TECHNOLOGY. Introduction to Automated Design Optimization

Transcription

1 ME Introduction to Automated Design Optimization 1

2 Analysis versus Design ME Analysis Given: system properties and loading conditions Find: responses of the system Design Given: loading conditions and targets for response Find: system properties that satisfy those targets 2

3 Design Complexity ME 3

4 Typical Design Process ME HEEDS Initial Design Concept Specific Design Candidate $ Time Money Intellectual Capital Modify Design (Intuition) No Build Analysis Model(s) Execute the Analyses Design Requirements Met? Yes Final Design 4

5 A General Optimization Solution ME Automotive Civil Infrastructure Biomedical Aerospace 5

6 Automated Design Optimization ME Basic Procedure: Plan Design Study Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization 6

7 Automated Design Optimization ME Plan Design Study Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Identify: Objective(s) Constraints Design Variables Analysis Methods Note: These definitions affect subsequent steps 7

8 Automated Design Optimization ME Plan Design Study Create CAD/CAE Models for a Representative Design Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Input File(s) Execute Solver(s) Output File(s) Validate Model 8

9 Automated Design Optimization ME Define Batch Execution Commands for Solvers Plan Design Study Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization Define Input Files and Output Files Define Design Variables and Responses Tag Variables in Input Files and Responses in Output Files Define Objectives, Constraints, and Search Method 9

10 Automated Design Optimization ME Plan Design Study Modify Variables in Input File Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization New Design (HEEDS) Execute Solver in Batch Mode Extract Results from Output File Converged? No Yes Optimized Design(s)

11 CAE Portals ME When What Where

12 Tangible Benefits* ME Crash rails: Composite wing: Bumper: Coronary stent: 100% increase in energy absorbed 20% uction in mass 80% increase in buckling load 15% increase in stiffness 20% uction in mass with ihequivalent performance 50% uction in strain * Percentages relative to best designs found by experienced engineers 12

13 Return on Investment ME Reduced Design Costs Time, labor, prototypes, tooling Reinvest savings in future innovation projects Reduced Warranty Costs Higher quality designs Greater customer satisfaction Increased Competitive Advantage Innovative designs Faster to market Savings on material, manufacturing, mass, etc. 13

14 Topology Optimization ME Suggests material placement or layout based on load path efficiency Maximizes stiffness Conceptual design tool Uses Abaqus Standard FEA solver 14

15 When to Use Topology Optimization ME Early in the design cycle to find shape concepts To suggest regions for mass uction 15

16 Design of Experiments ME B Determine how variables affect the response of a particular design Design sensitivities A Build models relating the response to the variables Surrogate models, response surface models 16

17 When to Use Design of Experiments ME Following optimization To identify parameters that cause greatest variation in your design 17

18 Parameter Optimization ME Minimize (or maximize): F(x 1,x 2,,x n ) such that: G i (x 1,x 2,,x n ) < 0, i=1,2,,p H j (x 1,x 2,,x n ) = 0, j=1 1,2,,q where: (x 1,x 2,,x n ) are the n design variables F(x 1,x 2,,x n ) is the objective (performance) function G i (x 1,x 2,,x n ) are the p inequality constraints H j (x 1,x 2,,x n ) are the q equality constraints 18

19 Parameter Optimization ME Objective: Search the performance design landscape to find the highest peak or lowest valley within the feasible range Typically don t know the nature of surface before search begins Search algorithm choice depends d on type of design landscape Local searches es may yield only incremental improvement Number of parameters may be large 19

20 Selecting an Optimization Method ME Gradient-Based Simplex Simulated Annealing Design Space depends on: Number, type and range of variables and responses Objectives and constraints Response Surface Genetic Algorithm Evolutionary Strategy Etc. 20

21 SHERPA Search Algorithm ME Hybrid Blend of methods used simultaneously, not sequentially Aspects of evolutionary methods, simulated annealing, response surface methods, gradient methods, and more Takes advantage of best attributes of each approach Global l and local l search performed together th Adaptive Each h method adapts itself lfto the design space Master controller determines the contribution of each method to the search process Efficiently learns about design space and effectively searches even very complicated spaces Both single and multi-objective capabilities 21

22 SHERPA Benchmark Example ME Find the cross-sectional shape of a cantileve I-beam with a tip load (4 design vars) P h1 H b2 L h1 b1 Design variables: H, h1, b1, b2 Objective: Minimize mass Constraints: Stress, Deflection 22

23 SHERPA Benchmark Example ME Find the cross-sectional shape of a cantileve I-beam with a tip load (4 design vars) Effectiveness eness and Efficiency of Search (Goal = 1) Nor rmalized ave erage best so olution SHERPA GA SA NLSQP RSM Maximum allowable evaluations 23

24 Advantages of SHERPA ME Efficienti Robust Requires fewer evaluations than other methods for many yproblems Rapid set up no tuning parameters Solution the first time more often, instead of iterating to identify the best method or the best tuning parameters Better solutions more often than other methods for broad classes of problems Global and local optimization at the same time Easy to Use Only one parameter number of allowable evaluations Need not be an expert in optimization theory 24

25 Nonlinear Optimization Problems ME Usually involve nonlinear or transient analysis Gradients not accurate, not available, or expensive Multi-modal and or noisy design landscape Moderate to large CPU time per evaluation In other words, most engineering problems 25

26 Example: Hydroformed Lower Rail ME Crush zone Crush zone 26

27 Shape Design Variables ME 67 design variables: 66 control points and one gage thickness z rigid wall y x lumped mass crush zone arrows indicate directions of offset cross-section 27

28 Optimization Statement ME Identify the rail shape and thickness Maximize energy absorbed in crush zone Subject to constraints on: Peak force Mass Manufacturability 28

29 Optimized Design ME 29

30 Validation ME 30

31 Lower Rail Benefits ME Compa to 6 month manual search: Peak force uction by 30% Energy absorption increased by 100% Weight uction by 20% Overall crash response resulted in equivalent of FIVE STAR rating 31

32 Future Gen Passenger Compartment ME Side Impact Roof Crush Mass improvement in safety cage: 30 kg (about 23%) 32

33 Sensor Magnetic Flux Linearity ME Displacement N S 6.0 mm Rack Holder Hall-effect Device S Magnetic Circuit N Cover Magnets 33

34 Sensor Magnetic Flux Linearity ME Compa to previous best design found: Linearity of response ~ 7 times better Volume uced by 50% Setup & solution time was 4 days, instead of 2-3 weeks 34

35 Front Suspension ME Picture taken from MSC/ADAMS Manual 35

36 Problem Statement ME Determine the optimum location of the front suspension hard points to produce the desi bump steer and camber gain. HEEDS Toe Curve Optimization HEEDS Camber Curve Optimization el Travel (mm) Jounce -> <- Rebound LF Whe 25 Toe - Initial Design 20 Toe - Target <- Rebound LF Whee el Travel (mm) Jounce -> Camber - Initial Design Camber - Target <- Toe Out (deg) Toe in -> -25 Camber (deg) 36

37 Results ME HEEDS Toe Curve Optimization HEEDS Camber Curve Optimization <- Re ebound LF Wheel Travel (mm) Jounce -> Toe - Initial Design Toe - Target Toe - Final Design <- Rebo ound LF Wheel Tr ravel (mm) Jounc ce -> 25 Camber - Initial Design 20 Camber - Target Camber - Final Design <- Toe Out (deg) Toe in -> -25 Camber (deg) 37

38 Piston Design for a Diesel Engine ME Piston pin location is optimized to uce piston slap in a diesel engine at 1100, 1500, 2000, and 2700 RPM Design Variables: Piston Pin X location Piston Pin Y location Design Objectives: Minimize maximum piston impact with the wall Minimize total piston impact with the wall throughout the engine cycle. 38

39 Piston Design for a Diesel Engine ME 110 designs were evaluated ated for each engine speed (440 runs of CASE) Total computational time was approximately 0.5 days using a 2.4 GHz processor. Optimized pin offset was essentially identical to what was found experimentally on the dynamometer. 39

40 Soft Tissue Membrane Inflation ME A biaxial stress state suitable for interrogating nonlinear anisotropic properties of membranous soft tissue can be realized using membrane inflation Orthotropic nonlinear elasticity: four material parameters Drexler et al., J. Biomech. 40 (2007), Courtesy of Jeffrey Bischoff, Zimmer Inc.

41 Optimization Progression ME R Iterationti

42 Polymer Property Calibration ME Rate Sensitive Polymer: Neo-Hookean material model with a four-term Prony series Five undetermined coefficients (design variables) 42

43 Stent Shape Optimization ME LOADCASE 1 Expand the stent in the radial direction by mm. LOADCASE 2 Crimptheannealedstentby20mm 2.0 mm. ANNEAL 43

44 Stent Subsystem Design Model ME 44

45 Stent Baseline and Final Designs ME BASELINE DESIGN (Provided) FINAL DESIGN (Found by HEEDS) Max. Strain = 3.3% Max. Strain = 0.99% 45

46 Example: Frame Torsional Stiffness ME Goal: Maximize torsional stiffness with no increase in mass 46

47 Loading and Optimization Statement ME Objective: Minimize deflection of unsupported corner Constraints: mass < baseline model max von mises stress < baseline model first 3 modal frequencies > baseline model 47

48 Design Variables ME 10 shape parameters: 5 each hfor two cross members 7 thickness variables: 3 each for two cross members 1 for the longitudinal rails x5 t4 x1 x2 t1 t2 x3 x4 t3 48

49 Design Results ME Torsional stiffness increased by 12% height of cross members increased cross member locations moved toward the ends connection plate thicknesses decreased cross member thicknesses increased thickness of the rails remained constant Baseline Design Optimized Design 49

50 Design of a Composite Wing ME Design variables: Number of plies Orientation of plies Skin, spars, tip Objectives, Constraints: Minimize mass Buckling, stiffness, failure constraints Analysis Tool: Abaqus 50

51 Failure Index ME Baseline HEEDS: 30% uction in failure index 51

52 Deflection ME Baseline HEEDS: 15% uction in deflection 52

53 Buckling ME Baseline HEEDS: 80% increase in buckling load 53

54 Design of a Composite Wing ME 1.6 nts & zed Constrain Objective Normaliz Mass Failure Index Deflection Cycle Number Buckling Load increased by 80% Failure index decreased by 30% Bending stiffness increased by 15% Mass increased by 6% 54

55 Rubber Bushing ME Parametric model: 6 parameters D2 D1 Fixed D1 θ D3 D1 D4 D5 55

56 Rubber Bushing Target Response ME F o r c e (N) Displacement (mm) 10 mm Load deflection curve when the bushing is loaded to the left Load deflection curve while the bushing is loaded to the right 56

57 Rubber Bushing Final Design ME Final design: 57

58 Rubber Bushing Response ME Stiffness Comparison Chart 9.00E E E+07 Design Curve Final Curve Fo orce (0.001N) 6.00E E E E E E E Deflection (mm) 58