dynamic software & engineering gmbh
DESCRIPTION
dynamic software & engineering GmbH. optiSLang. optiSLang is an algorithmic toolbox for sensitivity analysis, optimization, robustness evaluation, reliability analysis and robust design optimization. . optiSLang Process Integration. - PowerPoint PPT PresentationTRANSCRIPT
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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 IntegrationArbitrary 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 DefinitionStart
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Sensitivity Analysis1) 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
Robustness Evaluation
Reliability Analysis
Optimization
Multi objective (Pareto) optimization
Single objective optimization
Robust Design Optimization
Robust Design Methodology Definition
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Robustness Evaluation due to naturally given scatterGoal: measurement of variation and correlationMethodology: 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 Basement1. 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
Yiel
d st
ress
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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 optiSLang2) 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
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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1. Variation der Eingangsstreuungenmittels geeigneterSamplingverfahren
2. Simulation inkl.Mappingauf einheitlichesNetz
3. statistische Auswertungund Robustheitsbewertung
1. Variation der Eingangsstreuungenmittels geeigneterSamplingverfahren
2. Simulation inkl.Mappingauf einheitlichesNetz
3. statistische Auswertungund Robustheitsbewertung
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!
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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 ProcessingProductive 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 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 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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sigm
a =
+/-1
0kN
sigm
a =
+/-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
Robustness Evaluation
Reliability Analysis
Optimization
Multi objective (Pareto) optimization
Single objective optimization
Robust Design Optimization
Robust Design OptimizationStart
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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).