Flight Vehicle System Identification: A Time Domain Methodology

Transcription

1 Flight Vehicle System Identification: A Time Domain Methodology

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3 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 Alexander Bell Drive, Reston, VA 20191

4 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 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.

5 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

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7 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

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9 To Aai and Bapu, my Parents

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

12 xii TABLE OF CONTENTS The Maximum Likelihood Function for Estimation of Parameters in Dynamic Systems Basics of Cost Function Optimization Gauss Newton Algorithm Method of Quasi-linearization System Response and Sensitivity Coefficients Automatic Gradient Computation Step Size Control Bounded-variable Gauss Newton Method Constrained Gauss Newton Method Using the Interior-point Algorithm Levenberg Marquardt Method Direct Search Methods Regression Startup Procedure Estimation Accounting for a Priori Information Statistical Accuracy of Parameter Estimates Algorithmic Implementations OEM Software Examples Concluding Remarks Chapter 5. Filter Error Method Introduction Filter Error Method for Linear Systems Process Noise Formulations Filter Error Algorithm Filter Error Method for Nonlinear Systems Initial Noise Covariance Matrix Extension of Filter Error Method to Multiple Experiments Explicit Modeling of Gust Spectrum On the Equivalence of Output Error and Filter Error Methods FEM Software Examples Concluding Remarks Chapter 6. Equation Error Methods Introduction Least Squares Method Weighted Least Squares Method Nonlinear and Multi-output Regression Total Least Squares Instrumental Variable Method Data Partitioning Model Structure Determination Examples Concluding Remarks

13 TABLE OF CONTENTS xiii Chapter 7. Recursive Parameter Estimation Introduction Least Squares-based Recursive Methods Filtering Methods Algorithmic Implementation and Software Examples Comparative Evaluation of Recursive Algorithms Concluding Remarks Chapter 8. Artificial Neural Networks Introduction Basics of Neural Network Processing Training Algorithms Optimal Tuning Parameters Extraction of Stability and Control Derivatives from Trained FFNN FFNN Software Examples Concluding Remarks Chapter 9. Unstable Aircraft Identification Introduction Basics of Unstable Aircraft Identification Least Squares Method Total Least Squares Method Combined Output Error and Least Squares Approach Equation Decoupling Method Eigenvalue Transformation Method Filter Error Method Extended and Unscented Kalman Filters Output Error Method Output Error Method with Artificial Stabilization Multiple Shooting Method Output Error Method in Frequency Domain Separate Surface Excitation Programming Considerations Examples Concluding Remarks Chapter 10. Data Compatibility Check Introduction Kinematic Equations Flight Path Reconstruction Techniques Estimation-before-modeling Approach

14 xiv TABLE OF CONTENTS Example Calibration of Five-hole Flow Angle Probe Calibration of Static Pressure Ports Wind-box Maneuver Technique Concluding Remarks Chapter 11. Model Validation Introduction Statistical Accuracy of Parameter Estimates Residual Analysis Inverse Simulation Model Plausibility Model Predictive Capability Range of Model Applicability in Frequency Domain Concluding Remarks Chapter 12. Selected Advanced Examples Introduction Modeling of Transit Time Lag Effects Aerodynamic Effects of Landing Gear Control Surface Malfunction Effects Unsteady Aerodynamics Modeling Quasi-steady Stall Modeling Ground Effect Modeling High-fidelity Databases for Training Simulators X-31A Model Validation and Update Wake Vortex Aircraft Encounter Model Phoenix RLV Demonstrator Rotorcraft Modeling and Simulation Concluding Remarks Epilogue Appendix A. Power Spectrum of a Multistep Input Signal Appendix B. Identifiability of Initial Conditions and Bias Parameters 493 Appendix C. Derivation of the Likelihood Function Appendix D. Statistical Properties of Maximum Likelihood Estimates Asymptotic Consistency Asymptotic Normality Asymptotic Efficiency

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

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17 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

18 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