Efficiency improvement of evolutionary multiobjective optimization methods for CFD-based shape optimization [Elektronische Ressource] / von Hongtao Sun

Sujets

• Mathematics

Informations

• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2010
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Efficiency Improvement of Evolutionary
Multiobjective Optimization
Methods for CFD-Based Shape Optimization
Vom Fachbereich Maschinenbau
an der Technischen Universität Darmstadt
zur
Erlangung des Grades eines Doktor-Ingenieurs
(Dr.-Ing.)
genehmigte Dissertation
von
Hongtao Sun, M. Sc.
aus Liaoning, V. R. China
Berichterstatter: Prof. Dr. rer. nat. M. Schäfer
Mitberichterstatter: Prof. Dr. rer. nat. S. Ulbrich
Tag der Einreichung: 24. November 2009
Tag der mündlichen Prüfung: 14. April 2010
Darmstadt 2010
D17Preface
This thesis contains the outcome of my research in the last five years at the institute of
Numerical Methods in Mechanical Engineering at TU Darmstadt.
There are many people that helped, inspired and encouraged me to progress and complete
this thesis, to whom I am deeply thankful. First and foremost, I would like to express my
gratitude and appreciation towards Prof. Dr. rer. nat. Michael Schäfer for his great supervision,
support and encouragement during the whole work. I also thank Prof. Dr. rer. nat. Stefan
Ulbrich for kindly accepting to become the co-advisor of this thesis.
My gratitude is extended to all the colleagues at our institute for the support and friendship
that created a wonderful and motivating working environment. Particularly I would like to
thank Dr.-Ing. Zerrin Harth for the pleasant collaboration, thank Michael Kornhass, Plamen
Pironkov, Gerrit Becker, Johannes Siegmann, Dr.-Ing. Markus Heck, Yu Du, Dr.-Ing. Dörte
Sternel for the fruitful discussions. Special thanks go to our system administrator Michael
Fladerer for his availability and willingness to solve all kinds of software problems and our
secretary Monika Müller for her kind help on a lot of things. Furthermore I would like to thank
Dr. Andreas Schönfeld for his valuable suggestions on the efficient computing on HHLR, Gary
Hachadorian for the extensively grammatical and linguistic correction of this thesis.
I am also profoundly thankful to my parents who did all they could to support me. Last, but
not the least, I thank my husband, Yinghua Wang for all his enormous affection and incredible
patient during these five years. This dissertation is dedicated to my parents and my husband.
Hongtao Sun
Darmstadt, Germany
November 2009Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Scope of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Overview of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Foundations of Flow Shape Optimization . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Numerical Flow Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Shape Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Free Form Deformation . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Optimization Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Automated Shape Optimization Loop . . . . . . . . . . . . . . . . . . . . . . 14
3 Multiobjective Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 Multiobjective Optimization Problem . . . . . . . . . . . . . . . . . . . . . . 16
3.1.1 Pareto-optimal Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.2 Classical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.3 Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Modified NSGA-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 External Population and Final Selection . . . . . . . . . . . . . . . . . 24
3.2.3 Parallel Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.4 Optimization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 RBFN-Based Approximation Model . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
i4.1.2 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Network Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.1 Determination of Training Size . . . . . . . . . . . . . . . . . . . . . . 31
4.2.2 Determination of Output Coefficients . . . . . . . . . . . . . . . . . . 32
4.2.3 Determination of Network Centers . . . . . . . . . . . . . . . . . . . . 33
4.3 RBFN Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Hybrid Optimization Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1 Global Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1.1 Global Search Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1.2 Control Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2.1 Starting Points of Local Search . . . . . . . . . . . . . . . . . . . . . . 41
5.2.2 Multiobjective Problems . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2.3 Deterministic Optimization Methods . . . . . . . . . . . . . . . . . . . 45
5.2.4 Local Optimization Procedure . . . . . . . . . . . . . . . . . . . . . . 47
5.3 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.1 Analytical Test Case 1 - ZDT1 . . . . . . . . . . . . . . . . . . . . . . 50
5.3.2 Analytical Test Case 2 - FON . . . . . . . . . . . . . . . . . . . . . . 55
5.3.3 Numerical Test Case 1 - Pipe Junction . . . . . . . . . . . . . . . . . . 58
5.3.4 Numerical Test Case 2 - Heat Exchanger . . . . . . . . . . . . . . . . 65
6 Proper Orthogonal Decomposition (POD)-Based Reduced-Order Model . . . . 74
6.1 Proper Orthogonal Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2 Combined Interpolation Approach . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Optimization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.4 Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4.1 Test Case 1 - Pipe Junction . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4.2 Test Case 2 - Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . 83
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
iiList of Tables
4.1 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.1 Global optimization parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Approximation control parameters (ZDT1) . . . . . . . . . . . . . . . . . . . . 52
5.3 Performance comparison of the optimal solutions after global search (ZDT1) . 53
5.4 Performance comparison of Pareto solutions with different p (ZDT1) . . . . . 540
5.5 Approximation control parameters (FON) . . . . . . . . . . . . . . . . . . . . 57
5.6 Performance comparison of the optimal solutions after global search (FON) . . 58
5.7 Approximation control parameters (pipe - 8 DVs) . . . . . . . . . . . . . . . . 62
5.8 Optimization performance comparison (pipe - 8 DVs) . . . . . . . . . . . . . . 64
5.9 Optimal solution obtained by NSGA-II+CONDOR (pipe - 8 DVs) . . . . . . . 65
5.10 Approximation control parameters (heat exchanger - 4 pipes) . . . . . . . . . . 68
5.11 Performance comparison after global search (heat exchanger - 4 pipes) . . . . . 71
5.12 Final Pareto-optimal solutions (heat exchanger - 4 pipes) . . . . . . . . . . . . 71
6.1 Comparison of CPU time (pipe - 4 DVs) . . . . . . . . . . . . . . . . . . . . . 82
6.2 Comparison of optimization results (pipe - 4 DVs) . . . . . . . . . . . . . . . . 83
6.3 Comparison of CPU time (fin-tube heat exchanger) . . . . . . . . . . . . . . . 87
6.4 Four exemplary optimal solutions (fin-tube heat exchanger) . . . . . . . . . . . 90
6.5 Performance comparison of two optimization runs (fin-tube heat exchanger) . . 90
iiiList of Figures
2.1 Methodology of numerical flow shape optimization . . . . . . . . . . . . . . . 6
2.2 Illustration of original (left) and deformed shape (right) using FFD . . . . . . . 11
2.3 A general flowchart of CFD-based shape optimization . . . . . . . . . . . . . . 15
3.1 Illustration of dominance concept, Pareto-optimal and reference vectors . . . . 17
3.2 Illustration of weighte