Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1994-03 Artificial neural network modeling of damaged aircraft Brunger, Clifford A. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/42931 AD-A283IlIIhIiIhIIm IhIhili 227 . , NAVAL POSTGRADUATE SCHOOL Monterey, California DTIC AUG 11994 THESIS b, 7- ARTIFICIAL NEURAL NETWORK MODELING OF DAMAGED AIRCRAFT _• by Clifford A. Bnmger March, 1994 Thesis Advisor: Daniel J. Collins Approved for public release; distribution is unlimited. 94 8 10 002 Unclassified SECURITY CLASSIFICATION OF T-IS PAGE "I r oForm Approved,, REPORT DOCUMENTATION PAGE NMo Oils I& KkMiKr /5kLULU1 ICLAeJ"-ILAIgJIN lb. Kkb1IbL-Vk"MAICMNLgJ Unclassified 2& SECUU[[Y LA SU WATIU NiAUTUOIUTY 3. LDII 1R WUTI4AVAILA/U1 TY KZ" OTUKI __________________________________________ Approved for public release; ULU.A W.L.IU^.U~a,•wNU IU •JULL distribution is unlimited. 4. YW~tUiJMMNU UK(,AXZ142-AAIUf k¶KI I'4MUM~bK) 5. NMUNI MMI( 0K~iANUAIIUt XMMlIJ 4UhMAkRI) 6*NAM1 UP FtPELCMIU UKUANJAW-CIUN *. UiMk bymDsL U* NAME~ OF MONITUKINa UKRiADUA1UN Naval Posgraduate School I AA/PL Naval Postgraduate School MWontMaUy. 3 Er CBS50) I. AIMonte riey. 3-C934 L-50r Monterey. CA 93943-5000 Mont CA-. 93943-5000 NAREOF FORRM071MRrlj 16. UFmLB ITSMUU V. IKUMAULi 243 KlibQ2I LulNiIEILA1iN NummL OROANA•1ON (If aWhoebe) 5ce. AL)DKJXS (City. State, and•LW ie 10. .UKL;V" UP tPuN'X~lRF NUL/Mbb,", ACCESON NO. SNO. NO. Artificial Neural Network Modeling of Damaged Aircraft 14. IIMMNAL AUWHUK(b) Clifford A. Brunger IS. I TR• (R KKI 1*u. -IWm=* uu 14. VAIB Ur ROU (IfhlJy) VAL&"OUNI Master's Thesis I 01M92DI0M9 March 1994 - 7 109 l6r7PUEMXLKY NVI[AIRIM The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. L;UbAII tULX5 I&. bumLI 11MMl (LaaMe aU swe•e wy Ideiualy by bilack SUnaa) K"UA UKUUP Ig KU Neural Network, Parallel Processors UlnuereIa IFl=n by b10" metw) Aircraft design and control techniques rely on the proper modeling of the aircraft's equations of motion. Many of the variables used in these equations are aerodynamic coefficients which are obtained from scale models in wind tunnel tests. In order to model damaged aircraft, every aerodynamic coefficient must be determined for every possible damage mechanism in every flight coutdition. Designing a controller for a damaged aircraft is particularly burdensome because knowledge of the effect of each damage mechanism on the model is required bafoM the controller can be designed. Also, a monitoring system must be employed to decide when and how much damage has occurred in order to re configure the controller. Recent advances in artificial intelligence have made parallel distributed processors (artificial neural networks) feasible. Modeled on the human brain, the artificial neural network's strength lies in its ability to generalize from a given model. This thesis examines the robustness of the artificial neural network as a model for damaged aircraft. [E tNDAsz6JIEIU Q s Amsmrr. Q zncwas Unclassified Daniel J. Collins (408) 656 - 2311 fC S/N 0102-LX-014-6603 Unclassified Approved for public release; distribution is unlimited. Artificial Neural Network Modeling of Damaged Aircraft by Clifford A. Brunger Lieutenant, United States Navy B.S.E.E., United States Naval Academy, 1984 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL MARCH 1994 Author: Approved by: J. Colli, Thesis Advisor Richard M. Howard, Second Reader Daniel J. $llins, Chairman Department of Aeronautics and Astronautics ii ABSTRACT Aircraft design and control techniques rely on the proper modeling of the aircraft's equations of motion. Many of the variables used in these equations are aerodynamic coefficients which are obtained from scale models in wind tunnel tests. In order to model damaged aircraft, every aerodynamic coefficient must be determined for every possible damage mechanism in every flight condition. Designing a controller for a damaged aircraft is particularly burdensome because knowledge of the effect of each damage mechanism on the model is required before the controller can be designed. Also, a monitoring system must be employed to decide when and how much damage has occurred in order to re configure the controller. Recent advances in artificial intelligence have made parallel distributed processors (artificial neural networks) feasible. Modeled on the human brain, the artificial neural network's strength lies in its ability to generalize from a given model. This thesis examines the robustness of the artificial neural network as a model for damaged aircraft. Acoession For DTIC T.1.3 Unanuo,-a=o'wed 0 Just if tenion By- iii Dist TABLE OF CONTENTS 1. INTRODUCTION ......................................................................... I II. NEURAL NETWORK FUNDAMENTALS ....................................... 4 A. BIOL.OGICAL. NEURONS ................................................................................ 4 B. PROCESSING ELEMENTS ............................................................................. 6 C. ARTIFICIAL NEURAL NETWORKS ......................................................... 1 2 D. ARTIFICIAL NEURAL NETWORK OPERATION .................................... 13 1. L.earig ............................................................................................... 14 a. Supervised Lea ng ............................................................... 14 2. Tes g ................................................................................................. 16 3. Learning Algorithm ........................................................................ 17 E BACK-PROPAGATION ............................................................................... 17 1. Generalized Delta Rule ........................................................... 18 I I I. EXPERIMENTAL PROCEDURE .......................... ................... 2 2 A. HARDWARE-SOFTWARE .................................................................... 22 B. OVERVIEW .............................................................................................. 23 CL SETUP SPECIFICS ............................................................................... 23 1. Modeling of A-4D Longitudinal Motion .............................. 23 2. Generation of Learn and Test Files ................................... 28 a. Random Binary Sequence ................................................ 28 b. A-4D Learn and Test Data .............................................. 32 c. Damaged A-4D Learn and Test Data ........................... 33 3. Neural Network Configuration .............................................. 37 4. Network Validation ................................................................. 39 iv I V. RESULTS ................................................................................. 5 0 A. INTERPOLATION BETWEEN DAMAGE MECHANISMS ....................... 50 B. EXTRAPOLATING FROM A DAMAGED AIRCRAFT ........................ 59 C, DETECTING AND RESPONDING TO DAMAGE ................................ 61 V . CONCLUSIONS ......................................................................... 7 5 APPENDIX A: MATLAB PROGRAMS ............................................. 7 6 APPENDIX B: NEURALWORKS SETUP SPECIFICS ...................... 9 8 LIST OF REFERENCES ................................................................ 100 INITIAL DISTRIBUTION LIST ................................................... 102 V To my beautiful wife Joie, who makes life enjoyable. vi I. INTRODUCTION Designing modem aircraft controllers requires advance knowledge of aircraft dynamics. In order to determine these dynamics, the aircraft is usually modeled. First, the equations of motion (based on Newton's second law) are derived. Neglecting higher order derivatives and making small angle approximations, these equations are linearized around a trim position. The aircraft's equations of motion can then be written in the following state space format: X(t) = Ax(t) + Bu(t) Y(t) = Cx(t) + Du(t) where, x(t) = state vector u(t) = input vector Y(t) = output vector Although the previous steps can be carried out to a high degree of accuracy, the aerodynamicist's job is still daunting. Using wind tunnel tests on scale models, the numerous partial derivatives must be obtained in order to compute the state space matrices (A, B, C and D). Since a simple model of an aircraft is at least eighth order, and some models reach more than fiftieth order, this makes determining the partial derivatives an arduous task. Once the derivatives are known, the transfer functions can be computed and, therefore, the static and dynamic response of the aircraft can be determined. These responses, however, are valid only around the trimmed position. In order for the controller to function throughout the aircraft's entire flight regime, several other trim positions, or flight conditions, must be defined, the equations of motion must be linearized around these new trim positions, and the new aerodynamic derivatives must be determined or estimated. This results in additional A, B, C, and D matrices. The more trim positions selected, the more schedules or plants the controller has to pick from and, therefore, the more robust the controller. A problem arises, however, when the aircraft is damaged. The controller is hard-wired with the