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Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space

Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space Shigeru Obayashi Institute of Fluid Science Tohoku University. Outline. Background Flow Visualization Multidisciplinary Design Optimization (MDO) Self-Organizing Map (SOM) Rough Set

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Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space

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

  2. 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

  3. Flow Visualization -1 Flow transition: Reynolds number

  4. Flow Visualization -2 Stall: boundary layer separation

  5. Flow Visualization -3 Karman Votex

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

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

  8. f2 f2 f1 f1 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 = f1 + f2 • Other analytical methods • Normal-Boundary Intersection Method • Aspiration Level Method • Multi-Objective Evolutionary Algorithms (MOEAs) • Population-based search Gradient-based method MOEAs

  9. f1 Pareto Front f2 f1 f1 Pareto front Pareto front f2 f2 How to Understand MOP Extreme Pareto Solution f1 X Arithmatic Average Improvement Extreme Pareto Solution Pareto front f2 Global optimization is needed Visualization is essential! Data mining is required Design optimization→Design exploration

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

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

  12. 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

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

  14. Rough Set and Attribute

  15. U x1，x2，x3，x4，x5，x6，x7，ｘ８

  16. Propane Diesel x1 Good x2，x3，x4 U Gasoline x5，x6，x8，x7

  17. Propane Diesel x1 Good x2，x3，x4 U Upper approximation Gasoline x5，x6，x8，x7

  18. Propane Diesel x1 Good x2，x3，x4 U Lower approximation Gasoline x5，x6，x8，x7

  19. Diesel Good x2，x3，x4 U Lower approximation Propane x1 Gasoline x5，x6，x8，x7 Rule extraction by lower approximation：if propane then good

  20. Good U Engine + Size Diesel Medium ｘ2，x4 Propane Compact Diesel full x1 ｘ3 Gasoline Medium x6 Gasoline Compact Gasoline full ｘ7 ｘ5，x8

  21. Good U Engine + Color Diesel Gold ｘ2 Diesel White ｘ3 Propane Black x1 Diesel Red ｘ4 Gasoline Black Gasoline Silver x5 ｘ6，x8 Gasoline White ｘ7 Two attributes out of thee are sufficient → reduct (reduced set of attributes)

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

  23. FSW (Friction Stir Welding) New Light Composite Material Advanced Human-Centered Cockpit Small Jet Aircraft R&D Project 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) Research Collaboration Japan Aerospace Exploration Agency (JAXA) Mitsubishi Heavy Industries Tohoku University R&D Activities Fuji Heavy Industries Japan Aircraft Development Corporation (JADC)

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

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

  26. = 0.29 Definition of Optimization Problem -1 - Objective Functions - Minimize • Drag at the cruising condition (CD) • Shock strength near wing-pylon junction (-Cp,max) • Structural weight of main wing (wing weight) • Function evaluation tools ・ CFD： Euler code (TAS-code) ・ CSD/Flutter analysis： MSC. NASTRAN –Cp,max –Cp x/c -CP distribution of lower surface @η=0.29

  27. (dv12, dv13) (dv10, dv11) (0, dv1) (dv2, dv3) (dv8, dv9) (dv6, dv7) (dv4, dv5) 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 NURBS control points = 0.12 = 0.29

  28. Point A Point A Point A Optimum Direction Optimum Direction Optimum Direction 0.5 20 kg 0.2 20 kg 20 counts 20 counts Performances of baseline shape and sample points CD vs. –Cp,max –Cp,max vs. wing weight Point A is improved by 6.7 counts in CD, 0.61 in –Cp,max, and 12.2 kg in wing weight compared with the baseline CD vs. wing weight

  29. Definition of Configuration Variables for Data Mining XmaxL maxL XmaxTC maxTC sparTC At wing root and pylon locations ↓ 10 variables

  30. Visualization of Design Space SOM with 9 clusters

  31. Analysis of Sweet–Spot Cluster • Handpick • Parallel coordinates • Extraction of design rules by discretization of configuration variables • Visualization • Rough set

  32. -Cp -Cp Small dv6 Large dv6 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 Airfoil Airfoil -Cp -Cp x/c x/c XmaxTC@η=0.29 Handpick -Cp,maxand dv6 (XmaxTC at pylon) Others Analysis of Variance (ANOVA)

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

  34. Discretization of Configuration Variablesby Equal Frequency Binning Index

  35. Finding Design Rules by Visualization Sweet-spot cluster

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

  37. Generated rules to belong to sweet spot cluster with support of more than eight occurrence

  38. Statistics of rule conditions and comparison with previous results large small XmaxTC maxTC sparTC XmaxL maxL

  39. Statistics of rule conditions for all objectives large small No large dv10 XmaxTC maxTC sparTC XmaxL maxL

  40. 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 • SOM reveals the structure of design space and visualizes it • Analysis of the sweet-spot cluster leads to design rules

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

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

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