dynamic software & engineering

optiSLangSoS

Sensitivity analysis, multiobjective and multidisciplinary optimization, robustness evaluation, reliability analysis, robust design optimization

Software

optiSLang 4

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PRODUCT OVERVI EWSince market launch in 2002, optiSLang has established itself as one of the leading software tools for CAE-based optimization and CAE-based stochastic analysis. User - friendliness realized by automated fl ows, effi cient methods, clearly structured user interfaces as well as meaningful result visualization secure our customers the success and the benefi t of using optiSLang for CAE-based parametric studies.

Background and Benefi tsSince the beginning of numerical simulation, engineers have been using parametric studies to verify, understand and im-prove their designs, numerical models and results. optiSLang does the same, but it is expanding parametric studies to ar-bitrary dimensions, adds the infl uence of scattering inputs, using statistics to identify and explain correlations, using mathematical or evolutionary optimization algorithms to optimize a parameter set or identify a measurement as well as using stochastic analysis to estimate result variation or to calculate probabilities. So optiSLang can be used to X-ray your design space and your numerical model to verify and improve the understanding of parameter-based interactions between input and output as a base for design optimization or robustness evaluation. You may ask: What does optiSLang set apart? Parametric studies are available in almost every simulation environment. That is true but the very important difference is the effi ciency and safety to use a minimum of CAE-based design evaluations and provide a maximum of forecast quality and result reliability for real world task hav-ing a lot of optimization and scattering parameter as well as non-linear, non-perfect CAE simulation models and results. In combination with easy and safe to use fl ows and wizards of best practice, optiSLang is ready to provide you the next level of parametric studies to innovate your virtual product development.

Core competencyReliability analysis is one of the core competencies of the development groups behind DYNARDO who provide more than 25 years of practical experience. Combined with the state of the art in parameter optimization, we have the best and most effi cient toolbox for CAE-based optimization and robustness evaluation available on the market. One of the core requirements of modern CAE-based virtual product development is the verifi cation of the product robustness as early as possible in the development process. Continu-ously DYNARDO, together with some key customers such as Robert Bosch GmbH, BMW AG or Daimler AG, improves and optimizes the virtual product development processes by in-troducing stochastic analysis and combines the robustness evaluation or reliability analysis with the design optimiza-tion process.

Made in GermanyGermans are known to do things accurately. In the case of robust design optimization and product reliability, our accu-racy provides you with accurate processes, a reliable product and the best support available.

History of optiSLangWhen optiSLang started in 2002, the package had one of the most effi cient and robust genetic optimization algo-rithms to search for design improvements in discrete or continuous design spaces. In 2005, a customizable evolu-tionary algorithm toolbox and an effi cient multiobjective evolutionary algorithm were added. To complete the me-thodical spectrum of Natural inspired Optimization Algo-rithms (NOA) for single and multiobjective optimization in optiSLang we added Particle Swarm Optimization (PSO) algorithms in 2009. With the help of robust predefi ned settings and decision trees optiSLang users investigate successfully single objective or Pareto frontiers in case of confl icting objectives. With NLPQL from the beginning we provide one of the leading gradient-based mathematical optimization algorithms.

Coeffi cient of Prognosis (CoP) and Metamodel of Optimal Prognosis (MOP)Today users have access to very powerful parametric model-ing environments. As a consequence the number of optimiza-tion parameters rises. Traditional Design of Experiment (DOE) and Response Surface Methodology ask the user to reduce the set of variables, to choose an appropriate DOE scheme and an appropriate regression function and to test the result-ing Response Surface Model for accuracy. From the beginning our users asked us to support the variable reduction and to provide reliable, quantitative measures of variable impor-tance. With the development of the CoP and the automatic identifi cation of the MOP we provide outstanding algorithms for automatic detection of the most important parameters, automatic detection of the best possible metamodel and ver-ifi cation of forecast quality of the MOP. Together with our very robust and fully automatic adaptive response surface (ARSM) optimizer, the method of choice for optimization problems up to 20 parameters, we provide our users a fully automatic procedure to investigate large dimensions of optimization parameters and to optimize the design performance.

Robustness Evaluation and Reliability AnalysisSince the fi rst optiSLang version the implementation of ro-bustness evaluation using reliability analysis has been a key feature. Henceforth our powerful set of available fi rst class reliability analysis algorithms has been constantly improved, offering today the best available commercial implementa-tion for CAE-based robustness and reliability analysis avail-able on the market.

Robust design optimization (RDO)Nowadays RDO becomes the key feature of virtual prototyp-ing. Having all necessary functionality to run real world RDO applications, which have a large number of optimization parameters and uncertain variables, optiSLang provides the necessary functionality for successful application of RDO in virtual prototyping. Still an iterative approach of determin-istic optimization and robustness evaluation is often the method of choice. Of course, the fi nal dream of virtual prod-uct development is an automatic robust design optimization procedure, simultaneously dealing with optimization and uncertainty domain. Therefore in version 3 we developed a robust design optimization algorithmic toolbox which com-bines optiSLang’s capabilities in optimization, robustness evaluation and reliability analysis. The toolbox provides dif-ferent combinations in order to offer a payable balance (in terms of necessary external solver calls) between effi ciency and reliability. Especially the new generation of global adap-tive response surface methodology for reliability analysis promises to be very effi cient for many practical robust de-sign applications.

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PROCESS AUTOM ATION AN D I NTEGR ATIONEasy to use process automation and integration as well as smooth access to design parametric into optiSLang are the key for successful CAE - based parametric studies.

SENSITIVITY ANALYSISWith the help of sensitivity analysis the base for a successful optimization or parameter identifi cation task is set up. Focus of the sensitivity analysis is the identifi cation of the most important input variables, the quantifi cation of variable importance and optimization potentials as well as the identifi cation of the best possible surrogate model between model input and output variables.

optiSLang C++ algorithm librarySince version 4 the algorithmic optiSLang base was com-pletely restructured to a C++ Library. Now all algorithms of optimization, stochastic analysis or metamodeling can be approached via Python interfaces from our own GUI or any third party application. With that move our software struc-ture supports the integration of external CAE - processes into optiSLang as well as the integration of optiSLang methodolo-gy into third party parametric modeling environments. Thus optiSLang is ready for the future challenges of automation and integration.

optiSLang graphical user interfaceThe graphical user interface of optiSLang 4 was completely redesigned to provide a new level of user friendliness and functionality for process automation and process integration. Now optiSLang enables the user to connect arbitrary complex simulation processes of CAE solvers, pre- and postprocessors

in heterogeneous networks or clusters via graphical interface. With the help of wizards users have access to best practice use of optiSLang algorithmic. Together with robust default settings of optiSLang algorithms the GUI offers easy and safe to use leading edge functionality of CAE-based robust design optimization. Of course in optiSLang it is possible to parallelize and distribute design evaluations. This reduces the computing time for an optimization or robustness evaluation signifi cantly.

StrategyFor continuous design variables their lower and upper bounds have to be defi ned. In addition optiSLang supports discrete parameters. Using deterministic design schemes a classical Design of Experiments can be generated (e.g. full factorial, central composite, D-optimal). This approach is effi cient in small design spaces (5 variables). Alternatively in larger design space dimensions stochastic sampling methods including Ad-vanced Latin Hypercube Sampling to minimize input correla-tion errors and take into account previous sample points are recommended. Based on the response values of the samples, which are calculated by the external solver, an advanced varia-tion and correlation analysis including calculation of variable importance (CoI) and forecast quality of the metamodels us-ing the Coeffi cient of Prognosis (CoP) is performed.

Post processingFor statistical evaluation of the sampling, the statistical post processing offers histograms, correlation coeffi cients, Coef-fi cients of Determination (CoD) and Importance (CoI), 2D and 3D anthill plots and Principal Component Analysis (PCA). For visualization and verifi cation of the MOP the approximation post processing offers 2D and 3D plots of the MOP, the Co-effi cient of Prognosis (CoP) and statistical properties of the regression model.

Process integration and ParametrizationoptiSLang offers a wide range of direct integration nodes such as MATLAB, Excel or python. This offers the most com-fortable way to access the CAE-tool parametric. These tools are called directly or are running inside optiSLang. Addi-tionally, as a result design evaluation is much faster than calling external CAE processes. Widely used CAE-solvers like ANSYS or Abaqus are supported via solver specifi c dialogs and automatized design parameter interfaces. In cases where optiSLang offers no specifi c interface, users always can introduce CAE processes and design parametric manu-ally. The only necessary boundary conditions are that the CAE process has to run automated and should be batchable for the avoidance of user interaction. For ASCII fi le based design parametric defi nition we offer automatized local-ization of input parameters. The extraction of result values being scalar, vector or signal output is supported from ar-bitrary ASCII fi les as well as from a selected range of binary fi les of external CAE solvers such as ANSYS or ABAQUS by using the Extraction Tool Kit (ETK).

optiSLang inside ANSYS WorkbenchoptiSLang inside ANSYS Workbench realizes the fi rst full integration of optiSLang functionality inside a third party parametric modeling environment. Therefore it is not nec-essary to leave ANSYS Workbench to apply optiSLang para-metric studies.

Best PracticeThe design space to be examined is specifi ed by the defi nition of continuous design variables with upper and lower bounds. With the help of Advanced Latin Hypercube Sampling, a set of design realizations is generated and evaluated. Outlier or infeasible response values are removed from the sample set. Then the fully automatic MOP algorithm is started, which searches for the best possible subspace of important design variables and the best possible metamodel giving the best prognosis quality.

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OPTIMIZATIONoptiSLang offers best in class algorithms for design optimization with the focus to provide the best possible design improvement with an acceptable amount of solver runs. We provide optimizers which can deal with real world problems having a large number of continuous and discrete variables, lots of constraints, non-linear effects, noisy responses or even multiple regions of failed or constraint violating designs.

PAR A METER I DENTI FICATIONIn parameter identifi cation tasks the deviation between measures and the numerical results are minimized by identifying the input parameters of a model. Sensitivity analysis provides the required information whether the unknown parameters can be identifi ed based on the available measures. Using our effi cient optimization methods the optimal parameter values can be determined.

StrategyThe optimization can be performed based on the defi nition of design space using continuous, discrete and binary design variables; the defi nition of design and manufacturing con-straints and the defi nition of objective functions, including multiple terms and weights.For the optimization procedure gradient-based methods (NLPQL) as well as a library of Nature inspired Optimiza-tion Algorithms (NOA) including genetic algorithms, Evolu-tionary Strategies (ES), Particle Swarm Optimization (PSO) and Stochastic Design Improvement (SDI) are available. All optimizers can be used in real design space or using global response surface approximations – polynomial and Moving Least Square (MLS), preferable with the Metamodel of Opti-mal Prognosis (MOP). In addition, fully automatic Adaptive Response Surface Methods (ARSM) are available.

Post processingThe results of the optimization are visualized by an interac-tive post processing. The predefi ned post processing win-dows are adapted to the optimization algorithm and provide appropriate information for the fast investigation of optimi-zation performance using the different strategies.

Best PracticeAfter performing sensitivity analysis and identifying the MOP for every response, optimization using NOA on the MOP is performed to check for possible design improvement. Only

StrategyFor parameter identifi cation purposes optiSLang provides not only the consideration of scalar response values. Addi-tionally the defi nition of multi-channel signals is possible, e.g. time-displacement curves. Measurements are defi ned as a reference signal. With help of a substantial library of signal functions containing not only local values as maximum and minimum amplitudes but also global values as integrals of certain properties and more complex signal operations, indi-vidual objective functions can be defi ned. This functionality is very helpful for identifi cation tasks.Using the Metamodel of Optimal Prognosis the sensitivity of different signal properties can be evaluated and a MOP-based optimization can be used to get an initial guess of the optimal parameters. For the fi nal optimization procedure again several optimization algorithms are available. In case of a suffi ciently smooth objective function gradient based methods can be used very effi ciently. If this is not the case Nature inspired Op-timization Algorithms give a robust alternative.

Post processingThe results of the parameter identifi cation task are visualized by the sensitivity and optimization post processing. If signals have been defi ned, for all evaluated designs the corresponding signal functions can be visualized with respect to the reference solution.

one additional external solver run is necessary to verify the optimum found on the MOP. In addition sensitivity analysis allows the reduction of the number of most important opti-mization variables. If the remaining number is less than 20, local Adaptive Response Surface Method is the algorithm of choice. For further design improvement gradient based or NOA algorithms can be started using the best designs of prior evaluations as initial start generation.

Best PracticeThe sensitivity analysis is used initially to check if the un-known parameters have signifi cant infl uence on the model response. Using the CoP measures the best possible result extraction for deselection of phenomena and uniqueness of correlation analysis can be verifi ed. Also the range of the re-sponse values obtained from the samples shall be checked regarding to the inclusion of the measures. All together

this analysis provides all necessary information to result in a well defi ned identifi cation task, containing only sensitive optimization parameter as well as best possible measures of fi t which deselect all relevant phenomena between test and simulation results. That is the key for successful identifi ca-tion using optimization algorithms. The sensitivity analysis can be used furthermore to check for non-unique (multiple) solutions due to coupling of parameters which need to be identifi ed.

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Noisy signal measurements and corresponding optimized model response

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MU LTIOBJ ECTIVE OPTIMIZATIONIn case of confl icting objectives the calculation, visualization and investigation of the set of Pareto optimal solutions will give the base for decision making which of the designs could be chosen for production. In order to select one solution from the Pareto front, posterior preferences have to be defi ned and evaluated along the Pareto frontier.

ROBUSTN ESS EVALUATIONRobustness evaluation helps to quantify product quality in virtual prototyping. Investigating the sensitivity of responses with respect to all potentially effecting uncertainties optiSLang provides all necessary information to measure design robustness. As an important added value, optiSLang robustness evaluation quantifi es the infl uence of approximation errors (solver noise) on the response variation.

StrategyThe multiobjective optimization can be performed for con-tinuous, discrete and binary design variables under the con-sideration of design and manufacturing constraints. Multi-ple objective functions including multiple terms and weights can be defi ned. The use of evolutionary algorithms as well as Particle Swarm Optimization for solving multiobjective optimization prob-lems has been established for practical applications. The main advantage of the population based approaches is the parallel search for a set of Pareto-optimal solutions in a sin-gle optimization run. In these methods the fi tness function is assigned using Pareto strength ranking and diversity is pre-served by density estimation. Furthermore dominance based constraint handling is used.

Post processingThe main feature of the multiobjective post processing is the visualization of the objective space. If the problem defi ni-tion exceeds three dimensions, a 2D or 3D subspace can be selected and parallel coordinate plots can be used to select best designs out of the set of Pareto designs.

StrategyVariance based robustness evaluation analyzes the infl u-ence of the random input scatter onto the output variation, quantifi es the sensitivity of the scattering inputs, estimates the safety margins of critical response values in terms of sigma levels or failure probabilities. For this purpose the random scatter of the inputs has to be defi ned in terms of a distribution function (more than 20 classical distribution types are available) and an input correlation matrix. Based on this defi nition of uncertanties highly optimized Latin Hypercube Samples are generated and the output variation of each response are determined. Defi ning safety levels for the response values the corresponding safety margins are calculated. Using the Metamodel of Optimal Prognosis vari-ance based sensitivity indices quantify the infl uence of the scattering inputs on the responses.

Post processingThe robustness post processing provides anthill plots to-gether with histograms and the evaluation of statistical measures as distribution fi ts, correlation coeffi cients, Coef-

Best PracticeBefore starting Pareto optimization the detection of confl ict-ing objectives using sensitivity analysis and/or single objec-tive weighted optimization is recommended. Consideration of best designs out of sensitivity analysis and single objec-tive optimization runs in the start population signifi cantly improves the Pareto optimization performance.

fi cient of Importance as well as MOP based Coeffi cients of Prognosis. In order to check the output variation for critical responses the traffi c light plot shows statistical box plots to-gether with safety and failure limits.

Best PracticeInitially the scatter ranges of the inputs have to be defi ned with uniform distributions or more qualifi ed distribution types. Performing the robustness evaluation at a determin-istic optimum requires adjusting the mean values of design variables. After calculating the Latin Hypercube Samples the statistical and MOP analysis is carried out. If safety limits with small probabilities of failure are investigated the esti-mated sigma level shall be proven by an additional reliability analysis.

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Output histogram with distribution fi t and probability estimates

Traffi c light plot with indicated variation of the scattering outputs

Robustness post processing

Three-dimensional Pareto frontier

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RELIABI LITY ANALYSISVariance based robustness analysis is suitable up to a safety margin of two sigma. Larger safety margins up to six sigma imply small probabilities of failure. For such cases standard sampling methods are not applicable and more effi cient reliability methods are available in optiSLang.

ROBUST DESIGN OPTIMIZATION Robust Design Optimization (RDO) is optimizing the design under consideration of uncertainties. Quality and reliability are explicitly integrated in the optimization process. optiSLang RDO provides methods for Robust Design Optimization and Design for Six Sigma, which is a quality improvement process leading to products conforming to Six Sigma Quality.

StrategyAlthough Monte Carlo methods are mostly versatile, intui-tively clear and well understood, the computational cost is exorbitant in many cases. The effi ciency of further methods depends on the sigma level, the number of random variables, the number of possible failure mechanism and the proper-ties of the limit state functions. If these limit state functions are continuously differentiable the First Order Reliability Method (FORM) and Importance Sampling (ISPUD) are effi -cient but limited to only one dominant failure mechanism. Directional Sampling and Adaptive Sampling can be applied for a moderate number of random variables but also mul-tiple failure mechanisms and small probabilities of failure. If the number of random variables is not larger than 20 the Adaptive Response Surface Method (ARSM) provides the most effi cient approach. For a large number of random vari-ables and small failure probabilities Asymptotic Sampling is available.

Post processingThe reliability of post processing provides two and three-dimensional plots of the calculated samples used for the es-timation of the failure probability. In the ARSM the support points used for the approximation are shown as well. Addi-

StrategyBecause Robust Design Optimization simultaneously deals with optimization and robustness analysis, the computa-tional effort becomes very high. Therefore, the challenge in applying RDO is to fi nd a suitable balance between effort and accuracy of the robustness measures. Variance-based Robust Design Optimization addresses tasks with low sigma level. If the robustness requirements have to ensure small probabili-ties reliability based RDO becomes necessary. In optiSLang sequential RDO performing deterministic optimization with stepwise adjusted safety factors and simultaneously coupled RDO are available. As robustness measures the mean values, standard deviations, quantiles, failure probabilities and Tagu-chi loss functions of the response values can be fl exibly com-bined in constraints and objectives of the RDO problem.

Post processingAt fi rst glance the RDO post processing looks similar to that of a deterministic optimization. The defi ned robustness measures are treated as the deterministic response values at each optimization design. Additionally the samples used for the statistical evaluation of the robustness measures are shown in anthill plots. Using the RDO Design of Experiments also sensitivity indices of the robustness measures with re-spect to the design variables can be visualized.

tionally the convergence of the failure probability is plotted together with an estimate of its accuracy. Valuable informa-tion about the most probable failure point and algorithm specifi c details are given in additional windows.

Best PracticeDue to the limitation of some methods to a small number of random variables a sensitivity analysis should be performed initially in order to identify important random variables. With the remaining variables at least two different reliability methods shall be used to estimate and to compare the fail-ure probability. For this purpose a comparison of the Adap-tive Response Surface Method with the First Order Reliability Method or Directional Sampling is suggested.

Best PracticeDue to the higher computational effort of the simultaneously RDO procedure the sequential RDO is the preferable approach for time consuming solver runs. Introducing safety factors in the deterministic optimization constraints and their step-wise adjustment according to a variance based robustness analysis should lead to a robust optimal design. Neverthe-less, a fi nal reliability proof is necessary if a sigma level higher than three sigma (probability < 0,1%) is required.

Sampling based reliability analysis using Adaptive Response Surface approxi-mation

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Robust Design Optimization post processing

Variance-based Robust Design Optimization samples using ARSM in combina-tion with Advanced Latin Hypercube Sampling

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METHOD OVERVI EW

Process automation and process integration • Workfl ow defi nition via graphical user interface • Reliable use with help of wizards • robust default settings • Connection of arbitrary complex solver chains • Parallelization and distribution of design evaluation • Direct integration of MATLAB/Octave, Excel/OOCalc,

Python and SimulationX • Supported connection of ANSYS, Abaqus, LS-DYNA,

Adams, MADYMO • Arbitrary connection of ASCII fi le interfaced solvers • Full integration of optiSLang in ANSYS workbench • Python interfaces to optiSLang library

Sensitivity analysis • Classical Design of Experiments • Advanced Latin Hypercube Sampling • Correlation coeffi cients (linear, quadratic, rank-order) • Principal Component Analysis • Polynomial based Coeffi cient of Determination • Polynomial based Coeffi cient of Importance • Metamodel of Optimal Prognosis (MOP) with

Coeffi cient of Prognosis (CoP) • MOP/CoP based sensitivity indices for important variables

Multidisciplinary nonlinear optimization • Continuous, discrete and binary design variables • Gradient based optimization (NLPQL) • Global Response Surface optimization using MOP

with best design verifi cation • Adaptive Response Surface Method • Evolutionary Algorithms (EA) • Particle Swarm Optimization (PSO) • Stochastic Design Improvement • Multiobjective optimization using weighted objectives • Multiobjective Pareto optimization with EA and PSO • Start design import from previous samples

Parameter identifi cation • Parametrization of response signals • Signal function library including FFT, fi ltering etc. • Sensitivity analysis using MOP/CoP to check identifi ability • Flexible defi nition of identifi cation goal functions • Local and global optimization methods to search for

optimal parameters

Robustness evaluation • More then 20 probability distribution functions • Distribution fi ts using measurements • Continuous and discrete random variables • Correlated input variables using the Nataf model • Monte Carlo and Advanced Latin Hypercube Sampling • Statistical assessment of output variation including:

- histograms with automated distribution fi ts - stochastic moments - quantile and sigma level estimation • Sensitivity analysis using correlations and MOP/CoP

Reliability Analysis • Defi nition of arbitrary limit states • Monte Carlo and Latin Hypercube Sampling • First Order Reliability Method (FORM) • Importance Sampling Using Design Point (ISPUD) • Directional Sampling • Asymptotic Sampling • Adaptive Response Surface Method

Robust Design Optimization (RDO) • Sequential and fully coupled procedures • Variance based RDO • Reliability based RDO • Flexible defi nition of robustness measures using e.g.

mean values, variances, Taguchi loss functions and probability of failure • Consideration of robustness measures in optimization

constraints and objectives functions

Post processing • Statistic post processing including anthill plots,

correlation plots and sensitivity indices • Approximation post processing including 2D and 3D plots

of response surfaces and the MOP • Optimization post processing including Pareto frontier

and convergence history of design variables, responses, objectives and constraints • Parallel coordinates plot • Traffi c light plot • Full interaction of single plots • Design classifi cation using coloring, selection/deselection • High quality outputs in BMP, PNG, SVG, EPS and

PDF format

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STATISTICS ON STRUCTU RE (SoS)Statistics on Structure is DYNARDO’s post-processor for the visualization of statistical data on fi nite element structures to analyze the spatial distribution of variation and correlation as well as to detect “hot spots” of variation.

Why SoS?Any structure possesses some natural randomness due to material scatter or manufacturing tolerance. For CAE-based robustness evaluations, engineers need to evaluate statisti-cal data on fi nite element structures in order to locate “hot spots” of variation and investigate the cause of scatter by performing correlation analyses.

StatisticsThe following statistical measures can be plotted on the FE structure. • Descriptive statistics (like means, standard deviations,

coeffi cients of variation or quantiles) • Single designs and design differences • Statistics of eroded (failed) elements • Quality capability statistics

• Input/output correlation and Coeffi cient of Determination • Minimum, maximum, range

What is SoS?SoS reads structure discretizations (nodes, elements) and related results of structural computations with randomly simulated input. Based on these data, statistical measures are determined and visualized directly on the FE structure.

Visualization: Visualization of the statistical data is based on an interactive multi-window concept. Numerous possi-bilities are available for evaluation and documentation, and exporting of data for further analysis.

Data smoothing: The imported mesh can be reduced by SoS. Structure-related data is transferred to the new mesh by inter-polation, which leads to smoother representation of data.

Random fi eld projection: Based on random fi eld methodol-ogy, data are ex panded by a series of scatter shapes scaled by random amplitudes. The contributions of the series com-ponents to the total variation are ranked. With the identifi -cation of the most impor tant scatter shapes, the user can visualize different “mechanisms” of randomness. Export of the sample of am plitudes to optiSLang allows for correlation analyses with respect to the random input variables.

Eroded elements: Elements which failed during the previous structural analyses, e.g. in a crash analysis, are detected. The statistics of failed elements within the sample can be evalu-ated and visualized.

Interfacing: The reference structure and structure-related response data can be imported from several common FE pro grams. Samples of input data may be read from an optiSLang binary fi le or as text fi le. For further correla tion analysis, samples of selected output data and ran dom am-plitudes are exported as optiSLang result fi le.

Your benefi tSoS helps you to visualize and understand sources of scatter, assess the robustness of the structure and formulate quality requirements. By introducing SoS in the virtual product de-velopment process using stochastic analysis, you can:

• Locate “hot spots” of high scatter directly on the structure, • Analyse the most relevant shapes of imperfection or scatter, • Evaluate the infl uence of varying input on the structure’s

performance, • Identify correlations between input data and structural

results or mode shape amplitudes.

Example from crash simulation: Standard deviation of plastic strain (above) and fi rst two scatter shapes

SU PPORT, TR AI N I NGS, EVENTSWe provide our customers a full range of support offering consultancy services, seminars for beginners or more advanced users, tailored trainings for specifi c applications as well as user meetings to introduce you to new methods and current issues concerning CAE.

CUSTOMER STORI ESCustomers value our individual solutions and precise execution of analysis and optimization tasks in the fi elds of automotive, mechanical and civil engineering, geo-mechanics as well as micro-mechanics and process engineering. For detailed information about our consultancy expertise visit our web site.

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SupportThe main interest of the optiSLang support team is a suc-cessful customer. Therefore, we provide technical support to optiSLang users over the phone or e-mail where every sup-port request is processed thoroughly and promptly. We not only answer questions concerning the handling of optiSLang, but also give hints for an effi cient application of its various methods to solve our customers challenges.

TrainingIf you are looking for a competent and custom-made introduc-tion to optiSLang, visit our seminars which explain the theory and train the application of the methods of multidisciplinary optimization, robustness evaluation and robust design opti-mization in a compact way. Thereby, the areas and limits of applying the different methods in optiSLang to customers tasks are discussed. The well balanced ratio of lectures and ex-ercises is 50% each. Hence, the seminars are not only directed to engineers in the whole CAE-based simulation area. They are perfectly suited for decision makers in CAE, too.

ConsultingThe DYNARDO consulting team offers solutions for any part of your optimization or robustness task at our offi ces in Weimar and Vienna or directly at your company. Especially, when op-timization and robustness evaluation are introduced for the fi rst time into product development processes, a balanced mixture of customer product knowledge and DYNARDO’s con-sulting experience in CAE-based optimization and robustness evaluation will optimize our customers benefi t.

Annual Optimization and Stochastic Days With the Weimar Optimization and Stochastic Days (WOSD) an event was created which aims at promoting the success-ful application of CAE-based optimization and CAE-based sto-chastic analysis in virtual product design. Organized by the DYNARDO GmbH, a concerted exchange between scientifi c and industrial application is provided. It offers a good mixture between further education, qualifi ed workshops and practical oriented lectures. We explicitly do not only invite users as lec-turers or participants, we also offer optiSLang users the possi-bility of exchange with acknowledged specialists from science and industry for everyone who is interested in the topic.

BOSCH speaks optiSLangRobert Bosch GmbH was the fi rst optiSLang key customer. Starting at central depart-ments of research and development in 2002, today optiSLang is an integral part a large range of virtual product development processes at BOSCH. With the help of sensitivity studies, optimization and robustness evaluation Robert Bosch GmbH could improve its product performance signifi cantly. A strong partnership between Bosch and DYNARDO ensures a maximum of customer benefi t using CAE-based op-timization and robustness evaluation. Having many successful implementation of RDO procedures BOSCH is an early inventor of consequent implementation of CAE-based robust design optimization virtual prototyping.

Daimler evaluates robustness with optiSLangIn the framework of the virtual product development process of the Daimler AG, parametric CAE-models are employed for the evaluation and optimization of differ-ent functional requirements like driving comfort or crashworthiness behavior. Ro-bust dimensioning means to design a vehicle which is as insensitive as possible in relation to the existing scatter in material or production. In order to ensure robust-ness within the virtual prototyping Daimler started implementing optiSLang robust-ness evaluation as early as 2002 for NVH applications of driving comfort. Since then robustness applications have been rolled out to crashworthiness, brake squeal load cases as well as forming simulation.

NOKIA integrates sensitivity analysis and robustness evaluationFor high end consumer goods the robustness is a key functionality. Nokia imple-mented sensitivity analysis to identify critical drop direction of phone drop load cases as well as robustness evaluation of the drop test due to production toler-ances and material scatter into the virtual prototyping since 2008. With the help of optiSLang an robust product performance due to critical mobile phone drop condi-tions could be increased.

JapanTECOSIM Japan LimitedMimura K2 Bldg. 4011-10-17 Kami-kizakiUrawa-ku, Saitama-shiSaitama 330-0071 Japanwww.tecosim.co.jp

KoreaCAE Technology Inc.A-208, Seoul Hightech Venture Center29, Gonghang-daero 61-gil,Gangseo-gu, Seoul 157-030, Koreawww.caetech.co.kr

TaeSung S&E Inc.Kolon Digital Tower 210F, Seongsu-dong 2 gaSeongdong-guSeoul 333-140, Koreawww.tsne.co.kr

ChinaPERA GLOBAL Holdings Inc. Standard Chartered Tower 201Century Avenue, Suite 7 B-C Shanghai, 200120 www.peraglobal.com

Germany & worldwideDynardo GmbHSteubenstraße 2599423 WeimarTel.: +49 (0)3643 900 830Fax. +49 (0)3643 900 839www.dynardo.decontact@dynardo.de

Dynardo Austria GmbHWagenseilgasse 141120 Vienna Austriawww.dynardo.atcontact@dynardo.at

GermanyCADFEM GmbHMarktplatz 285567 Grafi ng b. MünchenGermanywww.cadfem.de

science + computing agHagellocher Weg 7372070 TübingenGermanywww.science-computing.de

AustriaCADFEM (Austria) GmbHWagenseilgasse 141120 WienAustriawww.cadfem.at

SwitzerlandCADFEM (Suisse) AGWittenwilerstrasse 258355 Aadorf www.cadfem.ch

Czech Republic, Slovakia, HungarySVS FEM s.r.o.Škrochova 3886/42615 00 Brno-ŽideniceCzech Republicwww.svsfem.cz

RussiaCADFEM CISSuzdalskaya Str. 46-203111672 Moscowwww.cadfem-cis.ru

IndiaCADFEM Engineering Services India6-3-887, MCP Arcade 4th FloorRaj Bhavan Road, SomajigudaHyderabad 500 082www.cadfem.in

USACADFEM US, Inc.3 Research DriveGreenville, SC 29607www.cadfem-us.com

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