Flight Vehicle System Identification: A Time Domain Methodology

Flight Vehicle System Identification: A Time Domain Methodology

Flight Vehicle System Identi cation: A Time Domain Methodology by Ravindra V. Jategaonkar Senior Scientist Institute of Flight Systems DLR German Aerospace Center Braunschweig, Germany Volume 216 PROGRESS IN ASTRONAUTICS AND AERONAUTICS Frank K. Lu, Editor-in-Chief University of Texas at Arlington Arlington, Texas Published by American Institute of Aeronautics and Astronautics, Inc. 1801 Alexander Bell Drive, Reston, VA 20191

American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia. Copyright # 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, distributed, or transmitted, in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. For the software, Copyright # 2006 by Ravindra V. Jategaonkar. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. 1-56347-836-6 Data and information appearing in this book are for informational purposes only. AIAA is not responsible for any injury or damage resulting from use or reliance, nor does AIAA warrant that use or reliance will be free from privately owned rights.

Progress in Astronautics and Aeronautics Editor-in-Chief Frank K. Lu University of Texas at Arlington Editorial Board David A. Bearden The Aerospace Corporation Richard C. Lind University of Florida John D. Binder viasolutions Steven A. Brandt U.S. Air Force Academy Fred R. DeJarnette North Carolina State University Philip D. Hattis Charles Stark Draper Laboratory Abdollah Khodadoust The Boeing Company Richard M. Lloyd Raytheon Electronics Company Ahmed K. Noor NASA Langley Research Center Albert C. Piccirillo Institute for Defense Analyses Ben T. Zinn Georgia Institute of Technology Peter H. Zipfel Air Force Research Laboratory

Foreword This book covers a timely subject in the development of flight vehicles in spite of the long history of this topic. For example, through the development of the F-35 Joint Strike Fighter and recent various proposals to incorporate VSTOL in unmanned flight vehicles, the subject addressed in the book continues to be of significant importance, and of current and future interest. Flight vehicle system identification is an area of aerospace engineering which requires a tight knitting of basic engineering disciplines, experience, wisdom, and intuition. Dr. Jategaonkar provides refreshing insights into flight vehicle system identification and clearly demonstrates its multiple facets by systematically developing the difficult topic. The author pulls together a wealth of knowledge from decades of experience. After an introductory chapter, Dr. Jategaonkar plunges right into the critical aspect of the issues of flight vehicle system identification by discussing flight testing, followed by the development of mathematical tools. Such an arrangement reveals the crucial linkage between analysis and practice. Dr. Jategaonkar then proceeds to introduce advanced topics, including nonlinear stochastic estimation, artificial neural networks and unstable aircraft identification. He rounds off the book, once again, by returning to flight testing for data compatibility and model validation. Finally, Dr. Jategaonkar provides examples that show the application of flight vehicle system identification. The wide selection of examples is useful for illustrating the principles discussed in the book. This volume provides a state-of-the-art overview that will also apeal to experts in the field. Frank K. Lu Editor-in-Chief Progress in Astronautics and Aeronautics vii

To Aai and Bapu, my Parents

Table of Contents Foreword... Preface... vii xvii Chapter 1. Introduction................................ 1 What is System Identification?.... 2 Model Characterization... 5 Interdisciplinary Flight Vehicle Modeling... 6 Why System Identification?...... 8 Parameter Estimation in Flight Mechanics... 9 Estimation Techniques of the Past.... 11 Modern Methods of Aircraft Parameter Estimation... 12 General Aspects... 14 Chapter 2. Data Gathering.............................. 25 Introduction.... 25 Flight Testing and Maneuvers.... 26 Optimal Input Design.... 33 Scope of Flight Testing... 46 Flight Test Instrumentation and Measurements...... 49 Concluding Remarks.... 54 Chapter 3. Model Postulates and Simulation.................. 59 Introduction.... 59 Model Description..... 60 Extensions of the Mathematical Models.... 61 Retarded Systems...... 63 Linearized Models...... 67 Pseudo-control Inputs... 69 Treatment of Initial Conditions.... 71 Simulation..... 71 Concluding Remarks.... 76 Chapter 4. Output Error Method......................... 79 Introduction.... 79 The Principle of Maximum Likelihood Estimation... 80 Properties of Maximum Likelihood Estimates...... 83 xi

xii TABLE OF CONTENTS The Maximum Likelihood Function for Estimation of Parameters in Dynamic Systems.... 84 Basics of Cost Function Optimization... 86 Gauss Newton Algorithm... 88 Method of Quasi-linearization... 90 System Response and Sensitivity Coefficients... 91 Automatic Gradient Computation..... 94 Step Size Control... 95 Bounded-variable Gauss Newton Method.... 98 Constrained Gauss Newton Method Using the Interior-point Algorithm... 100 Levenberg Marquardt Method.... 103 Direct Search Methods...... 105 Regression Startup Procedure... 107 Estimation Accounting for a Priori Information... 109 Statistical Accuracy of Parameter Estimates.... 111 Algorithmic Implementations.... 112 OEM Software..... 115 Examples... 119 Concluding Remarks... 124 Chapter 5. Filter Error Method.......................... 131 Introduction.... 131 Filter Error Method for Linear Systems...... 133 Process Noise Formulations.... 135 Filter Error Algorithm...... 138 Filter Error Method for Nonlinear Systems.... 145 Initial Noise Covariance Matrix...... 154 Extension of Filter Error Method to Multiple Experiments...... 155 Explicit Modeling of Gust Spectrum... 157 On the Equivalence of Output Error and Filter Error Methods.... 159 FEM Software..... 160 Examples... 164 Concluding Remarks... 174 Chapter 6. Equation Error Methods....................... 177 Introduction.... 177 Least Squares Method...... 178 Weighted Least Squares Method...... 188 Nonlinear and Multi-output Regression...... 189 Total Least Squares... 191 Instrumental Variable Method... 194 Data Partitioning.... 196 Model Structure Determination...... 197 Examples... 204 Concluding Remarks... 216

TABLE OF CONTENTS xiii Chapter 7. Recursive Parameter Estimation.................. 219 Introduction.... 219 Least Squares-based Recursive Methods.... 222 Filtering Methods...... 234 Algorithmic Implementation and Software... 245 Examples..... 248 Comparative Evaluation of Recursive Algorithms.... 260 Concluding Remarks.... 261 Chapter 8. Artificial Neural Networks...................... 265 Introduction.... 265 Basics of Neural Network Processing..... 268 Training Algorithms.... 270 Optimal Tuning Parameters...... 276 Extraction of Stability and Control Derivatives from Trained FFNN... 278 FFNN Software... 279 Examples..... 281 Concluding Remarks.... 289 Chapter 9. Unstable Aircraft Identification................... 295 Introduction.... 295 Basics of Unstable Aircraft Identification... 297 Least Squares Method... 299 Total Least Squares Method..... 303 Combined Output Error and Least Squares Approach...... 304 Equation Decoupling Method.... 304 Eigenvalue Transformation Method... 306 Filter Error Method..... 308 Extended and Unscented Kalman Filters.... 309 Output Error Method.... 310 Output Error Method with Artificial Stabilization.... 310 Multiple Shooting Method...... 311 Output Error Method in Frequency Domain... 313 Separate Surface Excitation...... 314 Programming Considerations..... 316 Examples..... 317 Concluding Remarks.... 331 Chapter 10. Data Compatibility Check...................... 335 Introduction.... 335 Kinematic Equations.... 336 Flight Path Reconstruction Techniques..... 344 Estimation-before-modeling Approach..... 350

xiv TABLE OF CONTENTS Example... 354 Calibration of Five-hole Flow Angle Probe.... 358 Calibration of Static Pressure Ports.... 363 Wind-box Maneuver Technique...... 368 Concluding Remarks... 371 Chapter 11. Model Validation............................ 375 Introduction.... 375 Statistical Accuracy of Parameter Estimates.... 376 Residual Analysis... 378 Inverse Simulation... 382 Model Plausibility.... 383 Model Predictive Capability... 386 Range of Model Applicability in Frequency Domain.... 389 Concluding Remarks... 392 Chapter 12. Selected Advanced Examples................... 395 Introduction.... 395 Modeling of Transit Time Lag Effects... 396 Aerodynamic Effects of Landing Gear... 409 Control Surface Malfunction Effects... 411 Unsteady Aerodynamics Modeling.... 414 Quasi-steady Stall Modeling... 418 Ground Effect Modeling..... 427 High-fidelity Databases for Training Simulators... 433 X-31A Model Validation and Update.... 448 Wake Vortex Aircraft Encounter Model...... 450 Phoenix RLV Demonstrator.... 455 Rotorcraft Modeling and Simulation... 465 Concluding Remarks... 479 Epilogue............................................. 485 Appendix A. Power Spectrum of a Multistep Input Signal........ 489 Appendix B. Identifiability of Initial Conditions and Bias Parameters 493 Appendix C. Derivation of the Likelihood Function............. 497 Appendix D. Statistical Properties of Maximum Likelihood Estimates.................................. 501 Asymptotic Consistency..... 501 Asymptotic Normality...... 503 Asymptotic Efficiency...... 505

TABLE OF CONTENTS xv Appendix E. Minimization of Likelihood Function with Respect to Covariance Matrix R... 507 Appendix F. Derivation of Kalman Filter and Extended Kalman Filter....................................... 511 Extended Kalman Filter... 518 Index.............................................. 521 Supporting Materials................................... 535

Preface THE OBJECTIVE of this book is to provide a consolidated account of flight vehicle system identification that has evolved during recent decades, focusing particularly on nonlinear systems and the time domain approach. It also aims to share the practical experience gained on aerodynamic modeling from flight data to a large number of flight vehicles, because experience and engineering judgment are critical to generate good results. Effective system identification becomes possible based on a coordinated approach and by following certain well-researched guidelines. This book attempts to provide not only details of such a systematic approach, summarizing the general underlying concepts, methodologies, and computational procedures, and present examples of practical applications, but also to show the pitfalls of these methods. It gives practical tips on how to overcome the problems one is likely to face in developing nonlinear, high-fidelity models and analyzing flight data from complex flight vehicles, for example, intermediate divergence of optimization algorithms or estimation subject to bounds, or application of filter error method to data with turbulence, which are generally not covered in theoretical books. The layout of the book and the material presented here is partly based on the short courses on Flight Vehicle System Identification in Time Domain delivered as a part of the AIAA Professional Development program and at other educational and research organizations during the last few years, partly on the personal notes of discussions and experience gathered over two and half decades, and partly on several technical papers published jointly with my colleagues, including several guest scientists who I had the pleasure of guiding. If you locate any errors in the text and software, or have any other comments or questions, please send your suggestions and queries to me ( jategaonkar@dlr.de). With great pleasure, I would like to acknowledge several individuals who helped me during the various phases of writing this book. First, I sincerely thank Professor Peter Hamel for his support and for the use of materials from some of his and our joint papers. My personal discussions with him have shaped the book layout to some extent. Next, I greatly appreciate the help provided by my colleague Wulf Mönnich in the tedious job of reading the draft manuscript and for making many helpful suggestions. It has helped me directly and indirectly in the thought processes reflected in the book. I would also like to acknowledge my former colleague Dr. Ermin Plaetschke for his comments on the draft version, for the use of material from our joint papers and other notes. I am thankful to my colleague Dietrich Fischenberg for providing the case study on modeling of wake vortex encounter and some material on other examples. Likewise, I extend my thanks to Dr. Wilhelm Gockel for the consent to report on the case study pertaining to reusable launch vehicle demonstrator. Help from Dr. Wolfgang von Grünhagen on rotorcraft example is appreciated. I am also thankful to Professor Stefan Levedag and Dr. Frank xvii

xviii PREFACE Thielecke for the facilities granted at the Institute. The interest of other present and former colleagues of the Institute is appreciated, particularly that of Dr. Karl Doherr. It has been a pleasure to work at the DLR Institute of Flight Systems for more than two decades. I also recall my past association with the former Systems Engineering Department of the National Aeronautical Laboratory, Bangalore, India. I would also like to extend my special appreciation to my wife, Padma, for her patience throughout the extended period of writing this book. Without her understanding and support, this book would not have been possible. I would also like to mention here our daughters, Smita and Swati, for their continued interest. Finally, I would like to acknowledge the interest of AIAA in publishing this book under the Progress Series. In particular, I would like to extend my appreciation to Dr. Peter Zipfel, member of the Editorial Board, for a discussion which led to embarking on this book project. I would like to acknowledge Rodger Williams, AIAA Publications Development for his help and encouragement. I extend my thanks to Alex McCray, Managing Editor, Books, AIAA, for overseeing the book production, to Janice Saylor, Marketing Strategist, AIAA, for the front and back cover design and marketing, and Nick Barber, Books Manager, Techset Composition Ltd., for copyediting, text composition and for incorporating text amendments efficiently. I am sure many other AIAA staff are involved down the line, whom I would like to thank as well. Ravindra V. Jategaonkar DLR Institute of Flight Systems December 2005