Optimization and Probabilistic Analysis Using LS-DYNA

Transcription

1 LS-OPT Optimization and Probabilistic Analysis Using LS-DYNA Nielen Stander Willem Roux Tushar Goel Livermore Software Technology Corporation

2 Overview Introduction: LS-OPT features overview Design improvement Reliability & Robustness LS-OPT technologies overview Examples Variable Screening Metamodel-based Optimization Multi-Objective Optimization Parameter Identification 2

3 LS-OPT Features Design Improvement and Optimization Best multi-criterion designs Parameters Continuous Discrete (underlying continuous, e.g. off-theshelf plate thickness) Integer (e.g. material types, binary) Multiple cases/disciplines 3

4 LS-OPT Features Reliability and Robustness Reliability: Constrain probability of failure Robust Design: Minimize Standard Deviation of response Consistent product performance Reliability-based Design Optimization (RBDO) Incorporates Reliability and Robustness into design improvement Identify sources of uncertainty in the FE models: Outlier Analysis 4

5 Outlier Analysis LS-OPT Features Objective: repeatable performance of design Standard deviation of x-displacements of each node (120 runs) Deterministic (Meta-Model) Residual (Outliers) Courtesy Daimler AG (2003) 5

6 LS-OPT Features Schedule/monitor multiple Dyna runs across network Queuing systems: LSF, PBS, SLURM, etc. Interfaces for pre-processors ANSA, TrueGrid, etc. LS-DYNA integration Checking of Dyna keyword files (*DATABASE_) Importation of design parameters from Dyna keyword files (*PARAMETER_) Monitoring of Dyna progress Result extraction of most Dyna response types D3plot compression (node and part selection) 6

7 LS-OPT Core Technologies Optimization methods Sequential Response Surface Method polynomials Sequentially Updated Metamodel Methods Uses global approximations e.g. Neural Nets (FF), RBF Updated Space Filling Experimental Design D-Optimality Criterion (polynomials) Space Filling (FF & RBF) Other Optimization solvers (core solvers) LFOPC Leapfrog Optimizer for Constrained Optimization. (Gradient-based) NSGA-II (Non-dominated Sorting Genetic Algorithm) Also used for direct solution 7

8 Metamodel Types in LS-OPT Response Surface Methodology (RSM) Polynomial-based Typically regional approximation (especially linear) Linear regression Feedforward Neural Networks (FF) Simulation of a biological network, sigmoid basis function Global approximation Nonlinear Regression: more expensive Radial Basis Function Networks (RBF) Bell curve type basis functions in a linear system Global approximation Linear Regression (assuming constant spread and center) User-defined Dynamically linked (.so,.dll) 8

9 Radial Basis Function Networks Network construction Linear output layer: Y ( x, a) H 0 + ah f h= 1 = a ( ρ ) h Hidden layer: ρ h f ( ρ) K 2 h0 ( xk X hk ) k = 1 = r = e ρ Center: X h = ( X h1,..., X hk ) 9

10 Applications of optimization Multidisciplinary Design Optimization Crashworthiness (full vehicle, head impact, knee impact) Biomechanical optimization (surgical procedures) System and Material Identification Biomechanical properties Sheet metal Concrete Airbag properties Dummy calibration Spring-damper systems Process design Metal forming (formability, springback) 10

11 Crash optimization Design of structures subject to impact and dynamic loading Computationally intensive: Requires compute clusters Courtesy Neal Patel Minimize effort by sparse sampling and surrogate models Can also use direct optimization: GA 11

12 Variable Screening From regression Analysis (sensitivity) 90% 0 Uncertainty of variable Importance of Variable 12

13 Variable Screening: ANOVA chart Normalized Sensitivity Error bar: 90% Confidence Interval Note: Values are normalized with respect to design space 13

14 Variable Screening: Example Crash model elements Displacement = 552mm Stage1Pulse = 14.34g Stage2Pulse = 17.57g Stage3Pulse = 20.76g BIW model elements Torsional mode 1 Frequency = 38.7Hz Courtesy DaimlerChrysler 14

15 Variable Screening: Parameters Left and right apron Shotgun outer and inner Left and right cradle rails Inner and outer rail Front cradle upper and lower cross members 15

16 Variable Screening: ANOVA 16

17 Variable Screening: ANOVA 17

18 Design Variable 2 Optimization Sequential Metamodel-based Optimization Region of interest 2 3 start optimum RSM: Use only points from current iteration NN, RBF: Use all available points Design Space Design Variable 1 18

19 Optimization: Example Crash model BIW model elements elements Intrusion = 552mm Torsional mode 1 Stage1Pulse = 14.34g Frequency = 38.7Hz Stage2Pulse = 17.57g Stage3Pulse = 20.76g Courtesy DaimlerChrysler 19

20 Two Design Variables (Thickness) Left and right cradle rails (X) Inner rails (Y) 20

21 Sampling: Space Filling Method Iteration 1 Start 21

22 Sampling: Space Filling Method Iteration 2 Opt 1 Start 22

23 Sampling: Space Filling Method Iteration 3 Opt 2 Start 23

24 Sampling: Space Filling Method Iteration 4 Opt 3 Start 24

25 Optimization Design Variables (Thickness) Left and right apron Shotgun outer and inner Left and right cradle rails Inner and outer rail Front cradle upper and lower cross members 25

26 Design Formulation Design Objective: Minimize (Mass of components) Design Constraints: Intrusion < mm Stage1Pulse > 14.58g Stage2Pulse > 17.47g Stage3Pulse > 20.59g 41.38Hz < Torsional mode 1 frequency < 42.38Hz Crashworthiness design variables: 4 screened out of 7 total Rails (inner and outer); Aprons; Cradle rails NVH design variables: 7 (all) Crashworthiness responses: Intrusion, Stage Pulses NVH responses: Mass, Frequency, Mode number (for tracking internally) 26

27 Metamodel comparison: Optimization % 0.98 Mass 28% Mass Constraint violation Mass (RSM) Mass (NN) Max. Viol. (RSM) (Computed) Max.Viol. (NN) (Computed) Max.Viol. (NN) (Predicted) Max. Viol. (RSM) (Predicted) 24% 20% 16% 12% 8% 4% Maximum Constraint Violation % Number of Crash Simulations -4% 27

28 Pareto Optimal Front Tradeoff: Mass (NVH model) vs. Intrusion (Crash model) Pareto Optimal Front Baseline Optimum 28

29 Instrument panel with knee bolster system Courtesy: Ford Motor Company 29

30 Instrument panel: LS-DYNA Simulation LS-POST 30

31 Instrument panel: Design Variables 4 Screened out of 11 total Width Gauge Radius Gauge Depth Width Radius Width Gauge Depth Depth 31

32 Instrument panel: Design Formulation Design Objective: min ( max (Knee_F_L, Knee_F_R) ) Design Constraints: Left Knee intrusion < 115mm Right Knee intrusion < 115mm Yoke intrusion < 85mm Design variables Reduced from 11 to 4 (ANOVA) 32

33 Instrument panel: Optimization Knee Force L Knee Force (RSM) L Knee Force (RSM) (pred) R Knee Force (RSM) R Knee Force (RSM) (pred) L Knee Force (NN) L Knee Force (NN) (Pred) R Knee Force (NN) R Knee Force (NN) (Pred) Number of Simulations 33

34 Instrument panel: Tradeoff plot Maximum knee force vs. R Knee Intrusion Baseline Line of optimum designs Opt 34

35 Example: Head Impact A-pillar Trim Rib 0 ms 7 ms 35

36 Head Impact Side View 36

37 Head Impact: Design Formulation Design objective Minimize hic-d = * hic Design variables Trim thickness Rib thickness { independent so they Rib height influence the positions of the outer ribs Number of ribs Rib spacing 37

38 Strategy TrueGrid pre-processor Parametric mesh adaptivity: constant element size = 7mm nribs is continuous: nearest integer used by TrueGrid (or LS-OPT) 38

39 Optimization History : HIC-d and Variables 39

40 BASELINE and OPTIMAL Designs: Variables 4 ribs Height = 6 11 ribs Height = 6.5 Optimum Baseline Thickness = 1 Thickness = 0.8 Thickness = 2 Thickness = 2.9 Spacing = 60 Spacing = 14 All dimensions in mm 40

41 Acceleration History: Baseline Vs. Optimal HIC-d = 1450 HIC-d =

42 Multi-Objective Optimization Many optimal solutions Solve using Multi- Objective Genetic Algorithm NSGA-II Algorithm requirements: Convergence Spread (diversity of solutions) Min f 2 Min f 1 42

43 Direct Multi-Objective Optimization Vehicle Crashworthiness Problem Crash Min. (Mass, Intrusion) Subject to: Intrusion 551mm Stage 1 pulse > 14.5g Stage 2 pulse > 17.6g Stage 3 pulse > 20.7g 41.38Hz freq 42.38Hz Vibration 7 Crash variables 7 Vibration variables (2 discrete) 43

44 Direct Multi-objective optimization Simulation statistics IBM x3455 cluster. 40 nodes (160 cores) Queuing through Loadleveler Crash simulation time 3,400-3,900 sec Modal analysis time 40 sec Population: 80 Generations: 100 Total of 8,000 crash runs + 8,000 modal analysis runs (run to convergence!) 44

45 Pareto optimal front history 45

46 Direct Multi-Objective Optimization Example 2: Crash 46

47 Design criteria Minimize Mass Acceleration Maximize Intrusion Time to zero velocity 9 thickness variables of main crash members Intrusion < 721 Stage 1 pulse < 7.5g Stage 2 pulse < 20.2g Stage 3 pulse < 24.5g 47

48 Simulation statistics 640-core HP XC cluster (Intel Xeon nodes of 2 quad-core) Queuing through LSF Elapsed time per generation ~ 6 hours Population: 50 Generations: 20 Total of 1,000 crash runs 48

49 Results Minimize Mass 0.3% Acceleration 45% Maximize Intrusion 1% Time to zero velocity 10% Intrusion < 721 ( ) Stage 1 pulse < 7.5g ( g) Stage 2 pulse < 20.2g ( g) Stage 3 pulse < 24.5g ( g) 49

50 Metal Forming Criteria Types Thickness, Thickness reduction Forming Limit criterion based on in-plane principal strains Average principal stress 50

51 Metal Forming Criteria FLD criterion 51

52 Metal Forming Criteria FLD Criterion 52

53 Metal Forming Criteria Example: Stamping With LS-DYNA 53

54 Metal Forming Deformed Blank 54

55 Metal Forming Parameters 55

56 Metal Forming Design criteria Design Objective: Minimize: Maximum Radius Design Constraints: Maximum thinning (Δt) < 20% FLD < 0 Radius design variables: 3 radii: r1, r2, r3 (see diagram) FE model: Adaptive meshing 56

57 Metal Forming Optimization History: Responses 57

58 Metal Forming Optimization History: Variables 58

59 Metal Forming FLD Improvement 59

60 Metal Forming Final Product Thickness Distribution Δt_max=

61 Parameter Identification Used for calibrating material or system properties Methodology uses optimization of the Mean Squared Error to minimize differences between test and computed results Response surfaces constructed at each point instead of for the total MSE MSE can be point-based or history-based Point-based: The target value has to be specified for each point (selected as a Composite in Responses panel) History-based: The target values can be specified in a history file and imported as a history. A single function computes the MSE 61

62 History-based Parameter Identification Test Points G Test results z 62

63 History-based Parameter Identification Test Points + Computed Curve G,F Computed curve: F(x,z) Response Surface constructed for each interpolated matching point Residual e Interpolated test curve G(z) Test results z 63

64 History-based Parameter Identification Mean Squared Error Weight (Importance of error) Response Surface Value Test Value Residual 1 P P W p= 1 i F i ( x) s i G i 2 = 1 P P W p= 1 i e i ( x) s i 2 Number of points Residual Scale factor (Normalization of error) Variables (material or system constants) 64

65 Material Identification: Concrete Material parameters, 9 test types, 20 different test sets Par. C00 UNC T00 DP PRS ISOcomp UNX UNX C07 TXC7 C14 TXC14 C20 TXC20 C34 TXC34 C69 TXC69 G K R X 0 W D 1 D 2 θ λ β η Multiple cases, shared variables 65

66 Material identification: Optimization (10 iterations) and stress vs. strain results Residual Principal Stress Difference (MPa) Triaxial (34MPa) A Triaxial (34MPa) B Triaxial (34MPa) C Computed Strain (zz) (%) Compressive Stress (zz) (MPa) Compressive strain (zz) (%) Computed UNC1 UNC3 UNC5 Tensile Stress (zz) (MPa) Computed Direct Pull A Direct Pull B Direct Pull C Direct Pull D Tensile Strain (zz) (%)