1. dynamic software & engineering GmbH

2. optiSLang
optiSLang is an algorithmic toolbox for sensitivity analysis, optimization, robustness evaluation, reliability analysis and robust design optimization.
We think that for real life problems, customers do not need one magic algorithm.
Instead, customers need a tool box with a set of the best algorithms for the different kind of problems in optimization and robustness/reliability analysis.

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
The CATIA interface is still beta.
ANSYS interface is very good.
The extraction tool kit was set up for our customer BOSCH and is now available for all users.
MADYMO positioner is important for passive safety applications for robustness evaluation.

4. optiSLang Preprocessor
Process Integration
optiSLang Preprocessor
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
The parameter editor is visualizing the data flow of all variables and responses as well the constraints, objectives and limit state functions. The user friendliness of the editor is good. The parameter editor writes the oS problem file in XML-format. If we have a very large number of parameters or responses we are usually writing a script to generate the XML file.
That is a nice flexibility of oS, that the whole problem definition can be written/edited with any external program/script.

5. Robust Design Methodology Definition
Start
Robust Design Optimization
Robustness
Robustness Evaluation
Reliability Analysis
Optimization
Sensitivity Analysis
Single & Multi objective
(Pareto) optimization
Very important is to explain that the reliability space is given by nature (scatter at loads, material, geometry & design variables) and the optimization space (design variables) is defined by the designer. For practical applications, the spaces may overlap, but they will never be the same.
Optimization can be treated as a black box. After an optimization, the user can judge easily by looking at the results of the optima for the success of the optimization. If an important design variable was missed, the design improvement may be pure, but still valid.
Very much in contrast to the optimization, the robustness evaluation produces statistical measurements which can only be verified with another stochastic analysis or massive testing. Again, very much in contrast to the optimization, if one important input scatter for the virtual tests (stochastic analysis) is missing, all statistical measurements are useless.
Therefore, the user really has to know something about the input scatter, has to understand the reliability domain and has to use stochastic methodology which produces reliable measurements of robustness/reliability. We strongly recommend to start with variance-based robustness evaluation.
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
The most important measurement of sensitivity/importance is the coefficient of determination. He explains how much of the variation can be explained with the found (linear/quadratic) correlations for every input variation.
If the response value coefficient of determination of the full model is smaller than 80%, there is a significant amount of non linearity (higher than quadratic) or/and significant amount of numerical noise and/or the result extraction is introducing scatter to the response value.

7. Optimization Algorithms
Genetic algorithms & evolution strategies
Local adaptive RSM
Gradient-based algorithms
Start
Response surface method (RSM)
Pareto Optimization
Global adaptive RSM
Limitations and recommendations using the different strategies are given above.
Using gradient algorithms and response surface algorithms, optiSLang provides high end state of the art.
ARSM and the genetic/evolutionary algorithms are worldwide one of the best commercially available algorithms. These algorithms have been continuously developed over the last 5 years and have proven there functionality and robustness several times. They are usually the main reason for the customers decision to use optiSLang.

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
For identification tasks, the search of a parameter set for the numerical model regarding the best fit between test and simulation (some time also called model update) is one of the most difficult optimization problems.
First, we recommend always performing a sensitivity analysis to ensure:
That the test is inside the variation space of the simulation (defined by the lower and upper bounds of varying parameter=identification space)
That a set of sensible input variables to the update criteria can be found
After achieving a set of sensitive parameter to tune regarding sensitive update criteria, starting from the best design of the sensitivity analysis the optimization part is often simple.
See also: J. Will: The Calibration of Measurement and Simulation as Optimization Problem, Proceeding NAFEMS Seminar Virtual Testing – Simulationsverfahren als integrierter Baustein einer effizienten Produktentwicklung“” April 2006, Wiesbaden, Germany,
In the example above 7 different test conditions are identified at the same time. In the beginning 6 input parameter are varied between physically useful lower and upper bounds. First it could be proven, that the tests are lying within the variation band of identification space. Second the sensitivity of that parameter was checked against different response values (integrals and peak values of acceleration, displacement and pressure curves) and a subset of 3 input variables (gas temperature, bag permeability and efficiency of the airbag opening) to three response values (acceleration integral+peak, pressure integral) are used for the identification.
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
For identification tasks, the search of a parameter set for the numerical model regarding the best fit between test and simulation (some time also called model update) is one of the most difficult optimization problems.
First, we recommend always performing a sensitivity analysis to ensure:
That the test is inside the variation space of the simulation (defined by the lower and upper bounds of varying parameter=identification space)
That a set of sensible input variables to the update criteria can be found
After achieving a set of sensitive parameter to tune regarding sensitive update criteria, starting from the best design of the sensitivity analysis the optimization part is often simple.
See also: J. Will: The Calibration of Measurement and Simulation as Optimization Problem, Proceeding NAFEMS Seminar Virtual Testing – Simulationsverfahren als integrierter Baustein einer effizienten Produktentwicklung“” April 2006, Wiesbaden, Germany,
In the example above 7 different test conditions are identified at the same time. In the beginning 6 input parameter are varied between physically useful lower and upper bounds. First it could be proven, that the tests are lying within the variation band of identification space. Second the sensitivity of that parameter was checked against different response values (integrals and peak values of acceleration, displacement and pressure curves) and a subset of 3 input variables (gas temperature, bag permeability and efficiency of the airbag opening) to three response values (acceleration integral+peak, pressure integral) are used for the identification.
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
Customer: TAKATA, Solver MADMYO
A genetic algorithm was used to find the best compromise between the 7 test configurations. Because of the fast simulation (MADYMO multi body approach), the 1050 simulations could run over night.
The identification result was better than before (tuning iteratively by hand).
The figures show the computation results of the optimal design compared with the experimental data. It also shows the matching of the accelerations and the matching of the pressures of high grade. The automated validation of the airbag models ought to be transferred to further airbag models and should complete restraint systems. With an increasing number of possible parameters of the design space, the importance of the sensitivity study increases in order to reduce parameters to identify and validate the applicability of the design space for the sought after calibration. With increasing computation times, it also has to be checked how far adaptive response surface methods can contribute to the reduction of the computation time.
See also: J. Will: The Calibration of Measurement and Simulation as Optimization Problem, Proceeding NAFEMS Seminar Virtual Testing – Simulationsverfahren als integrierter Baustein einer effizienten Produktentwicklung“” April 2006, Wiesbaden, Germany,
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
Very important is to explain that the reliability space is given by nature (scatter at loads, material, geometry & design variables) and the optimization space (design variables) is defined by the designer. For practical applications, the spaces may overlap, but they will never be the same.
Optimization can be treated as a black box. After an optimization, the user can judge easily by looking at the results of the optima for the success of the optimization. If an important design variable was missed, the design improvement may be pure, but still valid.
Very much in contrast to the optimization, the robustness evaluation produces statistical measurements which can only be verified with another stochastic analysis or massive testing. Again, very much in contrast to the optimization, if one important input scatter for the virtual tests (stochastic analysis) is missing, all statistical measurements are useless.
Therefore, the user really has to know something about the input scatter, has to understand the reliability domain and has to use stochastic methodology which produces reliable measurements of robustness/reliability. We strongly recommend to start with variance-based robustness evaluation.
CAE Process (FEM, CFD, MBD, Excel, Matlab, etc.)

12. 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: 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. Improved 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
Regression analysis in Anthill plots
The post processing of oS follows the concept of showing the most important results via an interactive mode.

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
The required number of solver runs depends on the (in the beginning unknown) dimensionality (how many scattering inputs significantly influence a response scatter) and on the non linearity of the response scatter correlation.
Because we are guessing statistical values (variation/correlation), the necessary number of solver runs also depends on the tolerable amount of statistical error (confidence level).
Usually, a 95% confidence interval (0.15) resulting in an uncertainty of at correlation coefficients of 0.50 is used. Therefore, we provide tables to estimate the number of solver calls for that interval.
If you have 40 scattering inputs, we suggest for confidence interval of 0.15 approx. 100.

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
For identification tasks, the search of a parameter set for the numerical model regarding the best fit between test and simulation (some time also called model update) is one of the most difficult optimization problems.
First, we recommend always performing a sensitivity analysis to ensure:
That the test is inside the variation space of the simulation (defined by the lower and upper bounds of varying parameter=identification space)
That a set of sensible input variables to the update criteria can be found
After achieving a set of sensitive parameter to tune regarding sensitive update criteria, starting from the best design of the sensitivity analysis the optimization part is often simple.
See also: J. Will: The Calibration of Measurement and Simulation as Optimization Problem, Proceeding NAFEMS Seminar Virtual Testing – Simulationsverfahren als integrierter Baustein einer effizienten Produktentwicklung“” April 2006, Wiesbaden, Germany,
In the example above 7 different test conditions are identified at the same time. In the beginning 6 input parameter are varied between physically useful lower and upper bounds. First it could be proven, that the tests are lying within the variation band of identification space. Second the sensitivity of that parameter was checked against different response values (integrals and peak values of acceleration, displacement and pressure curves) and a subset of 3 input variables (gas temperature, bag permeability and efficiency of the airbag opening) to three response values (acceleration integral+peak, pressure integral) are used for the identification.

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
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 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 ,

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 ,
by courtesy of

23. Robustness Evaluation of Forming Simulations
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
Start in since 2006 used for production level
by courtesy of
After a successful running, the robustness evaluation for forming simulation BMW is integrating robustness evaluations in the standard process.
Therefore, we developed the postprocessor Statistics on Structure. Since 2007 it is available to other customers.
See also
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
Will, J.; Grossenbacher, K.: Using Robustness and Sensitivity Evaluation for setting up a reliable Basement for Robust Design Optimization, Forming Technology Forum 2007, March 2007, ETHZ, Zürich,
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. Robustness Evaluation Crashworthiness
Start in 2004 – since 2007 use for Production Level
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
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 (

26. 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.

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=
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= )

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
We could find and explain the test results!
SoS - post prozessing Statistics_on_Structure

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

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
Response
CoV
CoD lin[%]
CoD lin adj [%]
CoD quad [%]
CoD quad adj [%]
UPR_RIB_DEFL [mm]
0.027 40 34 93 83
MID_RIB_DEFL [mm]
0.038 95 94 98 96
LWR_RIB_DEFL [mm]
0.046 75 72 82
VC_UPR_RIB [m/s]
0.161 84 91
VC_MID_RIB [m/s]
0.118 33 25 88 73
VC_LWR_RIB [m/s]
0.138
HIC36 [-]
0.048 87
ABDOMEN_SUM [N]
0.119 53 48
PELVIS_Fy [N]
0.051 97 99
SHOULDER_Fy [N]
0.179
100
T12_Fy [N]
0.127 51 46 90 77
T12_Mx [Nmm]
0.424 81 79 92
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. 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 = +/-10kN
sigma = +/-5kN
First industrial applications of the adaptive global response surface methodology show promising performances for small and medium parameter ranges.
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
Very important is to explain that the reliability space is given by nature (scatter at loads, material, geometry & design variables) and the optimization space (design variables) is defined by the designer. For practical applications, the spaces may overlap, but they will never be the same.
Optimization can be treated as a black box. After an optimization, the user can judge easily by looking at the results of the optima for the success of the optimization. If an important design variable was missed, the design improvement may be pure, but still valid.
Very much in contrast to the optimization, the robustness evaluation produces statistical measurements which can only be verified with another stochastic analysis or massive testing. Again, very much in contrast to the optimization, if one important input scatter for the virtual tests (stochastic analysis) is missing, all statistical measurements are useless.
Therefore, the user really has to know something about the input scatter, has to understand the reliability domain and has to use stochastic methodology which produces reliable measurements of robustness/reliability. We strongly recommend to start with variance-based robustness evaluation.
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
Since the beginning of engineering designer deal with safety factors (safety distances). For a lot of practical problems today we cannot effort the necessary solver runs or we cannot define a appropriate RDO problem. Therefore we usually start with a consecutively approach.
First do a sensitivity analysis to understand the optimization domain
Second do a robustness evaluation of the reference (best practise) design to understand the robustness domain and to quantify safety distances in term of probability
Third define safety factors (usually on constraints of a deterministic optimization problem)
Fourth run the deterministic optimization
Fifth check the optima for robustness
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
Example of iterative RDO
The reference design was violating the forming limit crack criteria. In a sensitivity study, the design space (twelve bead forces + tool binder force) was scanned and found to be 98% violating the forming limit constraints. For the best design (valid) of the sensitivity study, a robustness evaluation (all optimization variables scatter + material scatter [yield stress, thickness, plasticity values] + friction scatter) was performed and the failure probability (5%) was found to be not acceptable. Therefore, the safety factors (so far used was a FLD_crack value from 0.8 which contains a safety distance of 0.2 to the limit of 1.0) are increased (to max. FLD_crack of 0.7) and a deterministic optimization was performed. The optimal design was checked for robustness and robustness was proven (no failure was found).
Additionally to standard optiSLang, the post processor Statistic on Structure (SOS) was used to investigate statistical values on the finite element mesh.
Solver: LSDYNA
Number of simulation: 350 (sensitivity 100, robustness 50, optimization 100, final robustness 100)
See also:
Will, J.; Grossenbacher, K.: Using Robustness and Sensitivity Evaluation for setting up a reliable Basement for Robust Design Optimization, Forming Technology Forum 2007, March 2007, ETHZ, Zürich,
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,

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).