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Introduction to Automated Design Optimization

ME 475. Introduction to Automated Design Optimization. Analysis versus Design. ME 475. Analysis Given: system properties and loading conditions Find: responses of the system Design Given: loading conditions and targets for response

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Introduction to Automated Design Optimization

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  1. ME 475 Introduction to Automated Design Optimization

  2. Analysis versus Design ME 475 • 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

  3. Design Complexity ME 475 Design Complexity Design Time and Cost

  4. Specific Design Candidate Build Analysis Model(s) Modify Design (Intuition) $ Execute the Analyses Design Requirements Met? No Typical Design Process ME 475 Initial Design Concept HEEDS Time Money Intellectual Capital Yes Final Design

  5. A General Optimization Solution ME 475 Automotive Civil Infrastructure Biomedical Aerospace

  6. Automated Design Optimization ME 475 Basic Procedure: Plan Design Study Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization

  7. Automated Design Optimization ME 475 Identify: Objective(s) Constraints Design Variables Analysis Methods Note: These definitions affect subsequent steps Plan Design Study Create Parameterized Baseline Model Create HEEDS Design Model Execute HEEDS Optimization

  8. Automated Design Optimization ME 475 Create CAD/CAE Models for a Representative Design Plan Design Study Input File(s) Create Parameterized Baseline Model Execute Solver(s) Create HEEDS Design Model Output File(s) Execute HEEDS Optimization Validate Model

  9. Automated Design Optimization ME 475 Define Batch Execution Commands for Solvers Plan Design Study Define Input Files and Output Files Create Parameterized Baseline Model Define Design Variables and Responses Create HEEDS Design Model Tag Variables in Input Files and Responses in Output Files Execute HEEDS Optimization Define Objectives, Constraints, and Search Method

  10. Modify Variables in Input File Execute Solver in Batch Mode Automated Design Optimization ME 475 Plan Design Study Create Parameterized Baseline Model New Design (HEEDS) Extract Results from Output File Create HEEDS Design Model Converged? No Execute HEEDS Optimization Yes Optimized Design(s)

  11. CAE Portals ME 475 “When” “What” “Where”

  12. Tangible Benefits* ME 475 Crash rails: 100% increase in energy absorbed 20% reduction in mass Composite wing: 80% increase in buckling load 15% increase in stiffness Bumper: 20% reduction in mass with equivalent performance Coronary stent: 50% reduction in strain * Percentages relative to best designs found by experienced engineers

  13. Return on Investment ME 475 • 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.

  14. Topology Optimization ME 475 • Suggests material placement or layout based on load path efficiency • Maximizes stiffness • Conceptual design tool • Uses Abaqus Standard FEA solver

  15. Early in the design cycle to find shape concepts To suggest regions for mass reduction When to Use Topology Optimization ME 475

  16. B A Design of Experiments ME 475 • Determine how variables affect the response of a particular design • Design sensitivities • Build models relating the response to the variables • Surrogate models, response surface models

  17. When to Use Design of Experiments ME 475 • Following optimization • To identify parameters that cause greatest variation in your design

  18. Parameter Optimization ME 475 Minimize (or maximize): F(x1,x2,…,xn) such that: Gi(x1,x2,…,xn) < 0, i=1,2,…,p Hj(x1,x2,…,xn) = 0, j=1,2,…,q where: (x1,x2,…,xn) are the n design variables F(x1,x2,…,xn) is the objective (performance) function Gi(x1,x2,…,xn) are the p inequality constraints Hj(x1,x2,…,xn) are the q equality constraints

  19. Parameter Optimization ME 475 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 on type of design landscape • Local searches may yield only incremental improvement • Number of parameters may be large

  20. Selecting an Optimization Method ME 475 • Gradient-Based • Simplex • Simulated Annealing • Response Surface • Genetic Algorithm • Evolutionary Strategy • Etc. • Design Space depends on: • Number, type and range of variables and responses • Objectives and constraints

  21. SHERPA Search Algorithm ME 475 • 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 and local search performed together • Adaptive • Each “method” adapts itself to 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

  22. SHERPA Benchmark Example ME 475 Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars) Design variables: H, h1, b1, b2 Objective: Minimize mass Constraints: Stress, Deflection

  23. SHERPA Benchmark Example ME 475 Find the cross-sectional shape of a cantilevered I-beam with a tip load (4 design vars) Effectiveness and Efficiency of Search (Goal = 1)

  24. Advantages of SHERPA ME 475 • Efficient • Requires fewer evaluations than other methods for many problems • 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 • Robust • 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

  25. Nonlinear Optimization Problems ME 475 • 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

  26. Crush zone Crush zone Example: Hydroformed Lower Rail ME 475

  27. Shape Design Variables ME 475 67 design variables: 66 control points and one gage thickness z y rigid wall lumped mass x arrows indicate directions of offset crush zone cross-section

  28. Optimization Statement ME 475 • Identify the rail shape and thickness • Maximize energy absorbed in crush zone • Subject to constraints on: • Peak force • Mass • Manufacturability

  29. Optimized Design ME 475

  30. Validation ME 475

  31. Lower Rail Benefits ME 475 • Compared to 6 month manual search: • Peak force reduction by 30% • Energy absorption increased by 100% • Weight reduction by 20% • Overall crash response resulted in equivalent of FIVE STAR rating

  32. Future Gen Passenger Compartment ME 475 Side Impact Roof Crush Mass improvement in safety cage: 30 kg (about 23%)

  33. Rack Hall-effect Device Holder Cover Magnets Sensor – Magnetic Flux Linearity ME 475 Displacement S N 6.0 mm S N Magnetic Circuit

  34. Sensor – Magnetic Flux Linearity ME 475 Compared to previous best design found: • Linearity of response ~ 7 times better • Volume reduced by 50% • Setup & solution time was 4 days, instead of 2-3 weeks

  35. Front Suspension ME 475 Picture taken from MSC/ADAMS Manual

  36. Problem Statement ME 475 Determine the optimum location of the front suspension hard points to produce the desired bump steer and camber gain.

  37. Results ME 475

  38. Piston Design for a Diesel Engine ME 475 • Piston pin location is optimized to reduce 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.

  39. Piston Design for a Diesel Engine ME 475 • 110 designs were evaluated 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.

  40. Soft Tissue Membrane Inflation ME 475 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), 812-819 Courtesy of Jeffrey Bischoff, Zimmer Inc.

  41. Optimization Progression ME 475 R2 1.6 1.8 2.0 0 50 100 150 Iteration

  42. Polymer Property Calibration ME 475 Rate Sensitive Polymer: Neo-Hookean material model with a four-term Prony series Five undetermined coefficients (design variables)

  43. Stent Shape Optimization ME 475 LOADCASE 1 Expand the stent in the radial direction by 8.23226 mm. LOADCASE 2 Crimp the annealed stent by 2.0 mm. ANNEAL

  44. Stent – Subsystem Design Model ME 475

  45. BASELINE DESIGN (Provided) Stent – Baseline and Final Designs ME 475 FINAL DESIGN (Found by HEEDS) Max. Strain = 0.99% Max. Strain = 3.3%

  46. Example: Frame Torsional Stiffness ME 475 Goal: Maximize torsional stiffness with no increase in mass

  47. Loading and Optimization Statement ME 475 Objective: Minimize deflection of unsupported corner Constraints: mass < baseline model max von mises stress < baseline model first 3 modal frequencies > baseline model

  48. Design Variables ME 475 10 shape parameters: 5 each for two cross members 7 thickness variables: 3 each for two cross members 1 for the longitudinal rails

  49. Design Results ME 475 • 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

  50. Design of a Composite Wing ME 475 • Design variables: • Number of plies • Orientation of plies • Skin, spars, tip • Objectives, Constraints: • Minimize mass • Buckling, stiffness, failure constraints • Analysis Tool: • Abaqus

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