Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020 [1st ed.] 9783030477127, 9783030477134

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Conference Proceedings of the Society for Experimental Mechanics Series

Chad Walber Patrick Walter Steve Seidlitz  Editors

Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7 Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA

The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research.

More information about this series at http://www.springer.com/series/8922

Chad Walber • Patrick Walter • Steve Seidlitz Editors

Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7 Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020

Editors Chad Walber PCB Piezotronics, Inc. Depew, NY, USA

Patrick Walter Texas Christian University Fort Worth, TX, USA

Steve Seidlitz Cummins-Power Systems Minneapolis, MN, USA

ISSN 2191-5644 ISSN 2191-5652 (electronic) Conference Proceedings of the Society for Experimental Mechanics Series ISBN 978-3-030-47712-7 ISBN 978-3-030-47713-4 (eBook) https://doi.org/10.1007/978-3-030-47713-4 © The Society for Experimental Mechanics, Inc. 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing represent one of eight volumes of technical papers presented at the 38th IMAC, A Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held in Houston, Texas, February 10–13, 2020. The full proceedings also include volumes on Nonlinear Structures and Systems; Dynamic Substructures; Model Validation and Uncertainty Quantification; Dynamic Substructures; Special Topics in Structural Dynamics & Experimental Techniques; Rotating Machinery, Optical Methods & Scanning LDV Methods; and Topics in Modal Analysis &Testing. Each collection presents early findings from experimental and computational investigations on an important area within sensors and instrumentation and other structural dynamics areas. Topics represent papers on calibration, smart sensors, practical issues improving energy harvesting measurements, shock calibration and shock environment synthesis, and applications for aircraft/aerospace structures. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Depew, NY, USA Fort Worth, TX, USA Minneapolis, MN, USA

Chad Walber Patrick Walter Steve Seidlitz

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Contents

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Orion MPCV E-STA Nonlinear Dynamics Uncertainty Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matt Griebel, Adam Johnson, Brent Erickson, Andrew Doan, Chris Flanigan, Jesse Wilson, Paul Bremner, Joel Sills, and Erica Bruno

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The Vibration and Acoustic Effects of Prop Design and Unbalance on Small Unmanned Aircraft. . . . . . . . . . . . William H. Semke, Djedje-Kossu Zahui, and Joseph Schwalb

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3

A Deformed Geometry Synthesis Technique for Determining Stacking and Cryogenically Induced Preloads for the Space Launch System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joel Sills, Arya Majed, and Edwin Henkel

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End-to-End Assessment of Artemis-1 Development Flight Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrew Doan, Adam Johnson, Tony Loogman, Paul Bremner, Joel Sills, and Erica Bruno

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Space Launch System Mobile Launcher Modal Pretest Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . James C. Akers and Joel Sills

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Feasibility Study to Extract Artemis-1 Fixed Base Modes While Mounted on a Dynamically Active Mobile Launch Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kevin L. Napolitano

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Challenges to Develop and Design Ultra-high Temperature Piezoelectric Accelerometers . . . . . . . . . . . . . . . . . . . . . Chang Shu, Neill Ovenden, Sina Saremi-Yarahmadi, and Bala Vaidhyanathan

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Application of Quasi-Static Modal Analysis to an Orion Multi-Purpose Crew Vehicle Test . . . . . . . . . . . . . . . . . . . . Matthew S. Allen, Joe Schoneman, Wesley Scott, and Joel Sills

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Using BB-gun or Acoustic Excitation to Find High Frequency Modes in Additively Manufactured Parts . . . Aimee Allen, Kevin Johnson, Jason R. Blough, Andrew Barnard, Troy Hartwig, Ben Brown, David Soine, Tristan Cullom, Douglas Bristow, Robert Landers, and Edward Kinzel

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Parametric Analysis and Voltage Generation Performance of a Multi-directional MDOF Piezoelastic Vibration Energy Harvester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paulo S. Varoto, Elvio Bonisoli, and Domenico Lisitano

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Are We Nearly There Yet? Progress Towards the Fusion of Test and Analysis for Aerospace Structural Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David Ewins

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Feasibility Study of SDAS Instrumentation’s Ability to Identify Mobile Launcher (ML)/Crawler-Transporter (CT) Modes During Rollout Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 James P. Winkel, James C. Akers, and Erica Bruno

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The Integrated Modal Test-Analysis Process (2020 Challenges) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Robert N. Coppolino

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Roadmap for a Highly Improved Modal Test Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Robert N. Coppolino

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Using Low-Cost “Garage Band” Recording Technology for Acquiring High Resolution High-Speed Data . . 175 Randall Wetherington, Gregory Sheets, Tom Karnowski, Ryan Kerekes, Michael Vann, Michael Moore, and Eva Freer

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Hybrid Slab Systems in High-rises for More Sustainable Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Katherine Berger, Samuel Benzoni, Zhaoshuo Jiang, Wenshen Pong, Juan Caicedo, David Shook, and Christopher Horiuchi

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Ground Vibration Testing of the World’s Longest Wingspan Aircraft—Stratolaunch. . . . . . . . . . . . . . . . . . . . . . . . . . 193 Douglas J. Osterholt and Timothy Kelly

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Using Recorded Data to Improve SRS Test Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Joel Minderhoud

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Distributed Acquisition and Processing Network for Experimental Vibration Testing of Aero-Engine Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Michal J. Szydlowski, Christoph W. Schwingshackl, and Andrew Rix

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Modal Test of the NASA Mobile Launcher at Kennedy Space Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Eric C. Stasiunas, Russel A. Parks, Brendan D. Sontag, and Dana E. Chandler

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Using Deep-Learning Approach to Detect Anomalous Vibrations of Press Working Machine . . . . . . . . . . . . . . . . . 229 Kazuya Inagaki, Satoru Hayamizu, and Satoshi Tamura

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DAQ Evaluation and Specifications for Pyroshock Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Erica M. Jacobson, Jason R. Blough, James P. DeClerck, Charles D. Van Karsen, and David Soine

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Optimal Replicator Dynamic Controller via Load Balancing and Neural Dynamics for Semi-Active Vibration Control of Isolated Highway Bridge Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Sajad Javadinasab Hormozabad and Mariantonieta Gutierrez Soto

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Forcing Function Estimation for Space System Rollout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 George James, Robert Grady, Matt Allen, and Erica Bruno

Chapter 1

Orion MPCV E-STA Nonlinear Dynamics Uncertainty Factors Matt Griebel, Adam Johnson, Brent Erickson, Andrew Doan, Chris Flanigan, Jesse Wilson, Paul Bremner, Joel Sills, and Erica Bruno

Abstract NASA vibration testing of the European Service Module (ESM) Structural Test Article (E-STA) for the Orion Multi-Purpose Crew Vehicle (MPCV) program demonstrated significant nonlinear behaviors and response deviation from pre-test finite element analysis (FEA). A linear FEA correlation effort, previously performed in 2017, resulted in the creation of two finite element models (FEM) – one correlated to high-load level swept sine responses and one correlated to low-load level swept sine responses. Additional work was required to quantify the uncertainty introduced when applying these linear models to non-sinusoidal flight load cases. To do this, an additional nonlinear dynamics model was developed and correlated with sine sweep test responses for low load level and high load level load cases. Results showed that, when the appropriate linearized model was selected for each specific Coupled Loads Analysis (CLA) loading type (i.e. Liftoff, Transonic, etc . . . ), the linearized models closely matched predicted nonlinear responses with modest error (uncertainty factor). Results of this investigation have established a physics-based nonlinear dynamics approach that uses empirical test data to establish the credibility assumption for usage of linear FEM(s) in CLA. It is anticipated that the methodology employed can be extended for usage in correlation and flight loads analysis of subsequent spacecraft with major joint nonlinearities. Keywords Nonlinear Dynamics · Uncertainty · Orion MPCV · Coupled Loads Analysis (CLA)

1.1 Introduction MPCV E-STA sine vibration testing was performed at various flight-like load levels. Significant nonlinear behaviors were observed as well as response deviation from pre-test FEA. These nonlinearities were observable as significant frequency and damping shifts between the low-load level test cases (20% flight level loads) and the high-load level test cases (100% flight level loads). Sample sine sweep frequency response function (FRF) results are shown in Fig. 1.3. In addition, evidence of joint slipping onset was apparent in the test data FRFs, exhibited as nonlinear inflections in the ramp up to resonance. A previous investigation by Quartus and NESC identified and limited the primary nonlinearities to three major interface joints. A linear FEA correlation effort resulted in the creation of two linear FEMs intended for use in a CLA study. The purpose of this study was to inform the use of correlated linear FEM(s) in a comprehensive linear CLA of a truly nonlinear system. One linear FEM was correlated to high level E-STA load cases (HLL FEM) and the other was correlated to low level E-STA load cases (LLL FEM). These two linear FEMs effectively represented linearizations of the true E-STA response about two specific load levels. Figure 1.1 illustrates how these linearizations might not necessarily predict accurate responses of a nonlinear system at load levels about which they were not correlated. Because of this, a single nonlinear FEM was created to help quantify the error (or uncertainty) introduced from utilizing linearized models in a linear CLA. This nonlinear “truth” model was developed from the previously correlated linearized models and correlated to the same E-STA sine sweep test M. Griebel () · A. Johnson · B. Erickson · A. Doan · C. Flanigan · J. Wilson Quartus Engineering Incorporated, San Diego, CA, USA e-mail: [email protected] P. Bremner AeroHydroPLUS, Del Mar, CA, USA J. Sills NASA Engineering and Safety Center (NESC), Houston, TX, USA E. Bruno Analytical Mechanics Associates, Inc., Hampton, VA, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_1

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Fig. 1.1 Illustration of Linearization Uncertainty – A single nonlinear “truth” model can help quantify uncertainty introduced when the correlated HLL and LLL linear FEMs are used under a loading about which they were not correlated. (NOTE: Graphics generated in MATLAB 2018/2019 and MS Office 2016)

Fig. 1.2 CLA Study Outline – CLA response was compared between the linearized models and the nonlinear model resulting in the selection of a best-fit linearized model and corresponding LUF for each CLA loading type. (NOTE: Graphics generated in MATLAB 2018/2019 and MS Office 2016)

results. It included detailed representations of the nonlinear joints – primarily through the inclusion of Coulomb friction stick-slip conditions. The results of both the linear and nonlinear model correlation efforts are briefly summarized in this report; additional details of these correlation efforts can be found in their corresponding references [1, 2]. Figure 1.2 outlines the steps taken in a CLA study designed to assess the performance of the HLL and LLL FEM for a set of flight-like load cases. The study was performed using a subset of representative CLA load cases and compared the response of the HLL and LLL linearized models to the response of the nonlinear model. This subset of CLA load cases represented three distinct phases of flight: • 5 Liftoff cases • 6 Transonic cases • 5 Max Acceleration cases These CLA load cases (6 DOF acceleration time histories at the MPCV interface) were applied to all three models as a time domain base excitation (fixed base analysis). The HLL and LLL response time histories were then compared to the nonlinear response time histories and a best-fit linear FEM was selected to represent each CLA loading type. Linearization Uncertainty Factors (LUF) were then computed for each CLA loading type using the selected best-fit linear FEMs.

1.2 Analysis A previous investigation performed by Quartus and NESC resulted in the creation of three correlated FEMs for use in a CLA study: • LLL linearized model: Linear NASTRAN FEM correlated to E-STA response at 20% flight load levels • HLL linearized model: Linear NASTRAN FEM correlated to E-STA response at 100% flight load levels • Nonlinear “Truth” FEM: Single nonlinear Abaqus model representing E-STA response at all load levels The results of both the linear and nonlinear model correlation efforts are briefly summarized in this report; additional details of these correlation efforts can be found in their corresponding references [1, 2]. The nonlinear Abaqus model is a combination of nonlinear Abaqus joints and a Hurty-Craig/Bampton (HCB) reduced model of the majority of the E-STA structure (reduction performed on NASTRAN model and HCB matrices converted to Abaqus format).

1 Orion MPCV E-STA Nonlinear Dynamics Uncertainty Factors

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One of the primary metrics used in the model correlation process was comparing E-STA FEM and test FRFs based on the E-STA sine test drive inputs. The linearized model FRFs were directly computed in the frequency domain using NASTRAN (sol 111). Figure 1.3 shows a comparison between the E-STA measured sine test FRFs and the linearized model FRFs at the Launch Abort System (LAS) simulator (considered a representative response location for gauging primary mode responses). Results are shown for the high-load level sine sweep (100% flight loading shown in red) and low-load level sine sweep (20% flight loading shown in blue) load cases. In the case of the linear correlation, the high load level sine sweep was applied to the HLL FEM while the low load level sine sweep was applied to the LLL FEM. The two linearized models approximated the frequency and damping shift observed during the E-STA test, however effects of slipping joints observable in the test responses was not captured. The nonlinear model FRFs were computed by post-processing time histories from a nonlinear direct transient simulation of the E-STA high level and low level sine sweeps. These simulations were performed using Abaqus implicit dynamics. Figure 1.4 shows the same comparison with E-STA test FRFs using only a single correlated nonlinear model. In this case, both the high-load level and the low-load level sine sweep transient inputs were applied to the same correlated nonlinear model in direct transient simulations in Abaqus. The use of this single nonlinear model showed improved correlation over the use of the two separate linearized models and captured the slipping onsets observed in the measured test FRFs. Because of this, the nonlinear model was considered a “truth” model and acted as a surrogate for the E-STA true nonlinear response. A CLA response study was performed using the three correlated models discussed above. The purpose of this study was to determine a best-fit linearized model for each CLA loading type (i.e. Liftoff, Transonic, Max Acceleration) by comparing the linearized model responses to the response of the nonlinear “truth” model. Figures 1.5 and 1.6 show the ensemble of CLA response locations used in this study.

Fig. 1.3 Linear FEM Correlation Results (LAS Simulator FRF) – Two linear FEMs were able to approximate the frequency and damping shifts observed in test; however effects of joint slipping (evident in some test FRF peaks) could not be captured using two correlated linear FEMs. (NOTE: Graphics generated in MATLAB 2018/2019 and MS Office 2016)

Fig. 1.4 Nonlinear FEM Correlation Results (LAS Simulator FRF) – A single correlated nonlinear FEM was able to capture frequency and damping shifts as well as effects of joint slipping observed in test. (NOTE: Graphics generated in MATLAB 2018/2019 and MS Office 2016)

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Fig. 1.5 Nodal Response Locations – CLA transient acceleration response was recovered in all translation DOFs at 27 nodal locations for the HLL, LLL, and nonlinear FEM. (NOTE: Graphics generated in Siemens Femap 11.3) Fig. 1.6 Strain Response Locations – CLA transient strain response was recovered at 4 elemental locations for the HLL, LLL, and nonlinear FEM. (NOTE: Graphics generated in Siemens Femap 11.3)

Due to the large number of response outputs (i.e. locations, degrees of freedom [DOF], and load cases), Pearson Correlation Coefficients were used to compare the response of the HLL and LLL model to the nonlinear model for each output. A Pearson Correlation Coefficient is a time-integrated measure of the linear dependence of two variables (Eq. 1.1). When this is applied to two response time histories, it provides a high-level frequency and phase comparison. These are the most important metrics when determining which linearized model best represents the nonlinear response for any CLA loading type. It should be noted that the Pearson Correlation Coefficient is not sensitive to magnitude discrepancies between two time histories. These are accounted for in a subsequent computation of uncertainty factors after the best-fit linear models have been selected for each CLA loading type.   N  Bi − uB 1  Ai − uA ρ (A, B) = N −1 σA σB

(1.1)

i=1

Pearson Correlation Coefficient – N: Sample Size, A&B: Random Variables, σ : sample standard deviation, μ: sample mean Pearson correlation coefficients were calculated between each linearized model and the nonlinear model for all response locations over all load cases and grouped by their respective CLA loading types. Figure 1.7 shows histogram distributions of Pearson Correlation Coefficients representing the LLL and HLL acceleration response comparison with the nonlinear “truth” response. In addition, a representative sample transient response comparison is shown at a single node on the E-STA LAS simulator for each CLA loading type. For Liftoff and Transonic type load cases, a strong correlation was observed between the HLL linearized model and the nonlinear model. On the other hand, Max Acceleration load cases were a lower-level load case; therefore a strong correlation was observed between the LLL linearized model and the nonlinear model. The same trend was observed for strain response comparisons, but is not shown explicitly in this report. These trends informed the selection of the best-fit linearized models for each CLA loading type. The best-fit linearized model for Liftoff and Transonic CLA cases was the HLL FEM, while the best-fit linearized model for Max Acceleration CLA cases was the LLL FEM.

1 Orion MPCV E-STA Nonlinear Dynamics Uncertainty Factors

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Fig. 1.7 Pearson Correlation Coefficients for Acceleration Response – Pearson Correlation Coefficients were computed between each linear model (LLL and HLL) and the nonlinear FEM and represented by histogram distributions. This was done to determine the best fit linear model for each CLA loading type. (NOTE: Graphics generated in MATLAB 2018/2019 and MS Office 2016)

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Following the response comparison, Linearization Uncertainty Factors (LUF) were computed to represent the uncertainty that would be introduced using the selected best linear models in a comprehensive CLA. LUFs were computed for each CLA response location as a ratio of response magnitude between the nonlinear “truth” model and the selected best-fit linearized model (Eq. 1.2). Table 1.1 shows the selected response magnitude metrics for each CLA loading type. Because Liftoff and Max Acceleration load cases were non-stationary, peak-value was selected as the magnitude metric. Alternatively, since Transonic load cases were primarily random buffet loadings, root-mean-squared (RMS) was selected as the magnitude metric for these cases. LU F n =

RN Lin RLin

(1.2)

Linearization Uncertainty Factor – RLin : Linear response magnitude, RNLin : Nonlinear response magnitude By the definition in Eq. 1.2, the maximum LUF for any loading type was of primary interest as it represented instances in which the selected linear model was under-predicting the true nonlinear response. However, since this study was performed on only a subset of CLA load cases, a measure of statistical significance was desired to help characterize how well the computed max uncertainty factors can generalize a comprehensive CLA consisting of hundreds or thousands of load cases. Figure 1.8 shows Probability Density Functions (PDF) computed using LUFs from all response locations (including acceleration and strain). Statistical significance is typically given as a probability level (β) and confidence level (γ ) associated with a particular maximum value. In this case, it was observed that the LUF distributions were irregular (not Normal Gaussian distributions) rendering the standard Normal Tolerance methodology unusable within the current analysis parameters [3]. Investigation revealed that the irregularities observed were primarily due to the use of peak value as a magnitude metric for non-stationary load cases. For example, the Liftoff load cases consist of two distinct events – one in which the HLL model over-predicts the true nonlinear response, and another in which the HLL model under-predicts true nonlinear response. This results in the bi-modal probability distribution observed in the Fig. 1.8 Liftoff PDF. A non-parametric, distribution-free methodology exists that does not assume any distribution of the sample [3]. The Distribution-Free Tolerance Limit (DFL) is defined as a value which exceeds all values for at least β fraction of a sample with a confidence γ defined by Eq. 1.3. The primary limitation of the DFL methodology is that it does not permit independent Table 1.1 Determination of Response Magnitude Metric (R) for Each CLA Loading Type

Liftoff Transonic Max Acceleration

Type of Loading Low Frequency

Magnitude Metric Peak Value Buffet + Thrust Osc. RMS Thrust Osc. Peak Value

RSS DOFs All YZ Lateral All

Fig. 1.8 Probability Density Functions of LUFs Computed Using Best-fit Linear Models – Probability distributions were determined to be irregular (not Normal Gaussian distributions). (NOTE: Graphics generated in MS Office 2016)

1 Orion MPCV E-STA Nonlinear Dynamics Uncertainty Factors Table 1.2 Max Uncertainty Factors for Each CLA Loading Type

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Max Uncertainty Factor Selected Linear Model Probability Confidence

Liftoff 1.24

Transonic 1.01

Max Acceleration 0.99

High Load Level 98% 96%

High Load Low Load Level Level 98% 98% 98% 96%

selection of γ and β. Instead, β < β max is chosen to achieve desired confidence (where β max is the fractional portion of the data enveloped by the max value). Since the LUF PDFs in Fig. 1.8 were extremely irregular (particularly the Liftoff distribution), further development of this methodology should be done to arrive at more familiar LUF distributions. This would allow for a better estimation of statistical significance. γ = 1 − βN

(1.3)

Confidence of Distribution-free Tolerance Limit (DFL) – Confidence associated with a DFL that envelopes β fraction of a sample (sample size = N) Table 1.2 shows the max LUFs computed for each CLA loading type and an associated statistical probability and confidence (from the DFL methodology outlined above). Using the appropriate best-fit linear model for each loading type resulted in relatively modest maximum LUFs. It should be noted that inherent loads uncertainty as well as model uncertainty was not accounted for in this analysis. These additional sources of uncertainty would be combined with the LUFs to arrive at total CLA uncertainty.

1.3 Conclusion NASA vibration testing of the Orion E-STA demonstrated significant nonlinear behaviors and response deviation from pretest analysis. Because of this, two correlated linear FEMs were developed that acted as linearizations of E-STA response about low-load level (LLL FEM) and high-load level (HLL FEM). Additionally, a single correlated nonlinear “truth” model was developed to act as a surrogate for the E-STA true nonlinear response. A CLA response comparison study revealed that the linearized models can approximate the true nonlinear response and informed the selection of a best-fit linearized model. To account for the uncertainty introduced from performing a comprehensive linear CLA on a nonlinear system, Linearization Uncertainty Factors (LUF) were computed for each loading type. Using the best-fit linear FEM for each CLA loading type, it was found that modest LUFs could be applied to a comprehensive linear CLA. Acknowledgements Special thanks to Joel Sills at NASA’s Johnson Space Center (JSC) for his guidance and continued support of this assessment.

References 1. Doan, A., Erickson, B., Owen, T.: Orion MPCV E-STA Structural Dynamics Correlation for NASA NESC. El Segundo California, Spacecraft and Launch Vehicle (SCLV) Dynamic Environments Workshop (2018) 2. Griebel, M., Johnson, A., Erickson, B., Doan, A., Flanigan, C., Wilson, J., Bremner, P., Sills, J., Bruno, E.: Orion MPCV E-STA Nonlinear Correlation for NESC. El Segundo California, Spacecraft and Launch Vehicle (SCLV) Dynamic Environments Workshop (2019) 3. National Aeronautics and Space Administration: Computation of maximum expected environment. In: NASA Handbook 7005. Pasadena, CA: Jet Propulsion Laboratory, National Aeronautics and Space Administration (2017)

Chapter 2

The Vibration and Acoustic Effects of Prop Design and Unbalance on Small Unmanned Aircraft William H. Semke, Djedje-Kossu Zahui, and Joseph Schwalb

Abstract The vibration and acoustic effects due to prop design, damage, and unbalance on a popular small unmanned aircraft systems (sUAS) is presented. The use of sUAS or drones is becoming ever more popular for hobbyists, as well as in commercial and military operations, and the influence of props on the vibration and acoustic environment are of interest. Many types of props are available for use on sUAS that promise extended run times, increased performance, and quieter operation. While many systems promise these results, few studies have been conducted to measure and evaluate their true performance. Therefore, this review provides data obtained by experimentally measuring the vibration levels onboard the host aircraft as well as the acoustic levels produced. The data is analyzed to gain further understanding of the vibration and acoustic properties and make predictions on prop performance. The fundamental frequencies of the aircraft are found along with the acoustic signature. These two outcomes are compared and studied to find the correlation between them. The analysis will utilize an airframes that is commonly used in the UAS community along with frequently used props that are balanced and unbalanced and with and without damage. The data is obtained from aircraft fully powered and airborne in a hovering or level flight configuration. This study provides sUAS operators the information required for choosing the most effective prop design to effectively reduce vibration and acoustic sound levels. Keywords Unmanned aircraft · Remote sensing · Vibration · Sound levels · Acoustic testing

2.1 Introduction Among the growing userbase of small Unmanned Air Systems (sUAS), the academic community takes a special interest in investigating their mechanical characteristics. Our focus exists in the mechanical characteristics and acoustic profile of the sUAS as a result to different styles of props and prop damage. There are multitudes of sellers carrying different types of propellers for the DJI Phantom 4 Pro, but we focus on select venders of propellers of two types: Standard and Low Noise. For both types of props, we examine the affect imbalance has on the vibration of the vehicle, as well as the change in acoustics introduced by the imbalance. The magnitude and spectral response of the system vibration and acoustic levels are presented. Many types of props are available for use on sUAS that promise extended run times, increased performance, and quieter operation. A maritime engineering reference book examines different types of propellers and provides performance metrics and much of the analysis done by Carlson [1] assumes that the propeller is in an undamaged state. This tends to be a common assumption between similar works. The work presented here does not offer a fault-analysis of a damaged propeller, but the vibration characteristics and acoustic profile changes causal to a damaged propeller, in a controlled manner. The need to reduce or eliminate unwanted vibration in imaging systems is crucial in many applications of UAS. Researchers have carried out investigations into vibration isolation and active control for many years. Several studies [2–4] provide numerous resources into the basic principles. Given the limited range and payload capacity of these vehicles, vibration control is often carried out through passive means with vibration isolation and low noise and vibration blade design. Many researchers have carried out research into vibration isolation and active control over a long period of time and the fundamentals are explained in vibrations texts [5–7].

W. H. Semke () · D.-K. Zahui Department of Mechanical Engineering, University of North Dakota, Grand Forks, ND, USA e-mail: [email protected] J. Schwalb Department of Aerospace Sciences, University of North Dakota, Grand Forks, ND, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_2

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Part of the inspiration for this paper stems from the want to “cut the cord” that we use to measure mechanical vibration of the vehicle. Specifically, we wanted to see if good correlation between mechanical vibration and acoustic profile exists. Should a strong correlation exist, it would allow vibration analysis with a microphone as opposed to an accelerometer attached to a cable. In other works, similar ideas have been explored for different reasons. Sas et al. [8] introduces experimental and numerical analysis of a multirotor chassis, with the goal of isolating areas of lesser vibrations. Their goal was to identify places of lesser vibrations so they could mount the more sensitive electronics in those areas. Kloet et al. [9] has a journal publication identifying the ambient noise of a multirotor UAS. They map the sound profile in two planes, adjacent to the propellers, and under the propellers. Dissent on experimentation analysis was done in the scope of both U. S. A. and E. U. regulators and their views of noise pollution in civil aviation. In an interesting turn, Iannace et al. [10] offers a fault diagnosis method for UAVs using artificial neural networks. In the process of building a model, they examine different imbalances by placing makeshift (tape) weights to introduce vibration. The model was trained to recognize the acoustics of the imbalanced propeller, to a success rate of 97% in the environment they tested in. Previous work by Semke, [11], offers analysis of different types of mounting mechanisms onboard a quadcopter and the vibration characteristics of the sensor mounting mechanisms of both multirotor and fixed wing aircrafts. The vibration environment onboard fixed-wing and quadrotor sUAS and provides sensor data to assist in passive and active vibration control methodologies [12].

2.2 Experimental Testing In contrast to many related works today, the goal is to investigate and better understand what happens when there is a damage to the propeller. A critical question we draw attention to is how much damage influences the acceleration and acoustic levels and ultimately the flight performance of the sUAS. Testing was performed on a DJI Phantom 4 Pro sUAS as shown in Fig. 2.1 Table 2.1 provides a key list of the aircraft specifications. In this paper four sets of blades were tested in the laboratory. For each type of blade, vibration and acoustic measurements were simultaneously collected. Undamaged blades were tested first, then one centimeter from a single blade tip, on one side

Fig. 2.1 DJI Phantom 4 Pro UAS Table 2.1 DJI Phantom 4 Pro Specifications Weight Diagonal Size Max Speed Max Flight Time Hover Range Accuracy

1388 g 350 mm 2 m/s Approx. 30 minutes Vertical Accuracy: ±0.1 m (Vision Positioning), ±0.5 m (GPS Positioning) Horizontal Accuracy: ±0.3 m (Vision Positioning), ±1.5 m (GPS Positioning)

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Fig. 2.2 Damaged propeller (left) and undamaged propeller (right) for the Standard 9450S and Low Noise 9455S Table 2.2 Summary of Acceleration Testing of the DJI Phantom 4 Pro with Various Propeller Configurations Blade Type DJI OEM Standard DJI OEM Standard Damaged BTG Standard BTG Standard Damaged DJI OEM Low-Noise DJI OEM Low-Noise Damaged Helistar Low-Noise Helistar Low-Noise Damaged

Amplitude: pk-pk (m/s2 ) 72 127 67 160 70 93 138 197

Increase % 76 139 33 43

Standard Deviation (m/s2 ) 12 21 11 26 11 17 22 30

Increase % 75 136 55 36

of the propeller, was removed to emulate damage. Figure 2.2 shows the damaged and undamaged props for the 4 types of props studied.

2.3 Vibration Testing To measure vibrations, a PCB Model 333B30 single-axis accelerometer (10.5 mV/m/s2 ) was attached to the base of the aircraft and the data was collected using a Data Physics Abacus 901 at a rate of 1536 Hz. The data was collected while the aircraft was in a hovering configuration approximately 1–2 meters above ground level. The peak-to-peak amplitude and the standard deviation for the recorded accelerations are shown in Table 2.2. Table 2.2 illustrates several interesting findings observed from the accelerometer data. First, damage had a more dramatic impact on standard prop designs than it did with the low noise prop configurations. In the undamaged state, all props showed similar peak-to-peak and standard deviation amplitudes, except for the Helistar low noise prop. This prop design had significantly higher peak-to-peak and standard deviation amplitudes compared to all other undamaged prop formats. The highest increase in vibration amplitudes due to prop damage was observed in the BTG standard prop model. The lowest increased in vibration amplitudes due to prop damage was observed in the DJI OEM low noise prop model. The Fast Fourier Transform (FFT) of each of the propeller configurations tests are shown in Figs. 2.3, 2.4, 2.5 and 2.6. The FFT plots show the frequency response of the aircraft for frequencies up to 600 Hz.

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1 Undamaged

Damaged

Magnitude

0.1 0.01 0.001 0.0001 0.00001 0

100

200

300

400

500

600

Frequency (Hz) Fig. 2.3 DJI OEM 9450S Quick-Release Propellers FFT Comparison of Damaged and Undamaged Propellers

1 Undamaged

Damaged

Magnitude

0.1 0.01 0.001 0.0001 0.00001

0

100

200

300

400

500

600

Frequency (Hz) Fig. 2.4 BTG 9450S Quick-Release Propellers FFT Comparison of Damaged and Undamaged Propellers

1 Undamaged

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Magnitude

0.1

0.01 0.001 0.0001

0.00001 0

100

200

300

400

500

600

Frequncy (Hz) Fig. 2.5 DJI OEM 9455S Low-Noise Quick Release Propellers FFT Comparison of Damaged and Undamaged Propellers

The DJI OEM 9450S quick-release propellers FFT show a higher baseline and peak amplitudes across all frequencies with a damaged prop. The largest increase in amplitude occurred at frequencies under 150 Hz. The BTG 9450S quickrelease propellers FFT shows a higher baseline and peak amplitudes across all frequencies when damaged as well. The highest increases occurred at frequencies below 150 Hz and between 200 and 450 Hz. The DJI OEM 9455S low-noise quick release propellers FFT did not show significant increase for most frequencies. Interestingly, there was a decrease in amplitude for most frequencies under 100 Hz along with an additional peak in the FFT plot around 50 Hz when the prop was damaged.

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1 Undamaged

Damaged

Magnitude

0.1 0.01 0.001 0.0001 0.00001 0

100

200

300

400

500

600

Frequency (Hz) Fig. 2.6 Helistar 9455S Low-Noise Quick Release Propellers FFT Comparison of Damaged and Undamaged Propellers

The Helistar 9455S low-noise quick release propellers FFT only shows a slight increase across the frequencies studied with prop damage. This case showed the least impact of damage on the FFT results as the undamaged and damaged FFT plots closely mirrored each other.

2.4 Acoustic Testing To measure noise, the ACO Pacific 4012 - 1/2 Inch directional microphone with a PS9200 2-channel power supply was used. The raw data was recorded using a TEAC LX-10 and later imported into MALAB® for analysis. Using a MATLAB® power spectrum analyzer object, a voltage spectrum was generated. The spectrum was then converted into Sound Pressure Lever (SPL) using the microphone sensitivity (50 mV/Pa). The results were converted into sound level3 at each frequency in Pascal (Pa) and subsequently in dB with a 20μPa reference pressure using Eq. (2.1).   Li = 20log10 pi /pref

(2.1)

where Li is the sound pressure in dB of the ith frequency and pi sound pressure in Pa. We also calculated the overall sound pressure level by combining the individual levels using Eq. (2.2). L = 10log10

 i

10Li /10

 (2.2)

Figures 2.7a, 2.8a, 2.9a, and 2.10a depict the noise level spectrum and the overall SPL for the eight tests. The DJI and BTG standard blades show a 4 dB in noise level increase from the undamaged to the damaged props. The increase in noise level can also be related to the increased in vibration level for these blades as shown in Figs. 2.3, 2.4, 2.5, and 2.6 and Table 2.1. There was no significant change in noise level between the undamaged and damaged blades for both types of the low noise props. However, the vibration level was increased for these props. The overall sound pressure level results are summarized in Table 2.3. There were 4-dB increases in noise level for the DJI and BTG standard blades, while the low noise props by DJI and Helistar only saw 1 and 0 dB increases, respectively. Further analysis of the data was carried out in the low frequency range (0–600 Hz) to better understand the correlation between the props radiated noise and vibration levels. Figures 2.7b, 2.8b, 2.9b, and 2.10b were thus generated. These figures represent the spectrum plot in Pascal (Pa) zooming in frequencies from 0 to 600 Hz. It can be seen on these sound pressure figures the frequency peaks correspond to the same frequencies as the vibration response frequency peaks. However, the peaks do not relate to the increase in sound pressure level from the undamaged to the damaged blades that were measured. For example, in Fig. 2.9b, the acoustic level peaks from the undamaged blade is higher than that of the damaged blade even though the overall sound pressure level indicates that the damaged blades were louder. The Figs. 2.7b, 2.8b, 2.9b, and 2.10b

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Fig. 2.7 DJI OEM 9450S Quick-Release Propeller Comparison of Damaged and Undamaged Propellers. (a) Noise Level Spectrum (b) Sound Pressure Spectrum

Fig. 2.8 BTG 9450S Quick-Release Propeller Comparison of Damaged and Undamaged Propellers. (a) Noise Level Spectrum (b) Sound Pressure Spectrum Table 2.3 Summary of Sound Pressure Level of the DJI Phantom 4 Pro with Various Propeller Configurations Blade Type DJI OEM Standard DJI OEM Standard Damaged BTG Standard BTG Standard Damaged DJI OEM Low-Noise DJI OEM Low-Noise Damaged Helistar Low-Noise Helistar Low-Noise Damaged

Sound Pressure Level (dB) 74 78 76 80 74 75 74 74

Increase (dB) 4 4 1 0

clearly show a correlation in frequency peaks between vibration and noise measurements. However, no definite conclusion can be drawn for the amplitude correlation between those two types of measurements.

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Fig. 2.9 DJI OEM 9455S Low Noise Quick-Release Propeller Comparison of Damaged and Undamaged Propellers (a) Noise Level Spectrum (b) Sound Pressure Spectrum

Fig. 2.10 Helistar 9455S Low Noise Quick-Release Propeller Comparison of Damaged and Undamaged Propellers (a) Noise Level Spectrum (b) Sound Pressure Spectrum

2.5 Conclusions The extent of the damage to the props in this study did not greatly impact the flight performance of the aircraft. When the damage was introduced, the DJI Phantom 4 Pro did experience slight yawing when first taking off, but the internal flight controller quickly resolved this issue after becoming airborne and nominal flight performance was experienced. More significant, or damage to multiple props, may impart more dramatic and potentially catastrophic consequences resulting in an aircraft that is not airworthy. This greater damage was not studied in this analysis, only the relatively small damage that may result from small prop strikes or an unbalanced situation. The observed vibration shows that the damage to the props increased both the peak-to-peak and standard deviation amplitudes for all configurations, but the damage had greater impact on the standard prop configurations. There was less impact in vibration due to the damage in the low noise configurations. The FFT amplitudes of the standard prop configurations showed a greater increase with damage. In general, the natural frequencies did not shift with damage except for the formation of an additional peak near 50 Hz in the damaged DJI OEM low noise prop.

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The observed acoustics depicted an increase in sound pressure level and can be qualitatively related to the increase in vibration levels. It is therefore our belief that based on these preliminary findings a microphone or an array of microphones could be used to monitor the vibrations on a sUAV during mission. In the testing conducted only 2 microphones were used and the exact positioning of the aircraft was not maintained throughout all the testing. While the position was not exact, only small variations of less than 1 m were observed. Even though the direct amplitude correlation between increase noise level and increased vibration level could not be determined in the current data sets further testing could be done in the future to establish a clear relationship between the noise level of a sUAV with damaged props and the onboard vibration levels. The amplitude of the various acoustic results across the frequency bands investigated do not necessarily directly correlate with the amplitudes of the vibration modes experienced onboard the aircraft. We believe further tests are needed to gain a better understanding of the behavior of sUAS props with a special emphasis on the low noise style. Greater prop damage magnitude and damage types will be investigated as well as a more detailed study on the correlation of vibration and acoustic responses. In this manner, we believe a non-invasive damage detection algorithm is possible using acoustic methods. This system would be part of robust and economical safety assessment procedures and protocols for preflight testing of remote autonomous sUAS systems that are planned for the future.

References 1. Carlton, J.S.: In: marine propellers and propulsion,. Butterworth-Heinemann,. In: Chapter 2 - Propulsion Systems, Cambridge, MA, United States (2019) 2. Thomas, R., Zahui, M.: Small unmanned aerial vehicle fuselage dynamic model using wings vibrations, Proceedings of the 22th international congress on sound and vibration. Florence, 12–16 July, 2015 3. Katalin, A.: Engineering Society International Conference 2017, MESIC” 11th international conference interdisciplinarity in engineering, INTER-ENG 2017, Tirgu-Mures, Romania, 5–6 Oct, 2017 4. Barron, R.F.: Industrial Noise Control and Acoustics, 1st edn. CRC Press (2002) 5. Crede, C.E.: Vibration and Shock Isolation. Wiley, New York (1951) 6. Rao, S.S.: Mechanical Vibrations. Prentice Hall, New Jersey (2004) 7. Meirovitch, L.: Fundamentals of Vibrations. McGraw-Hill, New York, NY, United States (2001) 8. Sas, P., et al.: Vibration Analysis of a UAV Multirotor Frame. KU Leuven - Department Werktuigkunde (2016) 9. Kloet, N., et al.: Acoustic signature measurement of small multi-rotor unmanned aircraft systems. Int. J. Micro Air Veh. 3–14 (2017). https:// doi.org/10.1177/1756829316681868 10. Iannace, G., Ciaburro, G., Trematerra, A.: Fault diagnosis for UAV blades using artificial neural network. Robotics. 8, 59 (2019) 11. Semke, W.: Vibration reduction for camera systems onboard small unmanned aircraft, Proceedings of the international modal analysis conference (IMAC) XXXVII: a conference and exposition on structural dynamics, 2019 12. Semke, W., Dunlevy, M.: A review of the vibration environment onboard small unmanned aircraft, Proceedings of the international modal analysis conference (IMAC) XXXVI: a conference and exposition on structural dynamics, 2018

Chapter 3

A Deformed Geometry Synthesis Technique for Determining Stacking and Cryogenically Induced Preloads for the Space Launch System Joel Sills, Arya Majed, and Edwin Henkel

Abstract The Space Launch System (SLS) stacking and Core Stage (CS) fueling induce significant preloads that contribute to the liftoff pad separation “twang”. To accurately capture this, an approach is required that can replicate the physics of all SLS physical stacking steps, CS cryogenic shrinkage, associated geometric nonlinearities, and the transient behavior and decay of the preloads with changing boundary conditions as the vehicle separates from the pad. The Deformed Geometry Synthesis (DGS) approach presented here satisfies the above requirements. DGS determines induced preloads by modeling components in their deformed geometry states and then enforcing compatibility by closing the resulting “deadbands”. DGS seamlessly integrates into the multibody modal synthesis framework and does not require the use of artificial external loads to enforce preloads or post-processing steps to remove their influence. Since DGS iterates to solve for the deformed state inclusive of geometric nonlinearities, running linearized parametrics to exercise different potential orientations of ball jointed struts that connect the CS to Boosters for cryo-shrinkage analyses is entirely avoided. Relative to the transient behavior and decay of stacking and cryo-induced preloads with SLS liftoff pad separation, this is an area of considerable interest to the SLS program. To capture this in the most accurate way possible, DGS algorithms are designed to work with Henkel-Mar nonlinear pad separation algorithms which operate on the separating longitudinal and lateral degrees of freedom (DoFs) between the vehicle and the pad. As the separating DoFs release, in whatever manner as dictated by the interface geometries, interface loads and interface flexibilities as well as the external loading on the vehicle, the subject preloads generate a complex twang/decay time-trace as dictated by the physics of the problem. This paper presents DGS numerical verification against the closed-form solution for Timoshenko’s 3 ball-jointed strut preload problem. This problem is then extended by the authors to the geometric nonlinear case where DGS is compared to the Newton-Raphson solution of the nonlinear equations. Next, DGS is utilized to solve the SLS stacking and cryogenic shrinkage coupled loads analyses. Finally, Henkel-Mar pad separation simulations are executed that isolate the impact of the induced preloads’ twang and decay characteristics. Keywords Space launch system · Deformed geometry synthesis · Henkel-Mar pad separation · Geometric nonlinear

3.1 Introduction A new approach for coupling deformed geometries and determining vehicle load indicators inclusive of prelaunch stacking and cryogenic induced preloads has been developed. This Deformed Geometry Synthesis (DGS) technique [1] is a specialized procedure in modal synthesis where components are coupled in their deformed geometry states by enforcing compatibility at the interfaces via a process of statically closing the resulting deadbands to lock-in the preloads. The procedure evokes a static version of the nonlinear deadband methodology first developed for the Space Shuttle Program (SSP). It has the advantage of being NASA verified and validated against test and utilized in the SSP nonlinear coupled loads analyses (CLAs) from 2005 until final flight in 2011. To accurately capture the SLS stacking and cryo-induced preloads, DGS replicates the physics of all SLS physical stacking steps, Core Stage (CS) cryogenic shrinkage, associated geometric nonlinearities (e.g., aft strut rotations – a set of 3 ball

J. Sills () NASA Engineering and Safety Center (NESC), Houston, TX, USA e-mail: [email protected] A. Majed · E. Henkel Applied Structural Dynamics (ASD), Inc., Houston, TX, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_3

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jointed struts providing the aft connections for each booster to the CS), vehicle stabilizer system (VSS) coupling/preloads (see Sect. 3.4), mobile launcher (ML) extensible column/preloads (see Sect. 3.5), and the transient behavior and decay characteristics of the preloads with changing boundary conditions as the vehicle separates from the ML. DGS seamlessly integrates into the SLS multibody modal synthesis framework and accurately simulates all stacking without the use of artificial external loads. The preloads are automatically reflected in the load indicator recoveries without any corrections or post-processing steps. All stages of stacking can be simulated including booster “toe-in” (for CS installation) and CS fueling/cryogenic shrinkage. DGS starts with an initial deformed geometry state and solves for the final system deformed geometry state, inclusive of all preloads and geometric nonlinear effects. This process can proceed iteratively until desired convergence is achieved. With this, executing linearized parametrics to, for instance, exercise different potential aft strut orientations is avoided since geometric nonlinear effects are captured in the final deformed geometry. To reduce the number of iterations, the initial deformed geometry state can include 1G and thermal effects in order to quickly converge to the final state geometry. In practice, this is done and fully converged solutions are achieved in only two iteration steps. The transient contribution (twang) and decay characteristics of the stacking and cryo-induced preloads is of considerable interest to the SLS program. To accurately capture this, DGS algorithms work together with Henkel-Mar nonlinear pad separation algorithms [2] which operate on the longitudinal and lateral separating DoFs at the ML to booster interface. As these separating DoFs release in the manner dictated by the interface geometries, interface flexibilities, interface loads, and external loads, the interaction of DGS and Henkel-Mar automatically generates the transient time-history, inclusive of the twang and decay characteristics, of the internal strain energy release. A series of DGS verification problems involving a system of ball-jointed struts are provided in the next section to help make concepts crystal clear. The first set of these problems has a closed form solution provided by Timeshenko and Gere [3]. To verify DGS capability for capturing larger strut rotations, the Timshenko problem is extended to larger preloads. Here, the linear analytical solution no longer holds and DGS is compared with a Newton-Raphson nonlinear solution of the Timoshenko problem.

3.2 DGS Verification Problems 3.2.1 Verification Problem #1: Ball Jointed Strut Problem – Preloads (Linear Case) Figure 3.1 depicts the ball-joint strut problem Timoshenko and Gere [3] utilized as the verification example. The vertical strut has an unstressed length of initial length (L) + change in length (L). It is coupled into the diagonal struts resulting in compression of the vertical strut and associated extension/rotation of the inclined struts. The objective is to predict the strut loads, and the vertical displacement at the vertex. The parameters used were: E = 10e6 psi, A = 1 in2 , L = 10 in, and L = 0.125 in. Timoshenko and Gere [3] provided the following closed form solution for the strut loads as applicable for small displacements: F2 =

Fig. 3.1 Ball Jointed Strut Verification Problem (Timoshenko)

2EA (L) cos3 β   L 1 + 2cos3 β

3 A Deformed Geometry Synthesis Technique for Determining Stacking. . .

F1 = F3 =

δ=

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F2 2cosβ

F2 L 2EAcos3 β

From the above equations, it can be observed that the strut forces are a function of un-stressed strut lengths and undeformed orientation which is characteristics of a linear problem. The comparisons to DGS for three orientations are provided in Tables 3.1, 3.2 and 3.3. Note in: this context, the Timoshenko analytical solution assumes small displacements. This problem is later extended to larger displacements, where Timoshenko analytical solution no longer holds.

3.2.2 Verification Problem #2: Ball Jointed Strut Problem – Preloads (Nonlinear Case) For the nonlinear case, the L is increased to 1.75 in. With this, the small displacement solution no longer holds and DGS iterations are required. The angle between the vertical and diagonal struts, β, is initially set to 45◦ and is expected to decrease by a few degrees with the introduction of the preloaded vertical strut to the multibody system. The DGS solution is compared to the geometric nonlinear solution which utilizes Newton-Raphson. Results after 1 and 2 iterations are shown in Tables 3.4 and 3.5, respectively. Table 3.1 DGS Verification Problem 1 – Preloads Case 1: β = 50◦

Table 3.2 DGS Verification Problem 1 – Preloads Case 1: β = 5◦

Table 3.3 DGS Verification Problem 1 – Preloads Case 1: β = 85◦

Table 3.4 DGS Verification Problem 2 – Preloads Iteration Step 1

Table 3.5 DGS Verification Problem 2 – Preloads Iteration Step 2

F2 F1 F3 δ β

F2 F1 F3 δ β

F2 F1 F3 δ

Exact (analytical) −43363.01 33730.44 33730.44 8.1637e−2

DGS (numerical) −43363.01 33730.44 33730.44 8.1637e−2

Diff 0 0 0 0

F2 F1 F3 δ

Exact (analytical) −83015.02 41666.06 41666.06 4.1985e−2

DGS (numerical) −83015.02 41666.06 41666.06 4.1985e−2

Diff 0. 0. 0. 0.

F2 F1 F3 δ

Exact (analytical) −165.29 948.26 948.26 1.2483e−l

DGS (numerical) −165.29 948.26 948.26 1.2483e−l

Diff 0. 0. 0. 0.

Geometric Nonlinear* −699700. 474220. 474220. 9.2787e−01 42.461◦ Geometric Nonlinear* −699700. 474220. 474220. 9.2787e−01 42.461◦

DGS (numerical) −675880.90 477919.97 477919.97 9.5584e−01 42.388◦ DGS (numerical) −700161.04 473987.38 473987.38 9.2731e−01 42.4625◦

Diff 3.40% −0.78% −0.78% −3.01% 0.172% Diff 0.07% 0.05% 0.05% 0.06% 0.00%

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3.3 Application to the SLS System The SLS stacking procedures and cryogenic shrinkage due to the CS fueling induce significant preloads that contribute to the liftoff pad separation “twang”. These preloads re-distribute and increase loads at the ML to boosters’ separation interface and therefore impact the vehicle’s pad separation dynamics. Figure 3.2 provides a depiction of the ML, boosters, CS, and Upper Stage (US). Figure 3.3 provides a depiction of the aft struts connecting the CS to the boosters. When fueled, the CS shrinks both longitudinally and radially, rotating the aft struts in the longitudinal direction from the unfueled configuration and resulting in strut preloads. The stacking steps start with the booster stacking, which simulates the ML vehicle support posts (VSPs) (Fig. 3.4) leveling, spacing and shimming under 1G deformed geometry. The boosters naturally “toe-in” as the ML “bows” under 1G. The shims ensure that the booster’s forward attach interface (Fig. 3.5) to the CS is within the desired tolerance box to optimize the CS physical integration. The boosters are pulled apart for CS integration therefore inducing a “toe-in” preload and associated moment at the VSP interface which re-distributes the ML/booster interface loads. Given the unfueled CS CG off-set, the CS rotates away from the tower during stacking. This geometric nonlinear rotation step along with the delta rotation in the reverse direction to accommodate the integration of diagonal struts of a fixed length must be simulated in order to relieve this delta rotation which then preloads the diagonal struts. The next step in the stacking procedures involves simulating the upper and lower strut integrations which are adjusted to fill the space and therefore should have zero preloads at this stacking step. Next the US components are integrated: Launch Vehicle Stage Adapter (LVSA), Interim Cryogenic Propulsion Stage (ICPS), MPCV Stage Adapter (MSA), and Multi-Purpose Crew Vehicle (MPCV) (see Fig. 3.6). Note that with this, the upper and lower aft struts are now taking load. Fig. 3.2 SLS/ML Coupled System

3 A Deformed Geometry Synthesis Technique for Determining Stacking. . .

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Fig. 3.3 CS/Boosters Aft Struts

Fig. 3.4 Vehicle Support Posts (VSPs) Showing Inboard (odd) and Outboard (even) Numbering

The final step in the DGS simulations involves the CS cryogenic shrinkage which further adds to the vehicle preloads amplifying the pad separation twang.

3.4 DGS of Vehicle Stabilizer System (VSS) to the SLS Figure 3.7 depicts the VSS which is designed to provide additional constraints against lateral displacements during the rollout and prior to liftoff. The preloads at the VSS to CS interface are enforced via the DGS approach. At booster ignition, the VSS separates from the CS relieving the preloads at the subject interface. The VSS includes radial and tangential hydraulic struts which are nonlinear. It is important for the VSS to be modeled in the coupled system as nonlinear given that at larger displacement amplitudes, the behavior of the nonlinear vs linearized VSS

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Fig. 3.5 CS/Boosters Forward Attach Interface (shown with red circles)

system can be significantly different. Figure 3.8 provides the VSS tangential strut damping force for a nonlinear vs linear VSS model in a SLS coupled loads analysis (CLA) involving an initial 6 inch lateral displacement release at the forward attach (along with 1G and stacking/cryo-induced preloads). It is seen that the behavior of the two models is significantly different for larger amplitudes but converges as the amplitudes reduce. Note: the zero strut damping solution is also provided which should results in a zero force for this particular response item.

3.5 DGS of ML Extensible Columns (EC) For SLS, four removable ECs, in addition to the six fixed launch pad Mount Mechanisms (MMs), provide support for the ML during vehicle fueling and launch at the four corners of the ML exhaust opening. This column concept is based on the ML support developed and used during Apollo/Saturn-V fueling and launch. Figure 3.9 shows the relative positioning of two ECs and three fixed MMs on the right (East) underside of the ML at the launch pad. These ECs are designed to be preloaded to a pre-determined value to ensure no gapping between the ML and the ECs after pad release. For the EC inclusion in the system model, DGS implemented the methodology to (a) enforce contact between the top of the EC and ML and (b) enforce the preload requirements. Resulting transient loads from this DGS application in pad release will be shown in the next section.

3 A Deformed Geometry Synthesis Technique for Determining Stacking. . .

Fig. 3.6 Upper Stage (US) Components

Fig. 3.7 Vehicle Stabilizer System (VSS)

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Fig. 3.8 VSS Tangential Strut Damping Force due to 6 in. Twang (linear vs nonlinear)

Fig. 3.9 (Left) EC and MM Positioning on the East Underside of the ML at Launch Pad, (Right) EC Concept

3.6 Liftoff Pad Separation Twang – Release of Preloads The transient contribution (twang) and decay characteristics of the stacking and cryo-induced preloads is of considerable interest to the SLS program. For this, the DGS algorithms work alongside the Henkel-Mar pad release algorithms to ensure a physics-based approach to pad release and the relief of preloads. It is important to note that not all ML/booster interfaces separate at the same time; therefore, the release of strain energy due to preloads must be congruent with the sequence of separating DoFs. The DGS approach is designed for this to occur in an automated physics-based fashion. Figure 3.10 provides the forces in the upper and lower aft struts from a SLS liftoff transient CLA. The DGS enforced initial conditions, Henkel-Mar pad separation, and the joint workings of the two algorithms results in a “twang” at booster separation which is clearly seen. Figure 3.11 provides the right booster/CS forward attach time-history in the longitudinal direction again clearly demonstrating the impact of the strain relief of the “toe-in” loads. Figure 3.12 provides the EC interface forces in the longitudinal direction. From this figure, it is seen that for the scenario simulated, the forces stays positive (i.e., in contact) after the vehicle separates from the pad.

3 A Deformed Geometry Synthesis Technique for Determining Stacking. . .

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Fig. 3.10 Upper and Lower Aft Struts Twang and Decay Transient Dynamics

Fig. 3.11 Right Booster/CS Forward Attach Longitudinal Force

3.7 Conclusion A new approach for coupling deformed geometries and determining vehicle load indicators inclusive of prelaunch stacking and cryogenic induced preloads has been developed. This Deformed Geometry Synthesis (DGS) technique [1] is a specialized procedure in modal synthesis where components are coupled in their deformed geometry states by enforcing compatibility at the interfaces via a process of statically closing the resulting deadbands to lock-in the preloads. Verification exercises using the Timoshenko ball-jointed struts problem demonstrated the concept and provided confidence in the extension to large displacements/geometric nonlinear where DGS was compared to the Newton-Raphson solution of the Timoshenko problem. The technique was then applied to the SLS stacked system where the stacking and cryo-induced preloads are captured prior to the Henkel-Mar pad separation and the resulting liftoff twang. To accurately lock-in all preloads, DGS is utilized to simulate all stacking steps including cryo-shrinkage of the fuel tanks, VSS coupling with preloads, and ML EC contact/preloads.

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Fig. 3.12 ML EC Longitudinal Contact Force

The transient contribution of the stacking and cryo-induced preloads at liftoff is of considerable interest to the SLS program. To solve this, the DGS approach for preload enforcement has the added capability to work with Henkel-Mar and automatically relieve the strain energy as the SLS separates from the ML. As such, it provides a physics-based method for predicting the liftoff twang. Acknowledgements The authors would like to acknowledge the NASA Engineering Safety Center for their support of this work.

References 1. Sills, J., Majed, A., Henkel, E.: Independent verification of SLS Block 1 Pre-Launch, Liftoff, and Ascent Gust methodology and loads, Part 1: prelaunch stacking analysis, NASA TM-2018-220073, NESC-RP-16-01128 (2018. March 1) 2. Henkel, E., Mar, R.: Improved method for calculating booster to launch pad interface transient forces. AIAA J. Spacecraft. 25(6), 433–438 (1988) 3. Gere, J.M., Timoshenko, S.P.: Mechanics of Material, 2nd edn. PWS Publishers, Boston, MA (1987)

Chapter 4

End-to-End Assessment of Artemis-1 Development Flight Instrumentation Andrew Doan, Adam Johnson, Tony Loogman, Paul Bremner, Joel Sills, and Erica Bruno

Abstract As the space industry continues to strive for more efficient launch vehicles they must rely on increasingly accurate predictive models. Verification of models typically requires physical testing. Flight data measurements offer the most real and therefore the most accurate data for model correlation. As NASA prepares for the inaugural launch of their new Space Launch System (SLS), Artemis-1, they must rely heavily on predictive system models to ensure flight safety. Artemis-1 will be an unmanned scientific mission with the intent of blazing a trail for future manned missions. NASA has implemented a system of Development Flight Instrumentation (DFI) in the hopes of recovering useful flight data during liftoff and ascent to aid in correlating their predictive models to ensure human safety in future missions. An end-to-end assessment of the DFI system was performed to verify data acquired during Artemis-1 would be adequate for the targeted flight test objectives (FTOs). This was accomplished using a computational simulation of all sensors and Data Acquisition (DAQ) parameters to investigate any potential problem areas in the current architecture. Input nominal signals were approximated and injected into the system model. Synthesized acquired signals were recovered to verify FTO success. Keywords DAQ · Measurement · SLS · Artemis-1 · NASA

4.1 Introduction As NASA prepares for the inaugural launch of their new Space Launch System (SLS), Artemis-1, they must rely heavily on predictive system models to ensure flight safety. Artemis-1 will be an unmanned scientific mission with the intent of blazing a trail for future manned missions. NASA has implemented a system of Development Flight Instrumentation (DFI) in the hopes of recovering useful flight data during liftoff and ascent to aid in correlating their predictive models to ensure human safety in future missions. The ESD/CSI Loads and Dynamics team performed a system level assessment of the SLS DFI system to assess the adequacy of the system hardware and programmable parameters to achieve the desired FTOs.

4.2 Background As the space industry continues to strive for more efficient launch vehicles they must rely on increasingly accurate predictive models. Verification of models typically requires testing and correlation on flight-like parts. It follows that data measured directly during flight offers the most insight into dynamic performance. In addition to the clear benefit of acquiring data directly from a flight structure, there are several other benefits to acquiring flight data. First, flight systems have accurate A. Doan () · A. Johnson · T. Loogman Quartus Engineering Incorporated, San Diego, CA, USA e-mail: [email protected] P. Bremner AeroHydroPLUS, Del Mar, CA, USA J. Sills NASA Engineering and Safety Center (NESC), Houston, TX, USA E. Bruno Analytical Mechanics Associates, Inc., Hampton, VA, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_4

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boundary conditions. Boundary conditions can drastically change the result of any test. Throughout ascent launch vehicles operate without grounding constraints. This leads to a challenge during typical ground tests, as it is very hard to replicate a free condition when subject to earth’s gravity. Second, flight measurements capture actual loading conditions, including loads that may not have been predicted in mathematical models or ground tests. In that way flight measurement is as much about verification of loading assumptions as it is about the response of the structure to those loading conditions. Thirdly, flight measurements are able to capture dynamic fuel changes which occur during any launch. Both simulations and ground based tests are only run for a discrete set of fuel conditions thus limiting their ability to predict and correlate to all of ascent. Although flight measurements are of obvious gain to any launch vehicle program, they are not free of challenges. Figure 4.1 illustrates the advantages and challenges introduced with the three most common ways of acquiring data for dynamic analysis. Simulations offer the first step for system identification as they are the cheapest and quickest way to obtain data useful for processing. However, they are quite limited in utility as they are only as true as the assumptions used to generate them. They require accurate predictions of system models and loads to be useful. Ground tests can help reduce model uncertainties by measuring the real response of the physical test article due to predicted loading. However, the added fidelity of ground tests comes with increased complexity. Special care need be taken to ensure measurements are true and valid. Whereas simulations are typically free of data pollution, ground test data is subject to two main sources of data pollution. The first is data pollution introduced by the measurement system itself and the second is outside operational noise which may pollute the incoming signals during acquisition. Operational noise is typically minimal during ground tests and, if present, can be mostly mitigated using averaging techniques. As previously mentioned, flight test measurements offer the most information to systems engineers as they acquire data due to true loading conditions on the physical structure. However, as was true for ground tests, added fidelity comes with even more complexity. Whereas ground tests are typically able to overcome the several sources of data pollution with relatively simple fixes, reducing data pollution during flight test measurements requires more careful attention. Since flight loads rarely occur in isolation, operational noise can have a large impact in polluting a measured signal. In addition, the data acquisition itself is much more limited compared to ground based acquisition. Strict mass requirements and the need for reliable data storage even in the event of lost hardware impose tight restrictions on DAQ designers which limit hardware and total bandwidth. SLS Artemis-1 is no exception to these challenges. In light of these challenges an end-to-end system analysis was performed to ensure system parameters were appropriate to minimize the effect of potential data pollution sources and maximize the probability of FTO success.

Fig. 4.1 Advantages and Challenges of Flight Measurements

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4.2.1 Investigation An investigation was performed in order to predict the performance of the DFI system for the successful execution of the following FTOs: 1. 2. 3. 4.

Modal Extraction Vibration Environment Characterization POGO Aeroacoustic/Buffet Characterization

Sensor types for each FTO are listed in Table 4.1. A complete system model was required in order to perform the investigation. The system model is represented in the flow diagram in Fig. 4.2. The system model was designed to replicate the path a dynamic signal would take from its source to final data processing. The first step of the simulation process was to develop an approximation of the analog signal. It was assumed the analog signal would be comprised of two parts: the nominal signal and operational noise. According to the nomenclature used in this report, the nominal signal is the signal desired to be measured for the particular FTO. For example, if investigating the modal extraction FTO the nominal signal would be the structural response at a given location to a given dynamic loading exciting the modes of interest. The underlying assumption of this investigation was that recovering the nominal signal perfectly would give the data analyst the best chance of successfully completing the FTO. It follows that the goal of the data acquisition process should be to capture the nominal signal as accurately as possible. Nominal signals for the four FTOs assessed were derived from multiple sources as listed in the following bullets. 1. 2. 3. 4.

Modal Extraction: Coupled Loads Analysis (CLA) simulations Vibration Environment Characterization: Max Predicted Environments (MPEs) POGO: State Space Models and Heritage Flight Data Aeroacoustic/Buffet Characterization: Wind Tunnel Data

Figure 4.3 shows the loading matrix used to guide the derivation of the nominal signals for each sensor throughout ascent. As can be seen not all loads will be applicable at all times during flight. This ascent profile also highlights areas

Table 4.1 Sensors Assessed per FTO FTO Modal Extraction Vibration Characterization POGO Aero/Buffet

Sensors Low Freq Accels X

High Freq Accels

Internal Pressure

External Pressure

External Mics

X

X

X X

Fig. 4.2 DAQ Synthesis Model Flow Diagram

X

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Fig. 4.3 Liftoff and Ascent load matrix Fig. 4.4 Operational Noise Color Contoured Levels at Accelerometer Locations

of maximum operational noise. Operational noise is assumed to be any signal not desirable for assessment of the specific FTO. For example for modal extraction, operational noise would include any physical vibration of the structure not due to primary mode response. For this investigation the largest assumed contributor to operational noise was vibro-acoustics. NASA had previously performed a study to assess the MPEs due to vibro-acoustics. Acceptance levels from the reported MPEs were used to define operational noise levels at each sensor as shown in Fig. 4.4. However, as MPEs represent the maximum predicted environment at a given location, they are not applicable at all times of flight. MPEs are typically driven by three sequential phases of flight: liftoff, transonic, and max Q. During the more quiescent times of flight a knockdown factor of -12 dB was derived in order to account for a drop in vibro-acoustic noise levels. Once the analog signal had been derived and simulated the next step was to simulate the data acquisition circuitry illustrated in the flow diagram (Fig. 4.2). The DAQ for Artemis-1 was simulated using known equations for the various electrical components present using an algorithm developed in Matlab. All parameters needed to fully define the DAQ system were given in NASA documents and compiled into a single model. This simulation allowed the team to track deviations from the nominal signal at each point during the data acquisition process. Several DAQ parameters were found to be critical to the successful recovery of the nominal signal in the presence of operational noise as listed below.

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Fig. 4.5 Artemis-1 LFA Sensor Clipping Summary

Fig. 4.6 Effect of Clipped Signal on Spectral Content

• Clipping: sensor range, anti-aliasing filter, and digital range (set by analog gain) • Resolution: gain, word size (dynamic range/bit resolution) • Phase distortion: pre-sample filter settings As part of the end-to-end assessment a detailed investigation was performed for each of the listed items. To illustrate a typical process, the investigation performed for clipping is expanded below. A top level summary of the Artemis-1 low frequency accelerometer sensors with various clipping risks is shown in Fig. 4.5. It is important to note that clipping was rarely driven by the nominal signals. Instead clipping was largely due to out-of-band operational noise. Clipping of a signal is detrimental to signal quality as it tends to “wash out” the nominal signal. This occurs because the clipped peaks add random artificial impulses to the data set which in turn translate into artificial broad band frequency content. When the nominal signal is lower than the broad band clipping levels, the nominal signal spectral content will be “washed-out” and unrecoverable. Figure 4.6 illustrates this effect on a typical sensor’s nominal signal. The plot shows the

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progression of the signal’s spectral content at each step along the data acquisition chain. As noted, the nominal signal has distinct peaks at low frequencies corresponding to the target modal frequencies. The signal maintains this quality until the digitization (quantization) step where it experiences digital clipping. Once clipping is experienced, the low frequency peaks of interest are washed out and the data is no longer useful for the intended FTO. Figure 4.7 illustrates the flow of a signal through the two clipping gates common to the Artemis-1 DAQ system. The first gate is the sensor range. A sensor will clip if the total level within the sensor bandwidth (ie. nominal signal plus out-of-band operational signals) exceeds its internal voltage capacity. Sensor clipping has a large effect on signal quality as, once clipped, the electrical signal typically requires a long recovery time for the signal to decay back to its correct state. Assuming the original excitation did not clip the sensor it will travel to the digitizer which introduces the next gate. Prior to digitization, the signal can be amplified using an operational amplifier. The amount of gain is set based on the desired resolution of the output signal. As the voltage limits remain constant, this signal amplification induces a new clipping limit (digital range). The digital range of a signal is typically set at or below the sensor range. As Fig. 4.7 shows, if this is the case and no other mechanism exists in between the two gates to decrease the signal level, digital clipping may occur. This was found to be the common source of clipping on Artemis-1. Wherever such clipping problems were uncovered, the investigation sought to answer the question: what alterations should be made to the DAQ system in order to remove signal clipping and thus help ensure modal extraction success? To answer this question requires a complete understanding of the signal at risk and its intended purpose. For example, the first solution that may come to mind in this case would be to increase the digital range (decrease the gain amplification). At first glance that would be a workable solution. Unfortunately, since gain is inversely proportional to resolution, simply increasing the gain may lead to an intolerable loss in digital resolution of the nominal signal. Recall however, for modal extraction the bandwidth of interest is only low frequency modal response. Therefore, a better solution would be to apply an appropriate low-pass filter to remove the higher frequency vibro-acoustic noise causing clipping prior to digitization. This solution is illustrated in Fig. 4.8 by way of altering the anti-aliasing filter to cut-off at a much lower frequency then currently implemented. Figure 4.9 illustrates the effect of the change to the simulated signal DAQ process. As noted the updated filter alleviates the clipping risk and helps maintain nominal signal quality in the low frequency range of interest.

Fig. 4.7 Signal Range Gates Clipped Signal Example

Fig. 4.8 Effect of Modification to Anti-Aliasing Filter on Clipping

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Fig. 4.9 Effect of Modification of Anti-Aliasing Filter on Spectral Content

4.3 Conclusion Flight missions are a critical but expensive step in the validation of models and critical to ensuring human safety in space travel. Confidence in flight measurements begins with confidence in the DAQ system used for measurement. As this study illustrates, full system knowledge of a given system is necessary to define DAQ parameters. An end-to-end system assessment proved to be a very useful tool to investigate probable problem areas in the current DAQ set-up for Artemis-1. The methodology presented herein, gives the engineer the necessary information to make well informed decisions about how to fix potential problems and ensure successful execution of the flight test objectives (FTO). It is clear that an end-to-end assessment such as this would be a very useful step in the initial phase of DAQ system design. Flight missions will continue to present unique challenges for test engineers, but by using the right tools early in the process we can still have high confidence in our measurements. Acknowledgments Special thanks to Joel Sills at NASA’s Johnson Space Center (JSC) for his guidance and continued support of this assessment. In addition to JSC, this assessment relied on input from NASA Marshall, Langley, and Kennedy Space Center. Special thanks to all NASA employees and contractors who made this work possible.

Chapter 5

Space Launch System Mobile Launcher Modal Pretest Analysis James C. Akers and Joel Sills

Abstract NASA is developing an expendable heavy lift launch vehicle capability, the Space Launch System, to support lunar and deep space exploration. To support this capability, an updated ground infrastructure is required including modifying an existing Mobile Launcher system. The Mobile Launcher is a very large heavy beam/truss steel structure designed to support the Space Launch System during its buildup and integration in the Vehicle Assembly Building, transportation from the Vehicle Assembly Building out to the launch pad, and provides the launch platform at the launch pad. The previous Saturn/Apollo and Space Shuttle programs had integrated vehicle ground vibration tests of their integrated launch vehicles performed with simulated free-free boundary conditions to experimentally anchor and validate structural and flight controls analysis models. For the Space Launch System program, the Mobile Launcher will be used as the modal test fixture for the ground vibration test of the first Space Launch System flight vehicle, Artemis 1, programmatically referred to as the integrated vehicle modal test. The integrated vehicle modal test of the Artemis 1 integrated launch vehicle will have its core and second stages unfueled while mounted to the Mobile Launcher while inside the Vehicle Assembly Building, which is currently scheduled for the summer of 2020. The Space Launch System program has implemented a building block approach for dynamic model validation. The modal test of the Mobile Launcher is an important part of this building block approach in supporting the integrated vehicle modal test since the Mobile Launcher will serve as a structurally dynamic test fixture whose modes will couple with the modes of the Artemis 1 integrated vehicle. The Mobile Launcher modal test will further support understanding the structural dynamics of the Mobile Launcher and Space Launch System during rollout to the launch pad, which will play a key role in better understanding and prediction of the rollout forces acting on the launch vehicle. The Mobile Launcher modal test is currently scheduled for the summer of 2019. Due to a very tight modal testing schedule, this independent Mobile Launcher modal pretest analysis has been performed to ensure there is a high likelihood of successfully completing the modal test (i.e. identify the primary target modes) using the planned instrumentation, shakers, and excitation types. This paper will discuss this Mobile Launcher modal pretest analysis for its three test configurations and the unique challenges faced due to the Mobile Launcher’s size and weight, which are typically not faced when modal testing aerospace structures. Keywords Apollo · Artemis 1 · Building block approach · Dynamic test fixture · Experimental modal analysis · Ground vibration test · Integrated vehicle modal test · Mobile launcher · Modal test · Rollout · Rollout forces · Space launch system · Space shuttle · Vehicle assembly building

5.1 Background NASA is developing the expendable heavy lift launch vehicle, the Space Launch System (SLS), to support lunar and deep space exploration [1, 2]. The Mobile Launcher (ML) is a very large and very heavy open beam/truss steel structure designed to support SLS during its buildup and integration in the Vehicle Assembly Building (VAB), transportation from the VAB out to the launch pad, and provides the launch platform at the launch pad.

J. C. Akers () NASA Glenn Research Center, Cleveland, OH, USA e-mail: [email protected] J. Sills NASA Engineering and Safety Center (NESC), Houston, TX, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_5

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Fig. 5.1 MSFC Test Stand 4550

The Marshall Space Flight Center (MSFC) Test Stand (TS) 4550 was built in 1963, called the Advanced Saturn Dynamic Test Facility, and used for the Integrated Vehicle Ground Vibration Testing (IVGVT) for the Apollo Saturn V. Subsequently modified in 1975 for the GVT of the Space Shuttle and called the Space Shuttle Mated Ground Vibration Test Facility [3–6]. Figure 5.1 shows the TS 4550 exterior and interior layout. Figure 5.2 shows the Saturn V Dynamic Test Vehicle, referred to as SA-500D, installed in Advanced Saturn Dynamic Test Facility (TS 4550). Figure 5.3 shows the installation of the Shuttle Orbiter Enterprise in the Space Shuttle Mated Ground Vibration Test Facility (TS 4550). However, a programmatic decision was made to not refurbish TS 4550 and use it for the ground vibration test of the Artemis 1 integrated vehicle and referred to as the Integrated vehicle Modal Test (IMT). The Artemis 1 integrated vehicle consists of the SLS integrated with the Orion Multi-Purpose Crew Vehicle (MPCV) spacecraft and will have its core and its second stage, the Interim Cryogenic Propulsion Stage (iCPS), which is based upon the Delta IV Cryogenic Second Stage [7], unfueled. The ML will serve as the IMT modal test fixture supporting the Artemis 1 integrated vehicle. The ML weighs over ten million pounds and is over 360 feet tall [8, 9]. The ML Deck supports the SLS at eight attachment points located at the bottom of its two boosters, which connect to the ML Vehicle Support Posts (VSP). The ML Tower provides lateral support to the integrated SLS launch vehicle via the Vehicle Stabilization System (VSS) and supports the fuel, power, and data umbilicals running to SLS and MPCV. The ML Tower also provides crew access to the MPCV Crew Module (CM). Fig. 5.4 shows the Artemis 1 integrated vehicle on the ML. The ML as the IMT modal test fixture presents unique technical challenges due to the ML providing a flexible boundary condition and its structural dynamics coupling with the Artemis 1 integrated vehicle. In addition, the ML is significantly heavier that the Artemis 1 integrated vehicle and therefore motion in the ML will end up “driving” responses in the Artemis 1 integrated vehicle. This could make it very challenging to identifying the modes only pertaining to the Artemis 1 integrated vehicle. While there is no current plan for modally decoupling the dynamics of the ML and Artemis 1 integrated test vehicle, several modal decoupling methods have been considered [10–27]. Hence a well correlated ML finite element model (FEM) is needed going into the IMT in order for not only an accurate modal pretest analysis, but to allow the model correlation focus to be on the Artemis 1 integrated vehicle. However, it should be kept in mind the ML FEM correlated to the ML Only modal test and subsequent ML on Transporter (CT)-2 rollout test data may have significant residual uncertainty because there is no launch vehicle mass loading of the ML Deck in either of these tests. Subsequent testing has been baselined by the programs

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Fig. 5.2 MSFC advanced Saturn dynamic test facility (Test Stand 4550) with Apollo SA-500D installed

(i.e., Space Launch System, Exploration Ground System, etc.) to gather ML Deck stiffness data that should help to reduce uncertainty in the correlated ML FEM. As part of the risk reduction process, a building block approach [28] has been adopted and a key element is a modal test of the ML, referred to as the ML Only modal test. This modal test was performed in June 2019. This test will be vital in generating a well test correlated ML FEM. Immediately following the ML Only modal test, the ML on the CT-2 [29, 30] rolled out from the VAB to Launch Pad 39B and back, similar to a rollout performed in September 2018 and shown in Fig. 5.5. The ML FEM will also be correlated to the June 2019 rollout test data using Operational Modal Analysis (OMA). CT-2 is a recently upgraded version of one of the original CT’s used for the Apollo and Space Shuttle programs. The upgrades allow CT-2 to carry the heavier loading imposed by the integrated SLS launch vehicle and ML. It takes approximately 8 hours for the CT-2 to transport SLS on the ML from the VAB to launch pad 39B. CT-2 is the size of a baseball infield, with a top speed of 1 mph loaded and 2 mph unloaded. CT-2 weights over six million pounds, height of between 20 feet and 26 feet depending on its jacking level, and is able to transport 18 million pounds. Figure 5.5 shows CT-2 rolling on the crawler way to Launch Pad 39B in March of 2016. A separate modal pretest analysis was performed for the ML on CT-2 rollout configuration [31] and will not be addressed in this paper. Because the ML structural dynamic properties are of paramount importance in accurately predicting rollout environment, separation dynamics during liftoff, and now serving as the dynamic modal test fixture for the IMT, the ML should be thought of as the “0th stage” of the SLS launch vehicle and is a truly “complicated aerospace structure”.

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Fig. 5.3 MSFC space shuttle mated ground vibration test facility (Test Stand 4550) with shuttle orbiter enterprise being lowered into place (l) and being integrated to the external tank (r)

This paper discusses the ML Only modal pretest analysis, which in addition to standard pretest analysis checks verifying adequacy of the exciter and accelerometer layout also included a force response analysis to generate “test like” acceleration time histories from which modal parameters were extracted. All the three test configurations were looked at: ML on the VAB Support Posts, ML on CT-2, and ML on the VAB Support Posts and CT-2. For the force response analysis to generate “test like” acceleration time histories, the planned instrumentation, shakers, excitation types, expected range of modal damping values, estimated ambient and sensor noise levels were used. These “test like” acceleration time histories were processed and had modes extracted using the same data processing software available to the test team. This “as-run end-to-end” simulation aspect was done to ensure a high likelihood of successfully identifying the primary target modes.

5.2 Verifying Validity of Results A series of intermediate checks were built into the pretest analysis to support verifying the validity of the results. Model checks were performed on all FEM’s, which included computing mass properties, free-free normal modes, fixed-base normal modes, 1 g static loading in three orthogonal directions, unit displacement in three orthogonal directions, and static loadings applied in all three orthogonal directions at all excitation locations. All intermediate checks were successfully completed. Static loadings applied in all three orthogonal directions at all excitation locations were used to compute their local compliances. The shaker suitability study used force to acceleration (A/F) frequency response functions (FRF) synthesized from the FEM mode shapes and modal frequencies assuming 1% modal damping. These drive point A/F FRF were double integrated in the frequency-domain to obtain the corresponding force to displacement (D/F) FRF, which were compared to the statically derived drive point compliances to verify their validity. Finally, the force response analysis generate both clean and noisy “test like” acceleration response time histories. These “test like” acceleration response time histories were then processed into A/F FRF and compared to those from the shaker suitability study to verify the validity of the force response analysis. Figure 5.6 shows this comparison for one of the shaker drive point locations. The sensor and ambient background

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Fig. 5.4 SLS on mobile launcher at launch pad (l) and Umbilicals (r), (from http://NASASpaceFlight.com)

Fig. 5.5 SLS mobile launcher rolling out to launch pad 39B, September 2018 (l) and CT-2 rolling on crawler way (r)

noise effect the first three resonance speaks the most because the ML shaker force levels are lower in this frequency range due to their stroke limitations.

5.3 Residual Vectors and Accounting for Compliance Contribution of Out-of-Band Modes Residual vectors are required to accurately account for the compliance contribution of the out-of-band modes in the pretest analysis. Including elastic body modes up to four times the frequency range of interest were retained, but without residual vectors, erroneously showed the shaker and drop hammer drive points were less compliant (i.e. stiffer) than what they actually are, which in turn lead to the erroneous conclusion they were able to excite more modes then they actually could. Figure 5.7 shows the effect of including residual vectors on the D/F drive point FRF at two locations, one that is very stiff and the other that has significant compliance. This shows that even if the frequency range of interest is quadrupled, but residual vectors are

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Fig. 5.6 Drive point A/F FRF comparison: no noise 1% damping (blue), Noisy 1% modal damping (red), noisy 2% modal damping (green), noisy +3% modal damping (light blue)

Fig. 5.7 Residual vectors effect on drive point compliance: stiff location (l) and compliant location (r)

not included, the drive point compliance may have significant error (i.e. magnitude of the D/F FRF at 0 Hz does not match the statically derived drive point compliance). Modal damping values of 100% were used for all residual vectors in the force response analysis so that only their static elastic contribution and not their dynamic contribution was included.

5.4 Target Mode Selection Primary and secondary target mode selection plays a key role in a successful modal test, particularly when the testing schedule is tight. It can significantly help reduce the number of accelerometers and shakers and helps to focus the modal test team’s mode extraction effort. Primary target modes are the critical “must have” modes needed to successfully correlate the FEM. Secondary target modes are modes of interest that provide useful information. The model correlation team should concur with the final target mode set and ideally be present during the modal test. Primary and secondary target modes selection uses modal effective mass and engineering judgement to capture fundamental characteristics of the ML and CT-2. For the ML on CT-2 and the ML on VAB Support Posts and CT-2 test configurations, the CT-2 has a significant amount of grounded mass due to the way its four trucks are modeled and constrained to ground. The pretest analyst should keep in mind how much of the total FEM mass is “locked” up in the boundary conditions and take this into account when determining a “small” modal effective mass fraction threshold. Figure 5.8 shows the cumulative modal effective mass for the ML on the VAB Support Posts, which has the typical characteristics of the majority of the modal effective mass being accounted for with the fundamental low frequency modes. As already mentioned, the ML Deck will not be mass loaded by a launch

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Fig. 5.8 ML on VAB support posts cumulative modal effective mass: translational (l) and rotational (r)

vehicle, which would have driven the ML Deck modes down in frequency. Because of this, modes of the ML Deck during this modal test, which exhibited significant vertical deflection, were retained as primary target modes even if their modal effective mass fraction was small or their modal frequency was slightly outside the original frequency range of interest. For all three test configurations, approximately two dozen total primary and secondary target modes were selected.

5.5 Test DOF Selection The ML and CT-2 test DOF were determined during the course of several previous modal pretest analyses. Self and crossorthogonalities metrics were the criteria used to verify the ML and CT-2 test DOF were still adequate to identify all primary target modes. If the primary target modes self orthogonality off-diagonals magnitudes were 5% (10% is a more common threshold) or less and the magnitudes of the off-diagonals of the cross orthogonality of the primary target modes and all FEM modes within the frequency range of interest were 5% (10% is a more common threshold) or less, then the test DOF were judged to well (adequately) identify all primary target modes. However, the more rigorous criterion of 5% was considered in order to obtain a “well correlated” ML FEM. This pretest analysis showed the ML and CT-2 test DOF are well suited to identify all target modes in the frequency range of interest for all three test configurations. However, the ML test DOF by itself is not adequate to identify all target modes of the ML on CT-2 and ML on VAB Support Posts and CT-2 test configurations. Figure 5.9 shows the cross orthogonality of the primary and secondary target modes and all FEM modes in the frequency range of interest for the ML on CT-2 test configuration. This is not surprising since the CT-2 by itself has modes within the frequency range of interest, with its first mode being the vertical bounce mode of the CT-2 chassis. Hence, the CT-2 acts a large sprung mass attached to the underside of the ML. This pretest analysis did not show that shakers were required to drive directly on the CT-2 to adequately excite all primary target modes. Having additional shakers driving on the CT-2 would provide margin since both the ML and CT-2 FEM’s are not test correlated, to mitigate issues due to the relative mass of the CT-2, and CT-2 modes coupling with those of the ML. If time had allowed, prioritizing the test DOF would have provided insight into how sensitive the modal test is to loss of test DOF and to identify key test DOF for which testing must be halted until repaired. While this pretest analysis showed that test DOF were not required at the boundary of the ML and VAB Support Posts, test DOF should always be located at the boundaries to verify boundary conditions even if not needed from a self/crossorthogonality perspective. Not having test DOF at the boundary can lead to erroneously changing the test article to make up for unexpected compliance/dynamics in the boundary condition. The final checks of the adequacy of the selected test DOF is displaying them on the FEM and animating the target mode shapes with a Test Display Model (TDM), which has grid points only where test DOF are located. If the distribution of the test DOF on the FEM or the animations of the target mode using the TDM do not make sense, then a revision to the test DOF is required.

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Fig. 5.9 ML on CT-2 test configuration cross orthogonality

Fig. 5.10 ML Shaker Force #4 time history normal probability plot

5.6 ML Shakers The ML Only modal test shakers are inertial reaction mass shakers. There were three lateral (horizontal) ML shakers with their inertial reaction mass riding on bearing rails and two vertical ML shakers with their inertial reaction mass moving on vertical guide-posts. NASA/Marshall Space Flight Center (MSFC) test personnel designed and fabricated the ML shakers and incorporated the hydraulic actuators from their modal shakers used during the Ares I-X Flight Test Vehicle (FTV) modal test in 2009 [32–36]. Two lateral ML shakers were located on the ML Tower and two vertical and one lateral ML shaker were located on the ML Deck. Because the ML shakers are inertial reaction mass shakers, they have a corner frequency for which their peak force decreases for frequencies below this corner frequency and is proportional to frequency squared, due to shaker stroke length limits. Unfortunately, the ML shakers “knee” frequency was significantly above the lowest frequency primary target modes resulting in the ML shakers having limited force input into the lowest frequency primary target modes. Figure 5.10 shows the normal probability plot of the fourth ML shaker force time history MSFC engineers provided. Even though the shaker drive signal was a bandwidth limited Gaussian signal, the ML shaker force exhibits significant non-Gaussian behavior, which is due to the nonlinearities in the hydraulic actuators. These ML shaker forces were at a higher sampling frequency than used in the modal pretest force response analysis. They were appropriately lowpass filtered and down sampled to the modal pretest force response analysis sampling frequency and verified by comparing power spectral density (PSD). Figure 5.11 shows the Autocorrelation functions computed on all four MSFC provided ML shaker force time histories, which shows that correlation essentially ceases to exist for time lags greater than or equal to 5 seconds.

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Fig. 5.11 Autocorrelation function of ML Shaker Forces

From each MSFC provided ML shaker force time history, five uncorrelated ML shaker force time histories were generated for use in the modal pretest Multi-Input Multi-Output (MIMO) force response analysis. Since the data processing frame length used to process the force response analysis time histories into PSD, FRF, and coherence significantly exceeded 5 seconds, a “Slinky Approach” was used to generate five uncorrelated shaker force time histories. ML shaker #1 force time history was created by taking the original recorded lateral shaker force time history and appending it to itself as many times as necessary until the assembled time duration equaled or exceeded the desired time duration. ML shaker #2 force time history was generated by lopping off the first data processing frame length of ML Shaker #1 time history and appending it to its end. This process repeated for the remaining ML shaker force time histories. Because the data processing frame length was significantly longer than 5 seconds, lopping off only first 5 seconds would have end up with the five ML random shaker force time histories being correlated and having very high coherences. This is due to each ML shaker force time history essentially being time delayed versions of themselves [37].

5.7 Drop Hammer Forces The MSFC test group designed and fabricated a Drop Hammer to supplement the ML shakers excitation of the ML Deck to help identify higher frequency ML Deck primary target modes. The Drop Hammer can shape its impulsive force, both in terms of peak force and frequency bandwidth, by adjusting its drop height and shock absorber. MSFC test personnel recorded an impulse train from four drops of the Drop Hammer in their laboratory. These four impulse Drop Hammer force time history, after removing transients due to resetting of the Drop Hammer between drops, were converted into a 16 impulse Drop Hammer force time history having the same sampling frequency as the modal pretest analysis force response analysis. Validity of the 16 impulse Drop hammer force time histories was verified by comparison of its PSD’s to that of the MSFC supplied four impulse Drop Hammer force time history.

5.8 ML Shaker and Drop Hammer Suitability Study This study was performed to determine if the locations and orientations of the ML shakers and Drop Hammer were adequate to excite all target modes. FRF were synthesized from the FEM modes assuming 1% modal damping, since this was believed to be the lowest modal damping level present during the ML Only modal tests. A spectral resolution equal to 1/tenth the half power bandwidth of the lowest frequency target mode was selected to ensure all resonance peaks in the FRF were well captured. Normal Mode Indicator Functions (NMIF) and Multivariate Mode Indicator Functions (MMIF) were computed on these synthesized FRF to determine if the ML shakers and Drop Hammer were adequate to excite all of the target modes. NMIF and MMIF values below 0.25 indicated potentially well excited target modes, and between 0.25 and 0.4 indicated

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potentially adequate excitation. This study did not look at ML shaker and Drop Hammer excitation levels. This study showed that the ML shakers and Drop Hammer locations and orientations are adequate to excite all target modes.

5.9 Accelerometer Sensor Noise Accelerometer sensor noise models were based upon the accelerometer manufacture’s specification data sheets. The ML Only modal test used several different accelerometer models. For accelerometers having sensor noise specified as “broadband resolution” as a PSD in units of grms2/Hz, their sensor noise time histories was modeled as uncorrelated zero mean Gaussian random time histories having the correct spectral content using a Fast Fourier Transform (FFT) approach. For accelerometers having sensor noise specified as “resolution” in terms g’s, their sensor noise time histories were modeled as uncorrelated random time histories uniformly distributed on the interval of +/− αg, where αg was the specified resolution. For the accelerometers having sensor noise specified as “broadband resolution” only in terms of overall grms level, their sensor noise time histories were modeled as uncorrelated zero mean Gaussian random variables with a standard deviation equal to the “broadband resolution”.

5.10 Ambient Background Noise (Not Including Accelerometer and Data Acquisition Sensor/Signal Noise) Ambient background noise is comprised of ambient vibrations and electromagnetic interference effects (e.g., 60-Hz harmonics due to lighting, transformers, etc.). Ambient background vibration levels of the ML inside the VAB were not available for this pretest analysis. Instead, ambient dated collected during the Ares I-X Flight Test Vehicle (FTV) modal test, with the VAB doors closed, was used to estimate the ML ambient background noise levels [32–36]. Figure 5.12 shows the Ares I-X FTV inside the VAB. These ambient acceleration time histories were highest near the top of the Ares I-X FTV and smallest on the Mobile Launch Platform (MLP) to which the Ares I-X FTV was mounted to. PSD computed on these ambient acceleration time histories clearly showed resonance peaks corresponding to modes of Ares I-X FTV and the MLP (i.e. system modes). The overall maximum, overall average, and overall minimum PSD were compared to the manufacturer’s sensor noise spectrum for the accelerometers used during this modal test. The overall maximum PSD and the manufacturer’s sensor noise spectrum showed good agreement, with the exception the overall maximum PSD having exceedances due to the Ares I-X FTV system modes. The ML ambient background noise was chosen to have a constant magnitude PSD that envelopes the accelerometer sensor noise spectrum and the overall average PSD magnitude of the Ares I-X ambient acceleration time histories, except for a few small exceedances of the resonance peaks due to the Ares I-X FTV system modes. The ML ambient background noise time histories were modeled as uncorrelated zero mean Gaussian random time histories. As forward work, it will be important to compare this assumed ambient background noise level to the actual ambient background noise levels to increase the accuracy of the subsequent IMT pretest analysis.

5.11 Force Response Analysis Theory and Implementation The modal pretest force response analysis utilized an open-loop MIMO modal state-space approach when using the five uncorrelated random ML shaker force time histories and a Single-Input Multiple-Output (SIMO) modal state-space approach when using the drop hammer force time histories. Equation 5.1 shows the modal state-space model used to generate acceleration response time histories. Equation 5.1 Force to Acceleration Modal State-Space Model M x(t) ¨ + C x(t) ˙ + Kx(t) = F (t), T Mq(t) ¨ + T Cq(t) ˙ + T Kq(t) = T F (t) q(t) ¨ + CC q(t) ˙ + KKq(t) =  F (t), T







q(t) ˙ In q(t) 0n 0n F (t) = + − KK −CC T q(t) ¨ q(t) ˙

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Fig. 5.12 Ares I-X FTV inside VAB







 q(t) q(t) T ¨ =  [q(t)] ¨ =  −KK −CC +  F (t), [x(t)] ¨ = [−KK − CC] + T F (t) [q(t)] q(t) ˙ q(t) ˙ Three modal damping levels of 1%, 2%, and 3%, were investigated for all three test configurations as it was believed they covered the range of modal damping that could be present during testing. The modal state-space model generated “clean” acceleration response time histories to which the ambient background noise and sensor noise acceleration time histories were then added in order to obtain the “test like” acceleration response time histories. The validity of the “clean” and “test like” acceleration response time histories was verified by comparing their drive point force to acceleration (A/F) FRF to the A/F FRF computed from the ML shaker and Drop Hammer suitability study. The ML shaker drive point displacements and velocities showed that neither the shaker displacement nor velocity limits were exceeded and thus verified this open-loop approach was valid and that a close-loop simulation involving detailed modeling of ML shakers was not needed. These “test like” acceleration response time histories were processed into PSD, FRF, and coherence using the same analysis tools available to the test team. For the random shaker test runs, the time histories were block processed with a Hanning window, 90% overlap, and a rather large frame length (i.e. block size), which was necessitated by a very fine spectral resolution needed to identify very closely spaced modes. For the drop hammer test runs, the time histories were similarly block processed, except no window or overlapping were applied. These “test like” PSD, FRF, and coherence were then treated just like actual test data would be. Standard frequencydomain data quality checks were performed, which included overlaying the shaker force PSD, drive point coherence, and drive point A/F FRF; and computing coherences between the ML shaker force time histories to verify they were uncorrelated. Force response analysis with the ML shaker random forces and 1% modal damping, as expected, clearly showed the effect of the Hanning window on the distortion of the low frequency resonance peaks in the FRF. Also as expected, significant dropouts in the coherence at frequencies close to the A/F FRF resonance peak frequencies were clearly evident. The next step computed Multivariate Mode Indicator Function (MMIF) and or Complex Mode Indicator Function (CMIF) on selected FRF to obtain an estimate of the number of modes within the frequency range of interest. Then time-domain

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Fig. 5.13 CMIF overlaid with pole estimates

Fig. 5.14 Test vs FEM cross orthogonality

polyreference techniques extracted the majority of the test modes, with a Single Degree Of Freedom (SDOF) polynomial curve fitting tool used a few times. Advanced modal extraction techniques, such as mode enhancement and spatial filtering, were not used. Figure 5.13 shows a CMIF overlaid with pole estimates forming well behaved race track patterns indicating the test modes are straight forward to extract. Self and cross-orthogonality criteria were used to determine how well the “test” primary target modes could be identified. If the magnitudes of the off-diagonal of the self orthogonality of the “test” primary target modes and the cross orthogonality of the “test” and FEM primary target modes being 5% (10%) or less, and the magnitudes of the diagonals of the cross orthogonality of the “test” and FEM primary target modes being 95% (90%) or greater, then the “test” primary target modes were well (adequately) identified. Figure 5.14 shows the cross orthogonality between all identified “test” modes and FEM modes in the frequency range of interest with the ML having 1% modal damping and sensor and ambient background noise included. Figure 5.15 shows the corresponding cross orthogonality between just the identified “test” primary target modes

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Fig. 5.15 Test primary target modes vs FEM cross orthogonality

and all FEM modes in the frequency range of interest. This was looking at a subset of the accelerometers showing they will adequately identify the first 11 primary target modes.

5.12 Conclusions This pretest analysis showed the primary target modes for all three test configurations can be adequately identified, and many times well identified for 1–2% modal damping values. However, this requires running the ML shakers at their full force levels. Running the ML shakers at 50% and 20% of their full levels was investigated to determine if multi-force linearity studies (i.e. shakers run at 20%, 50%, 100% levels) were feasible. This type of linearity study is especially important to conduct during ML Only modal test since the ML Deck is not being mass loaded as it will be during the IMT. This pretest analysis predicts that running the ML shakers at 20% of their full level is insufficient if the modal damping is 3% or greater. This is due to ML shakers operating as inertial reaction mass shakers, the lowest frequency primary target modes being significantly below the corner frequency, and therefore the shaker force levels at the lowest frequency primary target modes being too low to generate acceleration responses levels sufficiently above the ambient and sensor noise levels. Hence multi-force level linearity studies may require multi-point sine sweeps [38, 39] or normal mode tuning [40] techniques. The recognized challenge with modal pretest analysis is it utilizes uncorrelated FEM’s, includes assumptions about the ambient and accelerometer sensor noise levels, and most importantly assumed the ML and CT-2 behave linearly. Therefore, margin needs to be included in the test planning and preparation, and most importantly during the ML Only modal test there should be technical flexibility and capability to make the necessary adjustments to shaker, hammer, and instrumentation locations/orientations to ensure identifying all primary target modes.

References 1. “SLS Fact Sheet.”, https://www.nasa.gov/exploration/systems/sls/factsheets.html 2. “NASA Facts: Space Launch System.”, https://www.nasa.gov/sites/default/ files/files/SLS-Fact-Sheet_aug2014-finalv3.pdf 3. “Environmental Assessment: Modification and Operation of Test Stand 4550 in Support of Integrated Vehicle Ground Vibration Testing for the Constellation Program Marshall Space Flight Center, Contract No. NNM05AB44C, Task Order No. CH338.”, https://www.nasa.gov/pdf/ 247125main_MSFC_TS4550_ EA_Final.pdf 4. “Saturn V Dynamic Test Vehicle.”, https://en.wikipedia.org/wiki/Saturn_V_ Dynamic_Test_Vehicle 5. Lemke, P., Tuma, M., Askins, B.: Integrated vehicle ground vibration testing of manned spacecraft: historical precedent. https://ntrs.nasa.gov/ archive/nasa/casi.ntrs.nasa.gov/20080031432.pdf 6. “NASA History, This Week in NASA History: Space Shuttle Program’s first Mated Vertical Ground Vibration Test Performed at Marshall – Oct 4, 1978.” https://www.nasa.gov/centers/marshall/history/this-week-in-nasa-history-space-shuttle-program-s-first-mated-vertical-ground.html 7. Henry, K.: Getting to know you, rocket edition: interim cryogenic propulsion stage. https://www.nasa.gov/sls/ interim_cryogenic_propulsion_stage_ 141030.html 8. “Mobile Launcher, NASA Fact Sheet.” https://www.nasa.gov/sites/default/files/ atoms/files/mobilelauncher_ factsheet_v2.pdf 9. “Mobile Launcher Umbilicals and Support, NASA Facts.” https://www.nasa.gov/ sites/default/files/atoms/files/ml_ umbilicals20160523.pdf

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10. Kerrian, P., Napolitano, K.: Pretest analysis for modal survey tests using fixed base correction method. Proceedings of the 37th International Modal analysis Conference, 2019 11. Napolitano, K.: Maximizing the quality of shape extractions from base shake modal tests. Proceedings of the 37th International Modal analysis Conference, 2019 12. Napolitano, K.: Fixing degrees of freedom of an aluminum beam by using accelerometers as references. Proceedings of the 37th International Modal Analysis Conference, 2019 13. Napolitano, K., Yoder, N., Fladung, W.: Extraction of fixed-base modes of a structure mounted on a shake table. Proceedings of the 31st International Modal Analysis Conference, 2013 14. Napolitano, K., Yoder, N.: Fixed base FRF using boundary measurements as references – analytical derivation. Proceedings of the 30th International Modal Analysis Conference, 2012 15. Allen, M.: Recent advances to estimation of fixed-interface modal models using dynamic substructuring. Proceedings of the 36th International Modal Analysis Conference, 2018 16. Allen, M., Gindlin, H., Mayes, R.: Experimental modal substructuring to estimate fixed-base modes from tests on a flexible fixture. J. Sound Vib. 330, 4413–4428 (2011) 17. Kaufmann, D., Majed, A.:Accelerance Decoupling (AD) Method, NESC-RP-17-01207 18. Crowley, J., Klosterman, A., Rocklin, G., Vold, H.: Direct structural modification using frequency response functions. Proceedings of the 2nd International Modal Analysis Conference, 1984, pp. 58–65 19. Beliveau, J.G., Vigneron, F.R., Soucy, Y., Draisey, S.: Modal parameter estimation from base excitation. J. Sound Vib. 107, 435–449 (1986) 20. Imregun, M., Robb, D.A., Ewins, D.J.: Structural modification and coupling dynamic analysis using measured FRF data. 5th International Modal Analysis Conference (IMAC V), London, England (1987) 21. Napolitano, K., Winkel, J., Akers, J., Suarez, V., Staab, L.: Modal survey of the MPCV Orion European Service module structural test article using a multi-axis shake table. Proceedings of the 36th International Modal Analysis Conference, 2018 22. Staab, L., Winkel, J., Suárez, V., Jones, T., Napolitano, K.: Fixed base modal testing using the mechanical vibration facility 3-axis base shake system. Proceedings of the 34th International Modal Analysis Conference, 2016 23. Carne, T.G., Martinez, D.R., Nord, A.R.: A comparison of fixed-base and driven base modal testing of an electronics package. Proceedings of the 7th International Modal Analysis Conference, 1989, pp. 672–679 24. Fullekrug, U.: Determination of effective masses and modal masses from base-driven tests. Proceedings of the 14th International Modal Analysis Conference, 1996, pp. 671–681 25. Sinapius, J.M.: Identification of fixed and free interface normal modes by base excitation. Proceedings of the 14th International Modal Analysis Conference, 1996, pp. 23–31 26. Mayes, R.L., Bridgers, L.D.: Extracting fixed base modal models from vibration tests on flexible tables. Proceedings of the 27th International Modal Analysis Conference, 2009 27. Mayes, R., Rohe, D., Blecke, J.: Extending the frequency band for fixed base modal analysis on a vibration SlipTable. Proceedings of the 31st International Modal Analysis Conference, 2013 28. Sills, J., Allen, M.: Historical review of ‘building block approach’ in validation for human space flight. Proceedings of the 37th International Modal Analysis Conference, 2019 29. “Ground Systems Development & Operations Highlights, March 2017.” https://www.nasa.gov/sites/default/files/atoms/files/ gsdohighlights_march2017.pdf 30. “Crawler-Transporter 2, NASA Fact Sheet.” https://www.nasa.gov/sites/default/ files/atoms/files/crawler-transporters-2-oct2016.pdf 31. Winkel, J., Akers, J., Bruno, E.: Feasibility study of SDAS instrumentation’s ability to capture mobile launcher/Crawler-transporter target modes during rollout operations. Proceedings of the 38th International Modal Analysis Conference, 2020 32. Buehrle, R., Templeton, J., Reaves, M., Horta, L., Gaspar, J., Barolotta, P., Parks, R., Lazor, D.: Ares I-X flight test vehicle modal test. NASA/TM-2010-216182 33. Buehrle, R., Templeton, J., Reaves, M., Horta, L., Gaspar, J., Barolotta, P., Parks, R., Lazor, D.: Ares I-X flight test vehicle: stack 1 modal test. NASA/TM-2010-216210 34. Buehrle, R., Templeton, J., Reaves, M., Horta, L., Gaspar, J., Barolotta, P., Parks, R., Lazor, D.: Ares I-X flight test vehicle: stack 5 modal test. NASA/TM-2010-216183 35. Buehrle, R., Templeton, J., Reaves, M., Horta, L., Gaspar, J., Barolotta, P., Parks, R., Lazor, D.: Ares I-X launch vehicle modal test overview. Proceedings of the 27th International Modal Analysis Conference, 2010 36. Buehrle, R., Templeton, J., Reaves, M., Horta, L., Gaspar, J., Barolotta, P., Parks, R., Lazor, D.: Ares I-X launch vehicle modal test measurements and data quality assessments. Proceedings of the 27th International Modal Analysis Conference, 2010 37. Paez Wirching, P., Paez, T., Ortiz, K.: Random Vibrations: Theory and Practice, Wiley, New York, Section 5.2.2, 141 (1995) 38. Napolitano, K., Yoder, N.: Optimal phasing combination for multiple source excitation. Proceedings of the 31st International Modal Analysis Conference, 2014 39. Napolitano, K., Linehan, D.: Multiple sine sweep excitation for ground vibration tests. Proceedings of the 27th International Modal Analysis Conference, 2009 40. Hunt, D.L., Matthews, J., Williams, R.: An automated tuning and data collection system for sine dwell modal testing. 25th Structures, Structural Dynamics and Materials Conference and AIAA Dynamics Specialists Conference, Palm Springs, CA, May, 1984

Chapter 6

Feasibility Study to Extract Artemis-1 Fixed Base Modes While Mounted on a Dynamically Active Mobile Launch Platform Kevin L. Napolitano

Abstract There are several challenges associated with the scheduled integrated modal test (IMT) of the Space Launch System (SLS) Artemis-1 flight vehicle mounted on the mobile launcher (ML). While the goal of the test is to characterize the Artemis-1, the inclusion of the ML as the support stand for the test means that the entire system must be well characterized. A considerable amount of effort and schedule will have to be devoted to understanding both the test stand (the ML) and the Artemis-1 flight vehicle, and there is a risk that the effort may not be completed in time for a successful launch. NASA has requested that alternative methods be investigated to generate test results that can remove the effects of the ML from the test. ATA Engineering, Inc., (ATA) was given a reduced model of the Artemis-1 flight vehicle’s IMT configuration containing the candidate set of accelerometers and interface degrees of freedom (DOF). The model was used to determine how well ATA’s fixed base correction technique is able to estimate fixed base modes from test data collected on the IMT. This paper presents the fixed base correction method results. Keywords Modal testing · Boundary conditions · Frequency response functions

Acronyms ATA CMIF DOF FRF IMT ML SLS

ATA Engineering, Inc. Complex mode-indicator function Degree of freedom Frequency response function Integrated modal test Mobile launcher Space Launch System

6.1 Introduction and Background ATA Engineering, Inc., (ATA) proposed to use our fixed base correction method to estimate fixed base modes of the Artemis1 flight vehicle while it is mounted to the mobile launcher (ML) in the Vehicle Assembly Building at Kennedy Space Center. The fixed base correction method is a proven method that has been applied to a number of structures with flexible bases. The method derives from the fact that frequency response functions (FRFs) that use accelerations as references correspond to structures with modes that are fixed at those same reference accelerometer locations and directions. In this case, the accelerations are associated with the interface between the Artemis-1 flight vehicle and the ML. Since the motion at every degree of freedom (DOF) at a structure interface is truly independent at lower frequencies, a smaller number of generalized DOF, hereafter called constraint shapes, are used as references. This assumption is valid as long as the constraint shapes can capture the motion of the interface. The key to implementing this method is that at least as many independent sources must be applied to the ML as there are constraint shapes used to construct an invertible reference autospectral matrix (which is

K. L. Napolitano () ATA Engineering, Inc., San Diego, CA, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_6

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required for high-quality FRFs). A full mathematical investigation of the technique is provided in reference [1], and several examples of its implementation are provided in references [2–6]. In this paper, however, the drive point accelerometers at the interface DOF were used as references instead of constraint shapes. The different shaker combinations were selected to ensure that rigid or flexible body motion of each set of interface points could be excited. One can think of a given set of drive point accelerometers as a linear combination of the same number of calculated constraint shapes using the same accelerometers. The actionable results from using this method are FRFs associated with the Artemis-1 flight vehicle mounted to a fixed base. These FRFs can be used as inputs into standard modal analysis software tools to extract fixed based modes. The resulting fixed base modes can then be compared to fixed base analysis modes of the Artemis-1 flight vehicle, both visually and mathematically, to make decisions about the validity of the analysis model. For the assessment of this method’s feasibility, ATA was given a reduced model of the integrated modal test (IMT) setup using 3926 DOF associated with the full candidate set of accelerometers, as well as all 24 interface DOF consisting of all three translational degrees at eight locations where the Space Launch System (SLS) connects to the ML. This 3926-DOF model is assumed in this study to be the truth model, and the FRFs generated from this model are considered to be truth data associated with the full system. The model was reduced to the SLS DOF by eliminating all rows and columns not associated with the Artemis-1 flight vehicle. The interface DOF were not included in the SLS DOF set. This reduced model, containing 2720 DOF, is considered the truth model associated with fixed base modes. This paper uses the ATA fixed base correction technique to transform FRFs associated with the system model to FRFs associated with the fixed base model. Five locations on the Artemis-1 analysis model were selected as shaker locations and were used to generate both the system-level FRFs and the fixed base FRFs. The analysis models are discussed below.

6.2 Analysis Model The DOF associated with a 4000-DOF system model and the 2200-DOF Artemis-1 fixed base model are presented in Fig. 6.1. The 2200-DOF fixed base model was created by fixing all DOF not associated with the Artemis-1 portion, including the 24 interface DOF associated with the interface, shown in Fig. 6.2. The interface DOF were also used as candidate shaker

Fig. 6.1 Left panel shows 3926-DOF system model and right panel shows 2720-DOF fixed base model

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Fig. 6.2 Interface DOF that define the fixed base of the SLS model. The analysis in this paper assumes that the base shakers are applied to these DOF. However, the base shakers can be applied at nearby locations if those are more readily accessible

DOF '4812597Y+' '4812633Z+' '4812743Y+' '1880067Y+' '2880067X+'

Description Near top of vehicle Near top of vehicle Near top of vehicle Y- SRB, Lateral Y+ SRB, Lateral

Purpose Excite Lateral Modes Excite Vertical Modes Excite Lateral Modes Excite Torsion Modes Excite Torsion Modes

Fig. 6.3 Shaker locations on the SLS portion of the analysis model

locations for shakers mounted to the ML. In addition, five shaker locations were selected on the SLS to excite the structure primary modes. These five locations, listed in Fig. 6.3, represent shakers that could be used for the overall modal survey. The objective of this effort was to convert system FRFs from these five shakers into fixed base FRFs. These shaker locations are not the specific shakers that will be used in the overall modal survey, but the effect of the ATA fixed base correction method will be the same for these shakers as they will be for other shakers mounted on the structure. Lists of the first 33 modes of the system and fixed base model are presented in Fig. 6.4. A comparison table between the two sets of modes is also presented. The comparison table maps the fixed base mode in column 1 to the analysis mode with the cross-orthogonality derived from the mass matrix of the fixed base model with 2720 DOF. The percent frequency difference and cross-orthogonality between the two modes are also presented. The cross-orthogonality calculation was performed using the fixed base model mass matrix. The modes with high effective mass and large frequency shifts are highlighted.

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Fig. 6.4 Comparison table between fixed and system modes (right), with primary target modes highlighted

Fixed System Mode Mode % Freq Cross No. No. Diff Ortho 1 3 -12.40 100 2 6 -9.36 100 3 8 -8.73 94 4 10 -6.85 99 5 12 -2.14 97 6 14 -3.43 100 7 18 1.39 98 8 19 -1.59 97 9 21 -2.21 99 10 23 0.64 90 11 25 -2.07 99 12 32 -2.16 99 13 34 -6.28 99 14 38 -1.60 85 15 37 -6.54 89 16 28 -35.22 88 17 53 -0.11 90 18 48 -9.49 81 19 55 -1.52 93 20 52 -6.90 98 21 64 3.91 86 22 60 -1.91 82 23 67 -0.44 99 24 70 0.00 100 25 71 0.00 98 26 73 0.00 89 27 72 -0.12 85 28 74 0.00 100 29 75 0.00 100 30 76 0.00 100 31 79 -0.26 73 32 80 0.00 100 33 82 0.00 96

Fixed to System Comparison

6.3 Analysis Strategy The analysis strategy was similar to the effort put forward in reference [7], except that instead of investigating just the primary vehicle vertical mode, the first 21 fixed base modes were investigated. FRFs were generated using the system-level model at the five locations on the vehicle and various subsets of the 24 interface DOF defined in Fig. 6.2. The FRF matrix was partially inverted such that the drive point accelerations of the shakers on the base were used as references instead of the forces. The resulting FRFs were then used to extract modal parameters. The resulting fixed base modes from the procedure were compared to the modes from the fixed base model. This procedure was performed for six different shaker combinations, each representing a different subset of the 24 interface DOF. The combinations at the base were as follows: • • • • • • •

All 24 DOF: 8 vertical, 16 lateral 16 DOF: 8 vertical, 8 lateral 14 DOF: 8 vertical, 6 lateral 12 DOF: 8 vertical, 4 lateral 12 DOF: 6 vertical, 6 lateral 11 DOF: 8 vertical, 3 lateral 9 DOF: 6 vertical, 3 lateral The specific locations and directions are plotted as arrows in Fig. 6.5.

6 Feasibility Study to Extract Artemis-1 Fixed Base Modes While Mounted on a Dynamically Active Mobile Launch Platform

16 DOF: 8 vertical, 8 lateral

12 DOF: 6 vertical, 6 lateral

14 DOF: 8 vertical, 6 lateral

11 DOF: 8 vertical, 3 lateral

53

12 DOF: 8 vertical, 4 lateral

9 DOF: 6 vertical, 3 lateral

Fig. 6.5 Base shaker location and directions are shown as arrows

The shaker locations were evenly spread across both interface sets. In the case of three lateral inputs, two inputs in the Y direction were assumed to be able to excite Y-direction motion and in-plane rotation of the interface, and one input in the Z direction to excite in-plane motion in the Z direction.

6.4 Results At the core of the ATA fixed base correction method is the generation of fixed base FRFs that can be used to extract fixed base modes. The percent frequency difference and cross-orthogonality between the fixed base modes and the corrected fixed base modes for each base shaker configuration are presented in Tables 6.1 and 6.2. The first three columns are associated with the fixed base model. The modes for each shaker case were extracted from the resulting FRFs. The results from the 24-shaker case should exactly match the fixed base results, and any very minor errors in the results are more likely due to the modal extraction algorithm. The modes listed for the system-level model with zero base shakers were copied directly from the comparison table in Fig. 6.4. The cross-orthogonality values are higher than the extracted modes for this reason. As expected, the accuracy of estimating the fixed base modes increases as the number of base shakers increases. The first case using nine shakers significantly shifts the frequencies of the modes to levels that may be acceptable for the IMT, and adding more than twelve shakers minimally improves the frequency and cross-orthogonality results. Although 21 modes that correspond to the 21 fixed base modes were extracted, there were also other modes observable in the corrected fixed base FRFs. The number of additional modes increased as the number of base shakers decreased. Figure 6.6 presents FRFs synthesized from the 21 extracted modes presented in Tables 6.1 and 6.2 overlaid with the corresponding simulated test data. Spurious modes are shown for the 9-DOF case, and one low-responding mode is observable in the 12DOF case. These spurious modes are identified by red arrows. Note that there are no spurious modes for the 24-DOF case. Thus, spurious dynamics (additional modes) from the ML are removed as more shakers are added to the base. The issue of spurious modes can be accounted for by using spatial filtering to deemphasize nontarget modes and simultaneously emphasize target modes. Spatial filtering can also help emphasize modes that may not be observable from the complex mode indicator function (CMIF) plot.

6.5 Technology Readiness Level This method has been used on funded projects, including the European Structural Test Article (E-STA) modal survey in 2016. Data processing scripts have been developed but have not yet been packaged into a commercially available format.

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Table 6.1 Percent frequency error of modal extractions using ATA fixed base correction method for various numbers of proposed shaker configurations No. Shakers Vertical Shakers Lateral Shakers Mode Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

24 16 14 12 8 8 8 8 16 8 6 4 % Frequency Difference From Fixed Base 0.0 −1.1 −1.5 −1.5 0.0 −2.4 −2.7 −4.5 0.0 −0.4 −0.5 −0.8 0.0 −1.5 −1.5 −2.1 0.0 −0.2 −0.3 −0.3 0.0 −1.3 −1.4 −2.8 0.0 −1.0 −1.0 −2.1 0.0 −1.6 −2.7 −3.0 0.0 −1.3 −1.4 −3.9 0.0 −0.1 −0.2 −0.3 0.0 −0.2 −0.4 −0.4 0.0 −0.8 −1.2 −1.0 0.0 −1.9 −2.7 −3.1 0.0 −1.2 0.8 0.7 0.0 −3.9 −4.4 −4.4 0.0 −0.3 −0.4 −3.3 0.0 −0.1 −0.1 −0.3 0.0 −2.1 −2.1 −2.6 0.0 −0.4 −0.4 −0.5 0.0 −3.1 −3.1 −3.7 0.0 −1.0 −1.2 −2.2

12 6 6

11 8 3

9 6 3

0 Full System

−2.6 −3.4 −0.8 −2.6 −0.6 −2.0 −1.7 −3.7 −1.7 −0.2 −0.6 −2.2 −2.8 0.7 −4.5 −2.9 −0.3 −3.9 −1.0 −3.6 −1.5

−1.6 −4.8 −1.6 −2.5 −0.5 −3.0 −4.9 −3.5 2.0 −0.3 −0.6 −1.5 −3.4 0.7 −5.1 −4.2 −0.4 −2.7 −0.9 −3.8 −2.4

−2.9 −5.0 −2.2 −3.6 −0.7 −3.8 −4.1 −3.8 −8.5 −0.4 −08 −2.1 −3.2 0.7 −4.6 −5.9 −0.8 −4.0 −1.5 −4.6 −2.5

−12.4 −9.4 −8.7 −6.8 −2.1 −3.4 1.4 −1.6 −2.2 0.6 −2.1 −2.2 −6.3 −1.6 −6.5 −35.2 −0.1 −9.5 −1.5 −6.9 3.9

Table 6.2 Cross-orthogonality of modal extractions using ATA fixed base correction method for various numbers of proposed shaker configurations No. Shakers Vertical Shakers Lateral Shakers Mode Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

24 16 14 8 8 8 16 8 6 Cross-Orthogonality w/Fixed Base 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 99 99 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 99 100 99 96 100 94 86 100 31 92 100 100 100 100 100 100 100 92 92 100 89 89 100 80 79 100 89 86

12 8 4

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100 100 100 100 100 100 99 100 96 100 100 99 92 85 90 99 98 93 91 91 94

100 100 99 99 100 99 98 97 99 100 100 99 99 85 91 99 93 61 82 80 88

100 100 100 100 100 100 99 100 96 100 100 99 92 85 90 99 98 93 91 91 94

100 100 91 90 100 94 97 93 77 90 100 99 86 86 87 98 82 55 76 93 58

100 100 94 99 97 100 98 97 99 90 99 99 99 85 89 88 90 81 93 98 86

6 Feasibility Study to Extract Artemis-1 Fixed Base Modes While Mounted on a Dynamically Active Mobile Launch Platform

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12 DOF

9 DOF

24 DOF Fig. 6.6 Comparison of CMIFs from synthesized FRFs from the 21 extracted modes to the FRFs from the fixed base correction method

6.6 Summary This paper presents the results using the ATA fixed base correction method to help generate fixed base FRFs of the Artemis-1 flight vehicle while it is mounted on the dynamically active ML. The method is better able to generate fixed base modes as the number of base shakers increases. Ultimately, however, the number of shakers needed for the base will depend on how closely the corrected fixed base modes will match the actual fixed base modes in frequency. Although there may be spurious modes in the frequency range of interest, methods such as spatial filtering of the testmeasured data can be used to help identify the target modes. For this study, the minimum number of base shakers was determined to be nine, and the maximum effective number of shakers is likely to be twelve, with six vertical and six lateral shakers mounted near the interface. The frequencies are predicted to be approximately within 2.5–3.5% of the fixed base modes for major target modes with high effective mass and closer in frequency for modes with lower effective mass.

References 1. Napolitano, K., Yoder, N.: Fixed base FRF using boundary measurements as references – analytical derivation. In Proceedings of the 30th International Modal Analysis Conference, 2012. 2. Yoder, N., Napolitano, K.: Fixed base FRF using boundary measurements as references – experimental results. In Proceedings of the 30th International Modal Analysis Conference, 2012 3. Napolitano, K., Yoder, N.: Extraction of fixed-base modes of a structure mounted on a shake table. In Proceedings of the 31th International Modal Analysis Conference, 2013. 4. Staab, L., Winkel, J., Suárez, J., Jones, T., Napolitano, K.: Fixed base modal testing using the mechanical vibration facility 3-axis base shake system. In Proceedings of the 34th International Modal Analysis Conference, 2016. 5. Napolitano, K.: Extraction of fixed base modes for structures on shake tables and inertia supports. In Spacecraft and Launch Vehicle Dynamic Environments Workshop, 2016. 6. Winkel, J., Staab, L., Akers, J., Napolitano, K.: Fixed base modal survey of the MPCV orion european service module structural test article. In 2017 (forthcoming). 7. Blelloch, P.: Review of Joint Loads Task Team (JLTT) Technical Interchange Meeting (TIM). In Section 3.4. ATA Engineering, Inc., Project No. 62094. May 27, 2016.

Chapter 7

Challenges to Develop and Design Ultra-high Temperature Piezoelectric Accelerometers Chang Shu, Neill Ovenden, Sina Saremi-Yarahmadi, and Bala Vaidhyanathan

Abstract Piezoelectric accelerometer sensors are widely used for testing and monitoring vibrations in automotive, aerospace or industrial applications. The temperature limitation of most piezoelectric accelerometers is below 500 ◦ C, which meets the requirements of typical vibration measurement applications. However, in extreme cases such as engine monitoring, measurements are required up to 900 ◦ C, where the ultra-high temperature accelerometers are needed. This research work focuses on the development of ultra-high temperature piezoelectric accelerometers using bismuth layer-structured ferroelectric piezoceramics as sensing elements. The challenges to develop these materials and create the corresponding ultra-high temperature accelerometers will be discussed in this paper. Keywords Vibration testing · Ultra-high temperature · Accelerometers · Piezoelectric ceramics · Bismuth layer-structured ferroelectrics

7.1 Introduction A piezoelectric accelerometer is an AC-response accelerometer, which is the preferred option for dynamic vibration testing and monitoring in automotive, aerospace and industrial applications. The operation principle of this accelerometer is based on the ‘piezoelectric effect’ whereby the acceleration (a) of a seismic mass (m) in the accelerometer applies dynamic force (Newton’s second law F = ma) on piezoelectric sensing material, the piezoelectric material then converts the mechanical stress into electrical charges on its surface. The charge output is converted to a voltage signal before being connected to a data acquisition system. In the case of a charge output accelerometer, an external signal conditioning device (charge amplifier) is used for the signal conversion. Alternatively, an electronic circuit can be integrated inside accelerometer unit as an Integrated Electronics Piezo-Electric (IEPE) accelerometer with direct voltage output. The operating temperature of IEPE accelerometers is typically limited to 125 ◦ C by the electronic circuit components, whereas charge output accelerometers are usually functional at higher temperatures due to their purely mechanical assembly. The operating temperature of piezoelectric charge output accelerometers is dependent on the Curie temperature (TC ) of the piezoelectric materials used, above TC the sensing element loses the piezoelectricity/sensitivity. Both piezoelectric crystal and piezoceramic are used in commercial accelerometers, single crystal materials such as quartz, tourmaline, and LiNbO3 are used, with temperature limitations of tourmaline and LiNbO3 accelerometers around 600 ◦ C [1]. However, the cut

C. Shu () DJB Instruments (UK) Ltd, Mildenhall, Suffolk, UK Department of Materials, Loughborough University, Loughborough, Leicestershire, UK e-mail: [email protected] N. Ovenden DJB Instruments (UK) Ltd, Mildenhall, Suffolk, UK S. Saremi-Yarahmadi Department of Materials, Loughborough University, Loughborough, Leicestershire, UK B. Vaidhyanathan Department of Materials, Loughborough University, Loughborough, Leicestershire, UK © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_7

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Table 7.1 Properties of doped CaBi2 Nb2 O9 piezoceramics Composition Ca0.9 (NaCe)0.1 Bi2 Nb2 O9 Ca0.9 (NaCe)0.05 Bi2 Nb2 O9 Ca0.95 La0.05 Bi2 Nb2 O9 Ca0.9 La0.1 Bi2 Nb2 O9 Ca0.90 (KCe)0.05 Bi2 Nb2 O9 Ca0.90 (Li0.5 Ce0.25 Pr0.25 )0.10 Bi2 Nb2 O9 Ca0.85 (Li0.5 Ce0.25 Nd0.25 )0.15 Bi2 Nb2 O9 Ca0.92 Li0.04 Ce0.03 Y0.01 Bi2 Nb2 O9 Ca0.6 (Li0.5 Bi0.5 )0.4 Bi2 Nb2 O9 CaBi2 Nb1.97 W0.03 O9 CaBi2 Nb1.97 Zr0.03 O9 Ca0.92 (Li,Ce)0.04 Bi2 Nb1.96 W0.04 O9

d33 (pC/N) 13 16 12.6 13 16 17.3 13.1 16.1 15.3 13 8.2 16.1

TC (◦ C) 898 900 911 889 868 939 > 900 926 937 941 945 925

Thermal stability Poor Stable to 800 ◦ C Stable to 800 ◦ C Stable to 800 ◦ C Stable to 800 ◦ C 12% deviation at 850 ◦ C 14% deviation at 850 ◦ C 15% deviation at 900 ◦ C – – – 17% deviation at 900 ◦ C

References [14] [10] [14] [14] [7] [11] [15] [12] [16] [17] [18] [13]

directions of crystalline materials limit the flexibility of accelerometer designs. Piezoceramics are the most commercially popular sensing elements for accelerometer applications, benefitting from easier fabrication and machining process than single crystals to suit accelerometer designs. Lead zirconate titanate (Pb(Zr,Ti)O3 , PZT) and lead metaniobate (PbNb2 O6 , PN) based piezoceramics are commercially available materials for accelerometers at temperature ranges of 260 ◦ C and 480 ◦ C, respectively. However, in extreme testing environments, such as exhaust testing, turbo charger testing, and aerospace engine monitoring where the operating temperature is required to exceed 900 ◦ C, ultra-high temperature accelerometers are required for vibration measurements. The development of piezoceramics with higher TC (≥900 ◦ C) is considered as the primary challenge for this project. Bismuth layer-structured ferroelectrics (BLSFs), where (Bi2 O2 )2+ bismuth oxide layers alternate with (An−1 Bn O3n+1 )2− perovskite layers, (in the perovskite layers, A is mono-, di- or trivalent ion or a mixture of them, B is a combination of cations enclosed by oxygen octahedral, n is the number of octahedral layers in perovskite slab). Yan et al. proved the high TC = 943 ◦ C and high annealing temperature (over 800 ◦ C) of CaBi2 Nb2 O9 (CBN, n = 2) piezoceramics [2, 3]. Along with its good thermal stability to hold piezoelectricity [2], CBN becomes a good lead-free piezoceramic candidate for hightemperature sensor applications. An accelerometer prototype using stacked CBN ceramics as sensing elements was then published by Endevco, indicating sustainable operating up to ~630 ◦ C with ~10% thermal deviation [4]. However, the conventionally-fabricated CBN has poor piezoelectricity (piezoelectric charge coefficient d33 ~4–6 pC/N) [5–8], which is expected to restrain the sensitivity output of accelerometers. Therefore, researchers have focused on improving the CBN’s piezoelectricity by controlling the microstructure or tailoring the composition. The d33 value of textured grained CBN was improved to 20 pC/N [2, 8]. The correlation between grain sizes and piezoelectric properties of CBN stipulated that finegrained (~1 μm) CBN ceramics had the optimised d33 value of 13 pC/N [5, 9]. The addition of dopants on A-site and/or B-site improved the d33 value to 16 pC/N [7, 10–13]. Properties of reported doped compositions are summarised in Table 7.1, where the high TC and good thermal stability of CBN are maintained in doped CBN piezoceramics. In this work,undoped CBN and Li, Ce, W, V-doped CBN piezoceramics are fabricated and integrated into accelerometer prototypes. The properties of ceramics and the performance of accelerometer prototypes are characterized and compared. The challenges to fabricate the ultra-high temperature piezoceramics and to create the accelerometer sensor will then be discussed.

7.2 Experimental Procedure The CaBi2 Nb2 O9 and Ca0.92 (LiCe)0.04 Bi2 Nb1.92 V0.04 W0.04 O9 (LCVW-CBN) ceramics were fabricated by conventional solid-state method, using CaCO3 (99.0% purity), Bi2 O3 (99.9%), Nb2 O5 (99.99%), Li2 CO3 (99%), CeO2 (99.9%), V2 O5 (99.6%), WO3 (99.9%) as reagents. The raw powders were mixed stoichiometrically before calcination at 850 ◦ C. The calcined powders were then planetary milled for 4 hours. 5 wt.% PVA binder was added and mixed with the milled powders; the mixed powders were sieved to 1) for the empty and fluidfilled shell. Additional modes associated with axial stretch, torsion and fluid free surface sloshing (for the fluid-filled tank) are present. A summary of this structure’s modal content in the 0–60 Hz frequency band is provided below in Table 13.2. Based on the above results and Abramson [4], the following observations are drawn for this “many modes” problem. 1. 2. 3. 4. 5. 6. 7.

Bulge (n = 0) and lateral (n = 1) modes are relatively insensitive to ullage pressure. Bulge (n = 0) and lateral (n = 1) modes are profoundly affected by the presence of fluid. The many shell breathing (n > 1) modes are sensitive to both ullage pressure and the presence of fluid. Axial (stretch) and torsion modes are unaffected by ullage pressure and the presence of fluid. Bulge (n = 0) and lateral (n = 1) modes are insensitive to shell flexural stiffness. The many shell breathing (n > 1) modes are increasingly sensitive to shell flexural stiffness with increasing “n”. The two fundamental slosh modes occur well below the lowest shell breathing frequency (~1.2 Hz, not shown)

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Table 13.2 Cylindrical Structure Modal Frequency Content

m 1 3 5 7 9 11 13

Type Slosh Axial-1 Torsion-1

Modal frequencies (Hz) Bulge modes (n = 0) Lateral modes (n = l) Empty Full Empty P0 = 0 P0 = 30 P0 = 0 P0–30 P0 = 0 P0–30 208.46 208.46 7.79 7.79 27.86 28.23 208.46 208.49 21.75 21.75 121.17 121.30 208.47 208.56 32.60 32.62 165.54 165.71 208.48 208.66 40.92 40.96 184.13 184.39 208.53 208.82 47.61 47.68 193.09 193.46 208.61 209.04 53.27 53.38 198.03 198.54 208.75 209.36 58.24 58.41 201.08 201.76 Number of breathing modes (n > l) below 60 Hz Empty (P0 = 0) Full (P0 = 0) Empty (P0 = 30) 88 328 58 Hz Comments 0.35 Two fundamentals, many higher modes typically ignored 81.86 Unaffected by fluid mass and ullage pressure 64.72

Full P0 = 0 3.82 18.75 29.99 38.54 45.56 51.55 56.81

P0 = 30 3.87 18.77 30.03 38.59 45.64 51.69 57.01

Full (P0 = 30) 284

13.4.4 Further Experimental Results for Cylindrical Tanks During the mid-1970’s experimental studies in support of Space Shuttle development were conducted at NASA LaRC, with support provided by Grumman Aerospace Corporation [5]. Specific results, summarized below in Fig. 13.3, associated with empty and fluid filled cylinders with ends welded to thick bulkheads offered some insightful results related to parametric sensitivities. Results of the NASA LaRC tests offer further confirmation of insights associated with the Abramson example. But most significantly, sensitivity to joint (weld) flexibility (“shear diaphragm” versus the anticipated “fixed” condition is clearly evident) is dramatically indicated in the test data. Since that time, the present writer has noted the significance of sensitivity to joint flexibility (and its aleatoric nature) on many structures.

13.4.5 On the Nature of Damping in Structures A recent paper [6] offered a summary of common misconceptions related to structural dynamic behavior. An enduring misconception in the structural dynamics community relates to the nature of damping (the “[B]” matrix in eq. 13.1). Most finite element codes include an option for “Rayleigh”, proportional damping, which states that,     ˙ (t) + [K] {U (t)} = [e ] {Fe (t)} → [B] ≈ α [M] + β [K] , resulting in ζn ≈ α + βωn . ¨ (t) + [B] U [M] U 2ωn 2

(13.3)

The fallacy of Rayleigh proportional damping is clearly illustrated by the summary of measured modal damping versus modal frequency parameters for two structures, as shown below in Fig. 13.4. Empirical measurement of damping in structures [6] indicates that it is generally concentrated in interconnecting joints, welds, etc., while machined and forged metallic components possess negligible damping. Since the damping matrix cannot be rigorously classified in any mathematically convenient form, the modes of an actual structure are generally complex. It is fortunate in many cases that experimental modes may be approximated as real modes. However, this approximation breaks down when modal frequencies are closely-spaced, as in the case of the “many modes” problem.

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Fig. 13.3 Parametric Sensitivity of Cylindrical Shells welded to Thick Bulkheads Modal Damping from ISS P5 and ISPE Tests and the “Proportional Damping Curve Fit”

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Fig. 13.4 Illustration of the Fallacy of Rayleigh Proportional Damping

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13.5 Systematic Modal Test Planning In order to develop a logical modal test plan, close attention must be placed on (1) understanding of the test article FEM modal characteristics, (2) target mode selection (especially for the “many modes” problem), and (3) response DOF and excitation allocations.

13.5.1 Understanding of Test Article Modal Characteristics Unit mass normalized modes of a linear structural dynamic system, governed by the real, undamped, symmetric eigenvalue problem, [K] {n } = [M] {n } λn ,

(13.4)

    T [M] [] = [] , T [K] [] = [λ] .

(13.5)

satisfy the orthogonality relationships,

An unpacking of the above orthogonality relationships produces, columns associated with modal kinetic and strain energy distributions, respectively, which for individual modes are, {KEn } = ([M] {n }) ⊗ {n } , {SEn } = ([K] {n }) ⊗ {n } /λn .

(13.6)

For an assembled system dynamic model, the modal kinetic and strain energy distributions are identical to one another. However, when the mass and stiffness matrices are divided into “component” partitions [7], illustrated by the example five segment shell structure in Fig. 13.5, the modal kinetic and strain energy distributions are distinct, as depicted below in Fig. 13.6, facilitating enhanced understanding of modal content (specifically highest KE at the top extreme, highest SE at the lowest extreme for mode 1).

Fig. 13.5 Five Segment Axisymmetric Shell Structure

Further understanding of a structure’s normal modes is realized by introduction of deformation shape families [8], in particular overall “body” displacement patterns, as described below by the distributions in Fig. 13.7. By organizing the above described geometric patterns as a body displacement transformation matrix, [ b ], the discrete FEM shell displacements, [], are expressed as,

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Fig. 13.6 Five Segment Axisymmetric Shell Structure Mode Shapes and Energy Distributions

Fig. 13.7 Axisymmetric Shell Cross-Sectional “Body” Deformation Patterns

[] = [b ] [ϕb ] + [r ] = [b ] + [r ]

(13.7)

where [b ] represents “body” displacements, and [r ] represents remaining (residual) displacements that are not represented by the body patterns. Employing weighted linear least-squares analysis, each system normal mode may be partitioned into mutually orthogonal, “body” and (remainder) “breathing” components. Ultimately, the modal kinetic energy for each mode can be separated into respective “body” and “breathing” contributions,

13 The Integrated Modal Test-Analysis Process (2020 Challenges)

[KEb ] = [Mb ] ⊗ [b ] , [KEr ] = [Mr ] ⊗ [r ] ,

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(13.8)

offering further understanding of the nature of system modes. In particular, for the example axisymmetric shell structure (described in Fig. 13.5), system modes associated with ideal axisymmetric and perturbed (slight mass asymmetry) models of the shell are readily classified as (a) body dominant and (b) breathing dominant modes, which are summarized below in Fig. 13.8.

Fig. 13.8 Body and Shell Breathing Modal Kinetic Energy Distributions

13.5.2 Target Mode Selection Now faced with the “many modes” problem, as noted in the Abramson cylinder [4] and segmented axisymmetric shell [7, 8] examples, the question of relative significance of system modes must be addressed. NASA STD-5002 [2] suggests, “The goal of the modal survey test shall be to measure and correlate all significant modes below the model upper bound frequency, consistent with the model resolution requirement . . . . Significant modes may be selected based on an effective mass calculation (modal effective mass), but this set should be augmented by modes which are critical for specific load or deflection definition.” While it can be demonstrated that modal effective mass offers a (primary structure loads) target mode selection criterion for structures excited by base or interface accelerations only, a more complete selection criterion (alluded to by the underlined phrase) is required to address (1) systems excited by general, distributed forcing functions, and (2) response loads on localized critical components. The desired target mode selection criterion is to be found in application of Williams’ monumental mode acceleration method [9], which is commonly employed in the aerospace community. The following demonstration analysis is applied to the axisymmetric shell finite element model, interpreting the results described in Sect. 13.5.1, as associated with a 1/20th sub-scale model. Thus, the full-scale modal frequencies are 1/20th of the sub-scale model. Consider four applied dynamic load distributions, [ ie ], applied in the two lateral directions, the axial

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direction, and locally normal to the shell wall, respectively (applied boundary accelerations are not included in this exercise), as depicted below in Fig. 13.9. In addition, the following time history force, {Fe }, along with its normalized shock spectrum, shown below in Fig. 13.10, is imposed separately on the applied load distributions,

Fig. 13.9 Applied Load Distributions

Applied Force Time History and Normalized SRS

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Fig. 13.10 Applied Force Time History and Normalized Shock Spectrum

The normalized shock spectrum associated with the applied force time history suggests a full-scale value for f*, the dynamic response cut-off frequency, on the order of 70–80 Hz. The 150th model of the shell finite element model is about 73 Hz (corresponding to the 1/20th sub-scale value of 1452 Hz). For the present example, the response of individual (real) modes is described by,     {¨qn } + [2ξn ωn ] {˙qn } + ω2n {qn } = Tn e {Fe } .

(13.9)

 The modal gains for each of the four applied load distributions are Tn e . Regarding the first three applied load distributions described in Fig. 13.9, the dynamic loads, {σ}, of interest are the cumulative “body” loads at a series of 26 axial stations, defined by the following particular mode acceleration equations:         {σ} = {σ}D + {σ}QS = LTMq¨ {¨qn } + LTMFe {Fe } , LTMq¨ = bT [M] [] , LTMFe = bT [e ] .

(13.10)

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For the fourth applied load distribution case, involving a single concentrated load and an associated coinciding local response load of interest, is described by the load transformation matrices,   LTMq¨ = mDOF [DOF ] , LTMFe = 1,

(13.11)

Mode-by-mode contributions to dynamic response for all four applied load distribution cases are summarized in below in Fig. 13.11. Applied Force-X Drivers & Peak Body Inertial Loads

Inertial Load (%) Modal Gain (%)

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Fig. 13.11 Mode-by-Mode Contributions to Dynamic Response

For each of the four applied load distributions, there are groupings of three plots; the top plot indicates the distribution of modal frequencies, the middle plot summarizes relative modal gain norms, and the lower plot indicates an absolute summation “norm” of all dynamic loads relevant for the particular applied load distribution case. The relative significance of quasi-static and modal dynamic contributions to system transient responses, for the first three applied load distribution cases is summarized below in Table 13.3. In all three distributed applied load distribution cases, the quasi-static contributions to system response are generally significant. However, the fourth concentrated applied load response case, depicted below in Fig. 13.12, is most interesting in that the local responding load is almost completely dominated by quasi-static response (in spite of the fact that many modes contribute to the minor, dynamic component of response. While the results for the fourth applied load case are anticlimactic, (i.e., (a) dynamic response is associated with the contributions of many modes, and (b) total response is nearly entirely due to quasi-static response), the vital role played by Williams’ mode acceleration method is most clearly evident.

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Table 13.3 Significance of Quasi-Static and Modal Dynamic Contributions to System Response Load case 1: distributed “X” loading Geometry |FX| |MY| R Z Static Total Static 400 0 15 10 400 −60 15 12 400 −200 15 13 400 −340 15 14 400 −480 15 15 400 −540 15 15 392 −80 9 352 −190 10 264 −300 8 152 −370 4 40 −398 1 400 60 15 9 400 200 15 8 400 340 15 10 400 480 15 5 400 540 15 6 400 600 15 9 400 740 15 22 400 880 15 26 400 1020 15 17 400 1080 15 11 392 1180 15 18 352 1270 15 25 264 1380 15 20 152 1450 15 11 40 1478 15 12

Total 47 37 40 25 6 13 37 36 16 3 44 72 81 62 43 64 96 100 75 52 67 65 30 6

Load case 2: distributed “Y” loading Geometry |FY| |MX| R Z Static Total Static 400 0 15 10 400 −60 15 12 400 −200 15 13 400 −340 15 14 400 −480 15 15 400 −540 15 15 392 −80 9 352 −190 10 264 −300 8 152 −370 4 40 −398 1 400 60 15 9 400 200 15 8 400 340 15 10 400 480 15 5 400 540 15 6 400 600 15 9 400 740 15 22 400 880 15 26 400 1020 15 17 400 1080 15 11 392 1180 15 18 352 1270 15 25 264 1380 15 20 152 1450 15 11 40 1478 15 12

Total 47 37 40 25 6 13 37 36 16 3 44 72 81 62 43 64 96 100 75 52 67 65 30 6

Load case 3: distributed “Z” loading Geometry |FZ| |FR| R Z Static Total Static 400 0 47 400 −60 32 400 −200 33 400 −340 15 400 −480 3 400 −540 1 392 −80 21 352 −190 39 264 −300 35 152 −370 19 40 −398 4 400 60 35 400 200 61 400 340 71 400 480 56 400 540 34 400 600 61 400 740 90 400 880 95 400 1020 71 400 1080 47 392 1180 62 81 352 1270 62 100 264 1380 62 90 152 1450 62 72 40 1478 62 64

Normalized Applied Load History

Applied Load

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Normalized Response History 100 Ouasi-Staic Component Modal Dynamic Component Total Response

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Fig. 13.12 Quasi-Static and Modal Dynamic Contributions to System Response (Load Case 4)

0.5

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Total 4 7 12 11 5 4 3 1

6 9 8 5 3 4 6 5 5 5 7 6 1

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The present illustrative “many modes” example demonstrates a clear strategy for target mode selection (facilitated by decomposition of loads associated with system response), which helps to remove any vagaries in the NASA STD-5002 guidance: “The goal of the modal survey test shall be to measure and correlate all significant modes below the model upper bound frequency, consistent with the model resolution requirement . . . . Significant modes may be selected based on an effective mass calculation (modal effective mass), but this set should be augmented by modes which are critical for specific load or deflection definition.”

13.5.3 Response DOF Selection for Mapping Experimental Modes (the RKE Method) The most commonly used approach for development of a TAM is Guyan reduction [10] in which the “measurement” DOFs are retained in the “analysis” set. The matrix dynamic equations for free vibration (with all physical constraints applied) are, [K] {} − [M] {} λ = {0} →



KAA1 KAO KOA KOO

A O



−

MAA1 MAO MOA MOO



   A 0 λ= , O 0

(13.12)

where the FEM modal matrix is expressed in terms of “analysis” and “omitted” partitions. Denoting the modal matrix as, [], perfect orthogonality of (unit mass normalized) modes is expressed as, [OR] = []T [M] [] = [I] .

(13.13)

The Guyan reduction transformation which is used to form an approximate test-analysis mass (TAM) mass matrix is, [TRED ] =



I

(13.14)

.

− K−1 OO KOA

The “analysis” set partition of the modal matrix represents “measured” modal DOFs, therefore the approximate TAM modal matrix is,

A O



=

I

− K−1 OO KOA

(13.15)

[A ] ,

where the partition,  O , represents the approximate “omitted” DOF partition. Moreover, the TAM mass matrix, [MAA ], is defined as, [MAA ] =

I

T

− K−1 OO KOA

MAA1 MAO MOA MOO



I

− K−1 OO KOA

.

(13.16)

Imperfect orthogonality of the modal partition, [A ], corresponding to the “measured” DOFs with respect to the TAM mass matrix (for unit mass normalized modes, [A ]) is expressed as, [ORA ] = [A ]T [MAA ] [A ] = [IAA ] .

(13.17)

The residual displacement error matrix based on the difference between the exact FEM and TAM (eq. 13.15) modal matrices is defined as, [R ] =





A 0 A − = . O O O − O

(13.18)

Note that the residual error associated with the “measured” or “analysis” DOF partition is null. The modal kinetic energy distribution for the complete system is, [KE ] = [M] ⊗ [] ,

(13.19)

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where the column sum for each individual mode is unity (if the modes are normalized to unit modal mass). The residual kinetic energy matrix is defined in a similar manner as, [KER ] = [MR] ⊗ [R] .

(13.20)

Like the residual displacement error, [R], the residual kinetic energy matrix is exactly “0” at the rows corresponding to measured DOFs. The expected characteristic that residual energy is pronounced at “omitted” yet dynamically significant DOFs in any particular mode will be demonstrated with the uniform, free-free rod described by a 19 grid point FEM, illustrated below in Fig. 13.13.

Fig. 13.13 Simple Rod Structure

The first six (6) axial vibration modes are graphically depicted below in Fig. 13.14. Mode 2

Mode 1

0.3

0.15

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–0.3

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0.3

Phi

Phi

10 DOF

15

–0.3

5

10 DOF

15

Fig. 13.14 Simple Bar Structure Modes

DOFs 1, 3, 5, 7, 9, and 19 were first selected as “measured” DOFs. The TAM orthogonality matrix and residual kinetic energy associated with this selected DOF set are illustrated in Fig. 13.15. The orthogonality matrix and residual kinetic energy plot indicate that the selected “measured” DOFs are inadequate for mapping of modes 3–6. Pronounced residual kinetic energy in DOFs 11–17 suggests addition of “measured” DOFs in modes that vicinity. Addition of accelerometers at DOFs 11, 13, 15, and 17 was found to improve both the orthogonality matrix (conforming to the NASA-STD-5002 and SMC-S-004 criteria) and residual kinetic energy, as indicated below in Fig. 13.16. Since its introduction in 1998 [11], the RKE method has been employed by many organizations in the US aerospace industry for modal test planning. A variety of enhancements by a number of authors, involving the application of iterative and genetic schemes and modifications to the basic Guyan reduction method, have been introduced over the years. However all of the enhancements are based on the original RKE formulation.

13 The Integrated Modal Test-Analysis Process (2020 Challenges)

137 Cumulative Sum of RKE

80

Cumsum (RKE) (%)

70 60 50 40 30 20 10

6 5 4 3 2 1

0 0

2

4

6

8

10

12

14

16

18

20

Fig. 13.15 TAM Orthogonality and Residual Kinetic Energy for the 6 DOF Accelerometer Set Cumulative Sum of RKE

80 Cumsum (RKE) (%)

70 60 50 40 30 20 10 6 5 4 3 2 1

0 2

4

6

8

10

12

14

16

18

Fig. 13.16 TAM Orthogonality and Residual Kinetic Energy for the 10 DOF Accelerometer Set

13.5.4 ISS P5 Modal Test Planning with the RKE Method The ISS (International Space Station) P5 Short Spacer was the subject an end-to-end exercise of the Integrated Test Analysis Process in 2001 [12]. Modal testing was conducted by a team composed of Boeing/Rocketdyne (the manufacturer), NASA/MSFC (the laboratory), and Measurement Analysis Corporation (the consultant). The 21,666 DOF (3611 grid points) finite-element model of the ISS P5 (weighing 3605 lb.) and test fixture is illustrated below in Fig. 13.17.

Fig. 13.17 ISS P5 and Test Fixture Finite Element Model

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The RKE method was employed for determination of accelerometer allocation for the ISS P5 Short Spacer modal test program. An allocation of 86 triaxial accelerometers (258 DOF) was selected, resulting in a TAM mass matrix that produced impressive orthogonality for the majority of 36 FEM modes, as indicated below in Fig. 13.18.

Fig. 13.18 ISS P5 Pre-Test Modal Orthogonality Prediction

The above summary suggests that the RKE derived modal test plan includes sufficient accelerometer channels to map modes (associated with the P5 test article and test fixture) in the 0–50 Hz frequency band, while satisfying NASA-STD-5002 TAM orthogonality criteria. Note modes 14–17 include non-negligible modal kinetic energy content in the test fixture.

13.6 Measured Data Analysis Measured data analysis owes much to the contributions of Julius S. Bendat and Allan G. Piersol [13, 14]. The most reliable general approach to this task involves (a) thorough, objective review of measured data quality and content (preliminary data analysis), followed by (b) employment of rigorous spectral and correlation procedures (detailed data analysis). While the majority of Bendat and Piersol’s works focused on “random” data analysis, their contributions are quite applicable to analysis of measured data associated with non-random environments.

13.6.1 Preliminary Measured Data Analysis The following single data channel analysis functions are essential components of preliminary measured data analysis: 1. 2. 3. 4.

Time history and “running” autospectrum Autospectrum (also called the power spectrum) Probability density Shock response spectrum.

Displays of applied load (stationary random) excitation and drive point acceleration response associated with a test article (ISPE, 2016) that exhibited linear behavior are shown below in Fig. 13.19. Each of the above single channel displays includes (a) spectrogram (upper left), (b) time history (lower left), (c) autospectrum (upper right), and (d) probability density (lower right). Preliminary review of these channels indicates (1) stationary random excitation and response (spectrogram and time history plots), (2) linear dynamic behavior (“Gaussian” excitation and response probability densities). Displays of response accelerations in the vicinity of structural joints for a truss-type test article subjected to swept-sine excitation (ISS P5, 2001) that indicated local nonlinear behavior are shown below in Fig. 13.20.

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Fig. 13.19 ISPE Test Article Broad Band Random Excitation (left) and Response (right)

Fig. 13.20 ISS P5 Responses to Swept-Sine Excitation

Spectrograms (upper left windows for each Trunnion) indicate the presence of second and third harmonic distortions. Closer examination of focused SRS functions, during time segments exhibiting harmonic distortion (inset displays for each) suggest pronounced nonlinear activity at the left Trunnion and minor nonlinear activity at the right Trunnion. Displays of probability density functions associated with broad band random dynamic testing aimed at characterization of wire rope isolators (US Army sponsored SBIR contract, 2007), shown below in Fig. 13.21, offer a clear indication of nonlinear behavior.

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Fig. 13.21 Wire Rope Isolator Deflection and Force Probability Densities

For each data channel, the solid yellow curve is the measured (normalized) probability density function and the black curve is the ideal Gaussian (normalized) probability density function. Pronounced kurtosis in the isolator force probability density function clearly indicates pronounced nonlinear behavior of the wire rope isolators.

13.6.2 Frequency Response Function Estimates from Measured Data Consider the time domain matrix equation set, which includes nonlinear force terms, {FN (t)},     ˙ (t) + [K] {U (t)} = [e ] {Fe (t)} + [N ] {FN (t)} . ¨ (t) + [B] U [M] U

(13.21)

The companion Fourier transform of the above equation set is expressed as,       ¨ (f) = [Z (f)]-1 e {Fe (f)} + [Z (f)]-1 N {FN (f)} = [He (f)] {Fe (f)} + [HN (f)] {FN (f)} . U

(13.22)

The FRF matrices and forces mat be “folded” into the all-encompassing matrices and arrays,  HUF ¨ (f) = [He (f) HN (f)] , {F (f)} =



 Fe (f) . FN (f)

(13.23)

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Therefore, the general FRF relationship that implicitly includes the nonlinear force terms adopts the common linear input-output relationship, 

  ¨ (f) = H ¨ (f) {F (f)} or more generally {Y (f)} = [HYX (f)] {X (f)} . U UF

(13.24)

Benefits associated with “folding” in of the nonlinear partitions into the more convenient linear form will be exploited in development of nonlinear system estimation strategy (for systems with “algebraic” nonlinearities).

13.6.3 MI/SO Frequency Response Function Estimation For the case of a single response, Y, and multiple excitations, [X], The MI/SO relationship describing measured data that includes noise is, Y (f) = [HYX (f)] {X (f)} + N (f) ,

(13.25)

Where {N(f)} represents noise sources that are assumed uncorrelated with the excitations, {X(f)}. The response autospectrum is related to the excitation and noise cross-spectra as,  GYY (f) = [HYX (f)] · [GXX (f)] · H∗YX (f) + GNN (f) = GYY,C (f) + GNN (f) ,

(13.26)

where, GYY,C (f) is the coherent output autospectrum. On the assumption that noise sources are not correlated with the excitations, the optimal estimate of frequency response functions is, [HYX (f)] = [GYX (f)] · [GXX (f)]−1 ,

(13.27)

and the total ordinary coherence function is defined as, 2 γYX (f) =

(GYY (f))C ≤ 1. GYY (f)

(13.28)

The above MI/SO formulation does not offer details related to contributions associated with the multiple excitations to the output response. An alternative MI/SO analysis formulation using Cholesky decomposition, which does provide insight into individual excitation contributions, is thoroughly developed by Bendat and Piersol [13].

13.6.4 MI/SO Frequency Response Function Estimation Using Cholesky Factorization Cholesky factorization of the excitation cross-spectral matrix, [GXX (f)] yields, [GXX (f)] = [XZ (f)] · [ZX (f)] ,

(13.29)

where [ XZ (f)] is a complex, lower triangular matrix and [ ZX (f)] is its upper triangular, Hermitian transpose. A triple product decomposition version of Cholesky factors is formed by unit diagonal normalization of [ XZ (f)] and [ ZX (f)] resulting in, [GXX (f)] = [LXZ (f)] · [GZZ (f)] · [LZX (f)] ,

(13.30)

where [LXZ (f)] and [LZX (f)] are lower and upper triangular, unit diagonal matrices, respectively, and [GZZ (f)] is a positivedefinite, diagonal matrix. Physical significance of the normalized triangular factors is recognized by noting the input variable transformation, {X (f)} = [LXZ (f)] · {Z (f)} .

(13.31)

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The successive terms in {Z(f)} are, Z1 (f) = X1 (f) ,

Z2 (f) = X2 (f)“ swept" of contributions from X1 (f) ,

(13.32)

Z3 (f) = X3 (f)“ swept" of contributions from X1 (f) and X2 (f) . . . .. Therefore, [GZZ (f)] is the diagonal autospectrum matrix of uncorrelated, generalized inputs, {Z(f)}. Substitution of the triple product [GXX (f)] decomposition relationship (eq. 13.30) into eq. 13.27 results in the frequency response functions associated with uncorrelated generalized inputs, {Z(f)}, [HYZ ] = [GYZ ] · [GZZ ]−1 ,

(13.33)

[HYZ ] = [HYX ] · [LXZ ] , [GYZ ] = [GYX ] · [LZX ]−1 .

(13.34)

where,

Therefore, the frequency responses associated with physical inputs, {X(f)}, are now expressed as, [HYX ] = [HYZ ] · [LXZ ]−1 .

(13.35)

The generalized MI/SO equation in terms of generalized inputs is defined as, Y (f) = [HYZ (f)] · {Z (f)} + N (f) .

(13.36)

Since the generalized inputs, are uncorrelated, the output autospectrum (dropping the “f” designation) is expressed as,



2

2

2 GYY = HYZ1 · GZ1 Z1 + HYZ2 · GZ2 Z2 + · · · + HYZN · GZK ZK + GNN ,

(13.37)

The cumulative coherence function family is therefore defined as follows:  

2 2 = HYZ1 · GZ1 Z1 /GYY , for input x1 (t) , γY1  

2

2

2 2 = HYZ1 · GZ1 Z1 + HYZ2 · GZ2 Z2 + .. + HYZN · GZK ZK /GYY , for inputs, x1 (t) + .. xk (t) . γYK

(13.38)

(13.39)

The cumulative coherence function family has the property, 2 2 2 ≤ γY2 ≤ · · · ≤ γYK ≤ 1. 0 ≤ γY1

(13.40)

When graphically displayed as a function of frequency, the coherence function family appears as a waterfall plot series that clearly indicates the relative contributions of the accumulated excitation sources. The benefits of such a display will be demonstrated in a series of illustrative examples. Finally it is noted that Multiple Input/Multiple Output or MI/MO analysis represents a simple extension to MI/SO analysis.

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13.6.5 Illustrative Example: ISPE Modal Test The ISPE test article was excited with broad band random excitation forces at four separate locations, and MI/MO correlation and spectral analysis was preformed employing 8192 length windows with 50% overlap processing. Cumulative coherences for all 265 TAM response channels plus 4 drive point response channels were computed. MI/MO plots associated with all 4 excitation forces and 4 drive point responses are detailed below in Fig. 13.22.

Fig. 13.22 Representative ISPE MI/MO FRF and Cumulative Coherence Plots

The plots in Fig. 13.22 are arranged in a 4X4 matrix “plot map”. For example, the plots in the (2,3) position correspond to excitation 2, drive point response 3. Each plot “i, j” entry includes the cumulative coherence (top), FRF phase angle (middle), and FRF magnitude (bottom). An important feature of the plot matrix is FRF “reciprocity” (e.g., the “i, j” component is consistent with the “j, i” component, with regard to both magnitude and phase of the FRF). Greater detail can be discerned from the plot group for the “1, 1” component shown below in Fig. 13.23. Of particular interest is the (top) cumulative coherence plot, which (a) indicates the successive contributions of the first three excitations (to drive point 1 response autospectum) that are substantially below unity and (b) indicates the significant role of the fourth excitation producing near unit cumulative coherence. The cumulative coherences associated with nearly all response channels were close to unity confirming extremely high quality FRF estimates.

13.6.6 Illustrative Example: Wire Rope Isolator Nonlinear Characterization Recalling the preliminary measured data analysis, summarized in Fig. 13.21, the hypothesized “algebraic” nonlinear system composed of measured time histories (applied force and acceleration response) and synthesized “measured” time histories (cubed displacement and velocity•|velocity|) depicted below in Fig. 13.24 was subjected to MI/SO analysis. The cumulative coherence plot, shown below in Fig. 13.25 indicates that incorporation of the two nonlinear terms produces a nearly unit value cumulative coherence (red curve), while the ordinary coherence associated with a linear model (blue curve) indicates reduced coherence [14]. The above results provide clear evidence that the behavior of the wire rope isolators is nonlinear. However, further definitive data analysis indicates that the nonlinear behavior is “hysteretic” rather than “algebraic” as currently hypothesized. That being said, the present “algebraic” nonlinear model serves an important role as an “intermediate” data analysis.

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Coherence

File: ISPETESTDFRFs...MI/MO: Navg=16, df=0.025, Input(1)=2302104X-,Output(1)=2302104X+ 21-Sep-2019 3:54 PM 1 0.5 0 15

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Fig. 13.23 ISPE MI/MO FRF and Cumulative Coherence Plots for Excitation 1, Drive Point Response 1

Fig. 13.24 Hypothesized MI/SO Nonlinear System

13.6.7 Illustrative Example: ISS P5 Modal Test The ISS P5 test article was excited with broad band random excitation forces at three separate locations, MI/MO correlation and spectral analysis was preformed employing 1024 length windows with 50% overlap processing. Cumulative coherences for all 261 TAM response channels plus 3 drive point response channels were computed. MI/MO plots associated with the three drive point FRFs are detailed below in Fig. 13.26. The reduced cumulative coherences in the 30–35 Hz frequency band were judged provide additional evidence of test article nonlinear behavior, which was noted in preliminary data analysis results summarized in Fig. 13.20.

13.7 Experimental Modal Analysis (EMA) Experimental modal analysis owes its present state-of-the-art contributions of many technologists [1, 15, 16]. The most reliable general approach to this task involves (a) thorough preliminary analysis employing graphical and numerical techniques dating back to the “analog” era [15] (before 1970), followed by (b) employment of rigorous experimental modal analysis procedures [1, 16] developed during the “digital” era (after 1970).

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File: WireNonR...MI/MO: Navg=9, DF=0,488, MI/SD Cumulative Coherence

1 0.9

Due to Force Due to Force + U3Z3

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Due to Force + U3Z3+V3Z+|V3Z|

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10

15

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25

30 Hz

35

40

45

50

Fig. 13.25 Hypothesized Nonlinear System Cumulative Coherence

Fig. 13.26 ISS P5 MI/MO FRF and Cumulative Coherence Plots

13.7.1 Preliminary Experimental Modal Analysis (ISPE Modal Test, 2016) Experimental FRF displays associated with drive point 1 provided below in Fig. 13.27. The above FRF function is displayed in a variety of formats, which offer insight into experimental modal content. Specifically, the upper window displays FRF magnitude vs. frequency, the lower left window displays FRF magnitude and

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Magnitude

FRF Display: File: ISPETESTDFRFs, mat, Input(1)=2302104X-, Output(1)=2302104X+ 24-Sep-2019 11:35 AM

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35 40 frq (Hz)

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55

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Real

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–0.02 –0.04 –0.06

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–100 20

30

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20 Phase (Deg)

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Imaginary

Magnitude

10

20

30

20

30

40

50

60

50

60

0.05 0

–0.05

60

40 frq (Hz)

Fig. 13.27 ISPE Drive Point 1 FRF Detail

phase, the lower center window displays a real vs. imaginary FRF components (polar plot), and the lower left window displays FRF real and imaginary components vs. frequency (popular called a co-quad plot). A more comprehensive overview of the “many modes” evident in the ISPE test article is evidenced by display of two composite signature functions, namely (a) a normalized square-root of the summation of the autospectra for all modal test response accelerations, and (b) a global FRF skyline function, defined as a complex frequency domain function whose real and imaginary parts are the sum of the absolute values of the real component of response FRFs and the sum of the absolute values of the imaginary component of response FRFs, that is, SKY (f) =

NH  k=1

|real (Hk (f))| + i

NH 

|imag (Hk (f))| .

(13.41)

k=1

A display of the two global skyline functions for the ISPE test article is provided below in Fig. 13.28. The phase FRF skyline offers the clearest indication of the presence of many modes in the 15–65 Hz frequency band. While the skylines indicate the presence of “many modes”, further investigation of local response FRFs will provide insight into the presence of additional localized modes (a difficult, slow task for a structural test article that is mapped by 265 response channels and 4 excitations, that is 1060 individual FRFs!). Other strategies for discerning the presence of “many modes” as well as closely-spaced modes have been developed and successfully applied by leaders in the experimental structural dynamics community [1].

13.7.2 Overview of the Simultaneous Frequency Domain (SFD) Method A thorough presentation of the SFD method is provided in a separate paper entitled, “Roadmap for a Highly Improved Modal Test Process” [17]. The SFD method has undergone substantial revision and refinement since its introduction in 1981, primarily by this writer and principals at The Aerospace Corporation. SFD assumes that FRFs associated with a series of “N” excitations may be described in terms of a transformation described by, 

 H1 (f) H2 (f) . . . HN (f) = [V] · ξ¨ 1 (f) ξ¨ 2 (f) . . . ξ¨ N (f) .

(13.42)

13 The Integrated Modal Test-Analysis Process (2020 Challenges) ISPESTSTD Skyline Functions

100 PSD1/2 Skyline

147

10–1 10–2 10–3 15

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40 Freq (Hz)

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30

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40 Freq (Hz)

45

50

55

60

65

|FRF| Skyline

100 10–1 10–2

phase(FRF) Skyline

10–3 15 1 0.8 0.6 0.4 0.2 0 15

Fig. 13.28 ISPE Test Article Global Skyline Functions

By performing singular value decomposition  (SVD) analysis of the FRF collection, a dominant set of real generalized trial vectors, [V], and complex generalized FRFs, ξ¨ 1 (f) ξ¨ 2 (f) . . . ξ¨ N (f) , is obtained. Unit normalization and orthogonality of the SVD trial vectors is expressed as, [V]T [V] = [I] .

(13.43)

The generalized FRF array assumes the following dynamic system equations associated with the individual applied forces,                ˜ [ξ (f)] = ˜ [F (f)] , where B ˜ = M−1 [K] . ˜ = M−1 [B] and K ξ¨ (f) + B˜ ξ˙ (f) + K

(13.44)

      ˜ , and ˜ , are estimated by linear least-squares analysis. The real, effective dynamic system matrices, B˜ , K Estimation of experimental modal parameters is performed by complex eigenvalue analysis of the state space form of the effective dynamic system,  

 

˜ ξ¨ −B˜ −K ξ˙ ˜ {F} , = + ξ˙ I 0 ξ 0

(13.45)

The SFD method (and more generally any method that performs similar system “plant” estimation operations) will pick up spurious “noise” degrees of freedom and associated spurious modes. Over the years since 1981, the writer has employed a heuristic practice in versions of SFD algorithms that select “authentic” modes from the complete set, which is estimated in selected frequency bands. The heuristic criteria include, (1) elimination of modes having negative damping, (2) modes with very low modal gain, and (3) other modes that appear spurious from any number of physical/experience based considerations. The theoretical relationship between FRFs and modal parameters (assuming that modal vectors are real) is, [H (f)] = [] · [h (f)] ,

(13.46)

where [] is the unknown real modal matrix and [h(f)] is the SDOF acceleration FRF matrix. The terms of [h(f)] are defined as,

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−(f/fn )2 hn (f) =  , 1 + 2iζn (f/fn ) − (f/fn )2

(13.47)

where the fn and ζn are the modal frequency and damping associated with the particular experimental mode. Since the modal SDOF acceleration matrix is completely known, the real modal matrix is obtained by linear least squares analysis. At the experimental modal analyst’s discretion (highly recommended), low and/or high frequency residual modal frequencies may be added to the set of identified eigenvalues (the low frequency residual FRF has a frequency close to “0” and a userselected damping value, e.g., ζn = .01, and the high frequency residual has a frequency substantially higher than the highest experimental modal frequency and a a user-selected damping value, e.g., ζn = .01) to enhance accuracy of modal vector estimates. The theoretical relationship between FRFs and modal parameters (assuming that modal vectors are complex) is, [H (f)] = − (2π · f) ·

N   n=1

 n ∗n + ∗ , λn − i (2π · f) λn − i (2π · f)

(13.48)

where n is the unknown nth complex modal residue vector and λn is the nth (positive imaginary part) complex eigenvalue. The complex modal residue vectors are proportional to the complex system modes. Complex eigenvalues (when critical damping ratio, ζJ , is less than 1.0) are, λn = −ζn ωn + iωn .

(13.49)

Since the complex eigenvalues are completely known, the complex modal residue vectors (proportional to the complex modal vectors) are obtained by linear least squares analysis. As for the case of real modes, low and/or high frequency residual modal frequencies may be added to the set of identified eigenvalues to enhance accuracy of modal vector estimates. In 2017, as a result of the “many modes” challenge presented by the ISPE modal test, the SFD procedure was modified to address two key requirements, namely (1) discrimination of authentic and spurious modes, and (2) estimation of complex system modes that result from close modal frequency spacing. The new SFD-2018 methodology avoids least square modal fitting (outlined in eqs. 13.46–13.49) and estimates complex experimental modes through back transformation of the effective dynamic system’s (eq. 13.45) complex modes by employing the SVD trial vectors (eqs. 13.42–13.43).

13.7.3 ISS P5 Modal Test Experimental Modal Analysis Detailed experimental modal analysis of one specific measured data set for the ISS P5 modal test article (TSS2), employing the (pre-2018) SFD method, resulted in estimation of 23 test article modes in the 0–63 Hz frequency band as summarized below in Fig. 13.29. Note the first 10 modes (shaded in yellow) were selected for subsequent test-analysis correlation and model reconciliation analyses.

Fig. 13.29 ISS P5 Experimental Modal Analysis (SFD Curve Fit and Modal Orthogonality)

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Review of the contents of the orthogonality matrix indicates that the NASA orthogonality criterion (goal) [2] was achieved for most of the 23 test modes, including modes 11–23 which had non-negligible kinetic energy content associated with the test fixture.

13.7.4 IS PE Modal Test Experimental Modal Analysis The Integrated Spacecraft Payload Element (ISPE) was the subject of modal testing at NASA/MSFC in the fall of 2016. Measured FRF data was quite extensive, and the NASA team had a great deal of difficulty in estimation of modal parameters in the 0–65 Hz frequency band due in part to close modal spacing and significant modal density. These challenges led to development of SFD-2018, which is thoroughly discussed in a separate paper [17]. Results of pre-2018 experimental modal analysis methodology and measured FRF reconstruction are illustrated in below Fig. 13.30.

Fig. 13.30 ISPE Experimental Modal Analysis (pre SFD-2018 Curve Fit and Modal Orthogonality)

Review of the contents of the orthogonality matrix indicates that the NASA orthogonality criterion (goal) [2] was achieved for many of the 35 lowest frequency test modes.

13.8 Systematic Test Analysis Correlation Developments in structural dynamic modeling and modal testing were strongly motivated by aircraft structural failures as early as the first decade of the twentieth century. The space race, dating back to the 1950’s, and its early failures resulted development of strict government modal test-analysis correlation standards [2, 3] based on mass-weighted orthogonality and cross-orthogonality metrics. The present discussion focuses on (1) review of mass weighted test mode orthogonality and test-analysis cross-orthogonality metrics, and (2) introduction of a modal coherence metric. All of the noted metrics are the consequence of a rigorous weighted least-squares formulation. Employment of the mass weighted correlation metrics is demonstrated on modal data associated with two modal test projects.

13.8.1 Derivation of Mass Weighted Test-Analysis Correlation Metrics The relationship between target test modes, [t ], and their analytical counterparts, [a ], is described by the transformation, [t ] = [a ] [COR] + [R] ,

(13.50)

where [COR] is the cross-orthogonality matrix and [R] is the residual error matrix. Employing the TAM mass matrix, [Maa ], as a weighting matrix, the least squares solution for cross-orthogonality is

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  [COR] = [ORa ]−1 Ta Maa t ,

(13.51)

where the analysis mode orthogonality matrix is   [ORa ] = Ta Maa a ≈ [I] .

(13.52)

and the residual error matrix is orthogonal to the test modes, i.e., [a ]T [Maa ] [R] ≡ [0] .

(13.53)

The modal coherence matrix, [COH], is defined based on manipulation of eqs. 13.50–13.53, resulting in,      [COH] = [I] − [ORt ]−1/2 RT MR [ORt ]−1/2 = [I] − [ORt ]−1/2 CORt ORa COR [ORt ]−1/2 ,

(13.54)

where the test mode orthogonality matrix is,   [ORt ] = Tt Maa t .

(13.55)

The modal coherence matrix, [COH], provides a metric of the ability of mathematical model modes, [a ], to reconstruct the measured modes, [t ]; in particular, if the diagonal term, |COHnn |, associated with measured mode “n” is unity, the measured mode is a perfect linear combination of the mathematical model modes, [a ].

13.8.2 NASA and USAF Space Command Test-Analisis Correlation Standards NASA STD-5002 [2] states “Agreement between test and analysis natural frequencies shall, as a goal, be within 5 percent for the significant modes (aka target modes) . . . Mode shape comparisons shall be required via cross-orthogonality checks using the test modes [t ], the analytical modes [a ], and the analytical mass matrix [Maa ]. The cross-orthogonality matrix is computed as [t ]T [Maa [a ]. As a goal, the absolute value of the cross-orthogonality between corresponding test and analytical mode shapes should be greater than 0.9; and all other terms of the matrix should be less than 0.1 for all significant modes”. It is also informative to note the somewhat stricter U.S. Air Force Space Command criterion [3] for test-analysis correlation, which states, “As a goal, the analytical model frequencies should be within three percent of the measured values, and the cross-orthogonality between the analytical and measured modes, each set normalized to yield a unit generalized mass matrix, should yield values equal to or greater than 0.95 on the diagonal, and equal to or less than 0.10 on the off-diagonal of the cross-orthogonality matrix. Any modeling adjustments/changes made to achieve the above-stated criteria must be consistent with the actual hardware and its drawings”.

13.8.3 ISS P5 Test-Analysis Correlation At the time of the ISS P5 modal test, the modal coherence matrix was not employed as part of the modal test-analysis correlation process. It is quite informative nevertheless to review results of cross-orthogonality analysis, which was employed for correlation of (pre-2018 SFD) test modes and FEM analytical modes. As noted previously in this paper, the ISS P5 modal test suffered from challenges associated with localized nonlinearity and non-repeatability of experimental modal data. It is informative to review cross-orthogonality results for the TSS2 data set associated with the ISS P5 pre-test and revised posttest models. A more extensive discussion of the ISS P5 test-analysis reconciliation process (model updating) is provided in Sect. 13.9 of this paper. A summary of pre-test ISS P5 modal frequencies, TSS2 data set modal frequencies and the test-FEM cross-orthogonality matrix (for the first 10 modes) is provided below in Table 13.4.

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Table 13.4 ISS P5 Data Set TSS2 Test to Pre-test FEM Modal Frequencies and Cross-Orthogonality Matrix

The TSS2 data set pre-test modal frequency correspondence and cross-orthogonality matrix do not satisfy NASA STD5002 test-analysis correlation criteria (goals). Model updating operations substantially improved the test-analysis correlation situation, as summarized below in Table 13.5. Table 13.5 ISS P5 Data Set TSS2 Test to Updated FEM Modal Frequencies and Cross-Orthogonality Matrix

The level of compliance of TSS2 modal test data and the updated P5 FEM model, with NASA STD-5002 test-analysis correlation goals, is summarized below in Table 13.6. Table 13.6 ISS P5 Data Set TSS2 Test to Updated FEM NASA STD-5002 Compliance Status Mode 1

Pre-test FEM Freq (Hz) 18.67

TSS2 Freq (Hz) 16.94

Post-test FEM Freq (Hz) F (%) 16.48 −2.72

COR (%) 98

2 3 4 5 6

19.31 24.88 28.68 29.37 30.07

17.58 25.19 28.44 31.12 32.6

18.08 25.66 28.65 30.74 32.28

2.84 1.87 0.74 −1.22 −0.98

97 96 92 94 83

7 8 9

34.01 34.65 35.22

33.66 35.19 36.39

33.32 34.64 36.58

−1.01 −1.56 0.52

82 85 90

10

35.61

38.38

36.98

−3.65

97

Comments Satisfies NASA-STD-5002 modal frequency and on-diagonal cross-orthogonality goals

Frequency band associated with reduced MI/MO coherence (strong nonlinearity)

Satisfies NASA-STD-5002 modal frequency and on-diagonal cross-orthogonality goals

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13.8.4 ISPE Test-Analysis Correlation (Using Pre-test Fem Data) ISPE modal test data, described in Fig. 13.30, and ISPE FEM modes are now compared employing the conventional mass weighted correlation procedure. Employing the real part of the ISPE (pre-SFD-2018) complex modes and ISPE FEM modes, test mode orthogonality, test-analysis cross-orthogonality, and modal coherence matrices are provided below in Fig. 13.31.

Fig. 13.31 ISPE Conventional Mass Weighted Test-Analysis Correlation Matrices

While the cross-orthogonality matrix indicates poor test-analysis modal correlation for many of the 63 SFD estimated modes, the modal coherence matrix indicates that approximately 50 of the SFD-2018 modes are linear combinations of the 75 lowest frequency FEM modes.

13.9 Reconciliation of Finite Element Models and Test Data Reconciliation of finite element models with modal test data depends upon two key technical components, namely, (a) efficient, accurate FEM modal sensitivity analysis, and (b) minimization (optimization) of appropriately defined cost functions.

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13.9.1 Modal Sensitivity and Structural Dynamics Modification Efficient computation of structural dynamic modal frequency and mode shape sensitivities associated with variation of physical stiffness and mass parameters is essential for (1) practical design sensitivity and uncertainty studies and (2) reconciliation of finite element models with modal test data. Sensitivity analysis procedures fall in two distinct categories, namely (a) modal derivatives for small parametric variation and (b) altered system modes associated with “large” parametric variation. The latter category is generally applicable to modal testing, which often requires significant local parameter changes at joints to effect FEM-test reconciliation. However, many investigators and commercial software packages employ estimated modal derivatives [18, 19] in optimization strategies, which address FEM-test reconciliation objectives. The matrix equations describing exact free vibration of baseline and altered structures, respectively, are [KO ] [O ] − [MO ] [O ] [λO ] = [0] ,

(13.56)

  KO + p · K [] − MO + p · M [] [λ] = [0] .

(13.57)

It is implicitly assumed that the stiffness and mass changes scale linearly with respect to the parameter, p. Therefore, changes in “beam” depth may not be directly applied, since the axial stiffness (AE) scales linearly with depth and the flexural stiffness (EI) scales as the cube of depth. The appropriate formulation for eq. 13.62 permits linear sensitivity of “AE” and “EI” separately. The fundamental Ritz [20] approximation that is used in Structural Dynamic Modification (SDM) [21] employs a truncated set of low frequency eigenvalues as the reduction transformation described by, [] = [OL ] [ϕ] .

(13.58)

The reduced baseline structure stiffness and mass matrices are, respectively,     [kO ] = TOL KO OL = [λOL ] , [mO ] = TOL MO OL = [IOL ] ,

(13.59)

and the reduced stiffness and mass sensitivity matrices are, respectively,     [k] = TOL KOL , [m] = TOL MOL .

(13.60)

Therefore, the reduced altered structure free vibration equation is,   λOL + p · k [ϕ] − IOL + p · m [ϕ] [λ] = [0] .

(13.61)

A well-known result of this type of trial vector reduction strategy is that the approximate altered structure eigenvalues are generally higher than results for the exact solution, and the approximate mode shapes do not closely follow the exact shapes when parametric alterations are large.

13.9.2 Residual Mode Augmentation (RMA) for Dispersed Alterations Definition of residual vectors associated with dispersed, independent alterations of a baseline structure, described by eq. 7.1, is accomplished by first computing the lowest frequency mode shapes of the baseline structure (eq. 13.56) as well as the lowest mode shapes associated with each independent alteration of the structure (see eq. 13.57),   KO + pi Ki [iL ] − MO + pi Mi [iL ] [λiL ] = [0] (for i = 1, . . . , N) .

(13.62)

The selected value of each independent scaling parameter,pi , is sufficiently large to produce a substantial change in mode shapes (with respect to the baseline structure). An initial set of trial vectors that adequately (and perhaps redundantly) encompass all potential (low frequency) altered system mode shapes is,

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 [] = Φ1L 2L . . . NL .

(13.63)

This set of trial vectors is expressible as the sum of (a) a linear combination of baseline system mode shapes and (b)

trial vectors, [ ], that are linearly independent of the baseline system mode shapes. The “purified” trial vector set, [ ] is defined in a manner similar to MacNeal’s residual vectors [22]. The “purified” trial vector set includes an unnecessarily large number of vectors. A substantially smaller set of residual vectors is identified by singular value decomposition [8], resulting in the augmented trial vector set,    (13.64) OL = OL  ’ . The form of the resulting SDM, multi-parameter sensitivity model is,  kO +

N 





pi [ki ] [ϕ] − mO +

i=1

N 

 pi [mi ] [ϕ] [λ] = [0] ,

(13.65)

i=1

where,         T T T T [kO ] = OL KO OL , [mO ] = OL MO OL , [ki ] = OL Ki 2 , [mi ] = OL Mi OL .

(13.66)

Recovery of mode shapes in terms of physical degrees-of-freedom is accomplished with,  [] = OL [ϕ] .

(13.67)

13.9.3 RMA Solution Qualities Since its introduction in 2001, RMA has exhibited the capability to accurately follow modal sensitivity trends over an extremely wide range of parametric variation. The simple cantilevered (planar) beam example, provided in Fig. 13.32 below, demonstrates typical RMA performance (“100%” is baseline). Actual cross-orthogonality checks are also excellent.

13.9.4 Test-Analysis Reconciliation Using Cost Function Optimization Reconciliation of a test article’s finite element model with experimental modal data, if conducted in an objective and systematic manner, requires minimization of a cost function. A variety of modal cost functions are employed by many investigators. The present discussion describes a particular cost function that describes a balanced modal frequency and mode shape “error” relationship. Minimization (or optimization) of the modal cost function’s error norm employing gradient based and Monte Carlo strategies are evaluated. Consider the standard expression for the undamped structural dynamics eigenvalue problem, [K] [] − [M] [] [λ] = [0] .

(13.68)

When modal test data is substituted into the above expression, [K] [t ] − [M] [t ] [λt ] = [R] ,

(13.69)

there is a residual error, [R], due to (a) differences between the FEM and modal test data and (2) measurement error. Premultiplication by the FEM mode shapes results in,       T Kt − T Mt [λt ] = T R .

(13.70)

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155

Illustrative Cantilevered Beam Modal Frequency Sensitivity

Modal Frequency (Hz)

103

102

101 Exact Reference Perturbed Modes Exact Extreme Perturbed Modes Augmented Mode Based Sensitivity

100 10–1

100

101

102

Percent of Baseline “E12”

Fig. 13.32 RMA Sensitivity Performance for a Cantilevered Beam Example

By substituting the transpose of [K][] from eq. (13.68), the above relationship becomes,       [λ] T Mt − T Mt [λt ] = T R .

(13.71)

Finally, pre-multiplication of the above result by the inverse of the FEM eigenvalues defines the modal cost function [Cλ ] as,     [Cλ ] = λ−1 T R = [COR] − [λ]−1 [COR] [λt ] , where [COR] = T Mt .

(13.72)

The FEM may be efficiently altered employing the RMA method for specific values of selected parameters. A reconciled FEM is therefore defined by the combination of selected parameter alterations, which minimize the norm of the modal cost function, [Cλ ]. This may be accomplished by use of a random, Monte-Carlo [23] parameter search strategy or the Nelder-Meade Simplex algorithm [24].

13.9.5 ISS-P5 Test-Analysis Reconciliation The ISS P5 modal test, conducted in 2001, was the first opportunity to employ RMA sensitivity and modal cost function (norm) minimization methodology on a “production” modal test. Before presenting results of this particular investigation, it is important to emphasize valuable “lessons learned” from this first experience, specifically, 1. Due to “noise” in the modal test data, gradients associated with the modal cost function, [Cλ ], were not sufficiently “smooth” for application of the Nelder-Meade Simplex method. Therefore the Monte-Carlo search analysis strategy was employed in this and all subsequent modal tests. 2. Error norm “clouds”, which are 2D projections of the multidimensional modal cost function norm and individual parametric variations (all parameters varied in the search process) indicate the relative significance of each parameter, as illustrated below in Fig. 13.33. During the course of ISS P5 modal testing, nonlinearity in the left trunnion joint interface caused the experimental modes to migrate whenever a new set of data was recorded and analyzed. More than 25 FEM parameters were initially considered

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Fig. 13.33 ISS P5 Typical Modal Cost Function Error Norms

in the modal test-analysis reconciliation exercise. It was initially concluded that 9 FEM parameters, when adjusted, effected satisfactory reconciliation for three selected modal test sets (specifically, TSS2, TSS4 and TSS17). The adjusted parameters are summarized in Table 13.7. Note that only the left forward-mid and mid-aft strut end stiffness (“LT FM Struts” and “LT MA Struts”), corresponding to joint play were altered from test to test to effect reconciliation. Table 13.7 Summary of FEM Parameters Adjusted for Reconciliation Parameter 1 2 3 4 5 6 7 8 9

Description Bot braces Lt FM struts Lt MA struts Grap Lat Spr Mid long I-1 Mid long I-2 Grap I-1 A Grap I-2 A Grap I’s B

Original value 3.00E+09 3.00E+09 3.00E+09 Baseline 4.56 4.56 I1 (non-uniform) I2(non-uniform) I1&I2(non-uniform)

TSS02 Update value 0 1.50E+05 2.40E+05 Baseline 5.077 5.248 1.49XBaseline 1.46XBaseline 1.42XBaseline

% Change −100 −99.995 −99.992 0 11.3 15.1 49 46 42

TSS04 Update value 0 6.00E+04 1.20E+05 Baseline 5.08 5.25 1.49XBaseline 1.46XBaseline 1.42XBaseline

% Change −100 −99.998 −99.996 0 11.3 15.1 49 46 42

TSS17 Update value 0 3.30E+05 3.30E+05 Baseline 5.08 5.25 1.49XBaseline 1.46XBaseline 1.42XBaseline

% Change −100 −99.989 −99.989 0 11.3 15.1 49 46 42

A summary of TSS2, TSS4, and TSS17 mode set reconciliations indicating compliance with NASA [3] modal frequency and cross-orthogonality goals is provided below in Table 13.8. The above model reconciliations were judged to be in appropriate compliance with NASA STD-5002 [3] goals for this challenging modal test (due to significant nonlinear dynamic behavior), by the test team and NASA management. The testanalysis reconciliation exercise was completed within 2 weeks of the completion of laboratory activities.

13.9.6 Wire Rope Isolator Nonlinear System Identification While the wire rope test article is a not modal test-correlation and reconciliation application, it provides an example of detailed nonlinear system identification for a dynamic system that possesses strong hysteretic behavior. It is instructive at this point to recall results of preliminary data analysis and nonlinear MI/SO spectral analysis discussed previously in this paper. Preliminary data analysis of the estimated isolator deflection and isolator internal force probability density functions was previously summarized in Fig. 13.21. A hypothesized “algebraic” nonlinear system composed of measured time histories (applied force and acceleration response) and synthesized “measured” time histories (cubed displacement and velocity•|velocity|) was previously summarized in Figs. 13.24 and 13.25. While the prior results provide clear evidence that the behavior of the wire rope isolators is nonlinear, closer examination of isolator response to swept-sine excitation suggests the wire rope isolator exhibits “hysteretic” nonlinear behavior. The hypothesized wire rope model consists of the linear spring and Iwan friction slip element [25], depicted below in Fig. 13.34. Unknown parameters for the model consist of (a) linear spring stiffness, K1, (b) total Iwan stiffness, KF, (c) total Iwan critical slip force, F0; the Iwan parameters are uniformly distributed among n = 5 sub-elements.

18.08 25.66 28.65 30.74 32.28

19.31 24.88 28.68 29.37 30.07

34.01 34.65 35.22

35.61

2 3 4 5 6

7 8 9

10

36.98

33.32 34.64 36.58

TSS2 Post-test (Hz) 16.48

Pre-test Mode Freq (Hz) 1 18.67

33.38

33.66 35.19 36.39

17.58 25.19 28.44 31.12 32.60

Test (Hz) 16.94

97 96 92 94 83

82 85 90

97

−1.01 −1.56 0.52

−3.65

COR (%) 98

2.84 1.87 0.74 −1.22 −0-98

F (%) −2.72

37.00

32.93 34.39 36.56

18.02 25.50 28.09 30.56 31.63

TSS4 Post-test (Hz) 15.31

38.58

33.49 35.32 36.34

17.92 25.17 28.51 31.32 32.45

Test (Hz) 15.20

4.27

87

72 85 92

98 97 92 89 84

−0.55 −1.29 1.50 2.49 2.59

1.70 2.70 −0.60

COR (%) 98

F (%) −0.72

Table 13.8 ISS P5 Data Sets TSS2, TSS4, and TSS17 Test to Updated FEM NASA STD-5002 Compliance Status

36.99

33.71 34.98 36.60

18.24 25.80 29.16 30.87 32.65

TSS17 Post-test (Hz) 17.31

38.32

33.64 35.08 36.32

17.61 25.12 28.30 31.08 32.66

Test (Hz) 17.37

3.60

−0.21 0.29 −0.77

−3.45 −2.64 −2.95 0.68 0.03

F (%) 0.35

97

89 87 91

98 94 92 94 77

COR (%) 98

Satisfies NASA STD-5002 modal frequency and on-diagonal crossorthogonality goals

Frequency band associated with reduced MI/MO coherence (strong nonlinearity)

Satisfies NASA STD-5002 modal frequency and on-diagonal crossorthogonality goals

Comments

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Fig. 13.34 Hypothesized Nonlinear Wire Rope Model

Estimation of the three unknown parameters was accomplished by minimization of the error norm defined by the square of the absolute difference between measured (swept-sine) and model force time histories. A Monte-Carlo search strategy was employed to determine optimum values for the three unknown parameters. Error norm projections for the three parameters are illustrated below in Fig. 13.35.

Fig. 13.35 Wire Rope Cost Function Error Norm Projections

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Fig. 13.36 Results of the Wire Rope Hysteretic Nonlinear Model System Identification

Effectiveness of the wire rope nonlinear system identification process is illustrated in comparison of the measured and fitted model load-deflection plots provided below in Fig. 13.36. The dashed and solid black lines indicate stiffness asymptotes associated with non-slip and fully-slipped behaviors. While the majority of this paper has been devoted to the integrated test analysis process for linear structural dynamic systems, this final illustrative example offers a glimpse of promising future developments that may expand the process to include systems with quite general nonlinear features.

13.10 Conclusions This rather lengthy paper provided a synopsis of the integrated test analysis process (ITAP) for structural dynamic systems, as employed in the U.S. aerospace community. ITAP follows seven essential tasks, namely (1) model development, (2) modal test planning, (3) measured data acquisition, (4) measured data analysis, (5) experimental modal analysis, (6) test analysis correlation, and (7) model reconciliation. The roles of six of the seven tasks (excluding measured data acquisition, which is the domain of highly experienced laboratory technologists) were demonstrated in this paper with examples from past modal testing projects. The “many modes” challenge associated with large, complex launch vehicle and spacecraft systems currently in development, is being met by innovations in understanding the modal content employing modal orthogonality “unpacking”, target mode selection based on dynamic response “decomposition”, and a major update in experimental modal analysis which is the subject of a separate paper on a “roadmap for a highly improved modal test process”.

References 1. Piersol, A.G., Paez, T.L. (eds.): Harris’ Shock and Vibration Handbook, 6th edn. McGraw-Hill (2010) 2. Load Analysis of Spacecraft and Payloads. NASA-STD-5002 (1996) 3. U.S. Air Force Space Command: Independent Structural Loads Analysis. SMC-S-004 (2008) 4. Abramson, H.N.: The Dynamic Behavior of Liquids in Moving Containers. NASA-SP-106 (1966) 5. Coppolino, R.N.: A Numerically Efficient Finite Element Hydroelastic Analysis, vol. 1. NASA CR-2662 (1975) 6. Coppolino, R.N.: Structural Dynamic Modeling–Tales of Sin and Redemption. IMAC XXXIII (2015) 7. Coppolino, R.N.: Understanding Large Order Finite Element Model Dynamic Characteristics. IMAC XXIX (2011) 8. Coppolino, R.N.: Methodologies for Verification and Validation of Space Launch System (SLS) Structural Dynamic Models, vol. 1. NASA/CR 2018–219800 (2018) 9. Williams, D.: Dynamic Loads on Aeroplanes under Given Impulsive Load with Particular Reference to Landing and Gust Loads on a Large Flying Boat. Great Britain Royal Aircraft Establishment Reports SME 3309 and 3316 (1945) 10. Guyan, R.: Reduction of stiffness and mass matrices. AIAA J. 3, (1965)

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11. Coppolino, R.N.: Automated Response DOF Selection for Mapping of Experimental Normal Modes. IMAC XVI (1998) 12. Coppolino, R.N.: The ISS-P5 Modal Survey: Test Planning through FEM Reconciliation. IMAC XX (2002) 13. Bendat, J.S., Piersol, A.G.: Random Data Analysis and Measurement Procedures, 4th edn. Wiley (2010) 14. Bendat, J.S.: Nonlinear Systems Techniques and Applications, 2nd edn. Wiley (1998) 15. Bishop, R.E.D., Gladwell, G.M.L.: An investigation into the theory of resonance testing. Philos. Trans. R. Soc. Lond. Ser. A. 225(A-1055), 241–280 (1963) 16. Brown, D.L., Allemang, R.J.: The Modern Era of Experimental Modal Analysis. Sound and Vibration Magazine (2007) 17. Coppolino, R.N.: Roadmap for a Highly Improved Modal Test Process. IMAC XXXVIII (2020) 18. Fox, R.I., Kapoor, M.P.: Rates of change of eigenvalues and eigenvectors. AIAA J. 6, (1968) 19. Nelson, R.B.: Simplified calculation of eigenvector derivatives. AIAA J. 14, (1976) 20. Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. Reine Angew. Math. 135, (1908) 21. Twenty Years of Structural Dynamic Modification-A Review. IMAC 20 (2002) 22. MacNeal, R.: A hybrid method for component mode synthesis. Comput. Struct. 1, (1971) 23. Metropolis, N., Ulam, S.: The Monte Carlo method. J. Am. Stat. Assoc. 44(247), 335–341 (1949) 24. Nelder, J., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965) 25. Iwan, W.: On a class of models for the yielding behavior of continuous composite systems. J. Appl. Mech. 89, 612–617 (1967)

Chapter 14

Roadmap for a Highly Improved Modal Test Process Robert N. Coppolino

Abstract Difficulties encountered in modal test planning and recent advances in experimental modal analysis of aerospace systems have resulted in a new paradigm for experimental modal analysis. The Simultaneous Frequency Domain (SFD) method, weighted complex linear least squares correlation methodology, and state space model left- and right- hand eigenvector properties combine to produce the following benefits that are independent of an explicit TAM mass matrix: (1) verification and validation of experimental modes via isolation of individual experimental modes, (2) automatic selforthogonality of experimental modes, (3) test- FEM cross orthogonality, and (4) experimental complex mode kinetic energy distribution. The new approach directly employs complex experimental modes (rather than real mode approximations) and frees experimental data from a potentially flawed TAM mass matrix. A roadmap for incorporation of the new paradigm into NASA and USAF standards and continued progress are outlined in this paper. Keywords Complex experimental modes · Test analysis correlation

14.1 Introduction Challenges encountered by NASA/MSFC on the Integrated Spacecraft Payload Element (ISPE) modal survey in the fall of 2016 bring an important challenge to the forefront. Specifically, which estimated test modes are “authentic”, and which modes are associated with “noise” associated with measured frequency response functions (FRFs)? The present discussion on experimental modal analysis (EMA) focuses on mathematical isolation of individual estimated test mode FRFs in a manner that is similar to the concept developed by Mayes and Klenke [1]. While the presently discussed EMA approach ought to be quite independent of the investigator’s choice of experimental modal analysis algorithm, the results herein apply to methods that explicitly estimate the tested system’s state-space plant matrix such as the Simultaneous Frequency Domain (SFD) method [2–4], which relies heavily on singular value decomposition [5]. The latest version of SFD (SFD-2018) employs mathematical operations aimed at isolating individual candidate experimental modes without direct reliance on information associated with the subject system’s TAM mass matrix. The key to mathematical and visual isolation of individual modes from measured data is the left-hand eigenvector. Virtually all modern experimental modal analysis techniques produce estimates of (right-hand) eigenvectors and eigenvalues (modal frequency and damping). While techniques for estimation of left-hand eigenvectors are well-known (e.g., the “real mode transpose times TAM mass matrix product” and the MoorePenrose pseudo-inverse [6]), they have been judged inadequate. The purest approach to estimation of left-hand eigenvectors is a consequence specifically those techniques that estimate the measured system’s plant or effective dynamic system matrix, such as SFD. Since a complete set of raw experimental modes are identified consistent with the order of the estimated plant, the left-hand eigenvectors are calculated exactly from the inverse of the complete, raw right-hand eigenvector set. Over many years, members of the experimental modal analysis community have been challenged over the use of NASA and USAF Space Command [7, 8] modal orthogonality and cross-orthogonality criteria for validation of experimental modal vectors and for assessment of test-analysis correlation, respectively. At the heart of the challenge is the role played by the potentially inaccurate TAM mass matrix, which is derived from a mathematical model. Recent work that exploits left-hand eigenvectors, estimated by the SFD-2018 technique [9], provides a promising way out of the TAM mass matrix impasse. Modal orthogonality, defined as the product of left- and right-handed experimental eigenvectors (real or complex) is

R. N. Coppolino () Measurement Analysis Corporation, Torrance, CA, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_14

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mathematically an identity matrix. This guarantees that SFD estimated modes are always perfectly orthogonal. An alternative cross-orthogonality definition, based on weighted complex linear least-squares analysis [10], is evaluated and found to possess the desired property. Employment of (1) the left- and right-handed experimental eigenvector based orthogonality matrix and (2) the weighted complex linear least-squares based cross-orthogonality matrix represents a “game changer” that potentially frees the experimental modal analysis community from the potentially inaccurate TAM mass matrix.

14.2 Nomenclature

[Aη ] [B] [COH] [COR] [F] [H(f)] [K] [KE] [M] [OR] [U] [V] f fn h(f) {q}

Plant state matrix Damping matrix Modal coherence matrix Cross-orthogonality matrix Force array Frequency response matrix Stiffness matrix Modal kinetic energy Mass matrix Orthogonality matrix Physical displacement array Generalized SFD vector matrix Frequency (Hz) Natural frequency (Hz) SDOF frequency response function Modal displacement array

 [] [I]

Mode shape Spatial force allocation Identity matrix

[γ] {η} λ ωn [ξ] ζn

Generalized modal gain matrix State variable array Eigenvalue Modal frequency (rad/sec) Generalized SFD displacement array Critical damping ratio

14.3 The Simultaneous Frequency Domain (SFD) Method The SFD method [2], introduced in 1981, has undergone substantial revision and refinement since that time [3, 4], primarily by this writer and principals at The Aerospace Corporation. SFD implicitly assumes that FRFs associated with a series of “N” excitations may be described in terms of a transformation described by,   ¨ 1 (f) U ¨ 2 (f) . . . U ¨ N (f) = [V] ξ¨ 1 (f) ξ¨ 2 (f) . . . ξ¨ N (f) . U

(14.1)

By performing singular value decomposition (SVD) analysis [5] of the FRF collection, a dominant set of real generalized  trial vectors, [V], and complex generalized FRFs, ξ¨ 1 (f) ξ¨ 2 (f) . . . ξ¨ N (f) , is obtained. Unit normalization of the SVD trial vectors is expressed as, [V]T [V] = [I] .

(14.2)

Theoretically, the generalized FRF array describes the following dynamic system equations associated with the individual applied forces,                ˜ [ξ (f)] = Γ˜ [F (f)] , where B˜ = M−1 [B] and K ˜ = M−1 [K] . ξ¨ (f) + B˜ ξ˙ (f) + K       ˜ , and Γ˜ , are estimated by linear least-squares analysis [6]. The real, effective dynamic system matrices, B˜ , K

(14.3)

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Estimation of experimental modal parameters is performed by complex eigenvalue analysis of the state variable form of the effective dynamic system,  

 

˜ ξ¨ −B˜ −K ξ˙ Γ˜ {F} , = + ξ˙ I 0 ξ 0

(14.4)

 {η} ˙ = [Ah ] {η} + Γη {F} .

(14.5)

which is of the general type,

Complex eigenvalue analysis of the effective dynamic system produces the following results: (a) (b) (c) (d)

{η} = [η ]{q}, where the “left-handed” eigenvectors are [ηL ] = [η ]−1 [ηL ] · [η ] = [I], [ηL ] · [Aη ][η ] = [λ] (complex eigenvalues) (14.6) [ηL ] · [ η ] = [γ] (modal gains) q˙ j − λj qj = (γ)j [F (f)] (frequency response of individual modes).

Recovery of experimental modes in terms of the physical DOFs involves back transformation employing the trial vector matrix, [V], specifically,     [] = [V] η , [L ] = ηL VT , [OR] = [L ] [] ≡ []

(14.7)

14.3.1 The SFD Method Prior to 2018 Estimation of the effective dynamic system with the SFD method (and more generally any method that performs similar system “plant” estimation operations) will pick up spurious “noise” degrees of freedom and associated spurious modes. Over the years since 1981, the writer has employed a heuristic practice in versions of SFD algorithms that select “authentic” modes from the complete set, which is estimated in selected frequency bands. The heuristic criteria include, (1) elimination of modes having negative damping, (2) modes with very low modal gain, and (3) other modes that appear spurious from any number of physical/experience based considerations. Prior to 2018, the SFD method (this writer’s version) did not make use of the complex modes associated with the effective dynamic system (eqs. 14.3–14.7). The theoretical relationship between FRFs and modal parameters (assuming that modal vectors are real) is [H (f)] = [] · [h (f)] ,

(14.8)

where [] is the unknown real modal matrix and [h(f)] is the SDOF acceleration FRF matrix. The terms of [h(f)] are defined as, −(f/fn )2 hn (f) =  , 1 + 2iζn (f/fn ) − (f/fn )2

(14.9)

where the fn and ζn are the modal frequency and damping associated with the particular experimental mode. Since the modal SDOF acceleration matrix is completely known, the real modal matrix is obtained by linear least squares analysis. At the experimental modal analyst’s discretion (highly recommended), low and/or high frequency residual modal frequencies may be added to the set of identified eigenvalues (the low frequency residual FRF has a frequency close to “0” and a userselected damping value, e.g., ζn = .01, and the high frequency residual has a frequency substantially higher than the highest experimental modal frequency and a a user-selected damping value, e.g., ζn = .01) to enhance accuracy of modal vector estimates. The theoretical relationship between FRFs and modal parameters (assuming that modal vectors are complex) is, [H (f)] = − (2π · f) ·

N   n=1

 n ∗n + ∗ , λn − i (2π · f) λn − i (2π · f)

(14.10)

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where n is the unknown nth complex modal residue vector and λn is the nth (positive imaginary part) complex eigenvalue. The complex modal residue vectors are proportional to the complex system modes. Complex eigenvalues (when critical damping ratio, ζJ , is less than 1.0) are λn = −ζn ωn + iωn .

(14.11)

Since the complex eigenvalues are completely known, the complex modal residue vectors (proportional to the complex modal vectors) are obtained by linear least squares analysis. As for the case of real modes, low and/or high frequency residual modal frequencies may be added to the set of identified eigenvalues to enhance accuracy of modal vector estimates. Regardless of whether the user chooses to estimate real or complex modal vectors, reconstructed FRFs calculated from identified modal parameters serve as a means for a quality check on the overall (pre-2018) SFD process.

14.3.2 SFD 2018: A Fresh Look at Experimental Modal Analysis The initial point of departure from pre-2018 SFD practice is estimation of an effective dynamic system over the entire frequency band of interest (rather than selected sub-frequency bands). In order to achieve a satisfactory estimation for the effective dynamic system, the “tolerance” factor (ε) employed in the SVD process is set to a sufficiently low value (10−5 ); in previous sub-frequency band SFD calculations, the SVD “tolerance” factor was set to a value of 10−2 . Computation of effective dynamic system modal parameters, from the first-order system described in eq. 14.5, yields complex modes with eigenvalues having negative and positive imaginary parts. The first level of mode down-selection is to eliminate all modal eigenvalues and eigenvectors that are outside the positive frequency band of interest. A vital component of the mode downselection process is selection of left-hand eigenvectors. [ηL ] that correspond to their [η ] counterparts; this circumvents issues associated with more involved procedures for computation of a truncated left-hand eigenvector set. Two computational procedures estimate uncoupled experimental modal FRFs. The first method computes the exact modal solution from the estimated modal parameters of eq. 14.6d. Specifically,     hj A = q˙ j A =



i2πf i2πf − λj



  γj .

(14.12)

The second method estimates uncoupled experimental modal FRFs from linear combinations of the generalized FRFs (see eq. 14.6a, b) as follows:      ˙ . hj E = q˙ j E = ηL j · (η)

(14.13)

Verification and validation of any candidate estimated experimental mode is now to be judged on the basis of (a) graphical displays of the modal FRFs, and (b) a new modal coherence metric, which is defined as,

 

hj (f) ∗ · hj (f) 2 A E COHj =     .

hj (f) ∗ · hj (f) · hj (f) ∗ · hj (f) A E A E

(14.14)

14.3.3 ISPE Experimental Modal Analysis (EMA) The Integrated Spacecraft Payload Element (ISPE) was the subject of modal testing at NASA/MSFC in the fall of 2016. Measured FRF data was quite extensive, and the NASA team had a great deal of difficulty in estimation of modal parameters in the 0–65 Hz frequency band due in part to close modal spacing and significant modal density. These challenges led to development of SFD-2018. For completeness, results of pre-2018 experimental modal analysis methodology and measured FRF reconstruction are illustrated in Fig. 14.1.

14 Roadmap for a Highly Improved Modal Test Process File: ISPETESTDFRF Global Real Mode Fit... Input=2302113X-, Output=2302113X+

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Establishment of a selected set of experimental modes employing uncoupled modal FRF estimates, computed using eq. 14.12 (red for reconstructed FRFs) and eq. 14.13 (blue for experimental FRFs) for several candidate modes is illustrated in Figs. 14.2, 14.3, and 14.4 include FRF magnitude, magnitude and phase, polar, and real and imaginary parts.

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It is clear in the above three figures that candidate modes 1 and 3 appear valid based on close agreement of the two types of uncoupled modal FRF estimates. In contrast, candidate mode 6 is clearly “spurious”.

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Fig. 14.4 EMA for SFD Candidate Mode 6, Excitation 4 (4% Coherence)

Table 14.1, shown below summarizes additional information related to the process of selection of 63 acceptable experimental modes from the 106 candidate modes (the first 30 candidate modes and associated modal coherences are illustrated). The above table provides a clear demonstration of the utility of the newly introduced EMA metric. In particular, the modal coherence metric, defined in eq. 14.14, for which a value of 85% or greater is assumed to indicate a validly estimated mode.

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Table 14.1 EMA Modal Selection Criterion (COHj ≥85%) for Candidate Modes 1–30 Candidate mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Eigenvalue FREQ (Hz) 16.74 17.03 18.12 18.16 18.79 19.40 20.08 20.31 20.96 21.01 23.23 24.05 24.07 24.26 24.95 25.82 25.89 27.70 27.79 28.91 30.15 32.52 32.52 33.42 33.65 34.61 35.53 35.76 36.24 36.46

Zeta (%) 2.32 2.25 0.12 0.12 0.12 0.05 3.22 3.07 0.10 0.09 2.14 0.02 0.48 0.45 1.81 0.15 0.12 1.40 1.69 –1.44 0.07 0.95 0.11 0.16 1.56 2.28 1.17 0.86 0.15 0.26

Modal coherences Excitation 1 99.15 72.99 70.97 97.08 94.47 2.80 93.57 95.26 86.89 96.43 39.31 27.91 83.55 99.71 36.78 99.69 78.20 98.84 96.85 0.76 87.03 8.29 28.00 87.29 66.09 90.14 83.46 72.07 95.91 99.76

Excitation 2 98.92 97.67 69.87 78.26 87.10 3.24 76.25 94.92 96.19 91.40 23.98 29.69 99.34 99.46 44.96 96.55 96.91 95.49 98.79 0.36 88.28 81.46 27.15 95.81 96.78 79.40 80.42 72.16 96.93 99.38

Excitation 3 98.31 98.62 73.51 85.15 97.41 1.91 94.66 90.67 93.10 89.50 4.12 18.24 98.94 99.33 54.73 95.00 89.74 95.59 98.58 1.09 69.70 91.37 3.47 95.64 93.51 65.22 64.20 62.79 80.51 99.68

Excitation 4 88.97 98.75 97.16 42.25 95.45 3.54 92.82 88.32 91.52 88.14 34.13 40.46 99.46 34.16 33.49 95.85 98.99 98.57 96.55 2.55 86.86 97.65 25.12 91.84 15.07 93.04 88.29 22.99 93.78 99.75

14.3.4 ISPE Test-Analysis Correlation (Using Conventional Metrics) NASA [7] (and USAF Space Command [8]) standards specify the following goal for orthogonality of experimental modes: “Accurate mass representation of the test article shall be demonstrated with orthogonality checks using the analytical mass matrix [MA ] and the test mode shapes [Φ T ]. The orthogonality matrix is computed as [Φ T ]T [MA ][Φ T ]. As a goal, the off-diagonal terms of the orthogonality matrix should be less than 0.1 for significant modes based on the diagonal terms normalized to 1.0.” It is quite informative to compare orthogonality matrices computed by (1) the conventional method based on weighted orthogonality of real modes (in this case the real part of the ISPE test modes) with respect to the TAM mass matrix, and (2) exact complex test mode orthogonality assured by left-hand eigenvectors (modes) based on Eq. 14.6b. Results for the 63 ISPE test modes are depicted below in Fig. 14.5. While results of orthogonality based on the NASA STD-5002 criterion indicate good to excellent orthogonality for the first 34 modes, the alternative based on the exact mathematical property of complex SFD-2018 estimated modes opens up the opportunity for automatic satisfaction of the orthogonality criterion without reliance on the (potentially flawed) FEM based TAM mass matrix. The NASA [7] standard specifies the following goal for cross-orthogonality of experimental and mathematical model predicted modes: “Mode shape comparisons shall be required via cross-orthogonality checks using the test modes [Φ T ], the analytical modes [Φ A ], and the analytical mass matrix [MA ]. The cross-orthogonality matrix is computed as [Φ T ]T [MA ][Φ A ]. As a goal, the absolute value of the cross-orthogonality between corresponding test and analytical mode shapes should be greater than 0.9; and all other terms of the matrix should be less than 0.1 for all significant

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modes. Additionally, qualitative comparisons between test modes and analytical modes using mode shape animation and/or deflection plots shall be performed”. The somewhat stricter U.S. Air Force Space Command standard [8] for test-analysis correlation, which states, “As a goal, the analytical model frequencies should be within three percent of the measured values, and the cross-orthogonality between the analytical and measured modes, each set normalized to yield a unit generalized mass matrix, should yield values equal to or greater than 0.95 on the diagonal, and equal to or less than 0.10 on the off-diagonal of the cross-orthogonality matrix. Any modeling adjustments/changes made to achieve the above-stated criteria must be consistent with the actual hardware and its drawings”. ISPE modal test data and ISPE FEM modes are now compared employing the conventional mass weighted correlation procedure. Employing the real part of the ISPE SFD-2018 complex modes and ISPE FEM modes, NASA STD-5002 test mode orthogonality, cross-orthogonality, and modal coherence matrices are provided below in Fig. 14.6. While the cross-orthogonality matrix indicates poor test-analysis modal correlation for many of the 63 SFD-2018 estimated modes, the modal coherence matrix indicates that approximately 50 of the SFD-2018 modes are linear combinations of the 75 lowest frequency FEM modes.

14.3.5 ISPE Test-Analysis Correlation (Using Left-Hand Eigenvectors) Systematic correlation of two sets of state-space, generally complex vectors (with identical DOF designations) is defined in a manner analogous to the case of real vector sets, wherein the transpose operator, is replaced by the complex conjugate transpose [10]. The correlation procedure is formally defined by the following steps: Step 1: Normalization of complex mode sets -1/2 −1/2   , [QTAM ] = diagonal ∗TAM TAM [QTEST ] = diagonal ∗TEST TEST

[TEST ]n = [TEST ] · [QTEST ] , [TAM ]n = [TAM ] · [QTAM ] .

(14.15)

Step 2: Pseudo-Orthogonalities and Pseudo Cross-Orthogonality (only used for Step 3 operations!) [ORTEST ] = [TEST ]∗n [TEST ]n , [ORTAM ] = [TAM ]∗n [TAM ]n , [COR] = [TAM ]∗n [TEST ]n .

(14.16)

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Step 3: Modal Coherence  ∗ [C] = [ORTAM ]−1 n [COR] , [R] = [TEST ]n − [TAM ]n [C] , [COH] = [ORTEST ] − R R .

(14.17)

Extensive evaluation of the complex least squares process indicates that both the complex cross-orthogonality and coherence matrices behave in a manner that parallels the behavior of their real eigenvector counterparts. Therefore, complex modal orthogonality and test-analysis mode correlation may be separated into a “recipe” composed of two distinct sub-tasks, namely: 1. Complex mode orthogonality is perfectly satisfied by left-hand eigenvector counterparts to state-space complex eigenvectors for test and TAM eigenvector sets (following eq. 14.6b). 2. Complex mode cross-orthogonality (correlation) and complex modal coherence are defined based on the complex leastsquares process (following eqs. 14.15–14.17) Following the above “recipe”, complex mode orthogonality, cross-orthogonality, and modal coherence matrices are illustrated in Fig. 14.7. The TAM and test mode orthogonality matrices are perfect identity matrices. The cross-orthogonality matrix appears similar in form to its state-space counterpart (see Fig. 14.6), and the modal coherence matrix indicates that the majority of lower frequency (~50%) of test modes are strong linear combinations of the TAM modes. Recalling the fact that the orthogonality matrix can be “unpacked” to describe a subject system’s modal kinetic energy distribution [9], a corresponding “unpacking” of the complex state-space mode orthogonality matrix (eq. 14.6b) similarly

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describes the kinetic energy distribution of the complex modes. In particular, the modal orthogonality and kinetic energy distribution relationship pair for a complex state-space modal set is defined below, in terms of left- and right-hand eigenvectors as,   [OR] = [L ] [] = V,L [V ] +  U,L [U ] ,    [KE ] = conj ∗L ⊗ [] = conj ∗V,L ⊗ [V ] + conj ∗U,L ⊗ [U ] .

(14.18)

Note that []* in the present context corresponds to the complex conjugate transpose of the matrix, []; the same operator designation applies to the left-hand eigenvector matrix. Partitioning of the complex state-space left- and righthand eigenvectors into “velocity” and “displacement” partitions (designated by the subscripts “V” and “U”, respectively), in order to describe the modal kinetic energy distributions in terms of the measured DOFs, the above definitions of complex state-space eigenvector orthogonality and modal kinetic energy distributions are independent of the TAM mass matrix.

14.4 The Roadmap for a Highly Improved Modal Test Process Introduction of the complex state-space viewpoint for experimental modal analysis (SFD-2018) and the TAM mass matrix independent metrics described in this paper as well as two recent papers [11, 12], suggests a potential paradigm shift for

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the integrated test-analysis process. A roadmap for this envisioned process, encompassing experimental modal analysis and systematic test analysis correlation, employing ISPE modal test data and mathematical model data, is outlined below (Figs. 14.8, 14.9, 14.10, and 14.11).

Fig. 14.8 ISPE Experimental Modal Analysis and Modal Orthogonality

Fig. 14.9 ISPE Test-Analysis Cross-Orthogonality and Modal Coherence

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Fig. 14.10 ISPE Test Mode 1 Mode Shape and Modal Kinetic Energy

Fig. 14.11 ISPE Test Mode 3 Mode Shape and Modal Kinetic Energy

The roadmap for a highly improved integrated test analysis process offers the following innovations: 1. Experimental modal analysis moves from the current, prevailing practice of verification and validation through curve fitting back to past (pre-digital era) practice of single mode isolation made possible by the SFD-2018 technique. 2. Established goals for experimental mode orthogonality (NASA STD-5002 and USAF Space Command SMC-S-004) are automatically satisfied, without dependence on a possibly flawed and/or inaccurate TAM mass matrix.

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3. Test-analysis cross-orthogonality goals (NASA STD-5002 and USAF Space Command SMC-S-004) are addressed without dependence on a possibly flawed and/or inaccurate TAM mass matrix. Moreover, the modal coherence analysis is defined independent of the TAM mass matrix. 4. While the conventionally used “real” test mode approximation often is similar in content to the corresponding SFD-2018 estimated test mode, modal kinetic energy distributions associated with the “real” and “complex” test modes may differ from one another. This is attributed to the fact that the conventional “real” test mode based modal kinetic energy depends on a possibly flawed and/or inaccurate TAM mass matrix. This is clearly demonstrated by the lack of agreement between conventional and complex modal kinetic energy distributions for ISPE mode 1, and close agreement between conventional and complex modal kinetic energy distributions for ISPE mode 3. 5. The emerging option for a highly improved integrated test analysis process must be reviewed, applied in parallel with established with established practice, and aggressively “poked and prodded” by the technical community before this “paradigm shift” is accepted.

14.5 Conclusions Experimental modal analysis (EMA) is a mature discipline in the structural dynamics community, which is as much an “art” as it is a “science”. Modern procedures for estimation of modal parameters from measured data are highly automated; however, applications involving complicated structural systems and/or systems with closely-spaced, parametrically sensitive modes require the test engineer’s experience and judgment (“art”) to discern the difference between authentic and spurious (“junk” or “noise”) system modes. A prevailing metric for experimental modal data validation is the orthogonality check, which relies on a model-based (TAM) mass matrix. In addition, reconstructive synthesis of measured frequency response function (FRF) data is another widely used strategy for experimental mode validation. The present EMA study employs mathematical operations aimed at isolating individual candidate experimental modes without reliance on a TAM mass matrix. The key to mathematical and visual isolation of individual modes from measured data is the left-hand eigenvector. The most effective approach to determination of left-hand eigenvectors stems from employment of techniques that estimate the measured system’s plant or effective dynamic system matrix. Since a complete set of (authentic and “noise”) system modes are estimated for the plant, left-hand eigenvectors are determined from the inverse of the complete right-hand eigenvector set. The following metrics provide a systematic basis for experimental modal analysis (EMA): 1. The estimated Single-Degree-of-Freedom (SDOF) modal FRF, formed by the product of a single estimated left-hand eigenvector and FRF matrix, is plotted in terms of real and imaginary components vs. frequency, magnitude and phase components vs. frequency, and polar real vs. imaginary components. Authenticity of an estimated mode is then judged on the basis of quality of the plots. 2. The SDOF modal FRF is also formed from exact mathematical solution of the estimated effective dynamic system. Graphical comparison of this result with the above left-handed product information offers further means of authentic vs. “junk” mode discrimination. 3. The coherence metric based on comparison of the results of “1” and “2” provides a 0-to-100% figure of merit for estimated experimental modes. The following additional metrics provide a systematic basis for test-analysis correlation: 4. The left-hand, right-hand eigenvector based state-space orthogonality matrix for complex experimental modes automatically satisfies NASA STD-5002 and USAF SMC-004 requirements. The orthogonality matrix for experimental modes is mathematically perfect by definition, and it is independent of the approximate TAM mass matrix. 5. Employment of the complex least-squares formulation for test-TAM correlation and modal coherence appears to be an appropriate enhancement for incorporation in NASA STD-5002 and USAF SMC-004 test-analysis correlation standards. It is recognized that the task of modal correlation does not specifically require perfectly orthogonal, real modes. 6. Introduction of the complex least-squares formulation for test-TAM correlation and modal coherence opens the opportunity for inclusion of damping in correlation and update endeavors, e.g., structures with non-negligible modal complexity due to localized, non-proportional damping mechanisms (joints). 7. Formation of complex mode kinetic energy distributions employing “unpacking” of complex (left- to right-hand eigenvector operations) provides additional means for test-analysis correlation analysis, which is independent of a theoretical mass matrix.

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References 1. Mayes, R., Klenke, S.: The SMAC Modal Parameter Extraction Package. IMAC XVII (1999) 2. Coppolino, R.: A Simultaneous Frequency Domain Technique for Estimation of Modal Parameters from Measured Data. SAE Paper 811046 (1981) 3. Coppolino, R., Stroud, R.: A Global Technique for Estimation of Modal Parameters from Measured Data. SAE Paper 851926 (1985) 4. Coppolino, R.: Efficient and Enhanced Options for Experimental Mode Identification. IMAC XXI (2003) 5. Golub, G.H., Reinsch, C.: Singular value decomposition and least squares solutions. Numer. Math. 14, 403–420 (1970) 6. A generalized inverse for matrices. R. Penrose Proc. Camb. Philos.Soc. 51, 406–413 (1955) 7. Load Analysis of Spacecraft and Payloads. NASA-STD-5002 (1996) 8. U.S. Air Force Space Command: Independent Structural Loads Analysis. SMC-S-004 (2008) 9. Coppolino, R.: The Integrated Modal Test-Analysis Process (2020 Challenges). IMAC XXXVIII (2020) 10. Miller, K.: Complex linear least squares. SIAM Rev. 15(4), 706–726 (1973) 11. Coppolino, R.: Experimental Mode Verification (EMV) Using Left-Hand Eigenvectors. IMAC XXXVII (2019) 12. Coppolino, R.: Modal Test-Analysis Correlation using Left-Hand Eigenvectors. IMAC XXXVII (2019)

Chapter 15

Using Low-Cost “Garage Band” Recording Technology for Acquiring High Resolution High-Speed Data Randall Wetherington, Gregory Sheets, Tom Karnowski, Ryan Kerekes, Michael Vann, Michael Moore, and Eva Freer

Abstract The Oak Ridge National Laboratory (ORNL) has developed and tested a novel system architecture for acquiring high fidelity high-speed data. The approach uses a consumer grade audio recording device that is normally associated with “garage band” recording of music. ORNL has coupled this low-cost data acquisition hardware with computing technology running open-source software. The main advantage of this approach is per-channel cost; an instrument grade data acquisition system typically costs between $800 to $2000 per channel compared to less than $50 per channel for these consumer grade components. Three systems, each featuring four channels, have been deployed for acquiring data from geophones and the electrical supply system that supports the High Flux Isotope Reactor (HFIR) and the Radiochemical Engineering Development Center (REDC) at ORNL. Each channel samples at 96 kHz at 24-bit resolution. The deployed systems operate continuously 24/7 and produce about 4 terabytes of data per month per system. This paper provides a technical overview of this approach, its implementation, and some preliminary results from qualification testing. This work was conducted in support of the Multi-Informatics for Nuclear Operations Scenarios (MINOS). Keywords Data acquisition · Measurement · Informatics

15.1 Background and Approach The impact of digital technologies has produced profound changes in all aspects of our lives. This includes the business of making high-speed measurements. In particular, the marriage of digital and low-noise analog technologies has resulted in data acquisition solutions that provide levels of performance that were a pipe dream only a few decades ago. Even so, the cost per channel of a quality high-speed data acquisition system can be high; starting at about $1 K per channel and going much higher. Yet there are creative approaches that can get this per channel cost down especially in cases where laboratory-grade measurements are not required such as machine monitoring or signature detection. This approach works especially well for applications where persistent data recording is required (i.e., data acquisition does not stop). The approach is based on leveraging the superb performance capabilities of consumer audio recording USB adapters with the robust data management capabilities of Linux when deployed on PC-level computers. The performance and robustness that can be achieved with this approach is quite impressive. The audio adapters, which are the analog-to-digital converters (ADCs) in this approach, are available as 2, 4, 8, and more channels per USB device. These units provide 16-bit or 24-bit digital representation with overall SNR specifications in the range of 90 dB to 120 dB. The channels are synchronously sampled and multiple units can be synchronized together. The dynamic range performance is usually better than 90 dB and tonal detectability with the correct processing can be in excess of −150 dB referenced to 1 Volt peak-to-peak. The big advantage of using USB audio adapters is cost. The per-channel cost is $25 to $400 per channel.

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). R. Wetherington () · G. Sheets · T. Karnowski · R. Kerekes · M. Vann · M. Moore · E. Freer Oak Ridge National Laboratory, Oak Ridge, TN, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_15

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Furthermore, the need for expensive anti-alias filters is eliminated since sigma-delta conversion technology is often used in these devices. There are some tradeoffs in using audio equipment for data acquisition. The most significant is the fact that most audio adapters are A/C coupled, which means they do not digitize DC values; however, many audio adapters will accurately resolve frequencies as low as 2–3 Hz, which in many cases is sufficient. There are a few audio adapters that claim to digitize all the way down to DC but these are less common and address a special focus of the audio market. Another tradeoff is latency (the delay between the sound input and the recording). Audio recording gear is designed for very low latency, resulting in very little digital buffering in the adapter. This characteristic has major impact on the computer and software that receives this digitized data in terms of the risk of missed samples. This can be an extremely difficult challenge to address. Some vendors address this challenge in specialized device drivers they provide with the equipment. These drivers are typically written for the Microsoft Windows operating system and may not be available for other operating systems. Some of the devices provide gain and filtering adjustments on a per channel basis. In some cases, these controls are available as knobs and switches on the front of the devices. While this can provide an incredible amount of flexibility when deploying the devices in the field, at some point the effects of the adjustments must be factored into the measurements before analytics can be performed. This can be problematic if note carefully planned for. Possibly the most imposing challenge to using audio adapters is the lack of vendor provided specifications and performance metrics. This means the burden is on the developer to determine how well this approach works and to what degree it can be certified. Environmental compliance is also important to consider. Testing and validation of these devices can be a sizeable amount of work because these devices are not marketed or intended for scientific research applications. Furthermore, the developer is essentially “on their own” for the applications software development and testing. This can be a significant commitment. However, the benefits of using audio adapters can be realized if the number of deployed units and channels is high. The investment to develop and qualify a design is then distributed across a large number of field deployments. ORNL has been using low-cost consumer grade audio devices for several years in high-speed data acquisition applications [1–4]. One of ORNL’s more recent adaptations of consumer audio gear for data acquisition is for a project that involves high-speed collection systems that are deployed around ORNL’s HFIR and REDC facilities. Data acquired by the collection systems is analyzed and correlated to operational ground truth information from the facilities. USB audio adapter are used as the foundation technology for three of the collection systems, which may be expanded in the near future.

15.2 Design The architecture of the MINOS high-speed collection systems is shown in Fig. 15.1. A Behringer UMC404HD audio adapter is coupled with a PC running Centos Linux. The Behringer unit digitizes four input channels by sampling each at 96 kHz with a resolution of 24-bits which is provided as a four-byte sample word. Advanced Linux Sound Architecture (ALSA)

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utilities are used for configuration and streaming control of the Behringer audio data. A Python script receives the data stream and accumulates it in a ring-buffer in memory. Data files are then sequentially saved that are 5 minutes in length. The file names contain the node IP-address identifier and a time stamp with microsecond resolution. The files are initially stored on a local solid-state disk drive. At a predetermined interval, the data is pushed to a file server using the Linux rsync command. Analysts typically use MATLAB or Python to analyze the data. Currently, three such systems are deployed for this project. They all run in a “persistent” mode which means they stream data all the time (it does not stop). And, there is no data loss. Each five-minute data file is approximately 480 Mbytes long. A single collector will generate about 4 Terabytes of data per month. While the signal sources for the input channels in our implementation are current transformers and geophones, virtually any analog signal source can be used for input that provides a signal level within the +/− 10-volt range. The Behringer audio adapters include a manual gain adjustment control for each channel that provides a lot of flexibility in the field. Development of this approach has occurred in several stages. An initial implementation based on Microsoft Windows and a C# application program was fielded for about a year. After its deployment, a periodic data loss condition was detected. This condition was infrequent yet persistent. Once identified, several attempts at streamlining the application software and adjusting task priorities were made without success. As a result, an approach that uses the Linux operating system was evaluated and found to work consistently with adequate performance. The Linux approach was fielded in August 2018.

15.3 Characterization of Performance Figure 15.2 shows a typical broadband frequency response curve for one of the collection systems. The input signal was a 1-Vpp sine wave at 1013 Hz. As noted later in this paper, many of the extraneous tones observed in Fig. 15.2 are from the signal source (i.e., the function generator). Figure 15.3 shows a narrowband plot (0–1500 Hz) for this same test signal. Figure 15.4 shows a lower narrowband showing the levels of 60 Hz and its first harmonics. Figures 15.5 and 15.6 show the measured roll-off response for the lower and upper frequency ranges of the Behringer. Broadband Response of Behringer with Input of 1,013 Hz 100

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Figures 15.7 and 15.8 show the measured response of the Behringer and another consumer USB audio adapter, the MOTU1 64, when terminated with a shorted and 50-ohm termination. These plots are important in that they show what the audio adapters is capable of producing. Much of the extraneous tone behavior shown in the previous figures were sourced from the function generator used for the testing. Based on the performance achieved in these last two figures, the user will realize much better measurements if the signal source driving the ADC is a “driven low-impedance output source”. This recommendation is similar what developers tried to achieve with older “flying capacitor” successive approximation ADCs that incorporated sample-hold inputs of each channel.

15.4 Special Considerations Many audio recording devices feature a manual gain adjustment along with its signal clipping indicator, which provides a lot of flexibility for dealing with a range of signal levels in the field. However, if a calibrated measurement is required, special considerations need to be made for a deployed system. Either an in-situ method of signal injection must be devised or an independent means of making a reference measurement must be included in the design for calibrating the measurements.

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The time accuracy of the sampling is also important. Most audio adapters generate their own sampling clock internally. This clock is the basis for any frequency domain analysis that may be planned. For several Behringer units we tested, a consistently “slow” sample clock was observed. By counting samples, we found that the Behringers lost about 14 seconds of data per day, which means the clock was slow by about 0.0162%. A slow sample clock means any resolved frequencies will appear higher than they actually are. Other manufacturers indicate they offer heater controlled crystal clock sampling signals, which may offer much better performance. They will be higher cost. Another challenge with using audio adapters is their low-latency design characteristics (i.e., these devices are designed for streaming data continuously with very little buffering). This means the devices have a small internal data buffer which places a challenging requirement on the responsiveness of the computer that must process this data. If the computer cannot service the data stream fast enough, samples are lost. ORNL spent a significant amount of effort testing these units to identify Behringer adapter, computer, and operating system combinations that would work. To qualify a design, we implemented a sample-loss detection scheme and ran the systems for a week to validate that the approach would be sample-loss-free. Additionally, we time stamp each data file with microsecond time resolution. This time stamp can be used to identify if sample loss occurs. The persistent nature of our application created the necessity for a means of operational monitoring that would not impede the continuous operation of the data acquisition function. We wanted an easy means of detecting when a system and its sensors were not operating properly. Our implementation approach was to create RMS values of each input channel and then plot those RMS features over a 7-day and 24-hour time span. This effectively produced a 48,000:1 data reduction in the presentation of the data. The resulting plots were emailed to our work accounts and also sent via text message to our

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phones every morning at 8 AM. This provided an easy means of checking on the systems operating state. Figure 15.9 shows a typical seven-day plot. The time stamps that were included in the data file names were also analyzed and used to detect when a sampling error occurred.

15.5 Conclusions ORNL has designed and deployed three high-speed data MINOS collection systems that utilize low-cost consumer grade audio recording adapters for gathering field data. Each system provides four channels of sensor data that are sampled at 96 ksamples/s each. Data is gathered continuously. The systems have been operating since August 2018 and produce approximately 4 Terabytes of data per month per system. The data quality is considered to be very good for conducting analysis of operational features in the data. A number of actions were required to prepare this technology for deployment including characterization of the device’s frequency response, software development of the main data acquisition process, verification that the implementation would not lose samples, taking independent field measurements that were then used to determine calibration coefficients, and the development of simple operational validators that would produce simple plots that could be reviewed to verify proper system operation. While there are other approaches to achieving high-speed data sampling, the use of consumer audio adapters offers a very cost effective solution if the user is prepared to invest some effort up front to develop test and qualify the system for use. This may not be a cost-effective solution for a single deployment, but it can very cost effective when multiple units and channels are fielded.

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References 1. Wetherington Jr., G.R., Van Hoy, B., Phillips, L., Damiano, B., Upadhyaya, B.: Evaluation of a Consumer Electronics-Based Data Acquisition System for Equipment Monitoring. NPIC/HMIT (2015) 2. Wetherington Jr., G.R., Van Hoy, B., Phillips, L., Damiano, B., Green, C.: Two-year operational evaluation of a consumer electronics-based data acquisition system for equipment monitoring. Proc. Soc. Exp. Mech. Ser. Sens. Instrum. 5, 99–109 (2017) 3. Wetherington Jr., G.R.: Performance assessment of several low-cost consumer-grade analog-to-digital conversion devices. Proc. Soc. Exp. Mech. Ser. Sens. Instrum. 8, 15–33 (2018) 4. G. R. Wetherington Jr., Gregory Sheets, Tom Karnowski, Ryan Kerekes, Michael Vann, Michael Moore, and Eva Freer, Novel LowCost Approach for Acquiring High Resolution High-Speed Data, Proceedings of the Annual Meeting of the Institute of Nuclear Material Management, online internal publication, pp. 1–8 (2019)

Chapter 16

Hybrid Slab Systems in High-rises for More Sustainable Design Katherine Berger, Samuel Benzoni, Zhaoshuo Jiang, Wenshen Pong, Juan Caicedo, David Shook, and Christopher Horiuchi

Abstract Greenhouse gases trap heat within our atmosphere, leading to an unnatural increase in temperature. Carbon dioxide and its equivalent emissions have been a large focus when considering sustainability in the civil engineering field, with a reduction of global warming potential being a top priority. According to a 2017 report by the World Green Building Council, the construction and usage of buildings account for 39 percent of human carbon emissions in the United States, almost one third of which are from the extraction, manufacturing, and transportation of materials. Substituting wood for high emission materials could greatly reduce carbon if harvested and disposed of in a controlled way. To investigate this important issue, San Francisco State University and University of South Carolina partnered with Skidmore, Owings & Merrill LLP, a world leader in designing high-rise buildings, through a National Science Foundation (NSF) Research Experience for Undergraduates (REU) Site program, to investigate and quantify the embodied carbons of various slab system designs using a high-rise residential complex in San Francisco as a case study. Three concept designs were considered: a concrete building with cementitious replacement, a concrete building without cementitious replacement, and a concrete building with cementitious replacement and nail-laminated timber wood inlays inserted into various areas of the superstructure slabs. The composite structural slab system has the potential to surpass the limitations of wood-framed structures yet incorporate the carbon sequestration that makes wood a more sustainable material. The results show that wood substitution could decrease overall emissions from the aforementioned designs and reduce the environmental footprint of the construction industry. Keywords Carbon · Emissions · Timber · Concrete · Sustainability

16.1 Introduction According to the National Oceanic and Atmospheric Administration, six of the past seven years fill several spots in the top seven warmest years on record [1]. The greenhouse effect is widely accepted to be the cause of this trend, and carbon dioxide (CO2 ) is the largest contributor to the greenhouse effect. If the temperature continues to climb the way it has been, it is predicted that the rising sea levels will inundate 48 square miles of the San Francisco Bay Area by the year 2100 [2]. Buildings are responsible for 39 percent of human greenhouse gas emissions [3]. These emissions can be categorized into a couple different areas. The main categories are the operational carbon and the embodied carbon. Operational carbon is defined as the emissions of greenhouse gases converted into their carbon dioxide equivalents resulting from building usage. This usage includes heating, cooling, lighting, and all other appliances that consume energy derived from fossil fuels [4]. As operational carbon has been widely studied and its emissions have been greatly reduced in the recent years, this paper will focus on embodied carbon. Embodied carbon refers to the emissions associated with the extraction, creation, processing, and manufacturing of materials used in buildings, as well as the emissions associated with building construction and demolition

K. Berger School of Engineering, The University of Texas at Austin, Austin, TX, USA S. Benzoni · Z. Jiang () · W. Pong School of Engineering, San Francisco State University, San Francisco, CA, USA e-mail: [email protected] J. Caicedo College of Engineering and Computing, University of South Carolina, Columbia, SC, USA D. Shook · C. Horiuchi Skidmore, Owings & Merrill LLP, San Francisco, CA, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_16

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[4]. Embodied carbon represents around 28% of the total carbon emissions associated with the building and construction industry, making it an area of interest for reducing global emissions [3]. Several studies were carried out to investigate and quantify the embodied carbon emissions. For example, Oka et al. [5] studied the energy consumption and resultant kg CO2 eq/m2 of six office buildings with a range of areas and structural compositions. The resultant energy consumption of the structure, finishing, equipment, and waste disposal was calculated for each building. This energy was then converted to kg CO2 eq through an inter-industry relations table. This study concluded that the structure of a building is one of the greatest contributors to embodied carbon emissions. It has been shown that the embodied carbon emissions associated with the production of wood are significantly lower than that of other common structural materials such as concrete and steel [6]. In addition to the fact that the processing of the material is severely less carbon-intensive, wood acquires and stores carbon during its life until a turning point where harvesting the material is optimal [7]. This carbon sequestration makes wood a very valuable material from an environmental standpoint. Buchanan and Honey [6] looked into different classifications of buildings and proposed various structural designs for each. The residential complex showed a comparison of the most common residential construction materials and sought to maximize and minimize the carbon impact based on these results. From this case study, the wood house was shown to sequester almost as much carbon as was emitted from the other material processes. The industrial complex compared a steel design and a glue-laminated timber design. The results showed that the steel building emitted twice as much CO2 eq as the glulam design. Finally, office building designs were compared for reinforced concrete and steel models, as well as for reinforced concrete and glulam models. These two cases showed that reinforced concrete is slightly lower in emissions than steel, but the glulam frame emits around one-fourth of the CO2 eq of the aforementioned designs. This study was one of the first to emphasize wood’s sequestration of carbon and note the impact that this could have on the neutrality of structural systems. In another study, Salazar and Meil [7] compared the emissions of a “wood-intensive” home and a standard woodframed home based on the harvesting of wood, the embodied carbon of the materials used, and the end of life disposal. Wood that is harvested during its late immature growth phase is shown to be most effective at sequestering carbon because the forest is forced to return to its pre-harvest state and take in carbon for regrowth. Trees that are not harvested can be subject to forest fires, which results in all stored carbon being released, and bacterial decomposition, which releases methane and other GHGs. Taking these into account, the wood-intensive home was shown to reduce more emissions and act as a net carbon sink when compared to the standard wood-framed home. The authors stressed the importance of properly disposing of wood and note the large impact that various disposal methods have on the environment. Although the quantification of embodied carbon emissions has been investigated by many, the scope of each study varies and can cause a misinterpretation of results. These methodologies include the comparison of structural material emissions, which can range from a narrow view of extraction, manufacturing, and processing to a broader analysis of the entire life cycle energy. It is important to note this scope to ensure an accurate comparison. From there, emissions are quantified through conversion factors for each material and process in the scope. Only structural materials and their emissions will be accounted for in this paper. This study intends to provide a quick and easily implementable approach to designing less carbon-intensive buildings by creating carbon-based design charts for designers. A concept design of a high-rise residential complex in San Francisco was first adopted to validate the methods used to quantify the carbon emissions. The validated method was then applied to a 30-story prototype residential building to study how the insertion of cross-laminated timber panels into slabs could reduce the carbon profile and help achieve carbon neutrality.

16.2 Method Validation To validate the quantification method of carbon emissions, concept designs of a high-rise residential complex in San Francisco were analyzed. The building was considered to be a sufficient representation of a typical residential structure. The carbon emissions profiles were developed for three case scenarios: (1) a concrete building with no cementitious replacement; (2) a concrete building with cementitious replacement; and (3) a concrete building with cementitious replacement and crosslaminated timber (CLT) inlays inserted into 40% of the superstructure floor area. This percentage acted as a starting point in the original design and was used to test the effect of these inlays on overall neutrality. The results were then compared to those from the Environmental Analysis (EA) Tool developed in-house by Skidmore, Owings & Merrill LLP, which can be used to quantify embodied carbon and give a general overview of emissions in the areas of materials, construction, and probabilistic failure. Note that these analyses will only account for the structural elements of a building. The case study building consists of an 8

post-tensioned flat slab system. The whole structure is around 320 ft tall and has approximately 484,341 ft2 gross floor area.

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Fig. 16.1 Typical floor plan of high-rise residential complex – green geometries represent wood inlays within slab Table 16.1 Carbon emissions result comparison between hand calculation and EA Tool Case scenario 1. Cement 2. Fly Ash/Slag Replacement 3. Slab with 40% Wood Inlay

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From the floor plan as shown in Fig. 16.1, the mass of concrete and steel of the superstructure was found for the first two designs (cases 1 & 2). These values were then converted to kg CO2 eq using conversion factors from the EA Tool user guide. For the wood inlay design (case 3), the emissions and sequestration of wood were taken into account. From previous studies, it is shown that the emissions of cross-laminated timber are around 0.39 kg CO2 eq/kg wood and its sequestration is around 1.8 kg CO2 eq/kg wood [8, 9]. The resultant CO2 eq was recorded for each concept design to analyze the impact of wood inlay slabs on reducing carbon emissions. The comparison results are shown in Table 16.1. As can been seen from the results, the comparisons in the first two designs showed reasonable consistence given the uncertainty involved in carbon emission quantification. This provides confidence to use hand calculation results for the quantification of the wood inlay slab system as there is no current way to check the carbon emission output with the EA Tool. Looking at the resultant outputs, it is shown that the insertion of wood inlays is promising to reduce carbon emissions with a 31% reduction comparing to the cement option.

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Fig. 16.2 Typical floor plan of the prototype building – the hatched regions represent the wood inlays in the slab

Fig. 16.3 Plans and sections through one bay of a wood inlay slab for various slab thicknesses

16.3 Case Study Given the promising results from the concept design study, a prototype of a 30-story residential building with 30 column spans and a 96 × 96 floor area was created to further investigate the effects of cross-laminated timber panels inserted into the slabs. In this study, the slab thickness of one level in the superstructure was varied from 6

to 18

with the wood inlays inserted to analyze the effects on the total embodied carbon footprint. A typical floor plan of the prototype building is shown in Fig. 16.2. Several assumptions were made throughout this study. In each scenario, the slab reinforcement was kept at 5.85 lbs rebar/ft3 concrete. This number was identified through experience and was considered sufficient for residential construction. A 2.5

layer of concrete at the top of the slab was kept consistent in each scenario for acoustic purposes, meaning that wood occupies the remaining thickness of the slab that is not occupied by this layer. Plans and sections through one bay of a wood inlay slab for various slab thicknesses are shown in Fig. 16.3 to demonstrate the configuration. The reduction of carbon is the goal of this study, with carbon neutrality being the higher goal that all designers must strive for to reduce environmental impact. In order to calculate the carbon footprint of this wood inlay slab system, it is necessary to clarify what carbon neutrality means. In this cradle-to-gate study, it is defined as the ratio of sequestered carbon from the wood inlays to the sum of all embodied carbon emissions from the concrete, steel, and wood used in the slab system. Given

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the construction constraints, a parameter named structural feasibility is defined for each slab thickness and is dependent on the minimum beam width that is necessary to transfer loads back to the core of the building. These beams act as areas where the wood inlays are not inserted, which limits the percent wood floor area allowed for each slab thickness. These structural feasibility values were based on practical experience and were linearly interpolated assuming that an 8

slab needs a 5 beam width, a 10

slab needs a 3 beam width, and the minimum allowable beam with is 1.5 . The structural feasibility can be seen in Fig. 16.3; as the slab thickness increases, there is less concrete allotted on either side of the wood inlay in order to maximize the floor area that contains CLT inlays. Keeping these assumptions and definitions in mind, the percent floor area of wood inlays necessary for 100% neutrality, 75% neutrality, and 50% neutrality was recorded. Once the percent wood floor area was found for each slab thickness, the carbon neutralization of other components of the superstructure from the wood inlay slab system was considered. The scope of this study included the core walls, link beams, and columns, and well as the original slab material quantities. To reduce carbon emissions as much as possible in the prototypical design, analyses were conducted to determine the minimum core wall thickness allowable for each slab thickness. ETABS, a structural analysis software by Computers and Structures Incorporated, was used to perform these analyses. The insertion of wood inlays into the concrete slabs led to a loss of seismic weight and lateral forces. In order to maintain a code-specified requirement for design-level earthquakes, the stiffness of the building, and therefore the core wall thickness, could reduce. This reduction of material could lead to a lower carbon footprint of the overall building and a greater likelihood that the wood inlays could completely neutralize the superstructure emissions. The parameters for this study were maximum interstory drift and maximum story shear and were based on requirements for design-level earthquakes. To achieve a building with reduced core wall thicknesses that performs at code level, the maximum interstory drift was 2% and the maximum story shear was considered to be  Vn = 0.6 ∗ Acv ∗ 6 f c

(16.1)

where Acv is the gross area acted upon in a seismic event and f c is 8000 psi for high strength concrete. Note that the story shear based on an ACI 318-R14 is given by  Vn = 0.75 ∗ Acv ∗ 8 f c

(16.2)

For this study, 0.75 was used instead of 0.6 and the factor of 8 was changed to 6 to provide conservative estimates for this prototype building in a seismic event. The definition of structural feasibility remained consistent from the study previously conducted. All additional structural elements in this study were considered as solid reinforced concrete members and were calculated accordingly. Similarly, these elements were all defined as high strength concrete with the core walls and columns having 15% cement replacement and the link beams having 50% cement replacement. With the ETABS results in mind, the emissions from the core walls, columns, link beams, and slabs were recorded and the percent floor area of wood inlays necessary for 100%, 75%, and 50% neutrality were found.

16.4 Results In an attempt to make these results more tangible and easily adoptable by designers, a chart was created for each scenario to show carbon neutrality possibilities. Figure 16.4 shows possibilities for carbon neutrality in the floor plan of a 96 × 96 slab with a 30 column span. The chart included four-point series overlaid to show overlap for what could be possible. Plotted are the structural feasibility line, the 100% carbon neutral line, the 75% carbon neutral line, and the 50% carbon neutral line. Each area in this plot has a different implication and is intended to give an idea for sustainable practices when designing a floor slab. Figure 16.5 shows another chart that incorporates the emissions of all structural elements of a single story, including those in Fig. 16.4 and elements such as columns, core walls, and link beams. Similarly, this chart serves to provide a sort of guideline for the design process. It indicates that there is a large amount of work to be done before carbon neutrality can be achieved on a larger scale, as it is much more difficult to achieve a 100% neutral superstructure than a 100% neutral slab.

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Fig. 16.5 Carbon-based design for an entire story of the prototypical building

In the design phases of a building, one might have a certain carbon reduction or neutrality that is desired. In this case, a user might use these charts and determine how much wood should be incorporated within the slab in order to achieve a certain neutrality, and how feasible this design may be. To provide an example on how to use these charts, a designer may produce a scheme that calls for an 8

floor slab. From Fig. 16.4, the designer could achieve over 75% carbon neutrality of the slab system by inserting wood inlays into 60% of the floor area. Since the carbon sequestered by the wood inlays is not enough to 100% neutralize the slabs, they may choose to increase the slab thickness or increase wood usage in other architectural areas for higher carbon sequestration potential. Using the same 8

floor slab with Fig. 16.5, the designer would note that the 60% wood inlay floor area prescribed by the structural feasibility line would provide less than 50% neutralization when considering all superstructure elements. In this scenario, it would be impossible to achieve 100% carbon neutrality of the superstructure at the given slab thickness.

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16.5 Conclusion With the amount of greenhouse gases currently in the atmosphere, it is crucial that everyone takes steps to reduce their emissions so that our environment may start to return to its natural state. The atmosphere has shown unprecedented heating trends due to carbon dioxide and equivalent greenhouse gases. In the building sector, the manufacturing and processing of structural materials are some of the largest contributions to these emissions. Since wood requires less manufacturing than other materials and trees intake carbon dioxide during their growth, it can act as a carbon sink when considering its overall footprint. The insertion of wood into a concrete slab could cause for reduction, or possible cancellation, of carbon emissions due to these properties. This paper studied the wood inlay slab system through several case studies and created two charts that can serve as guidelines for carbon-based design. The first chart can be used to estimate the percent floor area of wood inlays to achieve certain emission reductions or carbon neutrality within a single slab. The second chart shows how the carbon sequestration of the wood inlay slab system can reduce emissions beyond the slab, such as those associated with core walls, columns, and link beams. Inserting wood within concrete members has the potential to neutralize or offset the carbon footprint of structural systems while surpassing the building limitations of wood. Furthermore, it is a promising way for engineers to actively pursue the reduction of greenhouse gases, leading to restoration of the natural global climate. Acknowledgements The authors would like to acknowledge the supports from National Science Foundation EEC-1659877/ECC-1659507, the College of Science and Engineering and the School of Engineering at San Francisco State University, and College of Engineering and Computing at the University of South Carolina. Supports from the industrial collaborator, Skidmore, Owings & Merrill LLP, are also appreciated.

References 1. NOAA National Centers for Environmental Information. State of the climate: global climate report for annual 2017 (2018) 2. Shirzaei, M., Bürgmann, R.: Global climate change and local land subsidence exacerbate inundation risk to the San Francisco Bay Area. Sci. Adv. 4(3), 1 (2018) 3. UN Environment. Global Status Report 2017, 14 (2017) 4. Ding, G.K.: Developing a multicriteria approach for the measurement of sustainable performance. Building Res. Inf. 33(1), 67–70 (2005) 5. Oka, T., Suzuki, M., Konnya, T.: The estimation of energy consumption and amount of pollutants due to the construction of buildings. Energ. Buildings. 19(4), 303–311 (1993) 6. Buchanan, A.H., Honey, B.G.: Energy and carbon dioxide implications fo building construction. Energ. Buildings. 20(3), 205–217 (1994) 7. Salazar, J., Meil, J.: Prospects for carbon-neutral housing: the influence of greater wood use on the carbon footprint of a single-family residence. J. Clean. Prod. 17(17), 1563–1571 (2009) 8. Corradini, G., Pierobon, F., Zanetti, M.: Product environmental footprint of a cross-laminated timber system: a case study in Italy. Int. J. Life Cycle Assess. 24(5), 975–988 (2018) 9. Puettmann, M., Oniel, E., Johnson, L.: Cradle to gate life cycle assessment of glue-laminated timbers production from the Pacific Northwest. American Wood Council (2013)

Chapter 17

Ground Vibration Testing of the World’s Longest Wingspan Aircraft—Stratolaunch Douglas J. Osterholt and Timothy Kelly

Abstract The record-setting Stratolaunch (Roc) carrier aircraft first took to the skies on April 13, 2019, staying aloft for 149 minutes before successfully landing back in Mojave, California. Since 2012, Stratolaunch Systems Corporation, a space transportation venture created in part by Scaled Composites, has been designing, building, and testing the world’s largest composite aircraft. The goal of this mobile launch system is to make orbital access to space more convenient, reliable, and routine. To achieve the first successful flight of Roc, several ground vibration tests (GVTs) were necessary to characterize the modal properties of the composite aircraft and its subassemblies. ATA Engineering, Inc., (ATA) completed two partial GVTs and a full-scale GVT to help Stratolaunch Systems Corporation engineers achieve their successful first flight. The results of the GVTs were used to update the finite element models (FEMs) used for flutter and dynamic stability predictions. Testing an aircraft of this size imposed a number of challenges not encountered in most GVT programs; to efficiently conduct the tests, a distributed data acquisition system approach was used, and seismic accelerometers characterized the aircraft’s low-frequency rigid body modes. The distribution of shakers and sensors around the aircraft was addressed by the implementation of a new sensor cable system and the adaptation of multishaker excitation methods using temporary support structures. Keywords Modal survey · Ground vibration test · Distributed systems · Stratolaunch

Acronyms ATA FEM FRF GVT Hz IMAT Roc RMS TDM

ATA Engineering, Inc. finite element model frequency response function ground vibration test hertz Interface between MATLAB, Analysis, and Test Stratolaunch (Model 351) root mean square test display model

17.1 Introduction The record-setting Stratolaunch (Roc) carrier aircraft first took to the skies on April 13, 2019, staying aloft for 149 minutes before successfully landing back in Mojave, California. Since 2012, Stratolaunch Systems Corporation, a space transportation venture created in part by Scaled Composites, has been designing, building, and testing the world’s largest composite aircraft. The goal of this mobile launch system is to make orbital access to space more convenient, reliable, and routine. Before the

D. J. Osterholt () ATA Engineering, Inc, San Diego, CA, USA e-mail: [email protected] T. Kelly Scaled Composites, Mojave, CA, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_17

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first successful flight of Roc was achieved, however, there were many challenges in designing, manufacturing, testing, and flying the aircraft. A successful program such as the Roc program requires multiple ground tests to validate and update the finite element models (FEMs) used to predict safe flight, including predictions for flutter analysis, dynamic stability, and loads. With the support of ATA Engineering, Inc., (ATA), the successful ground vibration test (GVT) program for Roc was performed in three phases: (1) a single empennage test focused on the rudders and elevators; (2) a single wing test focused on the ailerons, flap, and engine; and (3) a full-scale aircraft test. The objective of the first and second GVTs was to measure the fundamental modal properties, including the frequency, damping, and mode shape, of each subsystem, and the third, full-scale GVT focused on the global modes of the entire aircraft. The three phases of the test program are discussed, including the challenges associated with each of them. Note that all data provided in this paper is unitless, not real, and presented as typical.

17.2 Phase 1: Empennage Stratolaunch Systems Corporation engineers were initially concerned with verifying the validity of the aft tail section (empennage) of their Roc FEM, so the initial GVT focused only on the right empennage, elevators, and rudders. Figure 17.1 shows the Roc aircraft from the aft. The test focused on the right-side rudder and elevator control surfaces to assess the nonlinearity of control surface modes under different hydraulic configurations. The initial challenge for this phase involved the provision of a shaker stand tall enough and stiff enough to allow proper excitation of the upper and lower rudders. The selection of accelerometer locations was relatively straightforward and resulted in 48 accelerometers arranged on the empennage components. Figure 17.2 shows the upper and lower rudder accelerometer locations, and Fig. 17.3 shows the test display model (TDM) used to visualize the animated mode shapes. The shaker support consisted of a welded steel frame that could be clamped to a large scissor lift as shown in Fig. 17.4. The lift was large and tall enough to allow high-force-level inputs on the upper rudder, lower rudder, and elevators. During the test of the empennage, a new accelerometer cable system was evaluated, which was later implemented in the full-scale aircraft GVT. The custom shaker support worked well and was utilized for the subsequent GVTs. Seventy-seven runs were recorded and ten sets of control surface sweeps performed. The runs consisted of all checkout runs, random excitation, and sine sweeps. A set of control surface sweeps included multiple levels of sine sweeps to characterize the nonlinear behavior of the rotation modes. The test, including all setup and teardown of instrumentation, was completed within three days.

Fig. 17.1 Overall view of Roc outside of test facility [1]

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Fig. 17.2 Photo of accelerometers on the upper and lower rudder

Fig. 17.3 TDM

There are several methods for testing the nonlinearity of control surfaces which come from the joints, free-play, and hydraulic system. The classic, nonlinear response of a control surface is often exhibited by a rotation mode frequency decrease with a corresponding damping increase when the surface excitation force or movement increases. The test proceeded smoothly, allowing the characterization of the nonlinear behavior of each control surface rotation mode and torsion mode for

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Fig. 17.4 Custom shaker platform

Frequency (Hz)

RHS Lower Rudder Frequency

Single Hydraulics Hydraulics Pressure Off Hydraulics Off Post 15 Minute Dwell Hydraulics Line Diconnected Hydraulics Diconnected 15 Minute Dwell

Force at Resonance (Ibf) Fig. 17.5 Example control surface nonlinearity plot showing frequency vs. force tracking for lower rudder. Data is not real and is provided for example only

multiple aircraft hydraulic system configurations. For each control surface and hydraulic system configuration, a low-forcelevel sine sweep was performed to identify the torsion and rotation mode of the control surface. The force levels were then increased while a narrow-band sine sweep was applied, and the modal frequencies and damping values were tracked relative to the force levels using standard orthogonal polynomial parameter estimation techniques [2]. Between six and eight force levels were applied to determine whether the frequency had stabilized. This method was repeated for each of the hydraulic system configurations. ATA obtained a unique test point by dwelling on the rotation mode for 15 minutes, allowing the hydraulic fluid to heat up, to see whether this would change the modal frequency. Figure 17.5 is an example of the mode tracking versus force for all hydraulic configurations for the lower rudder. This test method was repeated for the rest of the control surfaces to provide the range of frequencies to be used for updating the FEM in flutter and flight dynamics predictions.

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17.3 Phase 2: Aileron and Engine Several months after the first GVT was completed, the Roc aircraft was ready for the next-phase GVT. The second phase of the GVT program focused on the ailerons, of which the aircraft has twelve (six on each side). In this case, ATA tested only the six left-side ailerons due to schedule and budget constraints and the assumption of independence and symmetry between the two sides of the aircraft. One flap and one of the six engines were also tested. As was done for the empennage, the nonlinear behavior of the control surfaces was characterized for multiple hydraulic configurations. The same test method was applied: sine sweeps with increasing force to compute the frequency response functions (FRFs), followed by modal parameter estimation to compute the frequency, damping, and mode shape. A photo of the left outer wing is shown in Fig. 17.6, and the TDM of the left wing, aileron, flap, and outboard engine is shown in Fig. 17.7. Two shakers were used to excite the engine nacelle in the lateral and vertical directions as shown in Fig. 17.8. In total, 82 runs with different excitation types, which consisted of burst random, Multi-Sine1 [3], sine sweep, and impact, were performed. For the control surface rotation mode linearity assessment, at least four force levels were recorded and at most eight levels were required to assess the nonlinearity. A shaped sine-sweep method was used to characterize the control surface behavior. The initial sine sweep performed was a non-shaped, or flat, open-loop control sweep, in which the resulting force varies with time as the shaker sweeps through modes of the system. The force time history is inverted and used to scale the voltage signal sent to the shaker from the source module. The goal is to shape the force levels over the entire sweep so there is less amplitude variation in the force, decreasing the force required when the article under test is not shaking at resonance and increasing the force levels applied when it is shaking at resonance. To track the force at the mode, the force versus frequency is plotted to obtain the root-mean-square (RMS) force at the modal frequency of interest, as shown in Fig. 17.9. The figure shows the initial flat sweep and a higher-level shaped sweep. The shaped sweep is not perfectly flat because of the nonlinearity in the modes, but it has less variation in force over the entire sweep.

Fig. 17.6 Photo of left-side ailerons

1 ATA’s patented Multi-Sine excitation method dramatically reduces ground vibration (modal) test duration. The products, services, and technology

described here may be protected by U.S. Pat. No. 8,281,659.

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Fig. 17.7 TDM of left outboard wing

Fig. 17.8 Shakers and stand used for the engine excitation

This method was used for all the control surfaces. The interesting observation made during this phase of the GVT was that the three outer ailerons (1, 2, and 3) behaved as a stiffening spring system, where the rotation frequency increased as force increased. The three inner ailerons (4, 5, and 6) and the flap behaved as a softening spring system, where the rotation frequency decreased as force increased. Additional tests were performed on one of the outer ailerons to validate the results.

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The shaker was moved from the actuator location to the center of the trailing edge and the direction of the sweep signal was up in frequency instead of down. The investigation concluded that the behavior of the aileron was consistent throughout. The frequency increased with increased force, which is perhaps not as common, but can and does occur in control systems. An example of this type of behavior is shown in Fig. 17.10.

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17.4 Phase 3: Full-Scale Aircraft Almost immediately after the second GVT was complete, Scaled Composites requested that ATA perform a best-effort GVT of the full-scale Roc in support of the aircraft’s scheduled first flight, which constrained the amount of time allowed to complete the test. The two previously performed partial-aircraft GVTs provided good insight as to what would be required for the entire-aircraft test. The shaker stands were identified, the new cable system was implemented, and confidence that seismic accelerometers would help characterize the low-frequency modes of the aircraft was developed. One item that still needed evaluation was the aircraft boundary condition. It appeared that the only feasible option was to test Roc while the aircraft was on its landing gear. The Roc landing gear consists of two nose gears, one on each of the two fuselages’ forward ends, and three main landing gears on each fuselage. A sensitivity study was performed that evaluated combinations of the three main landing gears’ down and up positions to determine the best boundary condition. The study concluded the best configuration was the one in which the aircraft was supported by the forward and aft main landing gears while the nose gears and the center main landing gears were retracted. The tires were at nominal pressures. Pretest analysis was performed to identify accelerometer locations and to create back-expansion and mass matrices. Accelerometers were located at multiple nodes, and a number of those accelerometers were seismic sensors, which are 10× more sensitive than other standard modal accelerometers. These seismic accelerometers were placed at key locations to identify the aircraft’s overall rigid body behavior and the first several flexible modes that were low in frequency. The balance of the accelerometers had a sensitivity of 100 mV/g. In total, six shakers, located on the two wingtips and the four horizontal tailtips, were used to excite the overall aircraft. Additional impact testing was used to excite the six engines in the vertical and lateral directions (Figs. 17.11 and 17.12). The new accelerometer cable system consisted of a three-channel ribbon cable with JST connectors. Each accelerometer had a micro-dot to JST pigtail installed. Ribbon cables were routed to each node location before the correct number of channels were plugged into the cable. If there was a single accelerometer at the node, then ATA only connected one channel on the ribbon cable. If there was a tri-axial accelerometer, then ATA connected all three channels. Figure 17.13 shows a bi-axial node using the 100 mV/g accelerometers, and Fig. 17.14 shows a triaxial node using the seismic accelerometers. The node cables were each 25 long, but they were extended as needed as the ribbon cables were routed to PCB® 16-channel

Fig. 17.11 Photo of left side aircraft

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Fig. 17.12 TDM of full-scale aircraft

Fig. 17.13 Bi-axial accelerometer and cable

patch panels. From the patch panels, a 50-pin ribbon cable was routed to a distributed data acquisition system as shown in Fig. 17.15. There were multiple data acquisition systems, each consisting of 11-slot LAN-XI chasses with 12-channel 3053 modules. The systems were located under the left fuselage, right fuselage, and center wing. Ethernet Cat5 cables were used to connect all systems to a single data acquisition computer. The patch panels and distributed systems significantly reduced the cable runs required for each accelerometer. The shaker controller used is an EMX-1434 system driven by a custom MATLAB/IMAT™ software application. The data systems and shaker controller are shown in Figs. 17.16 and 17.17, respectively. The test consisted of multiple levels of Multi-Sine sweeps. In total, there were 85 modes extracted. Impact tests were performed on the engines to supplement the global shaker excitation. The impact tests helped identify lateral, vertical, yaw, roll, pitch, and higher-order pitch modes for all six engines. A four-shaker tail sweep was performed once with all four

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Fig. 17.14 Tri-axial accelerometer and cable

Fig. 17.15 PCB 16-channel patch panel and 50-pin ribbon cable

shakers in phase (symmetric) and again with the left-tail and right-tail shakers out of phase. These runs excited the rigid body pitch and fore-aft modes and the tail vertical out-of-phase mode. The final step involved computing the modal parameters, comparing them to the analysis predictions, and verifying all modes of interest were identified. Mode shapes were animated on the TDM and compared to analysis shapes. An example rigid body mode shape is shown in Fig. 17.18.

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Fig. 17.16 Distributed data system—LAN-XI

Fig. 17.17 Data system and shaker controller

17.5 Summary The three-phase modal test program for Roc allowed the initial focus to be on specific aircraft sections and components, which provided useful insight into the full-scale aircraft GVT. The lessons learned in the component and control surface GVTs were instrumental in enabling the full-scale aircraft GVT to be performed successfully in a limited amount of time. The implementation of a new cable system, seismic accelerometers, shaker stands, and distributed data acquisition systems

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Fig. 17.18 Example mode shape—fore-aft and pitch mode

were all key to the successful test program. The overall best-effort GVT provided valuable data that was used to update the FEM for flutter and controls predictions, which further led to a successful first flight.

References 1. Stratolaunch Systems Corporation. https://www.stratolaunch.com/news-and-features/galleries/ 2. Fladung, W., Vold, H.: An improved implementation of the orthogonal polynomial modal parameter estimation algorithm using the orthogonal complement. In: International Modal Analysis Conference (2015) 3. Hoople, G., Napolitano, K.: Implementation of multi-sine sweep excitation on a large-scale aircraft. In: 28th International Modal Analysis Conference (2010)

Chapter 18

Using Recorded Data to Improve SRS Test Development Joel Minderhoud

Abstract The Shock Response Spectrum (SRS) approach is an effective and widely used method for analyzing mechanical shock phenomena. Synthetic waveforms are commonly used in the development of an SRS; unfortunately, there is often no synthetic pulse with a frequency response that matches well to a given real-world transient event. This presentation describes a unique approach, where recordings from a field environment are modified to meet or exceed a specified SRS. Comparisons are made between a modified user waveform developed from this field-based SRS and waveforms developed with commonly applied synthetic pulses. Keywords Shock response spectrum · SRS · Mechanical shock · Transient event

18.1 Introduction Analyzing a shock pulse in the frequency domain provides much more insight than simply looking at the same pulse in the time domain. A Fast Fourier Transform (FFT) can make the conversion from time to frequency domain data, providing both the magnitude of the shock pulse accelerations and the phase information about the shock pulses at each frequency; from an FFT it is possible to recreate the original shock pulse. However, an FFT is not very useful in mechanical shock studies. Test engineers are interested in the maximum shock acceleration at each frequency bin rather than the average, because the large shock accelerations are what cause damage. This discrepancy leads test engineers to study mechanical shock using a Shock Response Spectrum (SRS) approach. An SRS models response channels using a theoretical series of single degree of freedom (SDOF) mass-damper-spring oscillators. The natural frequency of each SDOF oscillator defines the horizontal axis of a plot and a computed response for each oscillator is plotted on the vertical axis. This computed response is the absolute maximum acceleration of the SDOF oscillator to the pulse, referred to as the maximax, not the average acceleration (Fig. 18.1). The SRS calculation does not provide phase data, so it cannot be used to replicate the original shock pulse. Nor is the maximum acceleration value of the SRS the actual maximum acceleration of the original shock pulse. But despite not providing a replica of the original shock data, an SRS does provide highly valuable information to the test engineer about the maximum dynamic load as a function of frequency for a particular test.

18.2 Examples of Standard Synthetic Waverforms When producing an SRS waveform for a test to study mechanical shock, various parameters are used to synthesize a pulse that matches a specified SRS. While a range of waveforms can be created to achieve a required SRS, the testing industry usually relies on a set of standard synthetic waveforms; each of these waveforms is based on a specific set of equations and use a unique set of calculations to produce an SRS (Fig. 18.2).

J. Minderhoud () Vibration Research, Jenison, MI, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_18

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Fig. 18.1 A simple SRS model

Fig. 18.2 Definition of the WavSyn waveform

Selecting the appropriate synthetic waveform type depends on the application. For example, the WavSyn method produces short duration, high frequency waveforms appropriate for pyroshock tests and the Burst Random or Enveloped Burst Random methods produce long duration stationary random waveforms appropriate for earthquake tests.

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Unfortunately, there is often no synthetic pulse with a frequency response that matches well to a specific real-world transient event. To approximate a real event, the synthetic waveform must test the device under test (DUT) across the same range of frequencies found in the real-world waveform. A synthesized waveform test that misses either low frequency or high frequency vibrations will not result in a truly realistic test, while a waveform with excessive energy in a given frequency range will create an over-testing problem.

18.3 Using Field-recorded Data There is a unique approach, where the actual recorded field environment is modified to meet or exceed a specified SRS. This provides a time waveform similar to the original field environment and, more importantly, its frequency response function closely matches the original field environment. A real-world data set is representative of only a single unique event; using this one event as the basis for creating a synthesized SRS waveform gives an incomplete description of shock vibrations that may occur in a particular setting. A different approach is to use multiple real-world data sets and incorporate them into one representative waveform. For transient events, the proper way to combine multiple real-world data sets is not to find their average accelerations, but to find the maximum value at each frequency. This ‘max enveloping’ technique produces an SRS curve using the maximum acceleration value from a group of real-world data sets for each frequency. SRS synthesis parameters are then used within a specialized software module to create a pulse matching a specified SRS curve. The max envelope data set is used to develop a test maximax breakpoint table. An SRS is then synthesized by the software, followed by iterations that adjust wavelets to modify SRS synthesis parameters to create a pulse matching a specified SRS curve.

18.4 Comparing Waveforms Both a modified user waveform, developed from the enveloped environment, and standard synthesized waveforms can be evaluated by comparing them with a recorded waveform. Test engineers should consider three factors when they compare a synthetic waveform with a real-world recording. The first factor to consider is waveform shape; it is important because, to be realistic, a mechanical shock test needs to test the DUT at the correct amplitudes across the frequency domain. The second factor to consider is frequency content, as a useful synthetic waveform must test a DUT across the same range of frequencies found in the real-world waveform. A synthesized waveform test that misses either low frequency or high frequency vibrations will not result in a truly realistic test. Finally, test engineers should consider the energy or amplitude of the waveforms. While it is important for a test to have the correct waveform shape and the correct frequency content, a realistic test must also have the same amplitude as the real-world waveform.

18.5 Comparing the Modified User Waveform with an Original Real-World Recording This presentation offers real comparisons using various SRS generated from synthetic waveforms and an SRS generated from data recording a series of impacts of a golf club with a golf ball. Graphic comparisons highlight significant limitations of the standard synthetic waveforms. In contrast, the synthesized modified user waveform using recorded data matches the actual waveform very closely in terms of frequency content, waveform shape, and amplitudes across the frequency range (Fig. 18.3).

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Fig. 18.3 The modified user waveform overlaid on the original recording

18.6 Conclusion This study’s data clearly show that the modified user waveform generated with the max enveloping technique yields an SRS waveform closely matching the original real-world waveform in terms of waveform shape, frequency content, and amplitude. As demonstrated in the presentation, standard synthetic waveforms often do not closely match real-world transient events. They are generated from math algorithms and cannot duplicate the realistic qualities of a modified user waveform adjusted by a series of iterations to match a maximax SRS. The modified user waveform, based on an enveloped set of real-world recordings, maintains real-world characteristics and creates an SRS waveform that accurately reflects those recorded events.

Chapter 19

Distributed Acquisition and Processing Network for Experimental Vibration Testing of Aero-Engine Structures Michal J. Szydlowski, Christoph W. Schwingshackl, and Andrew Rix

Abstract Detailed vibration testing of large assembled structures, such as aeroengines, leads to significant requirements on data acquisition and processing. This can lead to high system cost and long post processing times, which often limit the amount of data that can be acquired. A novel hardware-software acquisition system combination is proposed here to overcome some of the challenges of large scale data acquisition, based on the idea to distribute the acquisition and data processing load between a network of specialized acquisition nodes. The nodes work in parallel and are independent of each other, while sharing a synchronization clock. Each node has the capability to process the data being acquired on-line. The network allows for testing of novel data analysis methods and its modular nature enables an easy expansion of the system when required. Keywords Vibration testing · Experimental · Data acquisition systems

19.1 Introduction Many factors influence the dynamic responses of complex rotating machinery. Gas turbine engines are good examples of such a complex system [1]. Experimental testing is a necessary tool in order to increase the understanding of the dynamic behaviour of such structures [2]. Engine vibration testing is a difficult task, the success of the testing procedure is dependent on many elements of the process [3–6]. From a technical stand point, it requires capturing large numbers of data points from multiple sensors at different sampling frequencies, that may come for a variety of sensors [7–10], such as accelerometers, blade tip timing systems, strain gauges, torque meters. Forced response analysis of a complex assembled structure may also require specialised multichannel signal generators for different types of exciters across the system. Normally very expensive high channel I/O testing systems will be used for this type of testing, which will be designed and optimised for a specific test setup, making them difficult to scale, and limiting their use for a research environment. Peeters et al. [4] shows in his paper modern approaches to on ground airplane vibration testing, where the acquisition system has seven hundredth channels. The setup is very complicated and requires several processing stations to go through the data. The complexity of engine testing programs is also shown by Howe and Carmichael [7]. To overcome some of the challenges for large scale data acquisition, the authors present a hardware-software signal acquisition architecture based on a network of specialized data capture and processing devices. The system is designed to meet the requirements of large scale vibration testing in a research environment, with a special focus of reasonable cost, flexibility and scalability.

19.2 System Concept Rather than using a single, powerful and expensive system that does it all, the system is designed so the data capture and processing loads are distributed between several nodes of a network, where each node consists of a lower cost data acquisition

M. J. Szydlowski () · C. W. Schwingshackl Imperial College London, South Kensington, London, UK e-mail: [email protected] A. Rix Rolls-Royce plc, 62 Buckingham Gate, London, UK © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_19

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Fig. 19.1 System architecture

system (DAQ). Four main types of nodes are proposed: (i) a control node (master) responsible for synchronisation, control of basic actuators (motors, pumps) and basic health monitoring of the system; (ii) excitation nodes that are multichannel signal generators driving various exciters at multiple frequencies; (iii) acquisition nodes that allow multichannel data capture with different sampling rates, reconfigurable data reduction and processing capabilities; (iv) storage nodes and processing nodes that provide additional processing resources as well as serve as a long-term data storage. Figure 19.1 depicts such a simple network consisting of a master node, N acquisition nodes and a storage node. All nodes of the network are synchronised using a distributed hardware clock and trigger system, ensuring minimal phase misalignment between the acquired signals.

19.3 Node Architecture Each of the nodes share the same basic architecture in order to be part of the network. Depending on the specialty of the node different functionalities are either added or disabled. Figure 19.2 presents the overall node architecture. Each node has three main layers, (i) a software layer that uses a real-time operating system (RTOS), (ii) a hardware layer using FPGA (Field Programable Gate Array) and (iii) a storage layer. The first two layers thereby have direct access to the on-board memory (DMA) and are capable of sharing and processing the data in it. The hardware layer is responsible for signal acquisition and signal output (if required). It controls the analogue to digital (ADC), digital to analogue (DAC), and fast digital inputs and outputs (DI/DO). It also ensures continuous node synchronization (SYNC module) and it can be used to apply a series of data pre-processing and reduction steps thanks to the FPGA (Field Programmable Gate Arrays) capability. The node sampling synchronization is implemented via hardware triggers (TRIG) and PLL (Phase Lock Loop) clocks with the master clock (CLK) running at 13 MHz. Due to the hardware implementation, pre-processing the data can be handled on the fly, leading to a significant reduction of what needs to be passed to the software layer via DMA (Direct Memory Access). The software part of each node is built in a RTOS (Real Time Operating System) to increase the speed and computational costs and ensure fast reaction time of the system. The heart of the software layer is the control module (CTRL) responsible of the systems operation. The built-in software enables further data processing (compression, scaling) which goes beyond the limits of the hardware layer. The processing is done in circular buffer with a fixed number of samples. This layer gives also access to the user interface (UI) in order to set up and provide information about the test progress. The CTRL module and Watchdog module ensure that the overall network and the node is operational and running as expected. The communication is

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Fig. 19.2 Node architecture

handled by the COM module. The communication is mostly using TCP/IP (Transmission Control Protocol/Internet Protocol) or UDP (User Datagram Protocol) messages. Once the required data processing and compression has been performed, it can either be stored temporarily in the internal memory of the unit for short term use, or it can be send to the final layer of the storage nodes.

19.4 Initial Trial Setup The above architecture is in principle independent of the used hardware, if it provides the required layers. The presented architecture was implemented on a National Instrument cRIO platform. A network consisting of two nodes was tested on the Asynchronous Rotor Excitation System (ARES) a rotor dynamic test facility at Imperial College London. One of the nodes was a control and excitation node while the second was an acquisition node. The control/excitation node was responsible for monitoring and running the system. The actuators and exciters where an electric servo motor powering the shaft and two linear piezo stacks connected to a flexible barring housing (enabling asynchronous excitation). The node also acquired signals from dynamic force gauges located on the piezo stacks, temperature signal form the bearings and the shaft rotary encoder. The acquisition node had 32 input channels acquiring with the sampling rate of 51,200 Hz. The sensors connected to the acquisition node were strain gauges, accelerometers and optical displacement probes.

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19.5 Conclusion A basic network needs at least two nodes, a control node and one acquisition node. To increase the number of acquired channel, or excitation sources one needs to add more nodes with desired capabilities. This makes the system scalable easily. Splitting the capture and processing load in to different units, using reprogrammable hardware and the proposed network architecture, the systems delivers high performance for the fraction of a cost of a standard multichannel acquisition system. Furthermore, the presented architecture unlocks the possibility of implementing novel online processing and data reduction algorithms. Acknowledgements Thanks to Rolls-Royce plc and the EPSRC for the support under the Prosperity Partnership Grant “Cornerstone: Mechanical Engineering Science to Enable Aero Propulsion Futures”, Grant Ref: EP/R004951/1 for supporting this work and allowing to publish its outcomes. Special thanks go to the team from National Instruments for the in-depth discussions about synchronisation methods, FPGA and modern acquisition system design.

References 1. Fawke, A.J., Saravanamuttoo, H.I.H., Holmes, M.: Experimental verification of a digital computer simulation method for predicting gas turbine dynamic behaviour. Proc. Inst. Mech. Eng. 186(1), 323–329 (1972) 2. Mongia, H.C., Held, T.J., Hsiao, G.C., Pandalai, R.P.: Challenges and progress in controlling dynamics in gas turbine combustors. J. Propuls. Power. 19(5), 822–829 (2003) 3. Göge, D., Böswald, M., Füllekrug, U., Lubrina, P.: Ground vibration testing of large aircraft–state-of-the-art and future perspectives. In: 25th International Modal Analysis Conference (2007) 4. Peeters, B., Hendricx, W., Debille, J., Climent, H.: Modern solutions for ground vibration testing of large aircraft. Sound Vib. 43(1), 8 (2009) 5. Boeswald, M., Goege, D., Fuellekrug, U., Govers, Y.: A review of experimental modal analysis methods with respect to their applicability to test data of large aircraft structures. In: Proc. of the International Conference on Noise and Vibration Engineering ISMA (2006) 6. Gil-García, J., Solís, A., Aranguren, G., Zubia, J.: An architecture for on-line measurement of the tip clearance and time of arrival of a bladed disk of an aircraft engine. Sensors. 17(10), 2162 (2017) 7. Howe, R., Carmichael, N.E.: “JET engine test strategy-program overview and objectives,” 2000 IEEE Autotestcon proceedings. In: IEEE Systems Readiness Technology Conference. Future Sustainment for Military Aerospace (Cat. No.00CH37057), pp. 284–289, Anaheim, CA, USA (2000) 8. Zielinski, M., Ziller, G.: Noncontact vibration measurements on compressor rotor blades. Meas. Sci. Technol. 11(7), 847 (2000) 9. Beauseroy, P., Lengellé, R.: Nonintrusive turbomachine blade vibration measurement system. Mech. Syst. Signal Process. 21(4), 1717–1738 (2007) 10. Heath, S., Imregun, M.: A survey of blade tip-timing measurement techniques for turbomachinery vibration. J. Eng. Gas Turbines Power. 120(4), 784–791 (1998)

Chapter 20

Modal Test of the NASA Mobile Launcher at Kennedy Space Center Eric C. Stasiunas, Russel A. Parks, Brendan D. Sontag, and Dana E. Chandler

Abstract The NASA Mobile Launcher (ML), located at Kennedy Space Center (KSC), has recently been modified to support the launch of the new NASA Space Launch System (SLS). The ML is a massive structure—consisting of a 345-foot tall tower attached to a two-story base, weighing approximately 10.5 million pounds—that will secure the SLS vehicle as it rolls to the launch pad on a Crawler Transporter, as well as provide a launch platform at the pad. The ML will also provide the boundary condition for an upcoming SLS Integrated Modal Test (IMT). To help correlate the ML math models prior to this modal test, and allow focus to remain on updating SLS vehicle models during the IMT, a ML-only experimental modal test was performed in June 2019. Excitation of the tower and platform was provided by five uniquely-designed test fixtures, each enclosing a hydraulic shaker, capable of exerting thousands of pounds of force into the structure. For modes not that were not sufficiently excited by the test fixture shakers, a specially-designed mobile drop tower provided impact excitation at additional locations of interest. The response of the ML was measured with a total of 361 accelerometers. Following the random vibration, sine sweep vibration, and modal impact testing, frequency response functions were calculated and modes were extracted for three different configurations of the ML in 0 Hz to 12 Hz frequency range. This paper will provide a case study in performing modal tests on large structures by discussing the Mobile Launcher, the test strategy, an overview of the test results, and recommendations for meeting a tight test schedule for a large-scale modal test. Keywords NASA · Large structures · Experimental modal analysis · Hydraulic shakers · Impact drop tower · Multi-sine sweep

20.1 Introduction and Motivation The National Aeronautics and Space Administration (NASA) has recently completed modification of the Mobile Launcher (ML), which will provide the launch platform for the new Space Launch System—a new heavy launch vehicle capable of launching both the Orion crew module and massive payloads to the Moon and beyond in a single launch. Before the SLS can receive launch certification, the finite element models of the fully integrated SLS—including the core stage, solid rocket boosters, and mission capsule—must be validated. Therefore, an experimental modal test, officially designated as the Integrated Modal Test (IMT), is scheduled to take place on the fully assembled SLS and will provide the data necessary to perform this model validation. Validated SLS models are critical to NASA, as they provide information for flight dynamic risk assessments, structural load analysis, and even launch control software. When performing an experimental modal test, particularly one as critical as the SLS IMT, it is important to fully understand the boundary conditions. Unintended interactions between the test item and the boundary constraints during a modal test can strongly influence the modes of interest. If this situation is unavoidable, it is important to understand these influences as it pertains to model verification and correlation. Because the Mobile Launcher will provide the SLS boundary condition during IMT, a Mobile Launcher-only experimental modal analysis test was performed at KSC in June 2019. Validating the finite element model of the Mobile Launcher with the resulting modal test data would define the SLS boundary condition during IMT, and allow the focus to remain on the SLS vehicle as well as increase the confidence of the resulting SLS model.

E. C. Stasiunas () · R. A. Parks · B. D. Sontag · D. E. Chandler NASA Marshall Space Flight Center, Huntsville, AL, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_20

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The Modal Test Team (ET40) from Marshall Flight Space Center (MSFC) in Huntsville, AL, planned and performed the experimental modal test on the Mobile Launcher in the requested frequency range from 0 Hz to 12 Hz. The ML was tested in three different support configurations: supported by six Vehicle Assembly Building (VAB) mount mechanism posts, supported by four Crawler Transporter (CT) posts, and supported by all 10 posts at once. Performing experimental modal analysis on a structure as immense as the ML required the use of uniquely-designed excitation fixtures, many response accelerometers, and various support equipment. This paper will discuss these in detail, as well as provide an overview of the test results and recommendations for future large-scale modal tests.

20.2 Mobile Launcher The NASA Mobile Launcher, located at Kennedy Space Center (KSC) and originally built for the Constellation program in the mid-2000s, has recently been modified to support the new SLS program. This immense structure consists of a two story, 25-foot tall base platform attached to a 355-ft tall tower for a total height of 380-ft and combined weight of approximately 10.5 million pounds. The base measures 165-ft long by 135-ft wide, and the tower measures 40-ft square. Normally, the base sits 22-feet off the ground, supported by six steel support posts that connect to support structures inside the Vehicle Assembly Building, as well as at the launch pad. The complete as-tested ML structure is shown in Fig. 20.1, secured to the Crawler Transporter during rollout to the launch pad. The VAB can be seen behind and to the right of the ML. The Mobile Launcher serves many functions in regards to the Space Launch System. During the SLS assembly process, the ML provides structural support and provides access to service the assembled vehicle. When ready for launch, the SLS and ML will be secured to the CT and moved from the VAB to Launch Pad 9, as seen in Fig. 20.1. At the launch pad, the ML provides power, communications, coolant, and fuel through umbilicals that reach from the ML tower to the SLS. Finally, the crew access arm (CAA) that provides a walkway for astronauts to access the Orion crew capsule is located at the 274-foot level of the ML tower. The umbilicals and the CAA all retract prior to, or during, lift-off [2, 3].

20.3 Modal Instrumentation Extensive pre-test analysis was performed on the Mobile Launcher analytical model by the Dynamic Test and Modal Sensitivity Study Team at MSFC in order to determine the most effective excitation and response measurement locations to capture a set of target modes. Additionally, the measurement degrees of freedom defined by the pretest analysis were selected

Fig. 20.1 Mobile launcher [1]

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Fig. 20.2 Modal test geometry (red = input, blue = response)

to minimize the off-diagonal terms of the test cross orthogonality matrix of the measured target modes. Five locations were selected for the modal excitation: two in the vertical direction and one in the lateral (horizontal) direction on the ML 0deck, one in the lateral direction at the 245-ft level (mid-tower), and one in the lateral directions at the 345-ft level (top of tower). For the response measurements, 235 locations were selected with a total of 361 degree-of-freedoms (DOFs). Note the resulting measurement set did not measure 3 degrees of freedom at every selected measurement node. The modal test geometry of the Mobile Launcher with the measurement locations, as determined by the pre-test analysis, is shown in Fig. 20.2. The five excitation locations are indicated by the red nodes at the base of the red arrows, which point in the direction of excitation. The 235 response locations are indicated by the blue nodes (DOFs not shown). Note that in addition to the ML tower and base, the umbilicals (nodes hanging off mid-point tower) and crew access arm (beam hanging off near the top of the tower) were of interest as well, as they exhibited local modes relative to the tower within the desired frequency range.

20.4 Modal Excitation – Shaker Test Fixtures Modal shaker tests are typically performed by exciting a test item with a shaker, while the shaker is either attached to, or suspended from, a rigid separate structure. Due to the immense size and weight of the Mobile Launcher, as well as a lack of available support structures for proper shaker mounting, an alternate shaker input method was required for the ML. For these reasons, five test fixtures were designed—each enclosing a hydraulic shaker that oscillated inertial masses on slip bearings—to provide adequate modal excitation into the Mobile Launcher. In order to excite the ML in all three axes, both lateral (horizontal) and vertical shaker test fixtures were built. The lateral shaker test fixture consisted of a hydraulic shaker and 2100-lbs of inertial mass plates attached to the top side of a slip plate. On the bottom side of the slip plate were linear bearing assemblies that rode on horizontal rails attached to a base plate that was bolted to the ML structure. The shaker armature was attached to a vertical arm on the base plate. Excitation forces were generated by oscillating the shaker and slip plate assembly relative to the vertical arm, for a total

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Fig. 20.3 Lateral shaker test fixture

Fig. 20.4 Vertical shaker test fixture

moving mass of 2867-lbs. Forces were measured with a PCB model 1381-01A rod-end load cell that was installed between the shaker armature and the vertical arm. A labeled drawing of the horizontal shaker test fixture, without the load cell, is shown in Fig. 20.3. The vertical shaker test fixture was similar to the lateral shaker test fixture in that it oscillated an inertial mass to produce an input force. However, in this case, the hydraulic shaker was positioned vertically and was attached to a reaction plate that was bolted to a base plate, with three PCB Model 202B ring-type load cell washers installed at the interface to measure the force. The hydraulic shaker armature drove into a top fixture assembly, guided by linear rails and bearings, which carried 2000-lbs of inertial mass plates, for a total moving mass of 2273-lbs. Three pneumatically pressurized air mounts supported the sliding top fixture, while providing the sufficient dynamic displacement. A labeled drawing of the vertical shaker test fixture is shown in Fig. 20.4. The rod-end and ring-type load cells installed in both shaker test fixtures provided the force measurements required for calculating driving point frequency response functions (FRFs). While only a single force was measured for the lateral fixture, three forces were measured for the vertical fixture—the sum of which equaled the input force into the ML structure. In order to provide force data for real-time FRF calculations, the three individual forces were summed using a Stanford Research System model SIM980 voltage-summing box and output to the data acquisition system. The individual forces were recorded as well, which allowed for post-test summation and processing of the total vertical force if desired. The hydraulic shakers used in the test fixtures were TEAM Model 24/0.8 shakers, selected primarily for their low frequency excitation capability from 0 Hz to 400 Hz, which included the ML modal test frequency range of interest.

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Additionally, with the rated 4-inch peak-to-peak armature displacement and the moving masses, these hydraulic shakers also provided sufficient force excitation down to very low frequencies (around 0.5 Hz). When powered by the TEAM model HPS-10A hydraulic pump operating at 3000 psi, the dynamic force rating of the shaker was 1560-lbf, which provided sufficient force excitation at the higher frequencies of interest. It is worthwhile to note that hydraulic shakers pose logistical challenges when compared to typical modal electrodynamic shakers, as they require hydraulic pumps, supply lines, hydraulic fluid, and spill containment measures. They also suffer from input harmonic distortions when exciting frequencies well below the hydraulic column frequency. However, hydraulic shakers have proved to be worth the effort due to their high force output, large peak-to-peak displacement, and low frequency limits down to 0 Hz. Comparatively, typical electrodynamic shakers have less force output, higher low frequency limits (around 5 Hz), and displacements no more than 2-in peak-to-peak at most, severely limiting low frequency excitation.

20.5 Modal Excitation – Impact Drop Tower Even though the pre-test analysis determined the effective shaker locations for the ML modal test, there was no guarantee that the shaker input would be sufficient to excite all the modes of interest, particularly vertical modes of the base platform. Therefore, a vertical, portable impact drop tower with removable wheels was designed and built that could be moved to any accessible node on the top floor of the base platform (0-Deck), and excite the structure with more force than obtainable with a typical impact hammer modal sledge. A labeled schematic of the impact drop tower, with the wheels removed, is shown in Fig. 20.5. The impact drop tower, constructed out of 8020 T-Slot aluminum, was operated by raising a 400-lbf stack of mass plates to a prescribed height—depending on the force needed—with an electric hoist located on the top of the tower. The mass plates were constrained by slip bearings on the tower frame. A quick-release mechanism would then release and drop the sliding mass plates onto a sandwich plate attached to a shock absorber. The shock absorber was purposefully selected to provide an impulse broad enough to excite up to 20 Hz (with 20 dB roll-off). The input force was measured with a ring-type PCB Model 206M06 load cell, installed between the base of the shock absorber and the base plate.

Fig. 20.5 Impact drop tower

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20.6 Modal Response – Accelerometers As with the hydraulic shaker selection, the accelerometer selection for the Mobile Launcher modal test was driven by the low frequency test requirements. For accurately measuring at frequencies below 1.5 Hz, PCB Model 393B04 accelerometers were selected due to their high sensitivity of 1000 mV/g, low frequency measurement range of 0.06 Hz to 450 Hz, and their low noise-floor characteristics. Because there were not enough 393B04 accelerometers for all the requested measurement locations on the ML, 181 of these accelerometers were installed at locations that participated heavily in the first few modes of the structure. Endevco 46A16 accelerometers, with a nominal sensitivity of 100 mV/g and frequency range of 1 Hz to 10,000 Hz, were used for the remaining measurement locations on the ML. Both accelerometer models were stud-mounted to an accelerometer block manufactured by MSFC, and adhered to the ML at the node locations (blue dots) of Fig. 20.2. The KSC instrumentation group performed the instrumentation work and used HBM-X60 dental cement on aluminum tape to apply the accelerometer blocks. Signal conditioning of both accelerometer models was provided by the B&K data acquisition hardware, which provided Constant Current Line Drive (CCLD) power with high-pass filtering set to 0.1 Hz. The high pass filtering setting removed DC offsets while allowing for accurate measurements, particularly with the low-frequency PCB 393B04 accelerometers. For past large-structure tests, such as the B2 Stand Modal Test [4], the MSFC Modal Test Team used capacitive-type accelerometers to measure low frequency response. However, these accelerometers were powered with an external signal conditioner that required manually zeroing out the DC offset due to gravity and DC drift prior to every test, which both complicated the test setup and extended the test time depending on the number of the capacitive-type accelerometers used. Despite attempts to minimize DC offset, the data would most often exhibit undesired amounts of DC drift that would typically require high-pass filtering. Therefore, low-frequency CCLD, or IEPE (integrated electronics piezo-electric), accelerometers were selected for the ML test, and have been proven easier to setup, operate reliably, and provide accurate response measurements of large structures in the low frequency regime.

20.7 Test Control Center The modal test control center, consisting of the data acquisition system (DAQ) and remote shaker monitoring systems, was located on the second floor, inside the Mobile Launcher base. This location was out of the way from the various SLS/ML support activities, protected from the elements, and provided enough power to operate the test equipment. Additionally, this area of the ML interior was air-conditioned for a majority of the testing, which was appreciated greatly by the test engineers. With the space available inside the ML, the test control center was arranged as seen Fig. 20.6. The DAQ hardware is seen on the left side of the figure, and the shaker monitor systems—which included a displacement monitoring system, a video surveillance system, and multiple oscilloscopes used to display the input force signals—are seen on the right of the figure. The data acquisition system used to record the 384 channels of data—including force, acceleration, displacement, and drive voltages—consisted of Bruel and Kjaer (B&K) LAN-XI front-end modules operated by BK Connect software, running on a Windows-based HP Z820 PC computer. The LAN-XI modules were distributed into three 19-inch racks holding two B&K mainframes each, and placed along the height of the ML tower. All transducers were connected to the mainframes at these locations via RG-174 co-axial cables. Ethernet cables of various lengths (6-ft to 300-ft) connected the mainframes to the DAQ PC via an Ethernet hub. A single 19-inch rack containing two B&K mainframes with 22 LAN-XI modules are shown with the Ethernet hub on the left side of Fig. 20.6; the PC (with a very, very large monitor) running the BK Connect software can be seen in the center of the figure. The shaker displacement monitoring system provided an efficient view of all five shaker displacements in addition to maximum armature stroke limit warnings and alarm indicators. A MATLAB executable running on a portable PC was used to operate an NI cDAQ-9174 chassis with two 4-channel NI-9239 input cards, which measured the built-in linear variable differential transformer (LVDT) signal from each hydraulic shaker; these signals were recorded by the DAQ as well. The MATLAB graphical user interface, shown in Fig. 20.7, allowed for adjustable measurement sample rates, LVDT sensitivity values, and peak hold values. Furthermore, the interface made it easier for the DAQ engineer to immediately detect displacement limit exceedances and decrease the hydraulic shaker gains as required to prevent banging of the fixture stops. The video surveillance system provided a real-time view of all five shaker test fixtures from the test control center. At each shaker location, an analog color camera was arranged on a tripod with a full-field view of each shaker test fixture (the adjacent 0-deck lateral and vertical fixtures were in the frame of a single camera). The camera signals were connected to a

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Fig. 20.6 Test control center (DAQ and shaker monitoring system)

Fig. 20.7 Hydraulic shaker displacement monitor interface

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16-channel video multiplexer via BNC co-axial cable, which displayed all fixtures on a large monitor simultaneously. The multiplexer also recorded the video signals, providing test documentation as well as a record of any test fixture malfunctions that were to occur during testing (note: no drastic test fixture malfunctions occurred during the ML modal test). The final component of the shaker monitoring system consisted of three 4-channel TDS1064 Tektronix oscilloscopes, installed in a 19-inch rack that provided a visual display of the shaker force input voltages. Viewing the raw force waveform was particularly useful if problematic force levels were detected on the DAQ during testing. As was discovered with the 0-Deck lateral shaker, being able to zoom in on the force signals helps immensely in diagnosing equipment issues. Additionally, the oscilloscopes provided RMS calculations, which was useful for adjusting hydraulic shaker gains on test startup. Altogether, these shaker monitoring systems proved to be very useful, as they provided immediate feedback to the DAQ engineer during shaker startup and testing, preventing possible damage to the test structure, shaker, or personnel.

20.8 Test Plan and Data Acquisition Parameters Based on a combination of pre-test analysis and dry runs performed with the hydraulic test fixtures in the lab at MSFC, it was determined that the requested test frequency bandwidth of 0 Hz to 12 Hz would be split into two smaller bandwidths for the random vibration modal tests. Driving the shakers with the smaller bandwidth random signals from the DAQ sources resulted in obtaining higher force levels. Therefore, a low frequency random test from 0 Hz to 3 Hz, and a high frequency random test from 3 Hz to 12 Hz would be performed with all five shaker test fixtures running simultaneously (multi-shaker) with uncorrelated output. This was particularly important for the low frequency bandwidth, where it was desired to provide as much drive force near 0 Hz as possible, in order to excite the first few modes of the ML. A fine frequency resolution was required for the multi-shaker random vibration modal testing due to the low response frequencies of interest. Therefore, a time window (T) of 256 seconds, with a corresponding frequency resolution (f) of 0.0039 Hz, was selected to calculate the frequency domain functions from the random vibration time data. To average out the non-biased noise in the spectral analysis calculations, 62 averages were measured with a Hanning broad window and 66.6% overlap, resulting in a total test time of approximately 92 minutes for each of the two frequency bandwidths (0 Hz to 3 Hz and 3 Hz to 12 Hz). These random vibration modal signal-processing parameters were proven sufficient from additional dry runs performed with the horizontal hydraulic test fixture on the historic 363-ft tall Saturn V Dynamic Test Stand, located at MSFC. In addition to the multi-shaker random vibration modal testing, plans were made to perform a multi-shaker sine (or multisine) sweep test if deemed necessary at test time. A multi-sine sweep test is defined as exciting a test structure with multiple shakers simultaneously, each outputting an uncorrelated sine sweep signal over the same frequency range. This test method is known for saving tremendous amounts of test time, as each shaker does not have to run a sine sweep individually. For the wrapped multi-sine method, each shaker starts at a different frequency within the sweep range, and once the shaker gets to the end of the frequency range, it ramps down, then ramps up to the beginning of the frequency range. Further detail of multi-shaker sine sweep testing can be found in [5, 6]. Based on the results from the multi-shaker random test, a wrapped, multi-sine sweep signal for up to four of the hydraulic shakers could be created with an ATA-MATLAB code over a desired frequency range and with a given sweep rate. The multi-sine sweep signals would then loaded into MATLAB and output as voltages from a 4-channel NI-9269 voltage output module, located in a NI cDAQ-9171 single-card chassis. The output voltages would be run directly into the hydraulic shaker inputs, disconnected from the DAQ outputs at the test control center, resulting in an open-loop, multi-sine sweep test. The final type of test planned for the ML was modal impact excitation, provided by the portable impact drop tower. Any locations on the ML 0-Deck that were not excited by the shaker test fixtures could be impacted by the drop tower and analyzed for modal frequencies. This test would provide verification that no global modes were missed during the random and multi-sine testing, particularly the vertical modes of the 0-Deck. Time histories were recorded by the BK Connect DAQ with the global sample rate of 512 Hz, resulting in a time resolution (t) of 0.00195 seconds for all modal test excitation methods (multi-shaker random, the multi-sine testing, and the impact tower). Real-time signal processing was performed by BK Connect during each modal test as well. The time histories allowed for the additional post-test processing by the modal teams with whatever method they deemed best for the test data.

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20.9 Test Configuration The Mobile Launcher modal testing was performed inside the KSC Vehicle Assembly Building from June 16 to June 24, 2019. Testing was performed at night, once all SLS/ML support work had ceased for the day, to minimize the amount of unmeasured noise into the modal measurements. Additionally, the high-bay doors of the VAB were closed during testing to prevent any wind from exciting the tower with unmeasured wind force. Two views of the ML during a night of modal testing are shown in Fig. 20.8—the tower as viewed from the 0-deck on the left, and the top of the tower as viewed from the VAB on the right. As seen in the photos, the VAB platforms used to service the SLS have been retracted from the ML. On the lower half of the tower, the grey umbilicals can be seen retracted to the tower, and the crew access arm is somewhat visible extending from the top half of the tower (a portion of the white roof at the end of the arm can be seen at the bottom of the right photo). The hydraulic shaker test fixtures were installed weeks prior to the modal test and operated locally, at very low levels, to determine proper assembly and operation. The hydraulic hoses from the shakers were run to their corresponding hydraulic pumps, which were all located on VAB platforms. Placing the pumps on the VAB eliminated the possibility of pump noise contaminating the modal data. Two of the operational shaker test fixtures are shown in Fig. 20.9. In the lateral shaker test fixture, the rod-end load cell can be seen installed between the shaker armature and the vertical arm. Also seen in the figure is the foam padding placed under the hydraulic hose to both reduce any undesired hose vibration into the ML platform as well as reduce friction between the hose and the fiberglass platform. Note that both shakers were installed with hydraulic fluid spill containment pans located between the shaker and the ML structure.

Fig. 20.8 Mobile launcher test configuration (a) view from 0-Deck and (b) view from VAB

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Fig. 20.9 Installed hydraulic shaker test fixtures, (a) Lateral and (b) Vertical

20.10 Test Results Ultimately, all three types of modal tests—multi-shaker random, multi-shaker sine sweep, and impact tower—were successfully performed on the Mobile Launcher in all three mount configurations, and completed ahead of schedule. The multi-shaker random modal testing provided sufficient excitation of the ML in the two frequency ranges (0 Hz to 3 Hz and 3 Hz to 12 Hz) to identify and extract the modal parameters of interest. Multi-shaker sine sweep testing was performed from 12 Hz to 3 Hz with the three shakers on the 0-deck to verify the random modal results. Finally, impact drop tower testing was performed at a few select accelerometer locations on the Mobile Launcher 0-Deck. The only major equipment problem experienced during the modal testing was with the 0-Deck lateral shaker test fixture, which began to decrease in force output following the first night of testing. Post-test investigation conducted at MSFC indicated that the shaker was misaligned with the vertical post, which increased bearing friction, and therefore decreased the available force output. This decreased force was first detected in the data measured during the first ML test configuration. The 0-Deck lateral shaker was determined ineffective during the second ML test configuration and was not used for the remainder of the testing. The subsequent data that will be discussed in this section was measured with the ML in the first configuration, so it will include data from this shaker test fixture. The results in this section will cover only the first Mobile Launcher test configuration, supported by the VAB mount mechanism points. Although this will not be discussed, each ML configuration resulted in different modal parameter estimates as expected, due to the change in ML boundary condition. Additionally, only the driving point functions will be displayed for each modal test due to the large number of frequency response functions calculated (5 uncorrelated force inputs with 361 accelerometer responses results in 1805 FRFs!). If the excitation locations are sufficiently selected, the driving points should exhibit all the modes of a structure. Finally, only representative plots will be shown, with no units displayed on the axes. The input force power spectral densities (PSD) achieved by the shaker test fixtures for the multi-shaker random modal tests are shown in Fig. 20.10 for both the low frequency band (0 Hz to 3 Hz) and high frequency band (3 Hz to 12 Hz). Both data sets are plotted on the x-axis with their respective input frequencies and have the same y-axis scale for comparison. The legend indicates the shaker configuration (lateral or vertical) and the ML level (0-deck, 240-ft, 345-ft), as well as the RMS force levels calculated from the data. As seen in the low frequency PSD of Fig. 20.10a, the force input values range from 367 lbf-RMS to 759 lbf-RMS, with the vertical shakers contributing to the lower force values. The magnitudes for the vertical shakers also drop off when approaching 0 Hz, as compared with the lateral shakers. This may have been due to the air bags in the vertical shakers that prevented the shaker from reaching full displacement when retracted, as a lower displacement results in a lower force. The lateral shakers however, did not use airbags and could travel a majority of the 4-inch displacement range, resulting in the higher force values near 0 Hz. Additionally, the lateral shakers had more inertial mass than the vertical shakers, which may also have resulted in more force output at lower frequencies. For the high frequency PSD of Fig. 20.10b, the force inputs range from 277 lbf-RMS to 1007 lbf-RMS, with the already discussed problematic shaker (0-Deck Lateral) being the outlier with the lowest force value.

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Fig. 20.10 Multi-shaker random input force PSD (a) low frequency and (b) high frequency

Fig. 20.11 Multi-shaker random driving point FRF (a) low frequency and (b) high frequency

The calculated frequency response functions (FRF) for the driving points (shaker locations) of the multi-shaker random modal tests are shown in Fig. 20.11, for both the low frequency excitation band (0 Hz to 3 Hz) and high frequency excitation band (3 Hz to 12 Hz). Again, the data sets are plotted on the x-axis with their respective input frequencies and have the same y-axis scale for comparison. The legend lists the FRF measurement locations and the colors correspond to the input force PSDs shown in Fig. 20.10. Several observations regarding the dynamic response of the Mobile Launcher can be made from the driving point FRFs in Fig. 20.11. First, the lateral shakers display an overall response of about an order of magnitude larger than the vertical shakers. This is expected, as the ML should be more dynamic and have more response in any lateral direction than in the vertical direction, primarily due to the tower. Second, the Level 345 and Level 240 lateral shakers, which were configured 90-degrees apart in the lateral plane, exhibit many clearly defined modes (peaks) of the tower. Third, the 0-Deck lateral shaker shows a few peaks with much less magnitude when compared with the tower lateral shakers in the low frequency plot, and hardly any peaks in the high frequency plot. Again, this is expected, as large responses in the lateral direction at the

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Fig. 20.12 Multi-shaker sine sweep (a) input force PSD and (b) driving point FRF

base of the tower should not be very large at higher frequencies. Finally, the 0-Deck vertical shakers exhibit very noisy FRFs at very low frequencies, which indicate the lack of response at these frequencies. However, at higher frequencies, there are definite peaks indicating contribution to the higher frequency, vertical modes. A multi-shaker sine sweep was performed with the three 0-Deck shaker test fixtures following the multi-shaker random testing to verify the results from the multi-shaker random data, particularly the vertical modes. While there are known equations to determine the adequate sweep rate based on damping values and frequencies of interest, due to the tight test schedule, the sweep rate for the ML was determined by frequency range and the desire to perform a multi-sine test with a one hour duration. Therefore, the multi-shaker inputs signals, created in MATLAB with ATA-authored software, consisted of a 4-Volt amplitude down sweep from 12 Hz to 3 Hz with a logarithmic sweep rate of 0.0107 dec/min for a total signal time of 3616 seconds. The ramp up/down time for each shaker was 8 seconds, and the wrap method was used. The multi-sine sweep results, consisting of the force input PSD and driving point FRF, are shown in Fig. 20.12. As before, the PSD legend indicates the shaker configuration (lateral or vertical) and the ML level (0-deck) as well as the RMS force levels calculated from the data. The FRF legend displays the measurement location, with the colors corresponding to those shown in the input force PSD. For ease of comparison, the colors for the each function are the same as in the multi-shaker random results of Figs. 20.10 and 20.11. In the PSD plot of Fig. 20.12a, the vertical force input values ranged from 1329 lbf-RMS to 1597 lbf-RMS, while the lateral force input was the lowest value of 794 lbf-RMS. Some of this difference may have been due to the 594-lbs difference in the moving mass between the lateral and vertical shaker test fixtures. However, upon closer inspection of the recorded time history, the lateral input signal did not appear as a clean sine wave, but appeared as a sine wave with additional higher frequency content present. Despite these additional frequencies, the force input into the ML by the 0-Deck lateral shaker was measured, so the data was considered valid for this multi-sine test. Despite the decreased force, the 0-Deck lateral shaker displayed a smooth PSD curve, whereas the 0-Deck vertical 1 shaker and vertical 2 shaker have large noisy blips. These larger blips are artifacts of using the wrap method when applying multi-sine with a sweep rate that may be too fast. With the wrap method, these shakers began and ended the sweep at these corresponding frequencies with an 8-second ramp up and ramp down. Even with a 95% overlap, the ramping causes some input frequencies to be improperly averaged or missed altogether. With a low enough sweep rate, this artifact would be reduced or go away completely. In the multi-sine sweep FRF plot of Fig. 20.12b, the 0-Deck lateral shaker appears to display a stiffness line leading to the first dominant lateral mode of the 0-Deck. The vertical shakers however, display many peaks in this frequency range, which indicate many vertical modes in the excitation frequency range. Additionally, the multi-sine FRF is much cleaner when compared with the multi-shaker random FRF of Fig. 20.11b, which can lead to much cleaner modal extraction with less scatter and uncertainty.

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Fig. 20.13 Impact drop tower time history (a) all impacts and (b) zoomed-in impact

The final test performed was the impact drop tower testing performed at three locations on the 0-Deck to verify the frequency response due to lack of input from the existing shaker locations. For each drop tower test, 10 impacts were performed with approximately 30 seconds between each impact while the data was recorded as one continuous time history. The time history of one of the impact test locations is shown in Fig. 20.13, where the entire time history is plotted on the left and a zoomed-in view of the second impact in plotted on the right. Disregarding the first impact, forces of about 1800-lbf were consistently achieved with the drop tower. The width of the second impact was approximately 0.05 seconds, which resulted in a 20 dB roll-off of the input power around 20 Hz, providing concentrated energy in the bandwidth of interest. This data was not fully analyzed by the MSFC Modal Test Team, but was recorded by request of the modal estimation team (which will be subsequently discussed), therefore, no spectral analysis results will be shown here. Both the multi-shaker random data and the multi-sine shaker data were used in the modal parameter estimation analysis performed by the MSFC Modal Test Team using Rational Fraction Polynomial-Z method in the BK Connect Modal Analysis software. For modes below 1 Hz, the low sensitivity (100 mV/g) accelerometers were removed from the data set, as the higher noise floor present in the data at these low frequencies resulted in false or inaccurate mode estimation. Because not every degree-of-freedom was measured for every node in the test display model of Fig. 20.2, a Guyan back expansion was performed on the measured, extracted mode shapes with the Test Analysis Model stiffness matrix, to fill-out the unmeasured modal vectors. A selection of the resulting, back-expanded mode shapes of the Mobile Launcher are shown in Fig. 20.14.

20.11 Recommendations The Mobile Launcher was only made available for modal testing for a short amount of time due ongoing preparations of the structure for the Space Launch System. To ensure that the available time would be used as efficiently as possible, all modal test equipment was thoroughly tested at MSFC, and once installed at KSC prior to the actual test date. A few examples include operating the B&K data acquisition system and hardware with all 400+ channels connected and recording data for hours at a time. The five hydraulic shaker test fixtures were assembled and operated all at once in the laboratory at MSFC to verify proper simultaneous operation and expected force levels. Once installed on the ML at KSC, the shakers were operated one at a time, locally, at very low levels. A full dry run integrating the DAQ, a lateral hydraulic shaker, accelerometers, and load cell was performed on the Saturn V Dynamic Test Stand at MSFC to simulate the data acquisition process on a similar

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Fig. 20.14 Select mode shapes of mobile launcher: (a) tower bending in z-axis, (b) tower bending in y-axis, (c) tower bending in z-axis with base motion, and (d) tower vertical with base motion

structure. Random vibration and sine sweep tests were run on the Test Stand, and the results helped determine optimal DAQ settings, sweep rates, and data analysis methods. This extensive pre-test work was vital to the completion of the Mobile Launcher modal testing within the allotted timeframe. The hydraulic shaker monitoring system proved to be a valuable addition to the test control center by providing immediate information regarding the status of all five shakers to the DAQ engineer during startup and testing. While the data acquisition system could provide the shaker displacement and force data during a test, it was also measuring 381 channels simultaneously, which complicates the display, even if the display is 42-inches large. Having a dedicated system for displaying this information during a test allows for quick adjustments to the shakers without scrolling through all

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the additional channels, saving time, mental stress, and eye strain. Diagnosing any problems with the shakers becomes immensely easier as well, as the raw data signals can be viewed for problems such as discontinuities or DC offsets. The video system was not as important, but served as a sanity check for the DAQ engineer and a video record of the test. The most vital aspect of keeping the modal test within schedule was the establishment of a completely separate data analysis team that operated onsite, in parallel to the data acquisition team. The data analysis team consisted of modal analysis engineers from other NASA facilities and industry. Following each modal test, the time history data was handed over to the analysis team, who would perform independent modal parameter estimation, allowing the test team to focus on performing the next test. Close communication between the two teams allowed for adjustments to the test procedure as necessary, in order to guarantee all target modes were measured. Most importantly, having two separate teams working in parallel allowed enough time for sleep between test days, which prevents exhaustion and encourages good critical thinking at test time. Finally, it is worth noting that insect repellant is required for any modal testing performed in Florida, USA. Even if the test item is in a large high-bay facility with the exterior doors closed, mosquitos and other insects will find test engineers and proceed to pester and bite them, predominantly at night. With insect repellant, modal tests can be performed in relative peace.

20.12 Conclusions A successful modal test was performed on the NASA Mobile Launcher at Kennedy Space Center by the Space Launch System Test Team to validate an analytical model of the launcher, in preparation of the upcoming SLS Integrated Modal Test. Excitation of the Mobile Launcher was achieved with five hydraulic shaker test fixtures, configured in the lateral and vertical directions, which were used to perform both multi-shaker random vibration as well as multi-shaker sine sweep modal tests. A portable drop tower was also used to perform impact modal testing on the 0-Deck platform at a few locations not sufficiently excited by the shakers. Response of the Mobile Launcher was measured with 361 accelerometers. Force, acceleration, displacement, and voltage drive time history signals were recorded with a B&K data acquisition system. Three Mobile Launcher support configurations were tested in the Vehicle Assembly Building over the frequency range of 0 Hz to 12 Hz. Modal parameters were estimated from the data and verified to include all target modes from the analytical model. The primary challenges met with this modal test included exciting such a large structure as well as testing within a short timeframe. The shaker test fixtures used for excitation implemented hydraulic shakers to move an inertial mass, providing inertial acceleration with 4-inches of displacement down to 0 Hz. Pre-test analysis ensured that the locations and directions of the shaker test fixtures would sufficiently excite all modes of interest, with an impact drop tower to excite a few additional locations. To meet the challenging schedule, all modal test equipment, from the shakers to the DAQ, was assembled and operated to their limits at MSFC, in order reduce time spent at the test site debugging or repairing equipment. At the Mobile Launcher test site, a shaker monitoring system was implemented with the data acquisitions system to provide immediate displacement and force information, as well as video, to the DAQ engineer during testing. Additionally, a second team of modal analysts was brought in to perform an independent modal parameter estimation on the data, while the MSFC test team continued to test. The division of test and data analysis responsibilities saved schedule time, allowed engineers to focus on their particular tasks, and most importantly, allowed for sufficient time for sleep between test days. Modal parameter estimates from the Mobile Launcher modal test will ultimately be used to validate an analytical model of the structure. Because the ML will provide the boundary condition for the upcoming SLS Integrated Modal Test, the validated ML model will allow focus to remain on SLS vehicle model correlation during the IMT. Since the validated SLS model is required for flight certification, the Mobile Launcher modal test can be considered an integral step toward NASA and the SLS successfully reaching deep space and beyond. Acknowledgements Modal testing the Mobile Launcher was a massive undertaking that the authors did not perform alone. Therefore, the authors would like to proudly thank Jason Perry, Alex McCool, and Felipe Mora of NASA Marshall Space Flight Center, James Bolding, Regina Chambers, and Josh Hicks of Aerie Aerospace, and Wulf Eckroth and Mark Tillet of KSC for all their work in preparing for, setting up, and assistance in performing a very large modal test in the hot, humid, and buggy Florida summer weather. Many thanks to Adam Carver, Jason Phelan, and Bryan Moran of the TOSC instrumentation crew for their very impressive, scary, and difficult job of instrumenting the Mobile Launcher. Critical onsite data quality assessments and mode extraction were performed by Vicente Suarez and Kenneth Pederson of Glenn Research Center, as well as, Kevin Napolitano of ATA Engineering. Finally, valuable pre-test analysis and test coordination support was provided by Clay Fulcher and Dan Lazor of MSFC and Chris Brown of KSC.

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References 1. Photo credit: NASA/Ben Smegelsky (2019) 2. Mobile launcher. NASAfacts. https://www.nasa.gov/sites/default/files/atoms/files/mobilelauncher_factsheet_v2.pdf (2018) 3. Mobile launcher tower umbilicals and launch accessories. NASAfacts. https://www.nasa.gov/sites/default/files/atoms/files/fs-2018-02-250-kscml_umbilical_fact_sheet.pdf, 2018 4. Stasiunas, E.C., Parks, R.A.: Performing a large-scale modal test on the B2 stand crane at NASA’s Stennis Space Center. In: IMAC-XXXVI Conference Proceedings, SEM (2018) 5. Napolitano, K., Linehan, D.: Multiple sine sweep excitation for ground vibration tests. In: IMAC-XXVII Conference Proceedings, SEM (2009) 6. Hoople, G., Napolitano, K.: Implementation of multi-sine sweep excitation on a large-scale aircraft. In: IMAC-XXVIII Conference Proceedings, SEM (2010)

Chapter 21

Using Deep-Learning Approach to Detect Anomalous Vibrations of Press Working Machine Kazuya Inagaki, Satoru Hayamizu, and Satoshi Tamura

Abstract In recent years, there has been a demand for advanced maintenance in factories. Data collection from factory equipment is being carried out, and the collected sensor data is widely used for statistical analysis in quality control and failure prediction by machine learning. For example, if it is possible to detect an abnormality using vibration data obtained from an equipment, increase in the operation rate of the plant can be expected. In this research, we aim at early detection of equipment failure by finding signs of abnormality from vibration data, using a deep-learning technique, particularly an autoencoder. In this paper, the following two methods were tested. The first scheme is based on the reconstruction error in an autoencoder. An autoencoder is trained using normal data only. Looking at the difference between input data and reconstructed data, we can regard the data having higher difference as abnormal. In the second approach, given the input data, values of the middle layer of the autoencoder are extracted, and we calculate the degree of abnormality using a Gaussian Mixture Model (GMM), representing a data set by superposition of a mixture of Gaussian distributions. In this framework, regarding an autoencoder structure, we tested both full-connection networks and convolutional networks. In this work, we chose a press machine. Frequency characteristics were acquired from the data in production mode of a press machine. Then using each method, we evaluated whether abnormality could be found by calculating the degree of abnormality. We employed two-day data without failure as training data, and another data set was prepared as forecast data obtained on the following days; on one of the days the machine stopped due to a sudden abnormality. Similar to time-series signal processing, we applied framing processing so that we can analyze data even in the case we can only get a small amount of data. As a result, our method succeeded in finding the day when the abnormality occurred and the machine stopped. In addition, the degree of abnormality became higher before the abnormality occurs, indicating we can detect signs of abnormality. In conclusion, the degree of abnormality could be calculated using the reconstruction error using an autoencoder from the vibration data during production, and the method using GMM from the middle layer of autoencoder. We consequently conclude it is possible to detect a sudden abnormality in which the device stopped, from actual vibration data. These results provide new solutions for equipment failure estimation. Keywords Autoencoder · Anomaly detection · IoT · Gaussian mixture model

21.1 Background Machines are essential components in a manufacturing process, and their sudden failures result in significant losses to the industry. Automatic anomaly detection before such the failures is thus quite useful but still challenging. In recent years, sensors have been used to collect data for advanced plant maintenance operations. These collected data are used for various purposes, such as quality control and failure prediction [1]. Among various kinds of sensor data, vibration data is considered as the most significant cause for equipment damage and failure. The number of defective products can be reduced by detecting vibration abnormalities in the equipment. Moreover, the operational productivity of a factory can also improve as a consequence.

K. Inagaki () · S. Hayamizu · S. Tamura Gifu University, Gifu, Japan e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_21

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Vibraon data

Cut out shot

Framing

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Fig. 21.1 Our feature extraction scheme

This study aims to develop an early detection method for equipment failure, by analyzing signs of abnormalities resulting from equipment vibration. Our final goal is to develop a high-accuracy and practical anomaly detection and estimation scheme. Thus we employ state-of-the-art machine learning and deep learning techniques for the purpose.

21.2 Methodology Figure 21.1 shows the flowchart for feature extraction. In this paper, we focus on a press machine, and put a vibration sensor in it. In every press (shot), we can observe a large amplitude (peak) in the vibration data. Based on the peak time, we then cut 500 msec previous and 500 msec following data, resulting one-second short-time data. Subsequently, frame analysis, windowing, and Fourier transform are performed to obtain the frequency spectrum. Through frame analysis, the number of data points can be increased, and this ensures that analysis can be performed even with limited data. By dividing the obtained frequency spectrum into 100 frequency bins with 50 Hz increments, a 100-dimensional frequency feature is obtained, which is then evaluated using a deep-learning framework, an autoencoder. An autoencoder is built on an unsupervised learning manner, which is an artificial neural network that can learn input data with efficient expression, called by encoder-decoder structure. An input vector is compressed using the encoder and subsequently restored using the decoder. In abnormality detection, only normal data are used for autoencoder training. The predicted data are correctly restored if it is normal, otherwise unrestored. Two evaluation methods are used in this study; one that uses the reconstruction errors between the input and output of the autoencoder, and another is the one that uses GMM to identify middle-layer values in the autoencoder. GMM describes a mixture of different probability distributions, under the assumption that they are actual values derived from multiple population distributions. In this scheme, we extract the values after the encoder part for the GMM.

21.3 Dataset The data used in this study was obtained from an acceleration sensor installed in a motor of the press machine. The vertical vibration of the motor was measured at every 10 seconds. Note that, throughout the data acquisition, the machine produced a uniform product under the same condition. The training data and test data used in this paper are shown in Table 21.1. We chose two-day data consisting of normal data only for training (2/5 and 2/6). For the prediction data, we employed the other data. The testing data has one-day data when we met failures, as abnormal data (2/21), in addition to data on the previous day (2/20) as well as data after repair (3/6). For comparison, data from which a product differs (2/8-610LOPG) and the production speed differs (2/7-SPM23) are also tested.

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Table 21.1 Training and test data used in this study Training data (month/day) Prediction data(month/day)

2/5 2/6 2/5 2/6 2/20 2/21 (anomaly) 3/6 2/7(High production speed) 2/8(Another product)

4917 items 5014 items 33 items 33 items 33 items 33 items 33 items 33 items 33 items

Fig. 21.2 Abnormality based on reconstruction error

21.4 Experiment Frequency features were acquired from the vibration data during operation, and degrees of abnormality were calculated using two methods, respectively. The results of the degree of abnormality using both the methods are shown in Figs. 21.2 and 21.3, respectively. The horizontal axis denotes the time transition. The vertical axis denotes the degree of abnormality. The different colors represent the different test dates. Based on the results, we can easily find the data on the day having sudden anomalies which represent a stoppage in machine operation. It is also notable that, on the day before the abnormality, the degree of abnormality seems to be higher. Focusing on the data obtained on the day when we had different production speed, we can find no significant difference in the degrees of abnormality. However, it is found that the degree of abnormality varied when producing different products. That indicates we need to build an appropriate model for each product when employing our methods.

21.5 Conclusion In this study, deep-learning-based models for anomaly detection in factory production were built and tested. Frequency features were obtained from vibration data acquired during production. The acquired data were used to train an autoencoder, which is a deep-learning scheme. We prepared two approaches using the autoencoder, based on a reconstruction error and GMM scoring to encoder results. The models were then used to obtain the degrees of abnormality. Through experiments we

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Fig. 21.3 Abnormality based on Autoencoder + GMM

find both models can detect sudden anomalies resulting from actual vibration data. It is also found data on the previous day of the failures showed higher degrees of abnormality, thereby enabling us to predict machine failures. From the results of this study, two prospects can be considered for future works. First, we must determine the threshold properly to detect abnormal events or alert future machine failures. Second, we will investigate our model for every type of product. Acknowledgements The authors would like to thank our collaboration partner for providing the data used in this paper.

Reference 1. Koizumi, Y., Saito, S., Uematsu, H., Harada, N.: Optimizing acoustic feature extractor for anomalous sound detection based on Neyman–Pearson lemma. In: Proceedings of EUSIPCO (2017)

Chapter 22

DAQ Evaluation and Specifications for Pyroshock Testing Erica M. Jacobson, Jason R. Blough, James P. DeClerck, Charles D. Van Karsen, and David Soine

Abstract Pyroshock events contain high-amplitude, extreme rise-time accelerations that can be damaging to electronics and small structures. Due to their extreme nature, these events can be difficult to capture, exceeding the performance limits of transducers, signal conditioning, and data acquisition (DAQ) equipment. This study assesses the ability of different data acquisition systems to record quality pyroshock data. Using a function generator and voltage input, different tests were performed to characterize the data acquisition systems’ anti-alias filter, out-of-band energy attenuation, number of effective bits, in-band gain, and slew rate. These tests include a shorted-input noise test, a sine sweep test, and a high amplitude low frequency square wave test. Although the data acquisition systems evaluated have similar specifications, their ability to record quality pyroshock data varied. Some of these data acquisition systems do not appropriately handle the rapid transient content and may have inadequate fidelity to record pyroshock data. Data acquisition system performance for pyroshock testing cannot be evaluated by the specification sheet alone. Keywords Data acquisition performance · Slew rate · Out-of-band energy · Anti-alias filter

22.1 Introduction Pyroshock events are short in duration (10,000 Gs) and frequency (>100,000 Hz). Pyroshock events are caused by a sudden release of energy at a point source, which causes strain energy to release and propagate through the structure under test. Due to the high frequencies and small wavelengths of the stress wave propagation, these events have no velocity change [1]. A few examples of pyroshock events in the service environment are live ordinance detonation or stages of a space vehicle launch. Pyroshock can be replicated in the laboratory environment with live ordinance detonation or mechanical shock. Mechanical shock is often simulated with a metal-on-metal impact; for example, a projectile impacting a resonant plate. Due to their violent nature, pyroshock events are difficult to measure in both the service and laboratory environment. The high-frequency, high-amplitude content of these events can contaminate recorded data without the test engineer’s knowledge. There exist system requirements and recommendations to avoid the collection of bad pyroshock data. Most of these requirements are based upon the data acquisition system (DAQ) specifications provided by the manufacturer and can be found in MIL-STD-810G Method 517 [1], as well as ECSS-E-HB-32-25A [2]. The slew rate limitations of a system are of particular interest since it is a value not listed on the manufacturer’s specification sheets but is listed as a requirement in MIL-STD-810G. There is little information about slew rate and how to determine if a DAQ meets the slew rate requirements listed in the standards. This study was initially performed to answer the question “did Michigan Tech collect contaminated shock data?” and eventually morphed into an investigation

The Department of Energy’s Kansas City National Security Campus is operated and managed by Honeywell Federal Manufacturing & Technologies, LLC under contract number DE-NA0002839 E. M. Jacobson () · J. R. Blough · J. P. DeClerck · C. D. Van Karsen Department of Mechanical Engineering & Engineering Mechanics, Michigan Technological University, Houghton, MI, USA e-mail: [email protected] D. Soine Kansas City National Security Campus, Kansas City, MO, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_22

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of how different DAQs attenuate data outside of the bandwidth of interest. This study also attempts to investigate how system slew rate is calculated and how it relates to other system specifications, like sample rate and anti-alias filter properties.

22.2 Background Below is a list of data acquisition system requirements for adequate shock data collection, from MIL-STD-810G change 1 Method 517 (Table 22.1). A sample rate of ten times the maximum frequency of interest is for amplitude accuracy when computing the absolute maximum shock response spectrum. Most accelerometers can accurately measure up to 10 kHz, so a sample rate of 100 kS/s would satisfy this sample rate requirement. Signal to noise ratio (SNR) is generally listed on the specification sheet and can also be verified experimentally. But how can the slew rate requirement be evaluated? Slew rate can be defined as the maximum change in voltage that a DAQ can detect without serious anomalies. These anomalies occur when a change in voltage is not detected and can show as clipping or a zero-offset in the collected pyroshock data [1]. It should be noted that other errors associated with pyroshock testing, such as accelerometer errors, also present themselves as clipping and zero-shift [3]. Slew rate specifications can be found for the system’s Analog to Digital Converter (ADC) chip, but the slew rate of interest is of the entire system, not the ADC chip. Slew rate can be defined as the change in the detected voltage (Vout ) with respect to time [4]: Vout = V ∗ sin (ωt) dVout = V ∗ ω ∗ cos (ωt) dt Slew rate is generally presented in volts per microsecond (V/μs). The gain-bandwidth product (V*ω) is a constant and can become saturated at high frequencies and high voltages [4]. This is also known as slew rate saturation and is the value of interest in this research. The maximum slew rate capabilities of a system can be found in a few ways. Smith [5] uses a sine sweep across a large frequency range and identifies discontinuities or anomalies, calculating the slew rate from that frequency. This method is attempted in this research. Another method, mentioned in IEEE-1057 section 9.3 [6] is to record the DAQ response to a step input, increasing the amplitude from 10% full scale. When the system does not detect a change proportional to the step response increase, the slew rate has been saturated. The slew rate of the system is equivalent to the largest recorded rate of change. A similar method is attempted in this research. Although slew rate requirements are mentioned in [1], no test method is described. However, examples of contaminated data are presented in Annex A. Most modern DAQs implement a sigma-delta ADC, which internally oversamples at a high rate (~9 MS/s), then uses an analog AAF for that internal sample rate. The ADC uses a one-bit comparator to toggle between a change in the voltage (the least significant bit). The digitized data is then downsampled (including a digital AAF) with the user-defined sample rate and reconstructed over the entire dynamic range (Fig. 22.1). This type of ADC is cost-effective and allows for a wide frequency and amplitude range while still providing alias protection. Three protocols were selected (or designed) to test a DAQs ability to detect abrupt changes, characterize the AAF, and compare calculations (slew rate, alias-free bandwidth, dynamic range) to the supplied specifications and test requirements.

Table 22.1 Minimum data acquisition system requirements for adequate shock data [1] Data Acquisition System Item Sample Rate Signal to Noise Ratio (SNR) Slew Rate

Recommended Value >10*Fmax ≥60 dB ≥0.5*Vmax /μs without distortion

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Fig. 22.1 Sigma-Delta system sample rates and anti-alias filters. (Inspired by [1])

Fig. 22.2 Change in voltage calculation using a low-frequency high-amplitude square wave

22.2.1 TEST 1: Change in the Voltage (Slew Rate) There is no unified method to test a system’s slew rate capabilities, though there are many different ways to do it. The method utilized in this test is to generate a low-frequency high-amplitude square wave and calculate the change in voltage across all samples (Fig. 22.2). There are groupings of values at the maximum positive and negative slew rates (rise and fall of the square wave), as well as around zero (the flat part of the square wave). The maximum absolute value was taken from these clusters. A 100 Hz square wave was generated at 50% Vmax using an NI VB-8012 digital oscilloscope and function generator. The DAQ’s ability to detect the abrupt change in voltage on a high-amplitude square wave is a simple representation of a pyroshock event, utilizing basic equipment and simple calculations. Below is the maximum change in voltage equation in relation to Fig. 22.2.  SR

V μs





V2 − V1 dVout

= max = dt (t2 − t1 ) ∗ 106

22.2.2 TEST 2: Sine Sweep A linear sine sweep test can visually reveal characteristics of the system’s anti-alias filter, in-band gain, and out-of-band attenuation. Ideally, the in-band gain is one, and the out-of-band energy is attenuated. This research generated a stepped sine from 100 Hz to 2.5 MHz in 20 seconds. The NI VB-8012 is controlled through a LabView 2017 VI, modified from [7]. Smith’s slew rate calculation method is also investigated using the equation below:

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 SR

V μs

 =

2πf Vmax dVout = dt 106

22.2.3 TEST 3: Short-Input Noise The “ideal input” is mimicked by connecting all DAQ inputs to each other and to a common ground. The measurements from the DAQ can be converted from voltage to the number of bins using the least significant bit (LSB). The noise floor is presented in percentage of total bins. SNR is also calculated. LSB (V ) =

Vmax Vmax = bits bins 2 

SN R (dB ref 1V ) = 20log10

Vmax mean (Vnoise )



22.3 Analysis Five data acquisition systems were selected from four different manufacturers for testing. Four of the systems implement sigma-delta ADCs and anti-alias filters, while one uses successive-approximation and no anti-alias filter. The five DAQs will be labeled A through E. • • • • •

ADC Type: sigma-delta, successive-approximation ADC Bits: 16, 24, 2 × 24 Highest Sample Rate: 102.4 kS/s, 204.8 kS/s, 500 kS/s, 2.5 MS/s Maximum Input Voltage: +/− 10 V, +/− 20 V Signal Coupling: AC, DC

The three tests mentioned above were performed on the five different data acquisition systems. Each test was repeated for a sample rate of 51.2 kS/s and the DAQ’s highest sample rate. The tests were also repeated for different signal couplings. The manufacturer and model will remain anonymous. Any information derived from the specifications or figures by the reader is purely incidental.

22.3.1 TEST 1: Change in Voltage (Slew Rate) The recorded square wave is characterized by percent overshoot and settling time (within 0.5%) for both maximum and common sample rates (Table 22.2). At the maximum sample rate, DAQs A and B have high overshoot but low settling time. At the common sample rate, DAQs B and C have both high overshoot and high settling times. DAQ D has a near-perfect square wave in the time domain, but the spectrum is full of aliasing; the anti-alias filter must manually be programmed for this unit. Figure 22.3 compares the recorded time response between DAQs D and E.

Table 22.2 Square wave characterization in the time domain DAQ A DC B AC C DC C AC E AC E DC

Common Sample Rate (51.2 kS/s) Percent Overshoot Settling Time (s) 11% 8E-05 17% 0.010309 18% 0.000938 n/a n/a 16% 0.000313 18% 0.000313

Maximum Sample Rate Percent Overshoot 19% 23% 7% 9% 17% 6%

Settling Time (s) 4E-06 7.86E-05 0.000176 0.000352 7E-05 0.000059

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Fig. 22.3 Square wave time response for DAQs D (no AAF) and E (Gibb’s phenomenon) at a sample rate of 51.2 kS/s

Fig. 22.4 Sine sweep results from 100 Hz to 2.5 MHz at a common sample rate of 51.2 kS/s

22.3.2 TEST 2: Sine Sweep The results of this test are very visual – it is obvious which DAQs properly attenuate high-frequency content (Fig. 22.4). The amplitude is normalized by the input voltage, so the in-band gain should be close to one. DAQ C has improper highfrequency attenuation that even amplifies the high-frequency content. DAQs C and E (AC coupling) show some undesired amplification in the pass band, especially near the Nyquist frequency. The DAQ closest to the ideal gain and attenuation is DAQ A. DAQ D has no anti-alias filter and does not attenuate high-frequency content. The points of anomalous behavior are shown as discontinuities outside of the pass band and are labeled with an arrow in the figure below.

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Table 22.3 Comparison of slew rate calculation results and requirements DAQ A B C D E

Test 1: Slew Rate (V/μs) Max Fs 21.2626 1.8419 1.2802 4.9893 1.6958

51.2 kS/s 0.2557 0.34528 0.7969 0.5262 0.3235

Test 2: [5] Slew Rate (V/μs) Max Fs None detected None detected 1.156 n/a 36.01

51.2 kS/s None detected None detected 0.435 n/a 35.91

22.3.3 TEST 3: Short-Input Noise The measured noise was statistically characterized. All dynamic range calculations were comparable to the manufacturer’s specifications and all passed the requirements of >60 dB inside the bandwidth of interest. This may no longer be an issue as it once was since high-bit systems are widely available and relatively inexpensive compared to previous technology.

22.3.4 Conclusion Table 22.3 compares the calculated slew rates from tests one (square wave) and two (sine sweep). The slew rate requirement is greater than one-half full-scale voltage per microsecond. Values that meet or exceed this requirement are marked with a green checkmark ( ). Examining the first test method, it can be concluded that the calculated maximum change in voltage is dependent on the sample rate. However, this may be closely linked to the AAF behavior than the sample rate. The change in voltage was calculated by taking the difference between two points on the slope of a square wave. Sampling at a higher rate allows for higher frequency detection. A square wave can be represented as a Fourier series including infinite harmonics – a higher sample rate correlates to more harmonics included in the summation, which leads to higher possible detection of voltage change. The results of this test may not be the best representation of slew rate saturation calculation. Examining the second test method, not all DAQs presented amplitude anomalies. DAQs A and B revealed no discontinuities or jumps in the sweep profile and can be said to have a slew rate greater than 140 V/μs (assuming an anomaly occurs at or beyond 2.5 MHz). However, DAQ D has no AAF and also did not display any anomalies. There are still differences between the calculated slew rates at different sample frequencies. The relationship between this calculation method and sample rate/AAF behavior must be investigated further. This method would also benefit from a set criterion of “anomalies”. Using the first test calculation method, only one system passes the requirement: DAQ A at the maximum sample rate. Using the second test calculation method, three (potentially four) systems pass the requirement: DAQs A, B, E, and possibly D. Using all the information collected across all DAQs and all tests, DAQ A passes all requirements and can be expected to take quality, contamination-free pyroshock data. However, when focusing on the sine sweep results, DAQ B also performed well in attenuating out-of-band energy and having a consistent gain in the pass-band. It should be noted that there are other ways to test and calculate a system’s specifications. More accurate test methods require better equipment, which not everyone has access to. For starters, the function generator used in these tests has similar specifications as the tested systems (SNR, dynamic range). There was also no ability to perform a true sine sweep, so a fast stepped-sine was substituted. Though these five DAQs appear similar when comparing their specifications, their performances for pyroshock data collection varied significantly. It is incredibly important to characterize the system before testing. The most shocking test results came from test 2 (sine sweep), which revealed that not all DAQs properly attenuate high-frequency content, meaning tests conducted with these devices could (most likely are) contaminated. This simple test can be done in a short amount of time with no calculations and minimal data processing. The most time-consuming process of this study was to set up each individual DAQ, acquisition software, and establish communication between the computer and DAQ. The relationship between slew rate and other requirements (AAF performance, sample rate) should be further investigated. There is potential for a system to meet multiple requirements simultaneously, especially if there is a strong relationship

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between AAF performance and maximum change in voltage detection. Slew rate (of the system, not the ADC chip) should be clearly defined in the standards, and a simple test procedure should be provided. Acknowledgements • Strether Smith, for his insight and discussions about pyroshock data collection, slew rate, and system test methods. • DAQ manufacturers, for sending loaner equipment and giving tech support assistance.

References 1. MIL-STD-810G chg.1: Environmental engineering considerations and laboratory tests (2014) 2. Space Engineering Mechanical Shock Design and Verification Handbook, ECSS-E-HB-32-25A (2015) 3. Agnello, A., Sill, R., Dosch, J., Smith, S., Walter, P.L.: Causes of zero offset in acceleration data acquired while measuring severe shock, White Paper no. WPL-61-ZERO-OFFSET 4. Bateman, V., Himelblau, H., Merritt, R.: Validation of Pyroshock data. Sound Vib. 46(3), 6–11,14 (2012) 5. Smith, S.: The effect of out-of-band energy on the measurement and analysis of Pyroshock Data (2009) 6. IEST.: IEEE Std 1057–2017 (Revision of IEEE Std 1057–2007): IEEE Standard for Digitizing Waveform Recorders (IEEE Std 1057–2017). IEEE (2018) 7. N. Instruments.: VirtualBench: frequency sweep generator and acquisition with the FGEN and MSO [Web Page]. (2015). Available: http:// www.ni.com/example/52075/en/

Chapter 23

Optimal Replicator Dynamic Controller via Load Balancing and Neural Dynamics for Semi-Active Vibration Control of Isolated Highway Bridge Structures Sajad Javadinasab Hormozabad and Mariantonieta Gutierrez Soto

Abstract During the past few decades, major structural damages due to natural disasters like earthquakes has led bridge engineers to develop structural control systems to mitigate damage and improve vibration reduction in real-time. Among different kinds of vibration control systems, base isolation is one of the most commonly used passive control strategies for civil structures. However, base isolators have their own limitations due to the lack of real-time adaptability and lower energy dissipation. In order to overcome this limitation, semi-active damping devices are installed between the deck and piers. In the present study, a semi-active control system comprised of magneto-rheological (MR) dampers is proposed for vibration mitigation of isolated bridge structures. Recently, inspired by evolutionary game theory, a replicator dynamic control algorithm was developed to allocate the input voltage of MR dampers. In this paper, a load balancing strategy is studied to reallocate additional resources and improve the power distribution over semi-active MR dampers. In order to achieve a high-performance design of the replicator controller, a modified patented Neural Dynamic (ND) model of Adeli and Park is used to optimize the load-balanced replicator control parameters. The ND model incorporates a penalty function, the Lyapunov stability theorem, and the Karush-Kuhn-Tucker conditions to guarantee the global convergence of the solution. The objective function is then defined to minimize the dynamic response of the bridge. The proposed methodology is evaluated using a benchmark control problem that is based on Interstate 5 overcrossing California State Route 91 bridge in Southern California subjected to near-field earthquake accelerograms. The performance of the proposed controller is evaluated and compared with conventional Lyapunov and fuzzy control algorithms in terms of 16 different performance criteria describing the reductions in dynamic response of the bridge structure. Keywords Isolated bridge · Replicator dynamics · Game theory · MR damper · Neural dynamic optimization · Load balancing

23.1 Introduction Extensive research about the economic consequences of failures and damages in bridges due to natural hazards especially earthquakes has highlighted the importance of control systems for bridges [1, 2]. Among different kinds of control systems used for seismic protection of bridges, base isolators are one of the most common systems [3]. Semi-active control devices like MR dampers can also significantly increase the seismic performance of isolated bridges. Different strategies have been suggested to control the performance of seismically excited bridges. Gutierrez Soto and Adeli [4] proposed a Replicator Dynamic Control (RDC) methodology for vibration mitigation of isolated bridges subjected to seismic loading. RDCs allocates the total available voltage to control devices based on the instantaneous fitness function of each device. Accordingly, control devices with higher fitness functions receive a larger input voltage and, in some cases, the voltage allocated to a device can be larger than its capacity. To resolve this issue, a load balancing strategy is devised to redistribute the extra available power. In this study, five different control systems, RDC1 to RDC5, are proposed. Each control system is designed as a RDC with a load balancing strategy. A Neural Dynamic (ND) model of Adeli and Park [5] is employed to optimize the control parameters of each RDCs. The proposed control methodologies are evaluated using a benchmark problem defined based on an actual isolated highway bridge located in Orange Country, California [6]. The performance of the proposed control methodologies is compared to conventional Lyapunov and fuzzy control algorithms.

S. Javadinasab Hormozabad () · M. Gutierrez Soto Department of Civil Engineering, University of Kentucky, Lexington, KY, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_23

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23.1.1 Background The game theory concept mathematically models decision-making problems when multiple dependent decision makers are interacting to change the properties of a system. Accordingly, the game theory can be used to develop data-driven control methodologies considering multiple control devices in a multi-agent system configuration. The game-theory data-driven control methodologies decide based on the data collected through the sensory system and do not require knowing the mathematical model of the structural system, which is often the case in conventional control methodologies. Gutierrez Soto and Adeli [4] proposed a hybrid control system for vibration mitigation of isolated bridges based on evolutionary game theory of replicator dynamics. This methodology was further modified to obtain optimal replicator control parameter using a patented neural dynamic model [7]. The results showed that the optimal replicator dynamics controller makes a remarkable reduction in seismic response of the bridge especially the midspan displacement of the deck. However, the game-theory replicator dynamics approach allocates the available resources to the control device that is experiencing the highest structural response. This leads to one control device reaching maximum force capacity, which could pose additional costs related to maintenance and long-term serviceability. In a multi-agent system designed to perform a specific task, load balancing or reallocation strategies are particularly useful to redistribute the task over under-loaded agents so that no agent be over-load and the task be carried out with a higher efficiency [8]. Load balancing mechanisms in software defined networks are reviewed by Neghabi et al. [9]. In present study, a new load balancing strategy tailored for the proposed semi-active controllers is devised. Due to this strategy, the resource allocation process is modified by redistributing additional voltage assigned to over-loaded MR dampers over the other devices. The proposed control methodology is compared with Lyupanov and Fuzzy logic methodologies. Fuzzy logic is a form of logic in which the degree of truth can be evaluated using any real number between zero and one, instead of conventional binary values [10]. Fuzzy controllers are known as effective tools to deal with complex and nonlinear control problems [11]. Ok et al. [12] used a fuzzy controller to determine the input voltage of MR dampers installed on cable-stayed bridges. Salari et al. [13] designed a variable tuned mass damper system comprised of MR dampers and fuzzy controllers for vibration mitigation of cable structures.

23.2 Analysis Figure 23.1 illustrates the overall architecture of the control system including the RDC and the load balancing strategy. In present study, five different fitness functions are defined to achieve five different replicator controllers represented as RDC1 to RDC5. The fitness function in each RDC is defined based on different types of structural responses measured at each control device. Relative acceleration across the damper, absolute acceleration of the deck, relative velocity across the damper, relative velocity multiplied by the relative displacement across the damper, and the sign of multiplication of relative velocity and displacement are used to define the fitness function respectively for RDC1 to RDC5. Therefore, RDC1 to RDC5 are achieved by implementing the related fitness function in RDC section of the configuration shown in Fig. 23.1. The relative displacement of the deck at midspan in x-direction for three different systems is shown in Fig. 23.2. The systems include the isolated bridge (without MR dampers), RDC1 without load balancing strategy, and RDC1 with load balancing strategy. To compare the performance of proposed RDCs with conventional Lyapunov and fuzzy controllers, 16 performance criteria as defined by Agrawal et al. [6] are calculated and presented in Table 23.1.

23.3 Conclusion In this paper, five RDCs were proposed for semi-active vibration control to mitigate the damage of isolated highway bridge structures equipped with MR dampers. The RDC methodology is a game theory-inspired approach that uses replicator dynamics in combination with load balancing. The RDCs were configured to allocate the total available voltage to the MR dampers. The allocation of total voltage of the replicator dynamics is modified using a load balancing strategy intended to reallocate additional voltage considering a maximum input voltage for each MR damper. The patented Neural Dynamic (ND) model of Adeli and Park, which integrates a neural network, Lyapunov stability theorem and the Karush-Kuhn-Tucker conditions, were used to optimize the control parameters of the RDCs including the total available voltage (e.g. emergency power generator) among the control devices and the growth rate of the RDCs. The proposed methodology is evaluated using the benchmark control problem of Interstate 5 overcrossing California State Route 91 bridge in Southern California subjected to near-field earthquake records. The performance of the proposed controllers was compared with conventional Lyapunov

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Fig. 23.1 Overall configuration of control system including the modified RDC with the load balancing (power reallocating) strategy

Fig. 23.2 Comparison of midspan displacement in x direction of the isolated bridge, RDC1 without load balancing strategy, and RDC1 with load balancing strategy

and fuzzy control algorithms in terms of 16 different performance criteria describing the reductions in dynamic response of the bridge. The results showed that the ND optimization procedure effectively optimizes the controller performance and achieves the optimal design variables. The optimal RDCs show a significant performance in improving the dynamic response

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Table 23.1 Performance criteria of different control systems subjected to Kobe earthquake Criteria J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11 J12 J13 J14 J15 J16

Description Peak base shear Peak overturning moment Peak mid-span displacement Peak mid-span acceleration Peak bearing deformation Peak bent column curvature Peak dissipated energy at bent column Number of plastic hinges Normed base shear Normed overturning moment Normed mid-span displacement Normed mid-span acceleration Normed bearing deformation Normed bent column curvature Peak control force in MR dampers Peak stroke of the MR dampers

RDC 1 0.7884 0.8974 0.2350 2.2204 0.2259 0.8974 0.0000 0.0000 0.5785 0.5726 0.1352 1.4753 0.1174 0.5726 0.0050 0.2259

RDC 2 0.6939 0.7453 0.2695 2.2090 0.2619 0.7453 0.0000 0.0000 0.4681 0.4623 0.2221 1.5379 0.2074 0.4623 0.0049 0.2619

RDC 3 0.7407 0.8437 0.3154 2.0606 0.3051 0.8437 0.0000 0.0000 0.5209 0.5150 0.1558 1.3768 0.1373 0.5150 0.0029 0.3051

RDC 4 0.7754 0.8322 0.3108 2.2950 0.3010 0.8322 0.0000 0.0000 0.5294 0.5238 0.2067 1.5093 0.2079 0.5238 0.0039 0.3010

RDC 5 0.7203 0.8014 0.2788 2.1843 0.2715 0.8014 0.0000 0.0000 0.5079 0.5019 0.1568 1.4950 0.1577 0.5019 0.0039 0.2715

Lyapunov 0.8922 0.8548 0.2609 1.9050 0.2659 0.8548 0.0000 0.0000 0.5257 0.5165 0.2777 1.1916 0.2799 0.5165 0.0050 0.2659

Fuzzy 0.8899 0.8817 0.6852 1.4457 0.6752 0.8817 0.0000 0.0000 0.8989 0.8909 0.8146 1.0847 0.8168 0.8909 0.0029 0.6752

of the bridge including the peak and normed values of base shear, overturning moment, mid-span displacement, bearing deformation, column curvature, dissipated energy, and the number of plastic hinges. This methodology can be adapted to mitigate the damage of other structures and for other control engineering problems where a data-driven controller based on load balancing and game-theory will be ideal. Acknowledgements The authors would like to acknowledge Professor Hojjat Adeli and Professor Hyo Seon Park’s permission to use the patented Neural Dynamic model for optimization problem.

References 1. Wardhana, K., Hadipriono, F.C.: Analysis of recent bridge failures in the United States. J. Perform. Constr. Facil. 17(3), 144–150 (2003) 2. Hsu, Y.T., Chung, C.F.: Seismic effect on highway bridges in Chi Chi earthquake. J. Perform. Constr. Facil. 18(1), 47–53 (2004) 3. Makris, N.: Seismic isolation: early history. Earthq. Eng. Struct. Dyn. 48(2), 269–283 (2019) 4. Gutierrez Soto, M., Adeli, H.: Semi-active vibration control of smart isolated highway bridge structures using replicator dynamics. Eng. Struct. 186, 536–552 (2019) 5. Adeli, H., Park, H.S.: Neurocomputing for Design Automation. CRC Press Taylor and Francis Group. Boca Raton, Florida (1998). https://doi.org/10.1201/9781315214764 6. Agrawal, A., Tan, P., Nagarajaiah, S., Zhang, J.: Benchmark structural control problem for a seismically excited highway bridge—part I: phase I problem definition. Struct. Control. Health Monit. 16(5), 509–529 (2009) 7. Gutierrez Soto, M.: Bio-inspired hybrid vibration control methodology for intelligent isolated bridge structures. In: Active and Passive Smart Structures and Integrated Systems XII, vol. 10595, p. 1059511. International Society for Optics and Photonics. Denver, Colorado (2018) 8. Banerjee, S., Hecker, J.P.: A multi-agent system approach to load-balancing and resource allocation for distributed computing. In: First Complex Systems Digital Campus World E-Conference 2015, pp. 41–54. Springer, Cham (2017) 9. Neghabi, A.A., Navimipour, N.J., Hosseinzadeh, M., Rezaee, A.: Load balancing mechanisms in the software defined networks: a systematic and comprehensive review of the literature. IEEE Access. 6, 14159–14178 (2018) 10. Zadeh, L.A.: Fuzzy logic. Computer. 21(4), 83–93 (1988) 11. De Silva, C.W.: Intelligent Control: Fuzzy Logic Applications. CRC Press Taylor and Francis Group. Boca Raton, Florida (2018) 12. Ok, S.Y., Kim, D.S., Park, K.S., Koh, H.M.: Semi-active fuzzy control of cable-stayed bridges using magneto-rheological dampers. Eng. Struct. 29(5), 776–788 (2007) 13. Salari, S., Hormozabad, S.J., Ghorbani-Tanha, A.K., Rahimian, M.: Innovative Mobile TMD system for semi-active vibration control of inclined sagged cables. KSCE J. Civ. Eng. 23(2), 641–653 (2019)

Chapter 24

Forcing Function Estimation for Space System Rollout George James, Robert Grady, Matt Allen, and Erica Bruno

Abstract American crewed spaceflight systems have used a significant tracked transportation system to rollout the stacked vehicle and launch platform from the Vehicle Assembly Building (VAB) to the launch pad. This system has been shown to produce specific narrow-band harmonic forces that can excite the complete system, including the ability to force a resonance for long periods of time. This work reports on the efforts to develop tools and processes to reconstruct rollout forcing functions to support advanced needs for the extraction of dynamic properties. The multi-step processes provided in this work include a hybrid version of a traditional force reconstruction approach; transfer of expected CG forces to the assumed force input locations; expansion of the forces to a full-rank set of input forces; application of known dynamic constraints; and joint updating of FRFs and the estimated forces. Three levels of success criteria are suggested for these processes as applied to analytical, laboratory, or measured field data: synthesizing output accelerometer data; reconstructing input forcing functions; and estimating modal properties. A dynamically simple system, limited instrumentation, and a simple single-speed forcing function are used to provide measured and analytical data to exercise and assess the tools of interest. Useful comparisons supporting the first success criteria are provided. Data and insight are also provided for the second success criteria. The simplicity of the example system supporting the work reported in this paper does not yet support the development of significant insight on the third success criteria. Follow-on activities are recommended to add additional insight into the process success with all three criteria. This work not only addresses engineering development work of specific and unique interest to spaceflight systems but also suggests general applicability for force estimation, dynamic property estimation, and operational testing situations. Specifically these tools are to enable the estimation of dynamic properties when the loading and constraint environments complicate traditional OMA techniques. Unique contributions of this process include: expanding inputs and constraints of traditional force reconstruction techniques; using null space vectors to complete the basis set for full rank force reconstruction; and constraining linear solutions to filter estimated forces for targeted force updating. Keywords Operational testing · Force reconstruction · Experimental modal analysis · Operational modal analysis · Harmonic loading

24.1 Introduction The current era of manned spaceflight development targets increasing efficiency in the use of test articles and flight hardware to maximize data return. When structural dynamic information is of interest, Operational Modal Analysis (OMA) techniques can be used to extract parameters from a wide variety of field, operations, and secondary situations [1–6]. However, OMA techniques can become difficult to use when the forcing functions become complicated [7] or the system changes rapidly [8]. One goal of this work is to identify the forcing function from OMA measurements, and then to use it as an input to standard input-output tools from experimental modal analysis (EMA), for example when estimating frequency-response

G. James () · R. Grady Structural Engineering Division, NASA Johnson Space Center, Houston, TX, USA e-mail: [email protected] M. Allen Engineering Physics Department, University of Wisconsin-Madison, Madison, WI, USA E. Bruno Analytical Mechanics Associates, Inc., Hampton, VA, USA © The Society for Experimental Mechanics, Inc. 2021 C. Walber et al. (eds.), Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47713-4_24

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Fig. 24.1 Space Shuttle Launch Vehicle Undergoing Rollout to the Pad for Launch

functions. The targeted operational scenario used in this paper is that of the rollout loading as a space system is transported to the launch pad. Many NASA manned vehicles have made the final transportation to the launch pad via a significant track/tread based system called the Crawler-Transporter (CT) coupled to a mobile version of the launch pad. Figure 24.1 depicts the Space Transportation System (STS) vehicle (Space Shuttle) and the associated Mobile Launch Platform (MLP) under transport to the launch site using this system. Besides the STS, the same CT system has been used to move multiple versions of the Apollo/Saturn vehicles, multiple test versions of the STS hardware, the Ares1-X vehicle, the Mobile Launcher (ML) for the now-cancelled Constellation systems, and the ML for the future Space Launch System (SLS) [9]. Based on this experience, this “Rollout” event has been found to have the potential to produce structural and fatigue loads on large flexible launch vehicles and spacecraft. On the other hand, this experience has shown that there is a potential to use the resultant rollout loading to exercise the vehicle for structural dynamic properties of the vehicle and launch platform [7, 9–12]. Dedicated tests have been used to exercise and develop this operational environment for use as supplemental modal tests. In previous STS-era work on the rollout forcing functions, the primary effort was to estimate the forcing functions at measured and interpolated speeds to identify speed ranges that caused undesired loading events [3, 7, 10]. The historical work is a useful basis for initiating the current effort but was not driven by the same high-fidelity need to exercise the forcing functions as the current work. Previously, the forcing functions were estimated using a modification of the Sandia National Laboratories-developed Sum of Weighted Accelerations Technique (SWAT) [13, 14]. The modifications to SWAT resulted in a hybrid approach that used the mode shapes of the structural model to estimate weighting matrices used to convert measured accelerations into estimated forces. Estimated six Degrees-Of-Freedom (DOF) forces then drove a free-free model (to meet the requirements of the traditional SWAT process [13]) of the STS vehicle and Mobile Launch Platform (MLP) at the centerof-mass. The resulting functions were then scaled to generate roll-out forcing functions at speeds between the measured data. This process allowed the dynamic model of the structure to be used to estimate the response at a wider range of speeds. The problems with this approach are the reliance on a CG input point, a limited frequency range constrained by the number of measurement locations, and the reliance on the analytical Finite Element Model (FEM) of the vehicle. Work with the Ares I-X vehicle, the cancelled Constellation Program systems, and the in-development SLS have highlighted potential uses of the expanded STS-era data to estimate rollout forcing functions, develop fatigue spectra, perform operational diagnostics, and extract structural dynamic properties. As a result, NASA has worked to overcome two STS-era

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shortcomings listed above (center-of-mass input and limited frequency range) and directly feed the processes reported in this work [15, 16]. The work reported in this paper includes the previous advances but also jointly estimates forcing functions and transfer functions without reliance on the dynamic FEM.

24.2 Data Processing Steps 24.2.1 Overview of Data Processing Steps A set of 14 data processing steps (some of which are optional) have been set up and coded to process the rollout data. A historical .9mph rollout data set has been used to exercise and assess the process. The process description, numerical examples, and experimental results were exercised using 63 measured accelerations from the CT+MLP system (as described in Appendix A) to estimate 12 input forces at locations on the CT trucks below the JEL system. The final products are estimated forcing functions, Frequency Response Functions (FRFs), and Impulse Response Functions (IRFs) that can be processed to extract modal parameters with little or no forcing function harmonics represented in the modal estimates. A summarized list of the processing steps follows: • Step #0 - Set Input Parameters and Filter Data – The original time history data is subjected to numerical transforms and filters to allow comparisons with reconstructed data; • Step #1 – Calculate Rigid Body Modes – Sensor geometry is used to estimate six rigid body modes in support of force reconstruction; • Step #2 – Remove Rigid Body Contribution from Original Data – Removing rigid body contributions from the measured data provides the residual flex-body data • Step #3 – Determine Basis Vectors for Residual Flex-Body Data – Left singular vectors become basis vectors for use in Step #4; • Step #4 – Determine SWAT Weight Matrix and CG Acceleration – Standard SWAT processing is used once the basis is known to enable Step #5 by providing the weight matrix and CG accelerations; • Step #5 – Define CG Forces, Below-JEL Transformation, and Below-JEL Forces – Forces and moments at the Center of Gravity (CG) are estimated and transferred to the input locations; • Step #6 – Define Below-JEL Null Space Transformation Vectors for Below-JEL Flex Forces – Transformation matrix null space vectors are estimated (for use as basis vectors to complete the input forces in Step #8 or Step #9); • Step #7 – Scale 12 Below-JEL Accelerations with Assumed Mass at Each Corner – Measured driving point accelerations are mass-scaled to provide an initial estimate of the Below-JEL forces (subject to modification in subsequent steps); • Step #8 – Estimate Total Below-JEL Forces – Initial force estimates from Step #7 (or updated force estimates of Step #11 or Step #12) are filtered to enforce known constraints; • Step #9 – Alternative Estimation of Total Below-JEL Forces – Alternate approach to Step #8 resulting in filtered force estimates with additional constraints; • Step #10 – Determine FRF between Total Below-JEL Forces and Original Accelerometer Data – Calculate a transfer function and inverse transfer function between estimated forces and measured outputs;

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• Step #11 – Iterate Using Inverse FRF – Use the measured outputs and estimated inverse transfer function to iteratively update the force estimates; • Step #12 – Iterate Using Assumed Residual Basis – Alternative iteration force updating using Step #8 or Step #9 force filtering; and • Step #13 – Final Averaged FRF – Create a final transfer function for modal processing from final forces and measured outputs.

Step #0 – Set Input Parameters and Filter Data Step #0 conducts initial filtering and sliding window processing of the measured acceleration data. Subsequent processes will utilize specific estimation and synthesis of acceleration time histories from weighted averages of windowed data segments generated from frequency domain processes using the same sliding window transform. Therefore, Step #0 subjects the original measured data to similar filter, segment, transform, weight, and average processing to allow direct comparisons to later synthesized data. A critical input parameter defined in Step #0 (and used in subsequent steps) is the data segment window size that is used (denoted as winsize). Additionally, there are two overlap or window increment parameters. The first increment (denoted as winskip0) defines the number of overlaps and the size of the increment from one window to the next to be used in frequency domain estimations of Frequency Response Function (FRF) transfer function spectra. The second incrementing parameter used (denoted as winskip1) is the increment used when reconstructing a time history from frequency domain estimates of the response of winsize lengths. The low-pass frequency cut-off is defined and applied to the measured data in this step as well. For the sliding window processing, a segment of winsize samples is extracted from the original data starting with time step 1 and incremented by winskip1 samples for subsequent segments. The data segment is converted to the frequency domain via a Fast Fourier Transform (FFT). Note that if the full length of the time history is not used in the defined segments, an additional segment ending with the last data point (and the necessary beginning point) will be used to assure that the total length of the filtered time history is unchanged. The frequency filtered response is then converted back to the time domain with a symmetric inverse Fourier transform. The resulting winsize time segment is scaled by the weight vector (defined below) and added to a data collector vector (maintaining the original segment times). The data collector is a running, weighted sum of the estimates of the filtered accelerations at each time step and is represented in Eq. (24.1):     XC tj : tj + Δt = XC tj : tj + Δt + weight. ∗ Xjo ;

(24.1)

where, XC (tj : tj + t) is the slice of the acceleration time history collector associated with the jth increment; Xjo is the original acceleration time history computed for the jth increment; j is the increment number; tj is the time step at which the jth increment starts; t is the time increment or winsize sample increments; weight is the numerical weighting vector; “.∗ ” is a numerical operation that multiplies each entry in the two vectors; and “:” is a function symbol for a sweep over the number of time steps in a time increment. The numerical weighting vector (denoted as weight), is composed of all integers starting with 1 and building sequentially to winsize/2 in the first half of weight. The values then reduce sequentially from winsize/2 to 1 for the last half of weight. The weight vector is to force time domain averages to place more emphasis on time points near the middle of a data window and de-emphasize the endpoints. An associated numerical collector, of the same length as each time history, is also updated by adding the weight vector to the same segment times. This numerical counter tracks how many weighted estimates have been added to the collector at each time step:     numC tj : tj + Δt = numC tj : tj + Δt + weight.

(24.2)

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The process is repeated by shifting the original time increment window forward in time by the chosen number of samples (winskip1). The ideal shift is one time sample per increment, which creates a slow process but eliminates periodic data spikes resulting in numerical frequency content due to the periodic window shifts. However, the weighting of the data and numerical counter reduce these data spikes by adding weight to the filtered data at the center of each segment. At the end of the process, the data collector value at each time step is divided by the counter value at each time step to weight average the collector estimates at each time step and generate the final updated force time history (X):     XC tj  . X tj = numC tj

(24.3)

Each original sensor time history is processed in this manner. It should be noted that a similar non-weighted version of this collector/averaging approach was used in Reference [15]. The filtered version of the original data enables the use of relevant convergence metrics and comparison plots in subsequent processing steps. It should be noted that, this sliding window processing has been shown to have minimal effect on the original measured data, which provides confidence that the technique will not add unwanted bias errors to subsequent processing steps.

Step #1 – Calculate Rigid Body Modes Step #1 uses the sensor geometry to estimate the six rigid body modes (denoted by ϕrb ) with respect to the Center of Gravity (CG) using the procedures provided in Reference [14]. Note that the size of ϕrb is nres x 6, where nres is the number of measured acceleration sensors. The following description will be limited to the case of each sensor output defined as a single orthogonal rectangular coordinate direction aligned with the system coordinate system. For this work, the translational rigid body shapes are denoted as the first 3 columns of ϕrb (X direction = 1, Y direction = 2, and Z direction = 3) and are defined as follows: ϕrb (i, j ) = δj k ;

(24.4)

where i denotes the sensor #, j denotes the rigid body shape translational direction (1, 2, or 3), k denotes the sensor direction (1, 2, or 3), and δ jk is the delta function which is only a non-zero value (1.0) if j = k (1, 2, or 3). For the rotation about the X, Y, or Z direction rigid body shapes (columns 4, 5, and 6 of ϕrb ): ⎫ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫⎤ ⎡⎧ ⎫ ⎧ ⎨ 1 ⎬ ⎨ LX δlk − CGX ⎬ ⎨ 0 ⎬ ⎨ LX δlk − CGX ⎬ ⎨ 0 ⎬ ⎨ LX δlk − CGX ⎬ ϕrb (i, j ) = ⎣ 0 × LY δlk − CGY 1 × L δ − CGY 0 × L δ − CGY ⎦ ; ⎩ ⎭ ⎩ ⎭ ⎩ ⎭ ⎩ Y lk ⎭ ⎩ ⎭ ⎩ Y lk ⎭ 0 0 1 LZ δlk − CGZ LZ δlk − CGZ LZ δlk − CGZ

(24.5)

where, i denotes the sensor #, j denotes the rigid body shape rotational direction (4, 5, or 6), k denotes the sensor direction (1 = X, 2 = Y, or 3 = Z), l denotes the relevant sensor coordinate (l = j – 3 and 1 = X, 2 = Y, or 3 = Z), δ lk is the delta function which is only a non-zero value (1.0) if l = k (1, 2, or 3), CGk is the CG location in the kth direction, and Lk is the geometric coordinate of sensor #i in the kth direction.

Step #2 – Remove Rigid Body Contribution from Original Data This step involves performing a least squares fit of the rigid body modes to the original data and remove the resulting contribution to estimate the residual flexible body acceleration time histories. The following equation exemplifies this

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process: ϕrb ∗ Xrb (t) = X(t);

(24.6)

where Xrb are the 6 x n rigid body amplitudes, X are the nres x n original measured accelerations, and n is the number of measured time points. The residual flexible body acceleration time histories (denoted by X1 (t) of size nres x n) are estimated as follows: X1 (t) = X(t) − ϕrb ∗ Xrb (t).

(24.7)

Step #3 – Determine Basis Vectors for Residual Flexible Body Data The Singular Value Decomposition (SVD) is used in this step to determine a set of basis vectors for the flexible body residuals, which are needed to build a modified SWAT weight matrix (described in References [9, 10, 12–14]): X1 = U1 ∗ S1 ∗ V1T ;

(24.8)

where U1 is the nres x nres matrix of left singular vectors and the source of the desired basis vectors, S1 is the diagonal matrix of nres singular values; and V1 is the n x nres matrix of right singular vectors. The flex body basis vectors (denoted by Ur6 of size nres x nr6 with nr6 = nres - 6) are taken to be the nr6 left singular vectors associated with the largest nr6 singular values. The use of these basis vectors instead of mode shape vectors is the primary modification to a traditional SWAT approach.

Step #4 – Determine SWAT Weight Matrix and CG Acceleration Step #4 uses the modified version of SWAT, which is a time-domain approach relating the forces at the CG to the accelerations at the CG. The initial step of SWAT involves developing a weight matrix (W of size 6 x nres ), which allows the estimation of the CG accelerations (Note that this matrix is distinct from the winsize x 1 weight vector of Step #0): XCG (t) = W ∗ X(t).

(24.9)

The weight matrix is chosen to sum the measured accelerations to generate estimates for each of the six rigid body accelerations at the CG. In performing this estimation, the chosen elastic body generalized DOFs and all rigid body generalized modes (except the single rigid body mode of interest) are zeroed out. The rigid body modes and flexible basis vectors are collected into a matrix ϕT of size nres x nres (with the first six vectors providing the rigid body modes), which will be used to build the weight matrix: ϕT = [ϕrb , Ur6 ] .

(24.10)

The weight matrix is estimated (which nulls the elastic mode shapes and unit normalizes the rigid body shapes) as depicted in Eqs. (24.6) and (24.7): Wi ∗ ϕT k = δik ; with i and k sweeping the columns of W and ϕ; and

(24.11)

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δ ik is the delta function which is only a non-zero value (1.0) if i = k (the first 6 vectors).

Step #5 – Define CG Forces, Below-JEL Transformation, and Below-JEL Forces The forces at the CG (denoted by FCG of size 6 x n) are related to the accelerations at the CG via the 6 x 6 global mass matrix defined at the CG (denoted as MCG ): FCG (t) = MCG XCG (t).

(24.12)

The global mass matrix is defined about the CG as follows: ⎡

MCG

MT ⎢ 0 ⎢ ⎢ ⎢ 0 =⎢ ⎢ ⎢ ⎣

⎤

0 0 MT 0 0 MT 0

0 IXX IY X IZX IXY IY Y IZY IXZ IY Z IZZ

⎥ ⎥ ⎥ ⎥ ⎥; ⎥ ⎥ ⎦

(24.13)

where MT is the total mass of the system; and IXX , IYY , IZZ , IXY , IXZ , IYZ , IZX , IZY , and IYX are the Moments Of Inertia (MOI) and Products Of Inertia (POI). Step #5 then uses the 3x3 Below-JEL force to CG moment transformation cross product matrices to convert forces at the CG to forces at the desired below-JEL locations, which are defined as: ⎫ ⎧ ⎫⎧ ⎫ ⎧ ⎫⎧ ⎫ ⎧ ⎫⎤ ⎡⎧ ⎨ LX − CGX ⎬ ⎨ 1 ⎬ ⎨ LX − CGX ⎬ ⎨ 0 ⎬ ⎨ LX − CGX ⎬ ⎨ 0 ⎬  χi = ⎣ LY − CGY × 0 LY − CGY × 1 LY − CGY × 0 ⎦ = Ri × eˆX Ri × eˆY Ri × eˆZ ; ⎩ ⎭ ⎩ ⎭⎩ ⎭ ⎩ ⎭⎩ ⎭ ⎩ ⎭ LZ − CGZ LZ − CGZ LZ − CGZ 0 0 1 (24.14) where, CGj is the CG location in the jth direction; Lj is the location of the ith Below-JEL force input location in the jth direction; Ri is the vector from the CG to the ith Below-JEL force input location; and eˆ are the basis unit vectors of each axis. Hence the 6 x 12 transformation matrix (Tχ and after normalization T) can be generated to convert the 6 DOF forces at the CG (FCG ) to the 12 DOF forces defined Below-JEL (Fbj of size 12 x n): FCGχ =

FF F Rχ



=

 I I I I χA χB χC χD

⎡

⎤ FA ⎢ FB ⎥ ⎢ ⎥ ⎣ FC ⎦ = Tχ ∗ Fbj ; FD

(24.15)

where, FA , FB , FC , and FD are the 3 x n Below-JEL estimated translational forces at each truck; χ A , χ B , χ C , and χ D are the Below-JEL force to CG moment transformation cross products; and I is the 3 x 3 identity matrix. It makes numerical sense to normalize FR to balance the Tχ matrix: χN =

' 2

 χA 2 + χB 2 + χC 2 + χD 2 ; and

(24.16)

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FCG =

FF FR



=

FF FR χ χN



 =



I I

I I

χA χB χN χN

χC χD χN χN

⎡

⎤ FA ⎢ FB ⎥ ⎢ ⎥ ⎣ FC ⎦ = T ∗ Fbj ; FD

(24.17)

Note that the order of the entries in the Fbj vector are as follows: ⎤ FbjAX (t0 ) · · · FbjAX (tn ) ⎥ ⎢ .. .. .. =⎣ ⎦; . . . FbjDZ (t0 ) . . . FbjDZ (tn ) ⎡

Fbj

(24.18)

where A, B, C, and D denote the corner; and X, Y, and Z denote direction of force. And the order of entries in the FCG matrix is as follows: ⎡

FCG

FFX (t0 ) · · · ⎢ F (t ) . . . F 0

⎢ ⎢ Y FF ⎢ FFZ (t0 ) . . . =⎢ = ⎢ FRX (t0 ) · · · FR ⎢ ⎣ FRY (t0 ) . . . FRZ (t0 ) . . .

FFX (tn ) FFY (tn ) FFZ (tn ) FRX (tn ) FRY (tn ) FRZ (tn )

⎤ ⎥ ⎥ ⎥ ⎥ ⎥; ⎥ ⎥ ⎦

(24.19)

where FF denotes translational force at the CG, and FR denotes rotational moment at the CG. At this point, the Below-JEL forces are a rank deficient partition that drives the CG accelerations via rigid body modes. Hence in order to solve Eq. (24.17) for Fbj , an SVD pseudo-inversion is used. The resulting answer will be of rank 6. However, a full rank rigid body plus flex body solution will result from later steps. Another solution approach is to assume that Fbj is defined to be a linear combination of the basis vectors (12 x 6 left singular vectors of TT denoted as U), which can be defined with a Singular Value Decomposition (SVD): U ∗S ∗VT = TT.

(24.20)

Fbj = U ∗ α;

(24.21)

where α is the 6 x n matrix of scale factors for the basis vectors of T to create Fbj . Note that system-level mass properties [MOI, POI, and CG location,] as well as sensor geometry are known and represent the only parameters that are extracted from an FEM.

Step #6 – Define Below-JEL Null Space Transformation Vectors for Below-JEL Flex Forces The Below-JEL forces (Fbj ) developed in the previous step are necessarily a rank deficient partition that drives the CG accelerations via rigid body modes. Hence the approach implemented in this step estimates the non-rigid body partition of the Below-JEL forces (Ff6 ) to complete the rank and drive the flex-body part of the measured accelerations: FT = Fbj + Ff 6 .

(24.22)

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The assumption is that Ff6 will be defined as a linear combination of the six vectors (denoted by N of size 12 x 6) that span the null space of the transformation matrix T: N = null(T ).

(24.23)

Ff 6 = N ∗ β;

(24.24)

where β is the 6 x n matrix of scale factors for the null space of T vectors to create Ff6 . Note that assessing the Step #6 process is one of the key contributions of this work, since this is a unique enhancement over previous work in these applications.

Step #7 – Scale 12 Below-JEL Accelerations with Assumed Mass at Each Corner Step #7 captures the fact that the CT system carries a different amount of the total weight at each corner truck. The weight ratios for each corner can be measured (using the CT JEL system pressures) or estimated from the mass properties of the system. Denote the scale factor for each corner as ∝A , ∝B , ∝C , and ∝D . Hence the mass at each corner is defined as: MA = ∝ A ∗ M T .

(24.25)

M B = ∝ B ∗ MT .

(24.26)

MC = ∝ C ∗ MT .

(24.27)

MD = ∝ D ∗ M T

(24.28)

Now it will become useful to scale the 12 measured Below-JEL measured accelerations by the mass carried at each corner to convert to force units: ⎤ ⎡ MA ∗ XbjAX (t0 ) · · · MA ∗ XbjAX (tn ) ⎥ ⎢ .. .. .. (24.29) FM = ⎣ ⎦ = Mbj ∗ Xbj . . . . MD ∗ XbjDZ (t0 ) · · · MD ∗ XbjDZ (tn ) In subsequent steps, FM takes on the roles of an initial starting estimate of a FF as well as a numerical tool to relate Below-JEL forces to Below-JEL accelerations. It should be noted that the definition of higher-fidelity starting estimates is an active area of development for this work.

Step #8 – Estimate Total Below-JEL Forces Step #8 and Step #9 are alternative approaches to refine the current estimates of the forcing function (including the Step #7 initial estimate). It should be noted that Step #9 is an expansion of Step #8, so it is useful to review Step #8 first (although the Step #8 is not used in the data presented in this paper). Also it should be noted that assessing the Step #8/Step #9 processes are another major contribution of this work, since these steps are an expansion over previous work in these applications. For Step #8, FM is related to FT via a residual Below-JEL acceleration matrix, which allows Eq. (24.22) to combine with Eq. (24.29): FM − Mbj ΔXbj = FT = Fbj + Ff 6 = U ∗ α + N ∗ β. And collecting Eqs. (24.30), (24.21), and (24.17):

(24.30)

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FT FCG





U N = T ∗U 0





B1 α A1 ∗ [C] = . ∗ = A2 B2 β

(24.31)

For the initial iteration, it is assumed that ΔXbj = [0]. Hence using Eq. (24.30), the initial FT is equal to FM . In later steps, Eq. (24.31) will be solved with more refined estimates of the total Below-JEL force. Equation (24.31) can be solved by constrained least squares as provided in Reference [17]. The upper partition is the primary linear problem and the lower partition becomes constraint equations as follows:   C = C + K B2 − A2 C ;

(24.32)

−1   −1 −1  ; and K = At1 ∗ A1 At2 A2 At1 ∗ A1 At2

(24.33)

−1  C = At1 ∗ A1 At1 B1

(24.34)

Note that it is assumed that U and N are normalized by definition, which makes A1 an orthonormal matrix and simplifies Eqs. (24.32), (24.33), and (24.34). After solution, Eq. (24.30) is used to generate the total force estimates at each time step since C is estimated at each time step. Although simpler solutions to Eq. (24.31) are available, Step #9 is an alternative to Step #8 and builds on this structure.

Step #9 – Alternative Estimation of Total Below-JEL Forces Step #9 provides an alternative and expanded approach to Step #8 (and the step actually used in the presented herein). It alternatively estimates the Below-JEL Forces by augmenting Eq. (24.31) with equations to drive the output accelerations to match the complete set of measured responses across the vehicle. This process can be enabled using the left singular vectors (U1 ) for the flexible-body part of the accelerations as in Eq. (24.8) or using the left singular vectors of the total measured acceleration matrix: X = U1 ∗ S1 ∗ V1T ;

(24.35)

Note that the matrix designation of U1 is used in both Eqs. (24.8) and (24.35), since X and X1 are largely interchangeable in Step #9. The remainder of this discussion will assume that X is used as opposed to X1 . It can therefore be assumed that the X matrix can be reconstructed with a linear combination of the left singular vectors scaled at each time step:

U1 U X = U1 ∗ γ = U1 L





XU ∗γ = XL





Xbj = ; XL

(24.36)

where the “U” denotes the first 12 entries which are assumed to be the Below-JEL measurements; and the “L” designator denotes the remaining nres – 12 = nr12 sensors. The full fit from Eq. (24.36) is used to augment the A1 and B1 matrices of Eq. (24.31):

FT X



⎡ ⎤

α U N 0 ∗ ⎣ β ⎦ = B1 = A1 C. = 0 0 U1 γ

As with Eq. (24.31), matrix A1 is orthonormal here as well and the transpose equals the inverse. The upper partition of Eq. (24.36) is combined with Eq. (24.30) to become an augmented constraint equation.

(24.37)

24 Forcing Function Estimation for Space System Rollout



FCG FT − FM



255



T ∗U 0 0 = U N −Mbj ∗ U1U



⎡ ⎤ α ⎣ ∗ β ⎦ = B2 = A2 C. γ

(24.38)

The constraint equations are used to assure that the rigid body part of the FF maintains the expected force at the CG as well as to assure that the flex body and rigid body part of the Below-JEL accelerations match up with the below JEL accelerations. Eqs. (24.32), (24.33), and (24.34) are again used to solve these equation and the updated total force is reconstructed using Eq. (24.30). Equation (24.38) can be used with an initial guess of FT = FM or can be used to modify an updated FT to assure that the constraints are met during iterative processing.

Step #10 – Determine FRF Between Total Below-JEL Forces and Original Data Estimate FRF Step #10 takes the current force estimates and the measured responses to estimate a Frequency Response Function (FRF). The Total Least Squares using an SVD approach as discussed in Reference [18] is the primary approach for FRF estimation (denoted as H4 ) used in this work. However, other common approaches as implemented in Reference [15] can be used (denoted as H1 , H2 , and H3 ). Under the H4 approach, the frequency domain version of the input and output for each winsize/winskip0 segment are collected (each row is a different segment and each column is a different force or measured acceleration) into the same matrix representation (Y):  [Y (ω)]H = [FT (ω)]H [X (ω)]H = [UY ] [SY ] [VY ]H ;

(24.39)

Where UY is the matrix of left singular vectors of Y; SY is the diagonal matrix of non-zero singular values of Y; and VY is the matrix of right singular vectors of Y. Therefore, the total least squares FRF is given by the following: [H4 ] = [VY X12 ] [VY F 12 ]−1 .

(24.40)

where: [VY ] = [[VY 12 ] [VY n12 ]] =

[VY F 12 ] [VY F n12 ] . [VY X12 ] [VY Xn12 ]

(24.41)

The subscripts defining the partitions of VY in Eq. (24.41) can be interpreted as follows: (1) F12 are first nref columns and nref rows; (2) X12 are the first nref columns and last nres rows; (3) Fn12 are the last nres columns and the first nref rows; and (4) Xn12 are the last nres columns and the last nres rows. The “nref ” descriptor refers to the number of assumed references or inputs (12 in the case of the data provided in this paper). The “nres” descriptor refers to the number of measured responses or outputs (63 in the case of the data provided in this paper).

Estimate Inverse FRF Step #10 also estimates an inverse transfer function called G4 by performing a pseudoinverse of H4 : [G4 ] = [VY F nres ] [VY Xnres ]−1 . Where:

(24.42)

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[VY ] = [[VY nres ] [VY 12 ]] =

[VY Xnres ] [VY X12 ] . [VY F nres ] [VY F 12 ]

(24.43)

Previous work on these systems directly applied Eqs. (24.39), (24.40), and (24.41) with the role of accelerations and forces reversed, but that option has not been exercised in this work reported in this paper [9].

Estimate Delta X For the full size FRF approach, the estimated forces and FRF can be used to reconstruct the measured sensors (X) and the resulting residuals (X ): [H4 (ω)] [F (ω)] = [Xs (ω)] = [X (ω)] + [ΔX (ω)] .

(24.44)

The full time history of the synthesized accelerations would use the process covered in Eqs. (24.1), (24.2), and (24.3). Subsequent iterations would attempt to drive the residual from Eq. (24.44) towards zero and therefore reproduce the measured accelerations.

Estimate Delta F The inverse FRF approach can be used to estimate updates to the 12 DOF forcing functions using the 1st order assumed FRF process (for the ith iteration): [Fi+1 (ω)] = [H4 (ω)]−1 [X (ω)] = [G4 (ω)] [X (ω)] = [Fi (ω)] + [ΔF i (ω)] .

(24.45)

In a similar fashion, the full time history of the updated Below-JEL forces use the same collector/averaging process as was used for the Step #0 acceleration measurement filtering and the Step #10 acceleration synthesis. After conversion of each increment to the time domain, the winsize length time records are weighted and added to a collector vector for each time record. The collector is a running weighted sum of the estimates of the updated forces at each time step (denoted as j):     FC tj : tj + Δt = FC tj : tj + Δt + weight ∗ Fj ;

(24.46)

where, FC (tj : tj + t) is the slice of the force time history collector associated with the jth increment; Fj is the force time history computed for the jth increment; j is the increment number; tj is the time step associated with the jth increment; t is the time increment; and : is a function symbol for a sweep over the number of time steps in a time increment. A numerical counter of the same length as each time history is updated when each time increment is added to the collector to track how many weighted estimates have been added to the collector at each time step:     numC tj : tj + Δt = numC tj : tj + Δt + weight.

(24.47)

The process is repeated by shifting the original time increment window forward in time by the chosen number of samples. The ideal shift is one time sample per increment, which creates a slow process but eliminates periodic data spikes resulting in numerical frequency content due to the periodic window shifts. However, the weighting process reduces the data spikes by giving more weight to the estimates in the middle of each segment. At the end of the process, the collector value at each time step is divided by the weighted numerical counter value at that time step to average the weighted estimates and generate an updated force time history: Fi+1 (t) =

FC . numC

(24.48)

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Convergence Metrics Since Step #10 may be performed multiple times to support either Step #11 or Step #12 iterations, therefore eight metrics have been identified to monitor the changes that result. The eight metrics include the following (where norm is the 2-norm of a matrix, max picks the maximum value, and abs calculates the absolute value): norm (X + ΔXi+1 ) − 1.0; norm(X)

(24.49)

max (abs (X + ΔX i+1 )) − 1.0; max (abs(X))

(24.50)

norm (Fi+1 ) − 1.0; norm (Fi )

(24.51)

max (abs (Fi+1 )) − 1.0. max (abs (Fi ))

(24.52)

Xnorm =

Xmax =

Fnorm =

Fmax =

Hnorm

Hmax

Gnorm

Gmax

  norm H4i+1 − 1.0; = norm (H4i )

   max abs H4i+1 − 1.0; = max (abs (H4i ))   norm G4i+1 − 1.0; and = norm (G4i )    max abs G4i+1 − 1.0. = max (abs (G4i ))

(24.53)

(24.54)

(24.55)

(24.56)

Step #11 – Iterate Using Inverse FRF Step #11 represents a simplistic approach to updating the forcing function estimates. It should be noted that Step #12 is used in the examples provided in this paper. However, it is instructive to review Step #11 before reviewing the more complex Step #12 (as with Step #8 and Step #9 previously). Step #11 (or Step #12) is initiated with one of three approaches (note option #3 coupled with Step #12 will be used in the examples reported herein): 1. Perform an initial Step #10 calculation process (with FT = FM ) and iterate using the results of Eq. (24.45) to Eq. (24.48); 2. Update FM with the Step #8 process to enforce the FCG forces, perform a Step #10 calculation process, and iterate using the results of Eq. (24.45) to Eq. (24.48); or 3. Update FM with the Step #9 process to enforce the FCG forces and enforce the link to vehicle acceleration, perform a Step #10 calculation process, and iterate using the results of Eq. (24.45) to Eq. (24.48);. Step #11 would continue using a second (and as needed subsequent) Step #10 update to the FRF Transfer Function feeding the subsequent reapplication of Eq. (24.57):  [Yi+1 ]H = [Fi+1 ]H [X]H .

(24.57)

The process would iterate until convergence with no additional per-iteration modification of the estimated forces from the Step #8 or Step #9 processes. Iterations end when either one of four metrics defined above (Xnorm , Xmax , Fnorm , or Fmax ) fall below a pre-defined threshold or when a maximum number of iterations are reached. Note that most exercises performed to-date terminate with the maximum number of iterations not via a convergence metric.

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Step #12 – Iterate Using Assumed Residual Basis Step #12 is initiated with one of the three iteration options listed above in Step #11. Unlike Step #11, Step #12 modifies the current FF estimates using either Step #8 or Step #9 to impose the implemented constraints. Hence, the major option choice for Step #12 is whether each iteration force update is filtered by a Step #8 or a Step #9 process before the reapplication of the Step #10 calculation. Note that Fi+1 is used to feed either Eqs. (24.31) or (24.37) for each iteration. As noted previously, Step #9 and Step #12 are used in the examples reported in this work. A second option includes a decision on keeping FCG constant from iteration to iteration or updating FCG each iteration using Eqs. (24.9) and (24.12). The examples reported in this work do not update FCG . FCG is also an input to either Step #8 via Eq. (24.31) or Step #9 via Eq. (24.38). Iteration convergence metrics used to-date are the same as those provided in the Eqs. (24.49)–(24.56). It should be noted that in the exercises performed to-date, little change in the convergence metrics are seen after the second iteration and the processing generally terminates after a defined number of iterations.

Step #13 – Final Averaged FRF Once the final full length force time history is generated from the final iteration of Step #11 or Step #12, a final averaged FRF is generated per Step #10 with the final estimated force. This final FRF is intended to be used as-is for frequency domain modal parameter extraction. The FRF matrix is converted to the time domain using a symmetric Inverse Fourier Transform to generate Impulse Response Functions (IRFs) to allow time domain modal parameter extraction approaches to be exercised as well.

24.2.2 Initial Recommended Approach Several processing options have been listed during the above description. Based on the experience to-date the following selections appear reasonable: 1. 2. 3. 4. 5. 6. 7.

Step #9 is used as the initial force estimate option; Full acceleration time histories (X) are used in Step #9 as opposed to flex-only accelerations (X1 ); Step #12 is used for iterations; Step #9 is used for each iteration force filter; FCG is not updated each iteration; Two forcing function iterations appear to be sufficient; and A convergence threshold of 10−6 is used (but iteration limiting appears to be sufficient).

24.3 Analytical Example 24.3.1 Success Criteria Evaluation of the processes listed above is by three success criteria. The first required success criteria is the estimated FF and FRF will reproduce the measured acceleration data as subjected to the filters of Step #0. Note that this success criteria can be applied to either analytical or experimental data. The second success criteria will be based on the proper breakdown of the FF vs. the transfer function. This success criteria can only be applied to analytical data sets where the input forcing functions are known. The third success criteria are the applicability of the FRF/IRF for driving modal parameter estimation tools. The direct comparison to known modal frequencies and known mode shapes can only be exercised with analytical data sets with known properties. However subjective assessments of the applicability and ease of use of modal estimation tools can be made using experimental data sets.

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Fig. 24.2 Modal Frequencies to 15 Hz from CT+MLP Finite Element Model (FEM)

24.3.2 Data Set and Processing Description An analytical data set was developed using a free-free FEM of the CT+MLP system. Figure 24.2 provides the first 100 modes of this system (up to 100 Hz). Note that the first elastic modes are a pair at 4.37 Hz. A FF previously estimated to represent this system operating at a speed of .9 mph for 10 minutes was simulated [15]. The 12 DOF inputs were applied at the Below-JEL locations denoted as sensors of 34, 35, 36, and 37 of Fig. 24.24 and Table 24.1. Acceleration outputs at the locations described in Tables 24.1 and 24.2 were simulated. The process was then applied to estimate the forcing functions and the system FRFs and IRFs. For this exercise, the simulated output data was frequency filtered to 60 Hz. A window size (winsize) of 16384 was used with a winskip0 increment of 8192 samples for FRF calculations. The winskip1 time domain averaging increment was 256 samples. When expanded views of the data are shown, the initial 1024 samples are used. Step #9 and Step #12 were used for two forcing function iterations. The FCG forces were not allowed to update each iteration. Two iterations were allowed with forcing function updates and a final FRF calculation was made using the final forcing functions.

24.3.3 Results and Discussion An example of the data driving success criteria 1 is shown in Fig. 24.3 which provides the simulated output at the driving point Below-JEL at Corner A in the vertical (X) direction. The upper part of the plot suggests that the general fit of the reconstructed to truth time signal is reasonable. The bottom plot shows that in the frequency domain some peaks were missed but the frequency content was captured fairly well overall. The middle plot shows an expanded time domain view of the first 1024 data points. This plot does show the effects of missing the amplitude of some of the higher amplitude peaks seen in the frequency domain. It should be noted that the first (and the last data points) of the reconstructed time history are the most challenging to fit due to the limited number of averages using the described approach. Figure 24.4 provides the same information for the lateral side-to-side (Y) direction above the JEL at the CT/MLP interface above Truck A. The fit up to 5 Hz is excellent but mismatch between truth and reconstruction sets in after 5 Hz. Figure 24.5 shows a fore/aft (Z) drive direction from the center of Side 3 of the upper MLP deck. This reconstruction is overall a better fit but does show some additional higher frequency mismatches. Overall, there is room for improvement in fitting the truth simulations.

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Fig. 24.3 Simulated Acceleration (Blue Line) Compared to Reconstructed Acceleration (Orange Line) in the Vertical (X) Direction Below-JEL Corner A for the CT+MLP System in Motion at .9mph

Fig. 24.4 Simulated Acceleration (Blue Line) Compared to Reconstructed Acceleration (Orange Line) in the Lateral (Y) Direction Above the JEL at Corner A for the CT+MLP System in Motion at .9mph

Figures 24.6, 24.7, and 24.8 provide examples of data that drives the second success criteria. These plots show the reconstructed force inputs in the X, Y, and Z directions respectively at the Below-JEL location on Truck A as compared to the known original forces. In all cases the upper time domain plot shows that globally the comparisons are fairly reasonable but room for improvement is seen. The middle plots are again the challenging first 1024 points of each time history comparison.

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Fig. 24.5 Simulated Acceleration (Blue Line) Compared to Reconstructed Acceleration (Orange Line) in the Fore/Aft (Z) Direction at Location 13 for the CT+MLP System in Motion at .9mph

Here it can be seen the some of the higher amplitude peaks were not fit as well as could be but the frequency content is likely reasonable captured. The bottom plots illustrate overall the frequency content is captured well but the amplitudes are off in some frequency bands. In the X direction of Fig. 24.6, the fit is very reasonable up to 5 Hz, but is significantly off between 5 and 10 Hz. In the Y direction of Fig. 24.7, the fit to 6 Hz is excellent. However, above 6 Hz there is a consistent bias in the reconstruction of the forcing function. The Z direction of Fig. 24.8 has frequency domain comparisons on the order of similar fits in the Y direction. Overall these reconstructed to original force comparisons are close enough to suggest that the procedures provided herein do hold promise for becoming a successful tool to support operational testing. One possible source of mismatch is the CT FEM which is not considered a correlated model. Additional sensors and speeds would improve the ability generate higher-fidelity force estimates by expanding the applicability of the SWAT forces. Figure 24.9 provides a comparison of the frequency content between the frequency average of all the FRFs and a frequency average of the associated forcing function. The lower plot shows the autospectra of the averaged forcing function. Superimposed on this are vertical lines showing where the anticipated narrow-band harmonics are when traveling at .9mph. As described in previous references such as [7, 9, 10], the harmonics expected while in motion at .9 mph include the following (in Hz): .5, .9, 1.1, 1.6, 1.8, 2.1, 2.6 (a strong combination harmonic), 3.2, 3.7, 4.2, 4.4, 4.8, 5.3 (a strong combination harmonic), 5.8, and 6.2 as well as weaker higher frequency continuations of this pattern. The peaks of the spectra line up with the anticipated frequencies, although there is a minor frequency dependent offset. This is likely due to numerical roundoff errors in determining the expected harmonics or a minor numerical error in the defined speed of travel. There are also significant amplitude variations in the different harmonics. The upper plot of Fig. 24.9 provides a high-level comparison of the frequency content of the FRF. The average amplitude of all 12 × 63 = 756 FRFs is plotted with vertical lines denoting the expected analytical frequencies. A couple of lower frequency peaks are seen below the first flexible modes that are likely residual effects from the forcing function. The peaks near the first pair of flexible modes at 4.4 Hz and the peak near the third flexible mode at 4.9 Hz are the only significantly identifiable comparisons. However, these are showing some offsets that suggest a more refined data analysis is needed. Also, when compared to the lower plot, there are expected harmonics nearby that may be affecting the amplitudes. Another block of potential flexible peaks can be seen in the 6 to 7 Hz region. A more detailed analysis utilized the full suite of 756 time domain Impulse Response Functions (IRFs) from the final FRF. The data analyzed were 8192 time steps in length. The quick-look assessment was made using the Eigensystem Realization Algorithm (ERA) with 1000 modes requested. The extracted modes were filtered for Consistent Mode Indicator (CMI) values greater than .1 and extracted damping values between 0% and 10%. Eleven modes were extracted and passed through these

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Fig. 24.6 Reconstructed Analytical Force (Blue Line) Compared to Original Force (Red Line) in the Vertical (X) Direction at Corner A BelowJEL for the CT+MLP System in Motion at .9mph

Fig. 24.7 Reconstructed Analytical Force (Blue Line) Compared to Original Force (Red Line) in the Lateral (Y) Direction at Corner A Below-JEL for the CT+MLP System in Motion at .9mph

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Fig. 24.8 Reconstructed Analytical Force (Blue Line) Compared to Original Force (Red Line) in the Fore/Aft (Z) Direction at Corner A BelowJEL for the CT+MLP System in Motion at .9mph

Fig. 24.9 Frequency Comparison of the Average FRF and Forcing Functions as Estimated from Analytical Data to the Expected Harmonics and Analytical Modal Frequencies

filters. Each of these extracted/filter modes were compared to each of the analytical modes of the system (as provided by the system FEM) below 12 Hz. The comparison results for the extracted mode at 5.92 Hz showed a reasonable correlation with

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Fig. 24.10 Modal Assurance Criteria (MAC), Damping, and Consistent Mode Indicator (CMI) Comparisons between the Extracted Modes and the Analytical 17th Mode at 5.94 Hz for the CT+MLP System

an analytical mode (the 17th mode at 5.94 Hz). Figure 24.10 shows the graphical comparison that captures these metrics to assess these extracted modes. The upper plot provides the Modal Assurance Criteria (MAC) comparison of the extracted modes to an individual analytical mode (the 17th analytical mode in this example) as red asterisks and the frequency of the analytical mode is denoted by the blue line. The successful extraction and comparison to an analytical of a mode is denoted by the blue line sitting on or near a red asterisk that has a high MAC value (MAC = .8 in Fig. 24.10 for the 5.92 Hz mode). The middle plot contains the extracted frequencies versus damping (in % of critical). Ideally the extracted mode of interest would occur near the analytically imposed value for damping (1% is expected here). And the plot contains extracted frequency to the CMI, with the relevant value as high as possible. The 5.92 Hz mode is a member of a group of four modes with very close modal frequencies, all with significant vertical motion. It can be seen from Fig. 24.2 that this model does have multiple sets of modes with very close frequencies (the regions of near vertical lines of points). The CT+MLP system has been used in force estimation of rollout due as it is the least “dynamically active” configuration. This allowed the development of processes and models to support generic rollout forcing functions for use in analytical studies with untested systems (as in Reference [15]). However, this feature of the CT+MLP system suggests that many of the flexible modes of the system are hard to excite and creates a limited opportunity to address the third success criteria. The data assessed to date supports this conclusion. However, past work with more “dynamically active” systems has shown that flexible modes can be excited and even tuned in to harmonic resonances. Highly active systems using higher channel counts and additional speed content will provide richer comparisons and assessments for the third success metric. The 17th mode of the system, the CT chassis trampoline mode, is one of the most dynamically active and easy to excite modes of the CT+MLP system. Hence it is useful to target this mode as an example as it provides a metric by which to assess later data sets with dynamically sensitive elements. Figure 24.11 provides a bar chart representation of this mode with the response of the axial (X direction) sensor at the center of the CT chassis dominating.

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Fig. 24.11 Bar Chart Representation of the Analytical 17th Mode at 5.94 Hz (CT Chassis Trampoline) for the CT+MLP System with Significant X Direction Motion at the Bottom Center of the Chassis

24.4 Experimental Example 24.4.1 Data Set and Processing Description A second example is provided using measured data from an actual rollout. Ten minutes of data taken at 320 samples/second was acquired with the CT+MLP system rolling at .9mph. Sixty-three accelerometer signals were acquired from the locations provided in Figs. 24.22, 24.24, 24.26, and 24.27 as well as Tables 24.1 and 24.2. The above process was then applied to estimate the forcing functions and the system FRFs and IRFs. For this exercise, the measured output data was frequency filtered to 60 Hz. A window size (winsize) of 16,384 was used with a winskip0 increment of 8192 samples for FRF calculations. The winskip1 time domain averaging increment was 256 samples. Step #9 and Step #12 were used for two forcing function iterations. The FCG forces were not allowed to update with each iteration.

24.4.2 Results and Discussion Figure 24.12 provides one of the 12 estimated forcing functions from this assessment. The harmonics expected during a roll at .9mph are seen in the estimated data. Figure 24.13 provides the corresponding accelerometer output at this location and direction. This location is a driving point location. Although there are some differences between the measured and reconstructed accelerations in the valleys and at the higher frequencies, the ability of the process to reproduce the measured data is clearly seen. Figure 24.14 provides the same information for the lateral (Y) direction at the CT/MLP interface above Truck A. The fit between reconstruction and measured data is very close. Figure 24.15 shows a fore/aft (Z) direction at the center of Side 3 of the upper MLP deck. This reconstruction is of the same quality as the other two directions. Overall, these reconstructions suggest that the process can be tuned to fit measured data with a reasonable chance of success. Note that the test-based Figs. 24.13, 24.14, and 24.15 use the same output locations as the analysis-based Figs. 24.3, 24.4, and 24.5. Figure 24.16 provides one of the IRFs and one of the FRFs that resulted from the processing of this system. The specific functions chosen are the response in the Z direction at the center of Side 3 on the Upper MLP deck due to the input at Corner A Below-JEL. Note that these are the same output and input presented in Figs. 24.12 and 24.15. The full IRF is in the top

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Fig. 24.12 Force in the Vertical (X) Direction at Corner A Below-JEL as Estimated for the CT+MLP System in Motion at .9mph

Fig. 24.13 Synthesized Acceleration (Red Line) Compared to Measured Acceleration (Orange Line) for the Vertical (X) Direction at Corner A Below-JEL for the CT+MLP System in Motion at .9mph

plot, the first 1024 time points of the IRF is in the second plot from the top. The amplitude of the FRF is in the third plot from the top, while the real and imaginary parts of the FRF are provided in the bottom plot. Note that the bottom two plots of Fig. 24.16 do not show any significant frequency content in the measured data example until approximately 6 Hz. That suggests that the significant peaks in Fig. 24.15 below 6 Hz are being driven largely from the forcing function harmonics without much dynamic amplification below the first dynamically active modes.

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Fig. 24.14 Synthesized Acceleration (Red Line) Compared to Measured Acceleration (Orange Line) for the Lateral (Y) Direction at the CT/MLP interface above Truck A for the CT+MLP System in Motion at .9mph

Fig. 24.15 Synthesized Acceleration (Red Line) Compared to Measured Acceleration (Orange Line) for the Fore/Aft (Z) Direction at the Center of Side 3 on the Upper MLP Deck for the CT+MLP System in Motion at .9mph

Figure 24.17 contains similar high-level frequency comparison data to Fig. 24.9, except the forcing function and FRF estimates are developed from measured data as opposed to analytical FEM-generated data. The lower plot shows that the forcing function peaks line up with the expected harmonics as seen with the analytical data. The upper plots show that there are more potential dynamics in the measured system, especially in the 5 to 7 Hz and 11 to 13 Hz regions. However there are

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Fig. 24.16 Estimated Impulse Response Function (IRF) and Frequency Response Function (FRF) between the Force Input at Corner A Below-JEL in the Vertical (X) Direction to the Fore/Aft (Z) Direction at the Center of Side 3 of the Upper MLP Deck for the CT+MLP System

potential bleed-through frequencies from the forcing function at 2 Hz and below. The ability to more completely filter out harmonic forcing function frequencies from the FRF will require future work and additional data sets. Since the analytical model is not assumed to be perfectly correlated the measured data and the expected analytical modes may be off due to model mis-match. Data containing multiple speeds and a larger number of acceleration sensors would enhance the ability to sort forcing function harmonics from flexible modes. Since precursor work with earlier versions of these processes have been successful at extracting system modes, it is expected that successful identification of the system dynamic properties will be found in later studies (References [1, 9, 10, 15, 16]). Figure 24.18 shows that an extracted mode at 6 Hz has a MAC value of almost .8 when compared to analytical model #18. Figure 24.19 provides a bar chart representation of the 18th analytical mode, while Fig. 24.20 provides a representation of the extracted mode with the closest MAC comparison (as seen in Fig. 24.18). It can be seen that the mode at 6 Hz extracted from measured data appears to be a combination of the 17th analytical mode (Fig. 24.11) and the 18th analytical mode (Fig. 24.19). Note that these two modes have the same analytical modal frequency.

24.5 Future Work The work reported in this paper represents an initial assessment into a larger more complete program. This work is intended to determine the applicability for larger scale diagnostic applications while at the same time focusing the efforts of smaller scale activities to develop process understanding. The detail-oriented side of these future efforts include potential tasks to more completely understand the foundational insight in these processes. These detail-oriented tasks include the following: 1. Laboratory scale articles where boundary conditions, forcing functions, and system dynamics are known; 2. Model sensitivity studies using the existing CT/MLP models, comparison of different FRF estimation schemes, and application of additional speed measurement sets; 3. Expanded analytical studies of full-scale systems with additional sensors, added dynamic receptivity, and more complex speeds/forcing functions; and 4. Application to existing rollout data sets with expanded sensor suites, system dynamics, and speed content.

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Fig. 24.17 Frequency Comparison of the Average FRF and Forcing Functions as Estimated from Measured Data to the Expected Harmonics and Analytical Modal Frequencies

Fig. 24.18 MAC, Damping, and CMI Comparisons between Extracted Modes and the Analytical 17th Mode at 5.94 Hz for the CT+MLP System

Potential tasks to prepare for larger scale diagnostic applications include the following: 1. Apply current modal analysis tools to FRFs/IRFs resulting from these processes; 2. Application to simulated data of an operational system;

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Fig. 24.19 Bar Chart Representation of the Analytical 18th Mode at 5.94 Hz (CT Truck Z Direction Out-Of-Phase with MLP) for the CT+MLP System (Repeated Mode with #17 Provided in Fig. 24.18)

Fig. 24.20 Bar Chart Representation of the Extracted Mode at 6 Hz (CT Truck Z Direction Combined with Chassis Trampoline) for the CT+MLP System (MAC .8 with Analytical Mode #18)

3. Application to rollout data with complex speed time histories, full sensor suites, realistic system dynamics, and operational constraints; and 4. Application to alternative systems in operational environments (such as launch vehicle in flight).

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24.6 Conclusion The process steps detailed herein are the result of efforts to implement tools to estimate a rollout FRF for the purpose of separating out the harmonics from the flexible body effects to allow estimation of the system’s structural dynamic properties. Alternative paths are provided to assess the fidelity and robustness of different processing steps. This set of processing steps have been subjected to limited initial data sets to exercise, assess, modify as-needed, and verify the applicability to the systems that will be enhanced via operational testing. Systems that are difficult to test in controlled laboratory environments or subject to unusual boundary conditions and/or loading such as full launch stacks, spacecraft in-flight, or systems in transportation are targeted stakeholders. The results, processing updates, and assessments have not been finalized but do provide evidence that the processing tools can be successfully applied. A process has been setup as a framework for the data analysis. Within this framework the following are unique contributions: 1. Expanding traditional CG centric force reconstruction techniques to expanded input locations and boundary conditions; 2. The use of CG force transformation matrix null space vectors as basis vectors to create full rank forces; and 3. Constrained least squares force updating to maintain targeted force updating. Success criteria have been identified and initial but limited application data is available. The first success criteria (reproduction of the input data) appears to be met with the current processes as forcing function/FRF calculations can be fit to match the measured data with the full system data example covering this example. The second success criteria (proper estimation of forcing functions and transfer functions) has shown to have a positive potential based on a comparisons presented herein. A reasonable assessment of the third success criteria will need a more dynamically active data set as well as a more complete assessment of FRF calculation. In summary, the processes developed herein hold promise to allow operational data to be used to derive structural dynamic parameters for multiple uses including but not limited to system identification, forcing function development, fatigue spectra generation, design assessment, and structural health monitoring, while expanding the reach of operational modal analysis. Acknowledgements The authors with to acknowledge Curt Larsen for his original insight to support this work. The team is also greatly indebted to Joel Sills for the continuing support and efforts to keep this work integrated into the larger scope of exploration initiatives within NASA. Multiple groups and individuals supporting the Space Launch System including structural dynamic, ground operations, and rollout analysis specifically have contributed significantly to this work, yet are too numerous to name here.

A Appendix A: Hardware and Data Background A.1 Crawler-Transporter (CT) Hardware Rollout forces are generated as the CT imposes a series of harmonic excitations (sine and cosine-like waveforms) onto the entire system under transport. Previous work during rollout of the STS system found two primary families of harmonics, which are characterized by a speed-dependent harmonic and integer frequency super harmonics [7, 12]. This loading is inherent in the tracked vehicle design of the CT. Figure 24.21 shows one of the four trucks on the CT and one of the eight tracks on the CT. The trucks contain the drive trains. A track is the continuous collection of shoes that transfers the motive force from the CT to the ground. The shoes are the structural contact between the CT and the ground. The rollers carry the transported weight to the shoes. The spacing between two of the 57 shoes on each track and the spacing between two of the 11 rollers on each track define the two harmonic families of the forcing functions of interest. Note that vehicle response can significantly increase when one of these forcing function harmonics created by the shoes and rollers is at or near one of the resonant frequencies of the transported vehicle. Previous work found that these forcing functions do not act as pure harmonics. The load paths through the trucks and rollers of the CT change over time during roll based on (as-yet) undetermined factors. Although harmonic frequencies of the forcing function may stay relatively constant at constant speed, other parameter changes (such as harmonic amplitudes and phase) make the forcing function difficult to model analytically. Each of the four trucks has a Jacking, Elevation, and Leveling (JEL) system and a guide tube system to properly support the CT chassis and the payload (launch platform and launch vehicle) as well as four electric track motors to provide motive force. The guide tube transfers all lateral loads from the CT chassis, the launch platform, and the launch vehicle into each of the four trucks. Figure 24.22 shows a schematic of a CT truck with the tracks, track motors, and guide tube marked.

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Fig. 24.21 Crawler-Transporter (CT) Truck and Track with Critical Spacing Locations Identified

All vertical forces generated to support the CT chassis, launch platform, and launch vehicle, are carried via the JEL systems. Each truck has four hydraulic cylinders that comprise the JEL system. The variability of the JEL system allows the CT to carry variable weight payloads, to handle uneven weight dispersions, to lift and lower the payload, and to level the payload when moving up or down the ramp at the pad. The CT chassis provides the structural framework to connect and control/steer all four trucks as well as interface to the payload. Also the chassis contains the diesel motors that drive the generators for motive and auxiliary power. The chassis contains the hydraulic systems for the JEL and steering functions. And finally all control interfaces to allow operation of the CT are housed in the chassis. Figure 24.4 shows a schematic and a photo showing the location and configuration of the JEL system on each truck, as well as the CT chassis. Note that one of the four payload support points is denoted in Fig. 24.23. There is a pickup point for the payload at the center of each set of 4 JEL cylinders.

A.2 Crawler-Transporter (CT) Sensor Suite The CT has triaxial accelerometers mounted at 9 locations. Figure 24.24 shows the CT with Sides, Trucks (Corners), and lateral sensor locations denoted (on the upper surface). Table 24.1 provides more details on the locations of the sensor suite.

A.3 STS Mobile Launch Platform and Sensor Suite The data in this paper will focus on an unloaded STS Mobile Launch Platform (MLP) carried by a CT. The MLPs were used to stack, transport, and launch the STS and Ares 1-X vehicles. Figure 24.25 shows an MLP on a CT system. The MLP weighs 8.2 million pounds without a vehicle. The CT weighs approximately one million pounds unloaded. The MLP/CT system represents a dynamically “simple” data set for a loaded CT. Since no vehicle is mounted on the MLP, there are no easily excited low frequency vehicle modes. The first major modes of this system are around 4.5 Hz. This configuration was operated for 10 minutes at five constant speeds (.5mph, .6mph, .7mph, .8mph, and .9mph) and at 0mph (stationary data).

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Fig. 24.22 Crawler-Transporter (CT) Drive Motors and Guide Tube Systems Identified

Fig. 24.23 Crawler-Transporter (CT) Chassis and Jacking, Elevation, and Leveling (JEL) Systems Identified

Only the .9mph data is used in the work reported herein. For the MLP, there were 12 triaxial sensor locations. Figure 24.26 shows the lateral locations of the sensors on Level B (the lower level). Figure 24.27 shows the lateral locations of the sensors on Level A (the upper level). Table 24.2 provides additional location information for the sensors.

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Fig. 24.24 Crawler-Transporter (CT) with Standard Sensor Suite Denoted

Table 24.1 Crawler-Transporter (CT) Sensor Locations # 30 31 32 33 34 35 36 37 38

Component Truck A Truck B Truck C Truck D Truck A Truck B Truck C Truck D Chassis

Vertical Location Above JEL Above JEL Above JEL Above JEL Below JEL Below JEL Below JEL Below JEL Bottom Center

Lateral Location Figure 24.24 as denoted Figure 24.24 as denoted Figure 24.24 as denoted Figure 24.24 as denoted Figure 24.22 Guide Tube Sleeve Figure 24.22 Guide Tube Sleeve Figure 24.22 Guide Tube Sleeve Figure 24.22 Guide Tube Sleeve Chassis Bottom Below Fig. 24.24 location

Channel Count Triax Triax Triax Triax Triax Triax Triax Triax Triax

Table 24.2 Mobile Launch Platform (MLP) Sensor Locations # 9 10 11 12 13 14 15 16 26 27 28 29

Component Level B Level B Level B Level B Level A Level A Level A Level A Pick-up Point Pick-up Point Pick-up Point Pick-up Point

Axial Location Lower Level Lower Level Lower Level Lower Level Upper Level Upper Level Upper Level Upper Level Bottom of MLP Bottom of MLP Bottom of MLP Bottom of MLP

Lateral Location Side 3 Side 1 Side 2 Side 4 Side 3 Side 1 Side 2 Side 4 Truck A Truck B Truck C Truck D

Channel Count Triax Triax Triax Triax Triax Triax Triax Triax Triax Triax Triax Triax

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Fig. 24.25 Crawler-Transporter (CT) Moving a Space Shuttle Mobile Launch Platform (MLP)

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Fig. 24.26 Mobile Launch Platform (MLP) Level B (Lower Level) with Sensor Locations Denoted

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Fig. 24.27 Mobile Launch Platform (MLP) Level A (Upper Level) with Sensor Locations Denoted

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