dynamic software & engineering GmbH

1. dynamic software & engineering GmbH

2. optiSLang optiSLang is an algorithmic toolbox for sensitivity analysis, optimization, robustness evaluation, reliability analysis and robust design optimization.

3. optiSLang Process Integration Arbitrary CAE-processes can be integrated with optiSLang. Default procedure is the introduction auf inputs and outputs via ASCII file parsing. Additionally interfaces to CAE-tools exist. Connected CAE-Solver: ANSYS, ABAQUS, NASTRAN, LS-DYNA, PERMAS, Fluent, CFX, Star-CD, MADYMO, Slang, Excel,… Available interfaces in optiSLang • CATIA v5 interface • ANSYS workbench interface • Extraction tool kit (ABAQUS, LS-DYNA) • Madymo positioner

4. optiSLang reads and writes parametric data to and from all ASCII input of any external solver Parameterize functionality Input file: Optimization variable Robustness variable Dependend variables Output file: Response variable Response vector Constraints Multiple objectives /terms Process Integration optiSLang Preprocessor

5. Robust Design Methodology Definition Start Robust Design Optimization Robustness Robustness Evaluation Reliability Analysis Optimization Sensitivity Analysis Single & Multi objective (Pareto) optimization CAE Process (FEM, CFD, MBD, Excel, Matlab, etc.)

6. Sensitivity Analysis 1) Scanning the design space with optimized LHS, investigation of variation and correlation • 2) Identify the important variables • Coefficient of determination • Matrix of linear/quadratic correlation • Anthill plots • Check the variation space

7. Optimization Algorithms Genetic algorithms & evolution strategies Local adaptive RSM Gradient-based algorithms Start Response surface method (RSM) Pareto Optimization Global adaptive RSM

8. Model Updating using optiSLang 1) Define the Design space using continuous or discrete optimization variables 2) Scan the Design Space • Check the variation • Identify sensible parameter and responses Simulation Test 3) Find the best possible fit - Choose an optimizer depending on the sensitive optimization parameter dimension/type optiSLang Best Fit

9. Model Updating using optiSLang • Validation of numerical models with test results (7 test configuration) • Modelling with Madymo • Sensitivity study to identify sensitive parameters and to verify prediction ability of the model. • Definition of the objective function Validation of Airbag Modeling via Identification Δamax Zeit Zeit Zeit acceleration integral acceleration peak pressure integral = α + β + γ

10. Model Updating using optiSLang Validation of Airbag Modeling via Identification • optiSLang’s genetic algorithm for global search • 15 generation *10 individuals *7 test configuration • (Total:11 h CPU) Simulation Test optiSLang Best Fit

11. Robust Design Methodology Definition Robust Design Optimization Optimization Multi objective (Pareto) optimization Single objective optimization Robustness Robustness Evaluation Reliability Analysis CAE Process (FEM, CFD, MBD, Excel, Matlab, etc.)

12. Which Robustness do You Mean? Robustness Evaluationdue to naturally given scatter Goal: measurement of variation and correlation Methodology:Variance based Robustness Evaluation Positive side effect of robustness evaluation: measurement of explainable physical scatter may answer the question: Does numerical scatter significantly influence the results?

13. Robustness Needs a Reliable Basement 1. Introduction of reliable scatter definitions  distribution function  correlations  stochastic fields 2. Using reliable stochastic methods  variance based Robustness Evaluation using optimized LHS 3. Development of reliable robustness measurements  standardized automatic post processing process  significance filter  reliable variation and correlation measurements

14. Definition of Uncertainties 1) Translate the know-how about uncertainties into a proper scatter definition Yield stress Correlation of single uncertain values Tensile strength Correlation is an important characteristic of stochastic variables. Distribution functions define variable scatter Spatial Correlation = random fields

15. Robustness Measurements 2) Scan the design space with optimized Latin Hypercube Sampling 3) Evaluation of robustness with statistical measurements • Variation analysis (histogram, coefficient of variation, standard variation, probabilities) • Correlation analysis (linear, quadratic, Spearman) including principal component analysis • Evaluation of coefficients of determination CoD and coefficient of importance CoI

16. Advanced histogram options PDF fit (automatic/manual) Number of histogram classes PDF values ready for optiSLang input Limits with probabilities Probabilities with limit Improved Statistic Measurements Regression analysis in Anthill plots

17. Costs of Robustness Evaluation • In large dimensions, the necessary number of solver runs for linear and quadratic correlation checks increase • But in reality, often only a small number of variables is important • Therefore, optiSLang includes filter technology to estimate significant correlation • Default use 99% significance level for linear & quadratic correlation and related CoI/CoD

18. Strategy “No Run to Much” Using advanced LHS sampling, significance filter technology, linear, quadratic and Spearman correlation, we can check after ≈ 50 runs ⇒ can we explain the variation ⇒ which input scatter is important ⇒ how large is the amount of unexplainable scatter (potentially noise, extraction problems or higher order non linearity)

19. Robustness Eavluation 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 3) Check the Variation interval 5) Identify the most important scattering variables 4) Check the CoD

20. 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.

21. Robustness Evaluation of 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 300 .. 600 scattering variables • Using filter technology to optimize the number of samples Start in 2002, since 2003 used for Production Level How does body and suspension system scatter influence the NVH performance? by courtesy of the Daimler AG [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.505-527, www.dynardo.de]

22. 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 Goal: Ensuring consumer ratings and regulations & improving the robustness of a system [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 851-873, www.dynardo.de] by courtesy of

23. 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 Robustness Evaluation of Forming Simulations Start in 2004 - since 2006 used for production level by courtesy of CAE-Solver: LS-DYNA, AUTOFORM and others [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]

24. SoS – Post Processing • Statistic Measurements of Variation • Single Designs • Differences between Designs • Variation interval • Minimum/Maximum • Mean Value • Standard deviation • Coefficient of variation • Quantile (± 3 σ) • Statistical Measurements of Correlation & CoD • Linear correlation & CoD • at nodal/element level • Process quality criteria • Cp, Cpk • process indices [Will, J.; Bucher, C.; Ganser, M.; Grossenbacher, K.: Berechnung und Visualisierung statistischer Maße auf FE-Strukturen für Umformsimulationen; Proceedings Weimarer Optimierung- und Stochastiktage 2.0, 2005]

25. Consideration of scatter of thickness, strength, geometry, friction and test condition Prognosis of intrusions, failure and plastic behavior Identify CoI and correlations due to the input scatter Check model quality and robustness CAE-Solver: LS-DYNA, ABAQUS Robustness Evaluation Crashworthiness Start in 2004 – since 2007 use for Production Level In comparison to robustness evaluations for NVH, forming or passive safety, crashworthiness has very high demands on methodology and software! Will, J.; Frank, T.: Robustness Evaluation of crashworthiness load cases at Daimler AG; Proceedings Weimarer Optimierung- und Stochastiktage 5.0, 2008, Weimar, Germany (www.dynardo.de)

26. Scatter definition (40..60 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 Application Crashworthiness AZT Insurance Crash Load Case 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.

27. Did You Include All Important Scatter? Scatter of uniform sheet thickness (cov=0.05), yield strength, friction, test conditions Insurance crash test Introduction of sheet metal thickness scatter per part - 100 LS-DYNA simulation - Extraction via LS-PREPOST We could not find or explain the test results! SoS -post processing Statistics_on_Structure

28. 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=0.03..0.05 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=0.01..0.03)

29. Did You Include All Important Scatter? Scatter of sheet thickness, forming process scatter covmax=0.05 yield strength, friction, test conditions + Insurance crash test Introduction of spatial correlated forming process scatter - 100 LS-DYNA simulation - Extraction via LS-PREPOST SoS - post prozessing Statistics_on_Structure We could find and explain the test results!

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

31. Benefits of Robustness Evaluation Results of Robustness Evaluation: • Estimation of result variation: By comparison of the variation with performance limits, we can answer the question: Is the design robust against expected material, environmental and test uncertainties? By comparison of the variation with test results, we can verify the prediction quality of the model. • Calculation of correlations, including the coefficient of determination, which quantify the “explainable” amount of response variation. Here, we identify the most important input scatter which are responsible for the response scatter. • Due to robustness evaluation, possible problems are identified early in the development process and design improvements are much cheaper than late in the development process. • Side effect: Validation of the modeling quality (quantification of numerical noise and identification of modeling errors)

32. Robustness and Stability of the Model “Which quantity of „numerical noise“ is acceptable?  quantification of correlations via coefficients of determination (COD)  estimation of numerical noise: 100% - (linear, quadratic, monotonic correlations - cluster - outlier) Experience in NVH, passive safety, forming and crash-worthiness tells that result values with lower COD than 80% show significantly: • High amount of numerical noise • Problems of result extractions

33. Numerical Robustness Passive Safety • Comparison of coefficients of determination (CoD) for different FE models (folded airbag/scaled airbag) The coefficients of determination of the folded airbag analysis show significantly lower values.  In this case, it could be shown that the folded airbag does have much more numerical noise than the unfolded! IIHS FMVSS

34. Numerical Robustness Side Crash ABAQUS Side Crash Case Robustness evaluation against airbag parameter, dummy position and loading scatter shows coefficients of determination between 73% and 99%. In qualified FE-models numerical scatter is not dominating important response values!

35. 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)

36. Methods of Reliability Analysis Due to the number of important scattering variables, the kind of failure mechanisms and the amount of numerical noise, you need different methodology for calculation of rare event probabilities. optiSLang has them all! • First and second order reliability method (FORM/SORM) • Monte-Carlo-Simulation (MCS) • Latin hyper cube sampling (LH) • Importance sampling using design point (ISPUD) • Adaptive importance sampling (AIS) • Directional sampling (DS) • Global response surface method (RSM) • Adaptive response surface method (ARSM)

37. sigma = +/-5kN sigma = +/-10kN 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)=2.3 10-4 (230 ppm) • Prestress II: P(f)=1.3 10-7 (0.13 ppm) ARSM N = 75 Solver evaluations by courtesy of ZF

38. Robust Design Optimization Start Robust Design Optimization Robustness Robustness Evaluation Reliability Analysis Optimization Multi objective (Pareto) optimization Single objective optimization CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)

39. Iterative RDO Procedure From our experience it is absolutely necessary to understand both domains, the design space of optimization and the reliability space, to be able to formulate a successive RDO problem. Therefore, starting with a consecutive approach is recommended. Define safety factors Robustness evaluation multi disziplinary optimization Robustness proof Sensitivity analysis

40. Example Iterative RDO Procedure Robustness evaluation Safety factor crack =1.3 Safety factor thinning =1.2 Safety factor hardening =1.1 Define safety factors Sensitivity analysis Deterministic optimization Robustness proof [Will, J.; Grossenbacher, K.: Using Robustness and sensitivity evaluation for setting up a reliable basement for robust design optimization, Forming Technolopgy Forum 2007, ETH Zürich, www.dynardo.de]

41. RDO at Restraint Systems • Identification of sensitive input parameter sets to fit experimental data • Identification of sensitive (most effective) optimization parameters • Single and multi objective optimization in the sensitive parameter space • Robustness evaluation of designs due to crash test load cases by courtesy of BMW AG and MINI

42. What‘s the difference to others Methodology • Sensitivity analysis and optimization for large (number of variables) non-linear problems • Optimization with robust defaults (ARSM, EA,GA,PARETO) • Complete methodology suite to run robustness evaluation, reliability analysis and robust design optimization Key Applications • 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 implement robustness evaluation at the automotive industry. We can show the success stories (BMW, BOSCH, DC).