CLEMSON UNIVERSITY S TACOM/ARC PROJECTS GEORGES FADEL MECHANICAL ENGINEERING

Transcription

1 1 CLEMSON UNIVERSITY S TACOM/ARC PROJECTS GEORGES FADEL MECHANICAL ENGINEERING

2 2 PROJECTS COMPUTER SCIENCE CORBA METRICS MODULE Drs. McGregor, Malloy PROBLEM SOLVING ENVIRONMENT Drs. Stevenson, Jacobs SOLDIER SCANNING MODULE Dr. Pargas VIRTUAL ENVIRONMENT MODULE Dr. Geist Microsoft PowerPoint Presentation Movie Clip (MOV) Microsoft PowerPoint Presentation

3 3 PROJECTS (cont.) MECHANICAL ENGINEERING COMPONENT CONFIGURATION Dr. Georges Fadel CONCEPT GENERATOR MODULE Dr. Wei Chen Microsoft PowerPoint Presentation Microsoft PowerPoint Presentation

4 4 ONGOING PROJECTS Investigate Multiobjective Optimization Approaches to Vehicle Suspension Design Develop Rubberband Optimization Algorithm to Facilitate Packing

5 1 Configuration Design Optimization Method Georges Fadel Mechanical Engineering Department Clemson University May 1999 Based on the work of: Pierre Grignon, Jinhua Huang, Oliver König, Yusheng Li

6 2 Real Configuration Design Problems Initial Goal Car Engine and Aerospace Components CDPs. Center of Gravity Volume Maintainability Cooling Vibrations Electromagnetic interference Connectivity... Introduction

7 3 Configuration Design Context System Design Part Design Connectors choice Shape design Materials Configuration choice 1 3 Product Design Understanding Specification Development Logistics 2 Conceptual Design Design Introduction

8 4 CDP Initial Basis Several Freeform Components Functional Connections Assembly Thousands of Variables Hundreds of Constraints Constraint Satisfaction Problem Analysis

9 5 CDPs As Multi Objective Optimization Problems Add Multiple Objectives Constrained Multi-criteria Optimization problem involving non-linear constraints and objectives. Analysis

10 6 Multi Objective Optimization Problem Formulation F : x -> {f1 [x], f2[x], f3 [x]} x = { x i } i = 1.. n H k : x -> H k [x] = (Functional Links -> Geometric Constraints) x li <= x i <= x ui for 1 <= i <= n Find Several a such that F[a]is non-inferior and H k [a] = ; for all k Formulation

11 7 Multi Objective optimization and Optimal Solutions Non-Inferiority Objective Space objective 4 B obj2 4 A t C obj1 Formulation

12 8 CDPs Status Non Linear (Discrete/Continuous) Objective Functions - Break Hierarchy Linear and Non Linear Equality Constraints Thousands of Variables Several Solutions CAR Front Under hood Motor Back Gas Tank Formulation

13 9 CDPs Simplifications Assumptions Too Many Variables Too Many Constraints Objectives Break Hierarchy Non Linear Objectives Several Solutions Parts are defined Variables = Authorized relative and absolute motion between components Selected Components Generalized Packing Problem Formulation

14 1 Genetic Algorithms Principles Coding: Individuals: x1 x2 X(x1,x2) -> genom e fitness fitness x1 P o p u latio n j x2 Selection - Two parents are selected according to their fitness. Reproduction - The two parents are m ated and "give birth" to two children. Mutation - The genom es of the children have a chance to be random ly altered in order to introduce diversity. x1 P o p u latio n j+ 1 x2 Reproduction process: Crossover Parents genom e parent 1 genom e parent 2 C h ild re n genom e child 1 genom e child 2 Method

15 11 Handling Non-linearity and Multiple Pareto Genetic Algorithms. P Conventional GA Population 1 Genome Objective 1 F1 ( X,.., X N-1) P1 P2 Variable Space X X1 XN-1 Pp Objective 2 F2 ( X,.., X N-1) solutions Select solutions based on ranking Problem requiring niching to diversify the solution Requires additional coding P (F1,F2) Pp (Fp1,Fp2) P1 (F11,F22) Objective Space Method

16 12 Handling Non-linearity and Multiple solutions Sets based Population with a Genetic Algorithm. C Sets GA Population C1 C2 CC Variable Space Ci (Fi) Objective Space F2 F2 F2 EP2 1 Genome P P1 P2... Pp X X1 XN-1 P (F1,F2) P1 (F11,F22)... Pp (Fp1,Fp2) Reference Pareto set Cloud to evaluate F1 F1 F1 Objective 1 F1 ( X,.., X N-1) Objective 2 F2 ( X,.., X N-1) Σ i Rank ( P i [ f1[xi], f2[xi], f3[xi] ] ) / (N+M) 2 Method

17 13 Method Status Number of Variables Equality Constraints Non Linear Objectives Multiple Solutions Reduced Constant shapes Selected Components Relative Motion GA Set based GA Populations

18 14 Unconstrained Non-Linear Multi Objective Optimization Problem? Interference between components G j : x -> Gj[x] < j = 1..N (Number of Components) Penalty Functions : Pty = f(gj[x] ) Σ i Rank ( P i [ f1[xi], f2[xi], f3[xi] ] ) / (N+M) 2 Σ i Rank ( P i [ f1[xi] - Pty, f2[xi] - Pty, f3[xi] - Pty] ) / (N+M) 2 Many Local Optima Method

19 15 Configuration Optimization Design Method Definition Start Encode each variable X i according to its bounds [Li, Ui ] Generate First Population of Clouds Randomly. Conventional GA Part Calculate Clouds Fitness Evolve 1 Generation End yes Maximum number of generation or convergence reached? yes Final Run? no Update the variables bounds [L i, Ui] Method

20 16 Complexity Classification Combinatorics Rg high N closely packed few solutions high N loosely packed few solutions GS + LS CDP 4 A high N loosely packed many solutions high N closely packed many solutions 2 CDP 1 CDP 3 CDP 2 low N closely packed few solutions LS low N closely packed many solutions low N loosely packed few solutions B Dil FA (Log) low N loosely packed many solutions Dil sol (Log) GS : Global Search. LS : Local Search. GS + LS : Global and Local Search Combined. Complexity

21 17 Three Criteria Characterizing the Pareto set Distances from the extreme planes. Objective 2 TEP2 TEPts 2 Real Pareto Set Point Spreading. Flatness. Objective2 EP 2 Bounds of the Real Pareto set Reference Pareto set (best found by CDOM) Best Solution So Far TEPts 1 EP 1 TEP 1 Objective 1 EP 2 TEPts 2 Ideal Reference Line Objective 2 Target Pareto Set Actual Reference Line TEPts 1 EP2 Best Solution So Far EP 1 Objective 1 A EP1 Objective 1 Bounds of the Real Pareto set (TEPs) Extreme Points Variation Region Solution Set Variation Region Bounds of the real Pareto set Reference Pareto set (best front) Quality

22 18 Test Cases Cubes Target Center of Gravity Removal Direction Compactness Engineering Applications Satellite Car Engine Tests

23 19 1 Results Cog (1) (5) 1 Maint 5 (6) (2) 39 Compacity Mnt Cog Compacity Tests

24 2 Car Engine CDP Description -1 y x z -1 y z -1-1 x 1 y z x y x z y -5 2 y 2-25 x x z z y z x 25 5 Tests

25 21 Car Engine CDP Results Inertia Mnt Cog.2 Tests

26 22 Achievements Configuration Design Optimization Method + Provides Multiple Optimal Solutions + No Assumptions on Objectives + Any type of System (Free form) + Respects Constraints + Easy Collaboration with the Engineer Complexity Classification + Gives accurate predictions Conclusion

27 23 Drawbacks - Small Number of Variables - Complexity Classification based on Approximation - Complexity Applied to Each Objective Alone Conclusion

28 24 Future Work No Clear Correspondence between Complexity Classifications Add Rotations More Realistic Solids and Assemblies Better Architecture of the Code Conclusion

29 25 Extensions of the Research Approximations of the Pareto Set Multi-Material Optimization Vehicle Dynamics Others...

30 26 Modeling of Heterogeneous Objects HD - Modeling of Heterogeneous Objects Consisting of a Finite Number of Distinct Materials Product space: T = R 3 I including material dimension Specific point: [ x, m( x)] with material type m(x) HC - Heterogeneous Objects Consisting of two or more primary materials with Continuous Material Variation n Product space: T = R 3 R with n primary materials Specific point: [ x, v( x)] with material fraction vector v(x) MODELING

31 27 Heterogeneous Flywheel Design Jinhua Huang Optimal HD Profile - Cell-Based Weighting Method (f 1 = f 2 =.5) Optimal HD Volume Fraction Distribution for Cobalt - Cell-Based Weighting Method (f i =.5)

32 28 Heterogeneous Flywheel Design Optimal HC Profile - Basis-Function-Based Weighting Method (f i =.5) Optimal HC Volume Fraction Distribution for Cobalt - Basis-Function-Based Weighting Method (f i =.5)

33 29 Heterogeneous Flywheel Design Pareto Curve of Normalized Optimal Energy and Difference between Max and Min Von-Mises Stresses for Multi-Objective HD Optimization Design with Weighting Method for f 1 Varying from to 1

34 3 Application 3. Turbine Blade Mesh: 951 Elements Materials Typical Titanium Alloy Silicon Nitride Boundary Conditions Boundary Temperatures No Convection & Radiation Fitness function score = N ele i= 1 ( T score i T norm 2 work ( mat) ) with T work ( Ti) = Temp. [K] T work ( SiNi) = 1 12

35 Turbine Blade: Outlook Problem: Thermal Stresses Thermal expansion coefficients α α Ti Ce = 1 µ m m K = 3.3 µ m m K Solution Approaches 1:Minimize thermal stresses 31 score = N ele i= 1 score norm ( σ th( i) σ ref ) 2 Subject to: max( T < T min( T > T Ti( i) ) Ce( i) ) 2:Two-objective optimization 3:Material modeling with HC work _ Ti work _ Ti Stress [N/mm2]

36 32 Closure Optimization as a Design tool can be applied to complex problems such as configuration design or multi-material optimization Multi-objective approaches are needed to obtain Pareto Optimal Solutions Application to multi-material manufacturing is a novel and challenging research area

37 Generating animated sequences from 3D wholebody scans Roy P. Pargas, Daniel Mulfinger, Pushkar Deshmukh, Vaishali Chitre Department of Computer Science Clemson University Clemson, SC

38 Objective To generate animated sequences from a single 3D scan Process Subdivide human image into segments Map the segments to those of a human model Use human-motion simulation package Capture snapshots of the movement Assemble snapshots to create animated sequence

39 Three views of original image

40 Uncapped leg and arm segments

41 Capped arm and leg segments

42 Animated sequences using segments Original 3D image brian.stills.gif Postures Jack.GIF brian.gif Animations animation.gif

43 Free-form deformation Objectives Provide continuous and smooth movement Avoid discontinuities at segment ends (shoulders, knees) Finer control over body movement

44 Free-form deformation Create lattice structure around image Map image points to lattice points

45 Animated sequences using freeform deformation Arm and torso movement: 1 frames/second (Click on image)

46 Applications Visualization tool for simulation of activities involving humans Vehicle crash simulations Information about the forces within the vehicle that may affect human passengers to predict severity of injuries. AI simulations of autonomous human behavior Independent AI routines may generate actions and movements to be performed by simulated humans, and then transmit the actions to a visualization tool which displays the individual and independent human motions.