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Wu Washington 0250E 15755.Pdf (3.086Mb) © Copyright 2016 Sang Wu Contributions to Physics-Based Aeroservoelastic Uncertainty Analysis Sang Wu A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2016 Reading Committee: Eli Livne, Chair Mehran Mesbahi Dorothy Reed Frode Engelsen Program Authorized to Offer Degree: Aeronautics and Astronautics University of Washington Abstract Contributions to Physics-Based Aeroservoelastic Uncertainty Analysis Sang Wu Chair of the Supervisory Committee: Professor Eli Livne The William E. Boeing Department of Aeronautics and Astronautics The thesis presents the development of a new fully-integrated, MATLAB based simulation capability for aeroservoelastic (ASE) uncertainty analysis that accounts for uncertainties in all disciplines as well as discipline interactions. This new capability allows probabilistic studies of complex configuration at a scope and with depth not known before. Several statistical tools and methods have been integrated into the capability to guide the tasks such as parameter prioritization, uncertainty reduction, and risk mitigation. The first task of the thesis focuses on aeroservoelastic uncertainty assessment considering control component uncertainty. The simulation has shown that attention has to be paid, if notch filters are used in the aeroservoelastic loop, to the variability and uncertainties of the aircraft involved. The second task introduces two innovative methodologies to characterize the unsteady aerodynamic uncertainty. One is a physically based aerodynamic influence coefficients element by element correction uncertainty scheme and the other is an alternative approach focusing on rational function approximation matrix uncertainties to evaluate the relative impact of uncertainty in aerodynamic stiffness, damping, inertia, or lag terms. Finally, the capability has been applied to obtain the gust load response statistics accounting for uncertainties in both aircraft and gust profiles. The gust response analysis shows a significant increase of the critical loads when system’s uncertainties are included. The work is expected to make a contribution to the understanding of the propagation of uncertainty and the resulting reliability of realistic integrated aeroservoelastic system inherent in real modern aircraft. This work will motivate more research in the aeroservoelastic uncertainty area regarding both methods development in general and reliability studies of different configurations of interest. The mathematical derivations which serve as the foundation of the capability are also well documented. TABLE OF CONTENTS List of Figures ................................................................................................................................. v List of Tables ................................................................................................................................. xi List of Symbols ............................................................................................................................. xii Chapter 1. Introduction ................................................................................................................... 1 1.1 Background and Challenges ........................................................................................... 1 1.2 The Needs and Goals ...................................................................................................... 7 Chapter 2. Tool Development ......................................................................................................... 9 2.1 The Matlab Based FEM Capability ................................................................................ 9 2.2 Unsteady Aerodynamics – The Doublet Lattice Method ............................................. 11 2.3 The Aeroservoelastic State-Space Model ..................................................................... 13 2.4 Aeroelastic System with Gust Excitation ..................................................................... 16 2.5 Probabilistic Aeroservoelastic Analysis ....................................................................... 18 Chapter 3. Probabilistic Aeroservoelastic Reliability Assessment Considering Control System Component Uncertainty ................................................................................................................ 21 3.1 Overview ....................................................................................................................... 21 3.2 Introduction ................................................................................................................... 22 3.3 Model Derivation .......................................................................................................... 24 3.3.1 The Aeroservoelastic State-Space Model ................................................................. 24 3.3.2 Model of Electrohydraulic Servo Actuator ............................................................... 24 i 3.4 Procedure of Uncertainty Mitigation ............................................................................ 27 3.4.1 Parameter Prioritization with Statistical Sensitivity Analysis .................................. 27 3.4.2 Bayesian Update and Risk Reduction ....................................................................... 29 3.5 Numerical Aeroservoelastic Reliability Analysis ......................................................... 32 3.5.1 The Nominal (Baseline) Case ................................................................................... 32 3.5.2 Uncertainty in the Actuator of the Outboard Elevon ................................................ 39 3.5.3 Uncertainty in the Actuator of the Outboard Elevon and the Structure .................... 43 3.5.4 Added Unsteady Aerodynamic Uncertainty ............................................................. 44 3.6 Application of Uncertainty Mitigation.......................................................................... 49 3.6.1 Parameter Prioritization ............................................................................................ 49 3.6.2 Risk Reduction .......................................................................................................... 50 3.7 Summary ....................................................................................................................... 53 Chapter 4. Alternative Aerodynamic Uncertainty Modeling Approaches for Flutter Reliability Analysis......................................................................................................................................... 56 4.1 Overview ....................................................................................................................... 56 4.2 Introduction ................................................................................................................... 56 4.3 AICs by Linear Panel Methods ..................................................................................... 60 4.4 Accounting for the Aerodynamic Uncertainty .............................................................. 65 4.5 Numerical Example ...................................................................................................... 69 4.5.1 Nominal Flutter Analysis .......................................................................................... 71 4.5.2 Aeroelastic Simulation Subject to Aerodynamic Uncertainty .................................. 76 4.5.3 Wing Section Prioritization with Statistical Sensitivity Analysis ............................ 81 4.5.4 Aerodynamic Uncertainty via Rational Function Approximation ............................ 86 ii 4.5.5 The Addition of Structural Uncertainty .................................................................... 89 4.6 Conclusion .................................................................................................................... 92 Chapter 5. Probabilistic Gust Loads Analysis Accounting for Aeroservoelastic System Uncertainty .................................................................................................................................... 95 5.1 Overview ....................................................................................................................... 95 5.2 Introduction ................................................................................................................... 95 5.3 Model Derivation .......................................................................................................... 98 5.3.1 Aeroelastic System with Gust Excitation ................................................................. 98 5.3.2 Gust Input Uncertainty in the Time Domain ............................................................ 98 5.3.3 Gust Input Uncertainty in the Frequency Domain .................................................. 100 5.3.4 The Addition of a Gust “Filter” to the Math Model of the System ........................ 102 5.4 Numerical Example of Gust Response with Uncertainty ........................................... 105 5.4.1 Discrete Gust Response with System Uncertainty .................................................. 106 5.4.2 Frequency Domain Gust Response Accounting for System Uncertainty ............... 110 5.4.3 Time Domain Turbulence Response with System Uncertainty .............................. 113 5.5 Summary ....................................................................................................................
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