Identifying Preferred Solutions for Multi-objective Aerodynamic Design Optimization DOCTOR OF ...

264 Pages·2012·12.64 MB·English

Identifying Preferred Solutions for Multi-objective
Aerodynamic Design Optimization
by
Robert Carrese, B.Eng. (Hons.)
A thesis submitted in fulfillment of the
requirements for the degree of
D O C T O R OF P H I L O S O P H Y
School of Aerospace Mechanical and Manufacturing Engineering
RMIT University
Melbourne, Australia
Declaration
Except where due references are made, the work reported in this thesis is solely that of
the author alone and has not been submitted or published previously, in whole or in part,
to qualify for any other academic award. The content of the thesis is the result of work
which has been carried out since the official commencement date of the approved research
program, 2nd of March 2009 at RMIT University.
Robert Carrese
Melbourne, June 2012
ii
Abstract
Aerodynamic designers rely on high-fidelity numerical models to approximate, within rea-
sonable accuracy, the flow around complex aerodynamic shapes. The ability to improve
the flow field behaviour through shape modifications has led to the use of optimization
techniques. A significant challenge to the application of evolutionary algorithms for aero-
dynamic shape optimization is the often excessive number of expensive computational
fluid dynamic evaluations required to identify optimal designs. The computational effort
is intensified when considering multiple competing objectives, where a host of trade-off
designs are possible. This research focuses on the development of control measures to
improve efficiency and incorporate the domain knowledge and experience of the designer
to facilitate the optimization process.
A multi-objective particle swarm optimization framework is developed, which incor-
porates designer preferences to provide further guidance in the search. A reference point
is projected on the objective landscape to guide the swarm towards solutions of interest.
This point reflects the preferred compromise and is used to focus all computing effort on
exploiting a preferred region of the Pareto front. Data mining tools are introduced to
statistically extract information from the design space and confirm the relative influence
of both variables and objectives to the preferred interests of the designer. The framework
is assisted by the construction of time-adaptive Kriging models, for the management of
high-fidelity problems restricted by a computational budget. A screening criterion to lo-
callyupdatetheKrigingmodelsinpromisingareasofthedesignspaceisdeveloped, which
ensures the swarm does not deviate from the preferred search trajectory. The successful
integration of these design tools is facilitated through the specification of the reference
point, which can ideally be based on an existing or target design.
The over-arching goal of the developmental effort is to reduce the often prohibitive
cost of multi-objective design to the level of practical affordability in aerospace problems.
The superiority of the proposed framework over more conventional search methods is
conclusively demonstrated via a series of experiments and aerodynamic design problems.
iii
Acknowledgments
I would first like to thank my thesis supervisor, Dr. Jon Watmuff, for his invaluable
time and support throughout my candidature. I am also very grateful to A/Prof. Hadi
Winarto,withwhomIdevelopedaveryproductiveworkingrelationship. Hisexpertiseand
patience have inspired me to complete this research project to the best of my abilities.
Considerable thanks also go to Dr. Xiaodong Li, and to Dr. András Sóbester of the
University of Southampton, whom with I collaborated extensively. Their guidance and
advicehaveaddedconsiderablytomyresearchexperience. IamalsoverygratefultoProf.
Sylvester Abanteriba for his continual support.
Throughout my candidature I had the privilege of working with some fantastic col-
leagues, and am especially grateful to Dr. Manas Khurana. His invaluable (often prob-
lematic) experiences have aided me considerably. I am also very grateful to Dr. Upali
Wickramasinghe, who first introduced me to the concept of preference-based optimiza-
tion. Special thanks also go to Lev Lafayette and Craig West from the VPAC labs, and to
SamuelEbenezerfromGridProforkindlyofferinghisassistance. Iwouldalsoliketothank
Viscovery Software GmbH for kindly offering a license for SOMine for the duration of this
research. I would also like to thank Tze Min Koh for his suggestions and his willingness
to always lend a hand. A big thanks to everyone at the Bundoora campus, particularly
Asintha, Sridhar, Xin, Ashwin and Ishan. Special thanks also to the administrative staff,
especially Melissa Sigismondo and Lina Bubic. These people and more have made my
postgraduate experience as enjoyable (and eventful) as possible.
I am particularly thankful to my family and friends for their continual support and
encouragement. Finally I would like to thank God for placing all these people in my path
and am deeply grateful to Him for making this research successful and my candidature as
enjoyable as possible.
iv
Publications
This thesis report is based on the following publications (or parts thereof):
Carrese, R., and Li, X., 2012. Preference-based multiobjective PSO for airfoil design.
Swarm Intelligence - Introduction and Applications, Springer (to be published).
Carrese, R., Winarto, H., Li, X., Sóbester, A., and Ebenezer, S., 2012. A comprehen-
sive preference-based optimization framework with application to high-lift aerodynamic
design. Engineering Optimization. 1–19.
Carrese, R., Sóbester, A., Winarto, H., and Li, X., 2011. Swarm heuristic for iden-
tifying preferred solutions in surrogate-based multi-objective engineering design. AIAA
Journal. 49(7), 1437–1449.
Carrese, R., Winarto, H., Watmuff, J., and Wickramasinghe, U. K., 2011. Benefits
of incorporating designer preferences within a multi-objective airfoil design framework.
Journal of Aircraft. 48(3), 832–844.
Carrese, R., Khurana, M., Winarto, H., and Li, X., 2011. An efficient strategy to
incorporate designer-preferences in automated airfoil design. In the 14th Australian Inter-
national Aerospace Congress. Melbourne, Australia.
Carrese, R., Winarto, H., and Li, X., 2011. Integrating user-preference swarm algo-
rithm and surrogate modeling for airfoil design. In the 49th AIAA Aerospace Sciences
Meeting. Orlando, Florida.
Carrese, R., Winarto, H., and Watmuff, J., 2010. User-preference particle swarm algo-
rithmforairfoildesignarchitecture. Inthe 27th International Congress of the Aeronautical
Sciences, Nice, France.
Wickramasinghe, U. K., Carrese, R. and Li, X., 2010. Designing airfoils using a
reference point based evolutionary many-objective particle swarm optimization algorithm.
In Proceedings of the Congress of Evolutionary Computation. Barcelona, Spain.
v
Contents
Declaration ii
Abstract iii
Acknowledgments iv
1 Introduction 2
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Research in Aerospace Design . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 The Role of the Designer . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Research Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Elements of Aerodynamic Design 10
2.1 Aerodynamic Design Architecture . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Inverse Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Direct Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Geometrical Shape Parameterization . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Discrete Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Spline-based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 The PARSEC Method . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 The CST Parametric Method . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Computational Flow Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 The Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Quantities in Aerodynamic Design . . . . . . . . . . . . . . . . . . . 22
2.3.3 Panel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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2.3.4 Full Potential Methods. . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.5 Euler Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.6 (Reynolds-Averaged) Navier-Stokes . . . . . . . . . . . . . . . . . . . 27
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Design and Optimization 30
3.1 Introduction to Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Optimization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Gradient Methods (GM) . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Evolutionary Algorithms (EAs) . . . . . . . . . . . . . . . . . . . . . 36
3.3 Particle Swarm Optimization (PSO) . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Swarm Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Swarm Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.3 Particle Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Multi-objective Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.2 Pareto Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.3 Pareto Front . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Solving Multi-objective Problems . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5.1 Weighted Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5.2 Evolutionary Multi-objective Optimization (EMO) . . . . . . . . . . 52
3.5.3 Multi-objective Particle Swarm Optimization (MOPSO) . . . . . . . 54
3.5.4 Preference-based Optimization . . . . . . . . . . . . . . . . . . . . . 56
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Surrogate Modelling 59
4.1 Surrogates in Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Constructing a Surrogate . . . . . . . . . . . . . . . . . . . . . . . . 60
4.1.2 Managing Surrogates in Evolutionary Optimization . . . . . . . . . . 61
4.2 Sampling Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.1 Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2 Latin Hypercube Design . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Kriging Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.1 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
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4.3.2 Model Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.3 Model Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.4 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Visualization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.1 Design Space Visualization . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.2 Variable Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.3 Self-organizing Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Novel Preference-based MOPSO Algorithm 86
5.1 Incorporating Designer Preferences . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.1 The Reference Point Method . . . . . . . . . . . . . . . . . . . . . . 87
5.1.2 The Reference Point Distance Metric . . . . . . . . . . . . . . . . . . 88
5.1.3 Defining the Preferred Region . . . . . . . . . . . . . . . . . . . . . . 89
5.1.4 Solution Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 Identifying Preferred Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.1 Global Best Selection Scheme . . . . . . . . . . . . . . . . . . . . . . 92
5.2.2 Personal Best Selection Scheme . . . . . . . . . . . . . . . . . . . . . 94
5.2.3 Constraint Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.4 Mutation Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2.5 UPMOPSO Pseudo Code . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 Test Function Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.1 Convergence Characteristics . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.2 Controlling the Preferred Region . . . . . . . . . . . . . . . . . . . . 100
5.3.3 Hyper-Volume Performance Metric . . . . . . . . . . . . . . . . . . . 102
5.3.4 Test Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.5 Low-fidelity Design: Wave Drag Optimization . . . . . . . . . . . . . 111
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6 Implementing Kriging and Visualization 117
6.1 Implementing the Kriging Method . . . . . . . . . . . . . . . . . . . . . . . 117
6.1.1 Update Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.1.2 Reference Point Screening Criterion . . . . . . . . . . . . . . . . . . 123
6.2 Kriging UPMOPSO Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.2.1 Schaffer Test Function . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2.2 Design of a Helical Compression Spring . . . . . . . . . . . . . . . . 130
6.2.3 Low-fidelity Design: Case-study Revisited . . . . . . . . . . . . . . . 132
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6.3 Visualization Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.3.1 Pre-optimization and Variable Screening . . . . . . . . . . . . . . . . 136
6.3.2 Post-optimization and trade-off visualization . . . . . . . . . . . . . 140
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7 Case-studies and Results 143
7.1 Multi-mission Airfoil Shape Optimization . . . . . . . . . . . . . . . . . . . 143
7.2 Supersonic Nozzle Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.3 Transonic Airfoil Shape Optimization . . . . . . . . . . . . . . . . . . . . . 164
7.4 Fuselage Cross-Sectional Design . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.5 Aeroacoustic Optimization of Trailing-Edge Flow . . . . . . . . . . . . . . . 188
7.6 Aerodynamic High-lift Configuration Design . . . . . . . . . . . . . . . . . . 199
8 Conclusion 213
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.2 Research Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.2.1 Research Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.2.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.2.3 Additional Findings and Interest . . . . . . . . . . . . . . . . . . . . 218
8.3 Recommendations for Future Study . . . . . . . . . . . . . . . . . . . . . . 219
A Mathematical Test Functions 223
Bibliography 231
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List of Figures
1.1 The conventional aerodynamic design optimization loop . . . . . . . . . . . 4
1.2 The preference-based aerodynamic design optimization loop . . . . . . . . . 5
2.1 Generalized process flowchart for direct aerodynamic shape optimization . . 12
2.2 Airfoil representation via the PARSEC method . . . . . . . . . . . . . . . . 17
2.3 Additional trailing edge curvature via the modified PARSEC method . . . . 19
2.4 Illustration of aerodynamic shapes via class function representation . . . . . 20
2.5 XFOIL simulation of NACA0015 airfoil at angle of incidence . . . . . . . . 24
2.7 Euler simulation illustrating Mach number contours for a supersonic nozzle 26
2.8 RANS simulation of a slat configuration illustrating confluent boundary layer 27
3.1 One-dimensional representation of a multi-modal objective landscape . . . . 32
3.2 Shift of global optimum as a result of boundary constraints . . . . . . . . . 33
3.3 Illustration of a constraint optimization problem . . . . . . . . . . . . . . . 34
3.4 De Jong’s convex function in two-dimensions . . . . . . . . . . . . . . . . . 35
3.5 Rastrigin’s multi-modal function in two-dimensions . . . . . . . . . . . . . . 37
3.6 Illustration of genetic operators . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.7 Illustration of main variations in swarm topology and social hierarchy . . . 42
3.8 Illustration of dominance on a bi-objective landscape . . . . . . . . . . . . . 47
3.10 Illustration of the weighted sum approach for a convex Pareto front. . . . . 50
3.11 Illustration of non-dominated sorting . . . . . . . . . . . . . . . . . . . . . . 53
3.12 Isolating the preferred region using the reference point compromise . . . . . 57
4.1 Constructing a surrogate to fit a one-dimensional function . . . . . . . . . . 60
4.4 Concentrated ln-likelihood function landscape for Branin test function . . . 69
4.6 Relationship between correlation and sample size for Branin function . . . . 72
4.7 Relationship between CV error and sample size for Branin function . . . . . 73
4.9 Matrix of two-dimensional contour plots . . . . . . . . . . . . . . . . . . . . 75
4.10 Two-dimensional contour of variables A and N . . . . . . . . . . . . . . . . 76
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