DYNARDO Dynardo GmbH Robustness & Reliability Analysis

Transcription

1 Robustness & Reliability Analysis 1

2 Start Robust Design Optimization Robust Design Variance based Robustness Evaluation Probability based Robustness Evaluation, (Reliability analysis) Optimization Sensitivity Study Single & Multi objective (Pareto) optimization CAE process (FEM, CFD, MBD, Excel, Matlab, etc.) Robust Design Optimization Methodology 2

3 How to define Robustness of a Design Intuitively: The performance of a robust design is largely unaffected by random perturbations Variance indicator: The coefficient of variation (CV) of the objective function and/or constraint values is smaller than the CV of the input variables Sigma level: The interval mean+/- sigma level does not reach an undesired performance (e.g. design for six-sigma) Probability indicator: The probability of reaching undesired performance is smaller than an acceptable value 3

4 Robustness Evaluation / Reliability Analysis Variance-based robustness evaluation measure product serviceability Safety and reliability for 1 & 2 (3) Sigma levels and identifies the most sensitive stochastic variables Possible with high number of stochastic variables Probability-based robustness evaluation (reliability analysis) measure product serviceability Safety and reliability for high reliability levels (3,4,5,6-Sigma) with small number of variables Possible with a limited number of stochastic variables 4

5 Definition of Uncertainties 5

6 Uncertainties and Tolerances Design variables Material, geometry, loads, constrains, Manufacturing Operating processes (misuse) Resulting from Deterioration Property SD/Mean % Metallic materiales, yield 15 Carbon fiber rupture 17 Metallic shells, buckling strength 14 Bond insert, axial load 12 Honeycomb, tension 16 Honeycomb, shear, compression 10 Honeycomb, face wrinkling 8 Launch vehicle, thrust 5 Transient loads 50 Thermal loads 7.5 Deployment shock 10 Acoustic loads 40 Vibration loads 20 Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace. Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris

7 DYNARDO ECCOMAS 2012 congress Dynardo GmbH 2012 Definition of Uncertainties Translate know how about uncertainties into proper scatter definition Yield stress Distribution functions define variable scatter Tensile strength Correlation of single uncertain values Correlation is an important characteristic of stochastic variables. spatial correlated thickness distribution 7

8 Design single scatter shapes Use of CAD-parameter or mesh morphing functions to design single scatter shapes Measured ed imperfection modelled imperfection Imperfection of cylindricity of truck wheel component by courtesy of Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, 8

9 Random Field Parametric Introduction of scatter of spatially correlated scatters need parametric of scatter shapes using random field theory. The correlation function represents the measure of waviness of random fields. The infinite correlation length reduced the random field to a simple random variable. Usually, there exist multiple scatter shapes representing different scatter sources. 9

10 DYNARDO RDO forming simulation Dynardo GmbH 2012 Use forming simulation to generate scatter fields 4. Mapping to crash mesh 3. Generation of n-imperfect formed parts using scatter field parametric 5. Run Robustness Evaluation of assembly including scatter from forming 2. Identification of most important scatter fields for scattering forming result values (thickness, hardening) 1. Running Robustness evaluation of forming simulation 10

11 Use measurements to generate Random Fields 4. Generate imperfect geometries using Random Field parametric 3. Identification tion of most important random fields for measured quantity (geometry) 5. Run Robustness s Evaluation to identify the most sensitive random fields 2. Trimming of initial FE-mesh regarding measurement or realization 1. Multiple Measurements from Manufacturing 11

12 Implementation of Random Field Parametric Introduction of spatial correlated scatter to CAE-Parameter (geometry, thickness, plastic values) 3. Generation of multiple imperfect structures using Random Field parametric 4. Running Robustness Evaluation including Random Field effects 2. Generation of scatter shapes using Random field parametric, quantify scatter shape importance 1. Input: process simulation or measurements 12

13 Variance-based Robustness Analysis 13

14 Which Robustness do You Mean? Robustness evaluation due to naturally given scatter Goal: measurement of variation and correlation Methodology: variance-based robustness evaluation Positive side effect of robustness evaluation: The measurement of prognosis quality of the response variation answer the question - Does numerical scatter significantly influence the results? 14

15 Statistic Measurements Evaluation of robustness with statistical measurements Variation analysis (histogram, coefficient of variation, standard variation, distribution fit, probabilities) Correlation analysis (linear, quadratic, nonlinear) including principal component analysis Forecast quality: Evaluation of Coefficient of Prognosis (CoP) including coefficients of determination (CoD)and coefficient of importance (CoI) 15

16 Advanced Statistic Measurements Advanced histogram options PDF fit (automatic/manual) Number of histogram classes PDF values ready for optislang input Limits with probabilities Probabilities with limit 16

17 Standardized and Automated Post Processing Example how the post processing is automated for passive safety at BMW The maximum from the time signal was taken. 17

18 Robustness Evaluation using optislang 1) Define the robustness space using scatter range, distribution and correlation 2) Scan the robustness space by producing and evaluating n (100) Designs 5) Identify the most important scattering variables 4) Check the CoI/CoP 3) Check the variation interval 18

19 Robustness Evaluation of NVH Performance Start in 2002, since 2003 used for Production Level How does body and suspension system scatter influence the NVH performance? Consideration of scatter of body in white, suspension system Prognosis of response value scatter Identify correlations due to the input scatter CAE-Solver: NASTRAN Up-to-date robustness evaluation of body in white have scattering variables Using filter technology to optimize the number of samples by courtesy of Will, J.; Möller, J-St.; Bauer, E.: Robustness evaluations of the NVH comfort using full vehicle models by means of stochastic analysis, VDI-Berichte Nr.1846, 2004, S , 19

20 DYNARDO ECCOMAS 2012 congress Dynardo GmbH 2012 Robustness Evaluation of break systems Start in 2007, since 2008 used for Production Level How does material and geometric scatter influence the break noise performance? Consideration of material and geometry scatter Break noise is a instability problem Identify correlations due to the input scatter CAE-Solver: NASTRAN, ABAQUS, ANSYS Up-to-date robustness evaluation have scattering variables Integration of geometric scatter via random fields 1. Define the Uncertainties 4. Post processing 2. Simulate random m parametersp 3. Generate set of random specimen, replace in FE assembly to compute by courtesy of X2 X1 Will, J.; Nunes, R.: Robustness evaluations of the break system concerning squeal noise problem, Weimarer Optimierungs- und Stochastiktage 2009, 20

21 Robustness Evaluation of Forming Simulations Start in since 2006 used for production level Consideration of process and material scatter Determination of process robustness based on 3- Sigma-values of quality criteria Projection and determination of statistical values on FE-structure necessary 1. Variation der Eingangsstreuungen mittels geeigneter Samplingverfahren 2. Simulation inkl. Mapping auf einheitliches Netz CAE-Solver: LS-DYNA, AUTOFORM and others 3. statistische Auswertung und Robustheitsbewertung by courtesy of Will, J.; Bucher, C.; Ganser, M.; Grossenbacher, K.: Computation and visualization of statistical measures on Finite Element structures for forming simulations; Proceedings Weimarer Optimierung- und Stochastiktage 2.0, 2005, Weimar, Germany 21

22 Das Bild kann zurzeit nicht angezeigt werden. DYNARDO Dynardo GmbH 2012 Why SoS and What is SoS? Why: Engineers need to evaluate statistical data on the structure to locate hot spots of variation as well as investigate correlations What: A post processor for Statistics on finite element Structures Visualization of descriptive statistics on the structure Visualization of correlations between random input and structural results Visualization of quality performance (QCS) Identification of scatter shapes using Random Fields Key features: locale hot spots of variation Data reduction and smoothing by mesh coarsening Identification of relevant scatter shapes Vizualisation statistics of eroded (failed) elements 22

23 Statistical post-processing on FE-meshes Motivation: - Visualization of statistical measurements - Identification of hot spots, - Identification of correlation structure (random fields) 1. Import data (multiple simulation runs or measurements) ments) 2. Visualize variation, correlation, identify ify random field shapes 3. Export local statistics and imperfection amplitudes to optislang for further post-processing 23

24 Statistical post-processing on FE-meshes SoS is the tool to answer the questions: Where? Locate hot spots of highest variation and/or extreme values, which may cause lack of performance or quality. Why? Find the input parameters which cause scatter of the results, by analysing correlation/cod between random inputs and spatially distributed results, export to optislang for MoP/CoP analysis. 24

25 SoS application crash simulation Stringer in a car body subject to crash simulation 55 random inputs: sheet thickness and material parameters (also of other parts), load parameters (velocity, barrier angle etc.) Observed result: remaining effective plastic strain [Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts. SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.] 25

26 SoS application crash simulation Analysis of a car structure subject to random crash load case Decomposition of plastic strain random field Analysis of largest influence by MoP/CoP in optislang [Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts. SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.] 26

27 SoS - Eroding elements Eroding percent plot shows the percentage of eroded elements. General eroding information. Green area: no elements eroded. Red area: there were eroded elements. 27

28 SoS Validated Global and Local Statistics Variation, mean value, correlation, Histogram, linear & quadratic QCS using SoS on FE-structure correlation, CoD, CoI, CoP and Anthill plots using optislang at local nodal or element values Selection of nodal/element results in SoS and export to optislang *.bin CoD linear base Correlation R-value Cotrrelation Y-tolerance 28

29 SoS - Applications - use SoS for robustness evaluation of forming processes - use SoS for visualization and hot spot investigation at robustness evaluations in crashworthiness or drop test applications - use SoS for the identification of random fields from simulation or measurements by courtesy of 29

30 Standardized and Automated Post Processing Productive Level needs standardized and automated post processing! 1. Check variation of plasticity, failure, intrusions. 2. Identify the beginning of the phenomena in time and use SoS to identify the source of variation 3. Summarize variation and correlation 30

31 Summary SoS Statistic on Structure The post processor for Statistics on finite element Structures - Statistic Measurements - Single Designs - Differences between Designs - Variation interval - Minimum/Maximum - Mean Value - Standard deviation - Coefficient of variation - Quantile (± - Correlation & CoD - Linear correlation & CoD - At nodal/element level - Process quality criteria Cp, Cpk process indices - Random field generation - Scatter shape extraction and visualisation 31

32 Robustness Evaluation of Passive Safety Consideration of scatter of material and load parameters as well as test conditions Prognosis of response value variation = is the design robust! Identify correlations due to the input scatter Quantify the amount of numerical noise CAE-Solver: MADYMO, ABAQUS Start in 2004, since 2005 used for productive level Goal: Ensuring Consumer Ratings and Regulations & Improving the Robustness of a System by courtesy of Will, J.; Baldauf, H.: Integration of Computational Robustness Evaluations in Virtual Dimensioning of Passive Passenger Safety at the BMW AG, VDI-Berichte Nr. 1976, 2006, Seite , 32

33 Robustness Evaluation Crashworthiness Start in 2004 since 2007 use for Production Level Consideration of scatter of thickness, strength, geometry, friction and test condition CAE-Solver: LS-DYNA, Abaqus Prognosis of intrusions, failure and plastic behavior Identify Coefficient of Prognosis and nonlinear correlations Check model robustness scattering variables Introduction of forming scatter via Random Fields by courtesy of the Daimler AG In comparison to robustness evaluations for NVH, forming or passive safety, crashworthiness has very high demands on methodology and software! by courtesy of Will, J.; Frank, T.: Robustness Evaluation of crashworthiness load cases at Daimler AG; Proceedings Weimarer Optimierung- und Stochastiktage 5.0, 2008, Weimar, Germany, 33

34 Summary Robustness Evaluation optislang + SoS have completed the necessary methodology to run robustness evaluation for NVH, passive safety, forming simulation or crashworthiness Success Key: Necessary distribution types and correlation definitions available Optimized LHS sampling Reliable measurements of variation, correlation and determination including filter technology Projection of statistic onto the FE-structure Main customer benefit: Identification of problems early in the virtual prototyping stage Measure, verify and finally significantly improve the modeling quality (reduce numerical scatter and modeling errors) 34

35 What is necessary for successful implementation? 1. Introduction of realistic scatter definitions Distribution function Correlations Random fields 2. Using of reliable stochastic methodology Variance-based robustness evaluation using optimized LHS 3. Development of reliable robustness measurements Standardized post processing Significance filter Reliable variation and correlation measurements Acceptance of method/result documentation/communication! 35

36 Robustness and Stability of the Model Which quantity of numerical noise is acceptable? Quantification via coefficients of prognosis (CoP) Estimation of numerical noise: 100% - CoP Experience in passive safety, CFD or crashworthiness tells that result values with lower CoP than 80% show: - High amount of numerical noise resulting from numerical approximation method (meshing, material, contact,..) - Problems of result extractions - Physically instable behavior 36

37 Robustness Insurance Crash Loading Response CoV CoD lin[%] CoD lin adj [%] CoD quad [%] CoD quad adj [%] max_int_energy max_hourglass_energy x_ _ x_ _ x_ x_ y_ y_ z_ z_ max_sec29_rforce max_sec29_xforce max_sec33_rforce max_sec33_xforce max_plast summ_plast LS-DYNA low speed structural crash case Robustness evaluation against structure and loading scatter show coefficients between 71 and 99 % In qualified FE-models numerical scatter is not dominating important response values! Model guidelines, model verification and robustness evaluation ensure a reasonable model quality. 37

38 Robustness check of optimized designs With the availability of parametric modeling environments like ANSYS workbench an robustness check becomes very easy! Menck see hammer for oil and gas exploration (up to 400m deep) Robustness evaluation against tolerances, material scatter and working and environmental conditions 60 scattering parameter Design Evaluations: 100 Process chain: ProE-ANSYS workbench- optislang 38

39 Robustness evaluation as early as possible Goal: Tolerance check before any hardware exist! Classical tolerance analysis tend to be very conservative Robustness evaluation against production tolerances and material scatter (43 scattering parameter) shows: - Press fit scatter is o.k. - only single tolerances are important (high cost saving potentials) Production shows good agreement! by courtesy of Design Evaluations: 150 solver: ANSYS/optiSLang Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, 39

40 Reliability Analysis 40

41 Dynardo GmbH 2012 Reliability analysis Limit state function g(x) divides random variable space X in safe domain g(x)>0 and failure domain g(x) Multiple failure criteria (limit state functions) are possible Failure probability is the probability that at least one failure criteria is violated (at least one limit state function is negative) Integration of joint probability density function over failure domain 41

42 Definition of limit state functions Dynardo optislang Seminar Example damped oscillator 42

43 Reliability Analysis Algorithms Gradient-based algorithms = First Order Reliability algorithm (FORM) ISPUD Importance Sampling using Design Point Adaptive Response Surface Method Monte Carlo Sampling X2 Latin Hypercube Sampling Directional Sampling X1 43

44 How choosing the right algorithm? Robustness Analysis provide the knowledge to choose the appropriate algorithm Robustness & Reliability Algorithms 44

45 Application Example ARSM for Reliability Fatigue life analysis of Pinion shaft Random variables Surface roughness Boundary residual stress Prestress of the shaft nut Target: calculate the probability of failure Probability of Failure: Prestress I: P(f)= (230 ppm) Prestress II: P(f)= (0.13 ppm) sigma = +/-5kN sigma = +/-10kN Solver: Permas Method: ARSM 75 Solver evaluations by courtesy of 45

46 Probability Assessment of Railways Goal: investigate the crosswind stability of Railway systems Sensitivity analysis against stochastic loading parameters followed by probability analysis Random variables crosswind amplitude, duration aerodynamic coefficients Solver: ADAMS + Matlab Methods: LHS, FORM, ISPUD Proppe, C.Wetzel, C.; Probabilitic Assessment of the Crossswind Stability of Railway Systems; Proceedings Weimarer Optimierung- und Stochastiktage 4.0, 2007, Weimar, Germany, 46

47 Robust Design Optimization 47

48 Design for Six Sigma Six Sigma is a concept to optimize the manufacturing processes such that automatically parts conforming to six sigma quality are produced Design for Six Sigma is a concept to optimize the design such that the parts conform to six sigma quality, i.e. quality and reliability are explicit optimization goals Because not only 6 Sigma values have to be used as measurement for a robust design, we use the more general classification Robust Design Optimization 48

49 Dynardo GmbH 2012 Dynardo GmbH Sigma level vs. failure probability The sigma level can be used to calculate the probability of exceeding a certain response value Since the distribution type is often unknown, this estimate may be very inaccurate for small probabilities The sigma level deals with single limit values, whereas the failure probability quantifies the event, that any of several limits is exceeded Reliability analysis should be applied to proof the required safety level Distribution Required sigma level (CV=20%) p F = 10-2 p F = 10-3 p F = 10-6 Normal Log-normal Rayleigh Weibull

50 Start Robust Design Optimization Robust Design Variance based Robustness Evaluation Probability based Robustness Evaluation, (Reliability analysis) Optimization Sensitivity Study Single & Multi objective (Pareto) optimization CAE process (FEM, CFD, MBD, Excel, Matlab, etc.) Robust Design Optimization Methodology 50

51 Robust Design Robust Design Optimization (RDO) optimize the design performance with consideration of scatter of design (optimization) variables as well as other tolerances or uncertainties. As a consequence of uncertainties the location of the optima as well as the contour lines of constraints scatters. To proof Robust Designs safety distances are quantified with variance or probability measurements using stochastic analysis. 51

52 Methods for Robust Design Optimization Variance-based RDO Safety margins of all critical responses are larger than a specified sigma level (e.g. Design for Six Sigma) Reliability-based RDO Failure probability with respect to given limit states is smaller as required value Taguchi-based RDO Taguchi loss functions Modified objective function 52

53 Robust Design Optimization - RDO Robust Design Optimization combines optimization and Robustness Evaluation. From our experience it is often necessary to investigate both domains separately to be able to formulate a RDO problem. optislang offers you either iterative or automatic RDO flows. Define safety factors Robustness evaluation Robust design optimization Sensitivity analysis Robustness proof! 53

54 Iterative RDO Application Connector 2) The DX Six Sigma design was checked in the space of 36 scattering variables using optislang Robustness evaluation. Some Criteria show high failure probabilities! 1) From the 31 optimization parameter the most effective one are selected ed with optislang Sensitivity analysis. 3) From optislang Robustness Evaluation safety margins are derived. 4) Three steps of optimization using optislang ARSM and EA optimizer improve the design to an optislang Six sigma design. 5) Reliability proof using ARSM to account the failure probability did proof six sigma quality. Start: Optimization using 5 Parameter using DX Six Sigma, then customer asked: How save is the design? by courtesy of 54

55 Robust Design Optimization of a rubber seal Using DesignModeler parametric was rebuild with 11 Parameter. Using optislang sensitivity analysis 7 effective parameter are identified. Using ARSM design was optimized to have minimal volume and sufficient pressure at all contact points. Including Uncertainty of loading and material 6 Sigma quality was violated. Therefore iterative RDO increasing safety margins was performed to reach 3 Sigma design level. Initial design Robust design Using optislang Reliability Analysis 3 sigma quality was proven. Customer started optimization with two parameter and found minimal improvement potential. 55

56 DYNARDO NAFEMS conference 2012 Dynardo GmbH 2012 Summary Stochastic analysis needs a balance between input definitions, stochastic analysis method and post processing Use specific/concrete robustness/reliability measurements RDO using one global response surface approximation for optimization and robustness space usually underrepresents the influence of scattering variables Because all RDO strategies will try to minimize solver runs for robustness measures, a final proof of robustness/reliability is mandatory Carefully translation and introduction of material scatter is crucial Start with robustness evaluation of start/optimal candidate design Continue with iterative RDO approach using safety distances If safety distances in optimization space vary significant automatic RDO is necessary 56

57 Part 7 Applications 57

58 Application Crashworthiness AZT Insurance Crash Load Case Scatter definition ( scattering parameter) Velocity, barrier angle and position Friction (Road to Car, Car to Barrier) Yield strength Spatially correlated sheet metal thickness Main result: Prognosis of plastic behavior CAE-Solver: LS-DYNA Deterministic analysis show no problems with an AZT load case. Tests frequently show plastic phenomena which Daimler would like to minimize. Motivation for the robustness evaluation was to find the test phenomena in the scatter bands of robustness evaluations, to understand the sources and to improve the robustness of the design. 58

59 Did You Include All Important Scatter? Scatter of uniform sheet thickness (cov=0.05), yield strength, friction, test conditions Introduction of sheet metal thickness scatter per part LS-DYNA simulation - Extraction via LS-PREPOST We could not find or explain the test results! SoS - post processing Statistics_on_Structure 59

60 Definition of Scatter is the Essential Input! Which degree of forming scatter discretization is becomes necessary? Level 1 - No distribution information: - increase uniform coil thickness scatter cov=0.02 to cov= Level 2 - Use deterministic distribution information: - use thickness reduction shape from deterministic forming simulation and superpose coil (cov=0.02) and forming process scatter (cov= ) 60

61 Did You Include All Important Scatter? Scatter of sheet thickness, forming process scatter covmax=0.05 yield strength, friction, test conditions + Introduction of spatial correlated forming process scatter LS-DYNA simulation - Extraction via LS-PREPOST SoS - post prozessing Statistics_on_Structure We could find and explain the test results! 61

62 Iterative Robust Design Optimization Design optimization task 4 continuous, 2 binary design variables Single objective formulations (maximal removal power) 2 optimization restrictions Robustness of performance should be preserved by courtesy of Könning, M; Plotzitza, A.: Optimierung und Robustheitsbewertung mit optislang bei der Robert Bosch GmbH, Proceeding Weimarer Optimierung- und Stochastiktage 1.0, 2004, 62

63 Iterative Robust Design Optimization With help of the sensitivity analysis, the optimization task was formulated. With help of genetic algorithms, the optimization was performed. With robustness evaluation, robustness and reliability were checked. The performance was increased by 25 %! The results of the digital product development were proven by testing! 63

64 RDO Centrifugal Compressor Parameterization Parametric geometry definition using ANSYS BladeModeler (17 geometric parameter) Model completion and meshing using ANSYS Workbench by courtesy of 64

65 RDO Centrifugal Compressor Fluid Structure Interaction (FSI) coupling Parametric fluid simulation setup using ANSYS CFX Parametric mechanical setup using ANSYS Workbench by courtesy of 65

66 RDO Centrifugal Compressor Optimization goal: increase efficiency Constraints: 2 pressure ratio s, 66 frequency constraints, Robustness Input Parameter 21 Output Parameter 43 Constraints 68 Tolerance limit 1.34< T <1.36 ~13% outside Initial SA ARSM I EA I ARSM II ARSM III Total Pressure Ratio Efficiency [%] #Designs by courtesy of 66

67 RDO Centrifugal Compressor Robust Design Optimization with respect to 21 design parameters and 20 random geometry parameters, including manufacturing tolerances. Robust Design was reached after =650 design evaluations consuming. Robustness evaluation RDO optimization Sensi + first optimization step by courtesy of Robustness proof using Reliability Analysis 67

68 Robust Design Optimization of a rubber seal Parametric model and Sensitivity Study Customer investigated Seal optimization using only 2 parameter Using DesignModeler parametric was rebuild with 11 parameter Initial design Sensitivity study Using optislang sensitivity approach 7 effective optimization parameter are identified 68

69 Robust Design Optimization of a rubber seal Deterministic optimization Using optislang ARSM algorithm design was optimized to have minimal volume and sufficient pressure at all contact points. Optimal design Initial design Including Uncertainty of loading and material 6 Sigma quality was violated. Therefore iterative RDO increasing safety margins of contact forces was performed to reach 3 Sigma design level. 69

70 Robust Design Optimization of a rubber seal Iterative Robust Design Optimization Required sigma level = 3 sigma 4 iterations of sequential optimization and robustness analysis Deterministic optimum (140 design evaluations): 14% failure Robust optimum (540 design evaluations): 0.3% failure Young s modulus is most important scattering variable 70

71 Robust Design Optimization of a rubber seal Iterative RDO Reliability proof 7 geometry + 2 material =9 important parameters detected from robustness analysis Directional Sampling on ARSM FORM failed ARSM: 116 design evaluations Failure probability = 0.07%, 3.2 sigma 71

72 RDO on global response surface Approximation of model responses in mixed optimization/stochastic space Simultaneous RDO is performed on a global response surface Applicable to variance-, reliabilityand Taguchi-based RDO Approximation quality significantly influences RDO results Final robustness/reliability proof is required Pure stochastic variables have small influence compared to design variables Important local effects in the stochastic space may be not represented 72

73 Robust Design Optimization of a rubber seal RDO on global response surface Optimization variables are varied in optimization space Pure stochastic variables are varied +/- 4 sigma 200 LHS samples generated with uniform distribution Approximation quality between 93% and 97% Young s modulus is in RDO space minor important but in robustness space most important Pure stochastic variables are unimportant Poor local approximation quality for robustness analysis 73

74 Robust Design Optimization of a rubber seal RDO on global response surface Evolutionary algorithm (444 designs) + 50 Robustness samples for each optimization design Mean values and standard deviation of contact pressures as robustness measures RDO-Optimization with constraints for all contacts: 3.5 sigma 74

75 Robust Design Optimization of a rubber seal RDO on global response surface Robustness proof Small approximation error Large approximation error Failure probability: Upper left contact pressure 2.2% (2.0 sigma) Lower left contact pressure 1.4% (2.2 Sigma) Optimal design is not robust! 75

76 Iterative RDO Application Connector Goal: high safety level of connector 10 contact forces have to be checked, failure may happen if N< 1 N The failure probability of single contact should be lower than 10% The failure probability of 5 contacts should be less than 1 out (6 Sigma Design) Status quo: pre optimized design using ANSYS DX and 5 optimization parameter Question: how optimal and robust is the design Solver: ANSYS Workbench by courtesy of 76

77 Step 1 - Sensitivity analysis The Sensitivity Analysis id done in the design space of 31 potential CAD (ProE) design parameters Identification of n=15 most important design parameters by courtesy of 77

78 Step 2 - Robustness analysis The failure probability of single contact failure is checked with Robustness evaluation. The Robustness Analysis is done in the Robustness space of 36 CAD tolerances Global variancebased robustness analysis using Advanced Latin hypercube sampling with 90 design evaluations Performance critical contact force F3o_v With failure probability of 89 %! by courtesy of 78

79 Step 3 - Optimization n=15 most important CAD design parameters Objective: minimal failure distance of every contact Step 1: ARSM - Stagnation after 5 Iterations (126 Design evaluations), contact force F3o_v still violating criteria Step 2: introducing of additions constraints Restart of Evolutionary Optimization using best Design_ARSM, stop after 390 Design evaluations with feasible design, but now other contact forces become critical Step 3: modifying the design space range and introducing additional constraints Restart using ARSM with best Design_EA, stop after 172 Design evaluations by courtesy of 79

80 Step 4 Robustness Analysis 36 scattering CAD tolerances Global variance-based robustness analysis using Advanced Latin hypercube sampling with N=50 design Failure probabilities of two forces higher than 1% Performance critical contact force F3o_v with failure probability 9 %! Contact force F2o_h with failure probability 1 %! by courtesy of 80

81 Step 5 - Reliability analysis Identification of n=12 most important random parameters using coefficients of importance Defining the limit state condition for violation more than 50% of the contact forces are lesser than 1N Reliability analysis using ARSM with N=137 D-optimal design of experiment Adaptive sampling on the MLS surrogate model without samples in the unsafe domain Probability of failure is near zero, assumption: normal distributed random parameters Optimized design is an Six Sigma Design by courtesy of 81

82 Results Variance and probability-based robust design optimization with 31 optimization parameters and 36 scattering parameters Increasing the performance critical contact force F3o_v according failure probability 89% -> 9% Failure probabilities of the other contact forces lesser than 1% System failure probability (more than 50% of the contact forces are lesser than 1) is near zero! (Six Sigma Design) N=950 parallel finite element calculations Total calculation time 1 week by courtesy of 82

83 Robustness Analysis drop test of mobile phone A robustness evaluation is a so called global variance-based stochastic analysis which addresses the question how much the response values scatter under the consideration of input parameter scatter. 209 scattering variables (drop position, material (E, ro, yield), geometry (thickness, radius), environment (friction) 150 Latin Hypercube Samples Statistical Post Processing include: The variation of the responses Coefficient of Determination/Importance, checking linear and non-linear correlation Coefficient of Prognosis Statistics on Structure for critical part by courtesy of 83

84 Process automation drop test Run the robustness analysis in optislang. 209 scattering inputs Run ABAQUS which creates *.csv files containing the results. 150 designs Run the robusteval script after the robustness analysis is finished. All the designs will be processed and *.rpt files are created. Post processing in optislang responses by courtesy of 84

85 Post Processing Robustness - drop test CoD lin adj CoD quad adj CoD lin Adj Spearman The Histogram shows a variation between and Probability of violating the limit is 9.33 % ( =0.0933) CoP Maximum Cop is 66 %, Inputs ANGLE_Y and ANLGE_X have the most significant influence by courtesy of Reference Maximum 85

86 Statistics on Structure (SoS) Based on Robustness analysis results (optislang) Visualization of statistics (Maxima, Minima, Mean value, Coefficient of variation, ) to locate hot spots of variation at the FE Structure Benefits: Visualization of Min/Max and scatter range on FE Structure Visualization of spatial Distribution of Variation and Correlation on FE- Structure Selecting and visualizing important regions and their correlations We have to select one time frame for every design by courtesy of 86

87 Combining SoS and optislang The picture above shows the maximum of S11 (positive - tension) In SoS it is possible to select elements at hot spots and generate optislang *.bin file (see black circles) Use the result_monotoring in optislang to identify local variation and correlation, The CoP plots below show that ANGLE_X and ANGLE_Y have strongest influence on S11 2to:Histogram for the to selected check elements variation Structure in ABAQUS viewer Element sets all glass element sets by courtesy of 87

88 Part 8 Costumers 88

89 Our Costumers agree 89

90 What s the Difference to Others? Methodology Sensitivity analysis and optimization for large (number of variables) non-linear problems COP/MOP to minimize the number of solver calls Optimization with robust defaults (ARSM, EA,GA,PARETO) Complete methodology suite to run robustness evaluation, reliability analysis and robust design optimization Key applications Optimization with large number of parameter (>10) having non linear effects, noise, design failure Model update and parameter identification using sensitivity study and optimization os (+SOS) have completed the functionality for robustness evaluation and reliability analysis and robust design optimization to be used in production We do not just offer a tool, we deliver a process. We are the ones who implemented robustness evaluation at different industries. 90

91 WOSD 2012 Dynardo GmbH 2012 optislang goes International DYNARDO, CADFEM (Germany, Austria, Swiss) SVSFEM (Czech Republic, Slovakia, Hungary) Pera Global (China, Shanghai) CADFEM India (India, Hyderabad) CAE Technology Inc. (Korea, Seoul) TaeSung S&E Inc. (Korea, Seoul) CADFEM CIS (Russia, Moscow) CADFEM US (USA) Tecosim Japan (Japan, Saitama) Introduction Weimar Optimization and Stochastic days