MultiObjective Design Exploration MODE Visualization and Mapping of

Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space Shigeru Obayashi Institute of Fluid Science Tohoku University 1

Outline Background Flow Visualization Multidisciplinary Design Optimization (MDO) Self-Organizing Map (SOM) Rough Set Multi-Objective Design Exploration (MODE) Application to Regional Jet Design Wing-Nacelle-Pylon-Body Configuration Analysis of Sweet-Spot Cluster Conclusion 2

Flow Visualization -1 Flow transition: Reynolds number 3

Flow Visualization -2 Stall: boundary layer separation 4

Flow Visualization -3 Karman Votex 5

Flow Visualization -4 Flow visualization: Seeing is believing (Seeing is understanding) (Picture is worth a thousand words) Drag divergence: shock wave 6

Aircraft Design Aerodynamics Propulsion Structure • Compromise of all disciplines • Multidisciplinary Design Optimization (MDO) as Multi-Objective Optimization (MOP) 7

How to Solve MOP Collection of non-dominated solutions that form trade-offs between multiple objectives Gradient-based method with weights between objectives Utility function: f = f 1 + f 2 Other analytical methods Normal-Boundary Intersection Method Aspiration Level Method Multi-Objective Evolutionary Algorithms (MOEAs) Population-based search f 2 Gradient-based method f 1 MOEAs f 1 8

How to Understand MOP f 1 Extreme Pareto Solution Pareto Front f 1 f 2 X Arithmatic Average f 1 Improvement Pareto front Extreme Pareto Solution Pareto front f 2 f 1 Global optimization is needed Visualization is essential! Data mining is required Design optimization→Design exploration Pareto front f 2 9

Visualization of Tradeoffs 3 objectives 4 objectives ? Minimization problems Projection 2 objectives 10

Self-Organizing Map（SOM） Neural network model proposed by Kohonen Unsupervised, competitive learning High-dimensional data → 2 D map Qualitative description of data • Node represents a neuron. SOM provides design visualization: -Neuron is a three-dimensional vector Seeing is understanding (Obj. 1, Obj. 2, Obj. 3) (Essential design tool) -Each neuron corresponds to a design. • Neuron is self-organized so that similar neurons are neighbored to each other. • Similar neurons form a cluster 11

How to understand SOM better? Colored SOMs identify the global structure of the design space Resulting clusters classify possible designs If a cluster has all objectives near optimal, it is called as sweet-spot cluster If the sweet-spot cluster exists, it should be analyzed in detail Visualization of design variables Data mining, such as decision tree and rough set 12

Rough Set - Pawlak(1982) - l Granulation of information l Reduction of information l Extraction of rules (knowledge acquisition) 13

Rough Set and Attribute U Condition attribute C Decision attribute D Vehicle type Engine Size Color Preference x 1 propane compact black good x 2 diesel medium gold bad x 3 diesel full white bad x 4 diesel medium red bad x 5 gasoline compact black good x 6 gasoline medium silver good x 7 gasoline full white bad x 8 gasoline compact silver good 14

U x 1，x 2，x 3，x 4，x 5，x 6，x 7，ｘ８ 15

U Diesel Good x 2，x 3，x 4 Propane x 1 Gasoline U x 5，x 6，x 8，x 7 Condition attribute C Decision attribute D Vehicle Engine Size Color Preference x 1 propane compact black good x 2 diesel medium gold bad x 3 diesel full white bad x 4 diesel medium red bad x 5 gasoline compact black good x 6 gasoline medium silver good x 7 gasoline full white bad x 8 gasoline compact silver 16 good

U Upper approximation Diesel Good x 2，x 3，x 4 Propane x 1 Gasoline x 5，x 6，x 8，x 7 17

U Lower approximation Diesel Good x 2，x 3，x 4 Propane x 1 Gasoline x 5，x 6，x 8，x 7 18

U Lower approximation Diesel Good x 2，x 3，x 4 Propane x 1 Gasoline x 5，x 6，x 8，x 7 Rule extraction by lower approximation：if propane then good 19

U Engine + Size Good Diesel Medium ｘ 2，x 4 Propane Compact x 1 Gasoline Compact ｘ 5，x 8 Gasoline Medium x 6 Diesel fullｘ 3 Gasoline full ｘ 7 20

U Engine + Color Good Diesel ｘ 2 Gold Propane Black x 1 Gasoline Silver ｘ 6，x 8 Gasoline Black x 5 Diesel ｘ 3 White Diesel ｘ 4 Red Gasoline ｘ 7 White Two attributes out of thee are sufficient → reduct (reduced set of attributes)21

What is MODE? Multi-Objective Design Exploration (MODE) Multi-objective Genetic Algorithm Computational Fluid Dynamics Step 1 Multi-objective Shape Optimization Design Database Visualization and Data Mining Design Knowledge Step 2 Knowledge Mining Data mining: maps, patterns, models, rules 22

Small Jet Aircraft R&D Project FSW (Friction Stir Welding) New Light Composite Material Advanced Human-Centered Cockpit Advanced Higher L/D Wing Health Monitoring System for LRU Optimized High Lift Device More Electric Aero-Structure Multi-Disciplinary Design Optimization R&D Organization New Energy and Industrial Technology Development Organization (NEDO) Mitsubishi Heavy Industries R&D Activities Research Collaboration Japan Aerospace Exploration Agency (JAXA) Tohoku University Fuji Heavy Industries Japan Aircraft Development Corporation (JADC) 23

Present MODE System START Latin Hypercube Sampling CFD mesh Design variables NURBS airfoil END FEM mesh 3 D wing Data mining Wing-body configuration Kriging model & optimization module Definition of Design Space Initial Kriging model CFD (FP/Euler) Pressure distribution Load condition MOGA (maximization of EIs) No Yes Continue ? FLEXCFD Static analysis model Flutter analysis model Strength & flutter requirements Structural optimization code + NASTRAN Selection of additional sample points Aerodynamic & structural performance CFD&CSD module Design variables Mesh generation Update of Kriging model Aerodynamic & structural performance CFD&CSD 24

Optimization of Wing-Nacelle-Pylon-Body Configuration Shock wave occuring at inboard of pylon may lead to separation and buffeting 25

Definition of Optimization Problem -1 - Objective Functions Minimize 1. 2. 3. Drag at the cruising condition (CD) Shock strength near wing-pylon junction (-Cp, max) Structural weight of main wing (wing weight) ü Function evaluation tools ・ CFD： Euler code (TAS-code) ・ CSD/Flutter analysis： MSC. NASTRAN –Cp, max = 0. 29 x/c -CP distribution of lower surface @η=0. 29 26

Definition of Optimization Problem -2 - Design Variables ・ Lower surface of Airfoil shapes at 2 spanwise sections (η= 0. 12, 0. 29) → 13 variables (NURBS) × 2 sections = 26 variables ・ Twist angles at 4 sections = 4 variables 30 variables in total (dv 12, dv 13) (0, dv 1) (dv 10, dv 11) (dv 2, dv 3) (dv 8, dv 9) (dv 4, dv 5) = 0. 29 = 0. 12 (dv 6, dv 7) NURBS control points 27

Performances of baseline shape and sample points 0. 2 CD vs. –Cp, max vs. wing weight 0. 5 20 counts 20 kg AAis improved by 6. 7 counts in CD, 0. 61 in –Cp, max, Point Optimum. Point A Direction and 12. 2 kg in wing weight compared with the baseline Direction 20 kg CD vs. wing weight 20 counts Optimum Direction Point A 28

Definition of Configuration Variables for Data Mining l Xmax. L l Xmax. TC l spar. TC At wing root and pylon locations ↓ 10 variables 29

Visualization of Design Space SOM with 9 clusters 30

Analysis of Sweet–Spot Cluster l Handpick l Parallel coordinates l Extraction of design rules by discretization of configuration variables üVisualization üRough set 31

Handpick -Cp, max and dv 6 (Xmax. TC at pylon) Small dv 6 -Cp Large dv 6 0. 00 0. 20 0. 40 0. 60 0. 80 1. 00 1. 20 0. 00 0. 20 0. 40 0. 60 0. 80 Airfoil 1. 20 Airfoil -Cp x/c 1. 00 -Cp x/c Others Xmax. TC@η=0. 29 Analysis of Variance (ANOVA) 32

Visualization of SOM Clusters by Parallel Coordinates 1 4 7 2 5 8 3 6 9 33

Discretization of Configuration Variables by Equal Frequency Binning Index 34

Finding Design Rules by Visualization Sweet-spot cluster Airfoil parameters dv 2 Xmax. L @ = 0. 29 dv 6 Xmax. TC @ = 0. 29 dv 9 spar. TC @ = 0. 12 dv 10 spar. TC @ = 0. 29 35

Flowchart of Data Mining Using Rough Set Preparation of data Discretization of numerical data Reduction Generation of rules Free software ROSETTA Filtering Interpretation of rules 36

Generated rules to belong to sweet spot cluster with support of more than eight occurrence Rule Count dv 1([33. 08, 39. 30)) AND dv 2([40. 69, *)) AND dv 5([29. 65, 33. 61)) AND dv 7([15. 09, 15. 83)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 10 dv 1([33. 08, 39. 30)) AND dv 2([40. 69, *)) AND dv 3([8. 88, 9. 57)) AND dv 5([29. 65, 33. 61)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 10 dv 1([33. 08, 39. 30)) AND dv 3([8. 88, 9. 57)) AND dv 5([29. 65, 33. 61)) AND dv 6([39. 25, *)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 10 dv 1([33. 08, 39. 30)) AND dv 5([29. 65, 33. 61)) AND dv 6([39. 25, *)) AND dv 7([15. 09, 15. 83)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 10 dv 1([33. 08, 39. 30)) AND dv 2([40. 69, *)) AND dv 5([29. 65, 33. 61)) AND dv 6([39. 25, *)) AND dv 7([15. 09, 15. 83)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 10 dv 1([33. 08, 39. 30)) AND dv 3([8. 88, 9. 57)) AND dv 4([7. 54, *)) AND dv 6([39. 25, *)) AND dv 10([*, 10. 58)) => Cluster(C 6) 9 dv 1([33. 08, 39. 30)) AND dv 2([40. 69, *)) AND dv 3([8. 88, 9. 57)) AND dv 4([7. 54, *)) AND dv 10([*, 10. 58)) => Cluster(C 6) 9 dv 3([8. 88, 9. 57)) AND dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 6([39. 25, *)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 2([40. 69, *)) AND dv 3([8. 88, 9. 57)) AND dv 5([29. 65, 33. 61)) AND dv 8([12. 82, 13. 32)) AND dv 9([*, 12. 62)) => Cluster(C 6) 8 dv 2([40. 69, *)) AND dv 5([29. 65, 33. 61)) AND dv 7([15. 09, 15. 83)) AND dv 8([12. 82, 13. 32)) AND dv 9([*, 12. 62)) => Cluster(C 6) 8 dv 1([33. 08, 39. 30)) AND dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 7([15. 09, 15. 83)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 1([33. 08, 39. 30)) AND dv 3([8. 88, 9. 57)) AND dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 1([33. 08, 39. 30)) AND dv 4([7. 54, *)) AND dv 6([39. 25, *)) AND dv 7([15. 09, 15. 83)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 1([33. 08, 39. 30)) AND dv 2([40. 69, *)) AND dv 4([7. 54, *)) AND dv 7([15. 09, 15. 83)) AND dv 9([*, 12. 62)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 2([40. 69, *)) AND dv 3([8. 88, 9. 57)) AND dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 2([40. 69, *)) AND dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 7([15. 09, 15. 83)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 dv 4([7. 54, *)) AND dv 5([29. 65, 33. 61)) AND dv 6([39. 25, *)) AND dv 7([15. 09, 15. 83)) AND dv 10([*, 10. 58)) => Cluster(C 6) 8 37

Statistics of rule conditions and comparison with previous results Sweet Number Airfoil parameters dv 1 11 dv 1 Xmax. L @ = 0. 12 dv 2 9 dv 2 Xmax. L @ = 0. 29 dv 3 8 dv 3 max. L @ = 0. 12 dv 4 10 dv 4 max. L @ = 0. 29 dv 5 13 dv 5 Xmax. TC @ = 0. 12 dv 6 7 dv 6 Xmax. TC @ = 0. 29 dv 7 max. TC @ = 0. 12 dv 8 max. TC @ = 0. 29 dv 9 spar. TC @ = 0. 12 dv 10 14 dv 10 spar. TC @ = 0. 29 large small Xmax. TC spar. TC Xmax. L 38

Statistics of rule conditions for all objectives Sweet Cd Cp WW Number Airfoil parameters dv 1 11 1 1 5 dv 1 Xmax. L @ = 0. 12 dv 2 9 2 6 3 dv 2 Xmax. L @ = 0. 29 dv 3 8 5 6 4 dv 3 max. L @ = 0. 12 dv 4 10 3 5 11 dv 4 max. L @ = 0. 29 dv 5 13 8 1 7 dv 5 Xmax. TC @ = 0. 12 dv 6 7 6 3 3 dv 6 Xmax. TC @ = 0. 29 dv 7 9 5 6 5 dv 7 max. TC @ = 0. 12 dv 8 2 4 3 2 dv 8 max. TC @ = 0. 29 dv 9 9 2 2 3 dv 9 spar. TC @ = 0. 12 dv 10 14 9 8 8 dv 10 spar. TC @ = 0. 29 large small No large dv 10 Xmax. TC spar. TC Xmax. L 39

Conclusions Multi-Objective Design Exploration (MODE) has been proposed Visualization and data mining based on SOM Regional-jet design has been demonstrated Wing-nacelle-pylon-body configuration üSOM reveals the structure of design space and visualizes it üAnalysis of the sweet-spot cluster leads to design rules 40

Acknowledgements l Prof. Shinkyu Jeong and Dr. Takayasu Kumano l Mitsubishi Heavy Industries l Supercomputer NEC SX-8 at Institute of Fluid Science l Prof. Yasushi Ito, University of Alabama at Birmingham, for Edge. Editor (mesh generator) l Prof. Kazuhiro Nakahashi, Tohoku University, for TAS (unstructured-mesh flow solver) l Mr. Hiroyuki Sakai, TIBCO Software Japan, Inc. , for Decision. Site (data visualization) 41

Mitsubishi Regional Jet (MRJ) l First flight due 2011 l Let me know if you are interested in a special offer! 42