1 dynamic software & engineering GmbH. 2 optiSLang optiSLang is an algorithmic toolbox for...

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dynamic software & engineering GmbH

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

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Available interfaces in optiSLang

CATIA v5 interfaceANSYS workbench

interfaceExtraction tool kit

(ABAQUS, LS-DYNA)Madymo positioner

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,…

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Process IntegrationoptiSLang 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

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CAE Process (FEM, CFD, MBD, Excel, Matlab, etc.)

Robustness

Robustness Evaluation

Reliability Analysis

Optimization

Sensitivity Analysis

Single & Multi objective

(Pareto) optimization

Robust Design Optimization

Robust Design Methodology Definition

Start

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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

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Gradient-based algorithms

Response surface method (RSM)

Genetic algorithms & evolution strategies

Start

Optimization Algorithms

Pareto Optimization

Local adaptive RSM

Global adaptive RSM

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1) Define the Design space using continuous or discrete optimization variables

Model Updating using optiSLang2) Scan the Design Space - Check the variation- Identify sensible parameter and

responses

3) Find the best possible fit- Choose an optimizer

depending on the sensitive optimization parameter dimension/type

Test

Best Fit

Simulation

optiSLang

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• 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

Model Updating using optiSLang

Δamax

pressure integral

acceleration integral

acceleration peak= α + β + γ

ZeitZeit Zeit

Validation of Airbag Modeling via Identification

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Model Updating using optiSLang

Test

Best Fit

Simulation

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)

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CAE Process (FEM, CFD, MBD, Excel, Matlab, etc.)

Robustness



Optimization

Multi objective (Pareto) optimization

Single objective optimization


Robust Design Methodology Definition

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Robustness Evaluation due to naturally given scatter

Goal: measurement of variation and correlation

Methodology: Variance based Robustness Evaluation

Which Robustness do You Mean?

Positive side effect of robustness evaluation: measurement of explainable physical scatter may answer the question: Does numerical scatter significantly influence the results?

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Robustness Needs a Reliable Basement

1. Introduction of reliablescatter 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

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Definition of Uncertainties

Correlation is an important characteristic of stochastic variables.

Distribution functions define variable scatter

Correlation of single uncertain values

Spatial Correlation = random fields

1) Translate the know-how about uncertainties into a proper scatter definition

Tensile strength

Yie

ld s

tress

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Robustness Measurements2) 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

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• 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

Improved Statistic Measurements

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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

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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)

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1) Define the Robustness space using scatter range, distribution and correlation

Robustness Eavluation using optiSLang

2) Scan the Robustness Space by producing and evaluating n (100) Designs

3) Check the Variation interval

4) Check the CoD5) Identify the most important scattering variables

1. Variation der Eingangsstreuungenmittels geeigneterSamplingverfahren

2. Simulation inkl.Mappingauf einheitlichesNetz

3. statistische Auswertungund Robustheitsbewertung




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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.

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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

How does body and suspension system scatter influence the NVH performance?

by courtesy of the Daimler AG

Start in 2002, since 2003 used for Production Level

[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]

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by courtesy of

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 2004Goal: 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]

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Robustness Evaluation of Forming SimulationsStart in 2004 - 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

CAE-Solver: LS-DYNA, AUTOFORM and others

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]

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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

SoS – Post Processing

[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]

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Robustness Evaluation CrashworthinessStart 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

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)

In comparison to robustness evaluations for NVH, forming or passive safety, crashworthiness has very high demands on methodology and software!

http://www.dynardo.de/

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Application CrashworthinessAZT Insurance Crash Load Case

• 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

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.

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Did You Include All Important Scatter?

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!

Scatter ofuniform sheet thickness (cov=0.05),yield strength, friction, test conditions

SoS - post processing Statistics_on_Structure

Insurance crash test

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?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)

Definition of Scatter is the Essential Input!

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We could find and explain the test results!

Introduction of spatial correlated forming process scatter - 100 LS-DYNA simulation- Extraction via LS-PREPOST

Scatter ofsheet thickness, forming process scatter covmax=0.05yield strength, friction, test conditions

SoS - post prozessing Statistics_on_Structure

+

Insurance crash test

Did You Include All Important Scatter?

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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

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Benefits of Robustness Evaluation Results of Robustness Evaluation:

1) 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.

2) 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.

3) 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.

4) Side effect: Validation of the modeling quality (quantification of numerical noise and identification of modeling errors)

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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

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Numerical Robustness Passive Safety• Comparison of coefficients of determination (CoD) for

different FE models (folded airbag/scaled airbag)

IIHS FMVSS

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!

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Response CoVCoD

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 93 82

VC_UPR_RIB [m/s] 0.161 84 82 96 91

VC_MID_RIB [m/s] 0.118 33 25 88 73

VC_LWR_RIB [m/s] 0.138 84 83 96 91

HIC36 [-] 0.048 84 82 95 87

ABDOMEN_SUM [N] 0.119 53 48 93 84

PELVIS_Fy [N] 0.051 97 96 99 98

SHOULDER_Fy [N] 0.179 98 98 100 99

T12_Fy [N] 0.127 51 46 90 77

T12_Mx [Nmm] 0.424 81 79 92 82

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!

Numerical Robustness Side Crash

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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)

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Methods of Reliability AnalysisDue 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)

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sig

ma

= +

/-1

0k

N

sig

ma

= +

/-5

kN

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)

by courtesy of ZF

ARSMN = 75 Solver

evaluations

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CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)

Robustness



Optimization

Multi objective (Pareto) optimization

Single objective optimization



Start

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Iterative RDO Procedure

Sensitivity analysis

Robustness evaluation

Define safety factors

Robustness proof

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.

multi disziplinary optimization

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Example Iterative RDO Procedure

Sensitivity analysisDefine safety factors

Deterministic optimization

Robustness evaluation

Robustness proof

Safety factor crack =1.3Safety factor thinning =1.2Safety factor hardening =1.1

[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]

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by courtesy of BMW AG and MINI

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

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What‘s the difference to othersMethodology• 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 optimizationKey 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).

1 dynamic software & engineering GmbH. 2 optiSLang optiSLang is an algorithmic toolbox for...

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