dynamic software & engineering
CAE-Software
Sensitivity analysis Multiobjective optimization Multidisciplinary optimization Robustness evaluation Reliability analysis Robust Design Optimization (RDO) optiSLang
optiSLang multiPlas ETK SoS ANSYS optiSLang
ANSYS optiSLang
Combining powerful parametric model capabilities with Robust Design Optimization
ANSYS Workbench provides leading technology for parametric and persistent CAD and CAE modelling for simulation driven product development. optiSLang focuses on effi ciency and automation of RDO methods for complex non-linear analysis models with many parameters, including stochastic variables. ANSYS Workbench project screen with the three optiSLang drag and drop modules sensitivity analysis, optimization and robustness evaluation to defi ne an RDO analysis. This includes robust handling of design failures and solver noise.
ANSYS optiSLang offers several modes of interoperability • using parametric ANSYS Workbench models with the In addition ANSYS optiSLang provides eral cores with ANSYS Remote Solve Manager and the use • using the optiSLang Workbench plugin to expose optiSLang GUI with the help of the optiSLang ANSYS • Flexible text-based interfacing tools that can connect of ANSYS HPC Pack Parametric Licenses for simultaneous optiSLang technology within the ANSYS Workbench GUI Workbench integration node ANSYS products, or any scriptable products, that may be computing of different designs are fully integrated. With • using text-based interfacing between ANSYS and optiS- part of your engineering process the continue crashed session option, further processing of Lang The optiSLang Workbench plugin toolbox includes the • Interfacing between optiSLang GUI and parametric aborted analyses is secured using all previously computed modules for sensitivity analysis, optimization and robust- ANSYS Workbench models via optiSLang’s ANSYS Work- data. All successful designs are stored in optiSLang’s data- ness evaluation which can easily be dragged and dropped bench integration node base and can be used independently from the ANSYS Work- onto the desktop to form an interactive process chain. • Easy to switch from Workbench integrated to interfacing bench design table. Furthermore, adding designs or recal- mode at any time culation is possible at any time. • Full functionality, including support for parameters and optiSLang Workbench plugin - General Features responses not extractable or integrated in ANSYS Work- • Automatic identifi cation of important parameters dur- bench, e.g. non-scalable responses such as load displace- ing sensitivity analysis ment curves • Automatic buildup of best possible regression functions • Flexilbity to include 3rd party solvers, along with ANSYS (meta models) having best possible forecast quality to technology, in the process chain response variation in a given sample set • Multidisciplinary and multiobjective optimization • Robustness evaluation Application • optiSLang’s minimalist philosophy reduces the number From ANSYS Workbench version 14.0, the optiSLang inte- of CAE solver runs gration can be used easily with drag and drop functional- • Designed for large numbers of parameters and non- ity. The user only needs to set up the variation space and linear RDO tasks the objectives. Then, optiSLang automatically identifi es • Predefi ned insightful and effi cient result post-processing the Metamodel of Optimal Prognosis. Afterwards, a Best- module Practice-Management generates the appropriate methods for optimization. The options for parallel computing at sev- Wizard to select the most appropriate optimization algorithms Extensive GUI for MOP-Postprocessing
1 www.dynardo.de 2 ANSYS optiSLang
PRODUCT OVERVIEW ANSYS OPTISLANG
Since market launch in 2002, optiSLang has evolved into one of the leading software solutions for CAE- based sensitivity analysis, optimization and robustness evaluation. Due to user-friendly automated workfl ows, effi cient methods and a powerful post-processing, optiSLang provides the basis for your Typical workfl ow using sensitivity analysis, optimization using meta-models and validation of the best design effi cient CAE-based Robust Design Optimization (RDO).
RDO in virtual prototyping The goal of CAE-based optimization in virtual prototyping tify the important scattering variables and quantifi es and making while only requiring a minimum of solver runs. appropriate functional model is chosen to result in the best is often to achieve an optimal product performance with explains result variations of product behavior. The distinc- Consequently, even RDO tasks involving a large number possible prognosis quality of variation based on a given set a minimal usage of resources (e.g. material, energy). This tive features of optiSLang provide you with a maximum of of optimization variables, scattering parameter as well as of designs. Here, the MOP represents the most important pushes designs to the boundaries of tolerable stresses, de- variation prognosis quality and result reliability for decision non-linear system behavior can be effi ciently solved. Dur- correlations between parameter input and result variation. formations or other critical responses. As a result, the prod- ing this process, optiSLang’s Best-Practice-Management If the prognosis quality of variation is high, MOPs can be uct behavior may become sensitive to scatter with regard feature automatically selects the appropriate optimization used to replace the CAE-calculations in optimization proce- to material, geometric or environmental conditions. Subse- algorithms and their settings. The procedures are guided dures or robustness evaluations. quently, a robustness evaluation has to be implemented in by intuitive drag & drop-workfl ows and powerful post-pro- the optimization task leading to a Robust Design Optimiza- cessing tools. Within a controlling workfl ow, any CAE simu- tion (RDO) strategy that consists of: lation data can easily be integrated and again made acces- Robustness Evaluation and Reliability Analysis sible for external solvers as well as pre and post processors. When optimized designs are sensitive toward scattering ge- 1. Sensitivity analyses to identify the most affecting pa- Thus, optiSLang gives you the opportunity to benefi t from ometry, material parameters, boundary conditions or loads, rameters regarding the optimization task the full capabilities of parametric studies in order to inno- a verifi cation of product robustness as early as possible in 2. Multi-disciplinary and multi-objective optimizations to vate and accelerate your virtual product development. the development process becomes a core requirement of determine the optimal design CAE-based virtual product development. The implementa- 3. Robustness evaluations to verify robustness values and tion of robustness evaluation procedures has always been failure probabilities Coeffi cient of Prognosis (CoP) and the a key feature in Dynardo’s software development. Today, Metamodel of Optimal Prognosis (MOP) optiSLang provides one of the most powerful sets of algo- Variable reduction and the application of reliable quanti- rithms available for commercial application. It enables the RDO with optiSLang tative measures of variable importance are the main chal- user to conduct a reliable determination of failure probabil- optiSLang expands the capabilities of parametric optimi- lenges in parametric sensitivity analysis. optiSLang’s sensi- ities by evaluating the result value variation including the zation studies to RDO. For example, the software includes tivity module generates the CoP which enables you to fi lter identifi cation and consideration of relevant scatter input the infl uence of scattering inputs, uses statistics to iden- the relevant input parameters. This ensures that the most parameters. 3D visualization of the Metamodel of Optimal Prognosis
3 www.dynardo.de 4 RDO–Methodology
MASTER OF DESIGN – CAE-BASED ROBUST DESIGN OPTIMIZATION WITH OPTISLANG
Sensitivity analysis, optimization and robustness evaluation with a minimum amount of user input and solver runs for your effective virtual product development
A U T L T S O M A F A U T E • Identifi cation of the relevant input parameters and D E D L M response values (sensitivity analysis + CoP/MOP) A O • Stochastic sampling (LHS) for optimized scanning M D • Pre-optimization of the parameter sets with MOP T I U of multi-dimensional parameter spaces L P A without additional solver runs O R • Quantifi cation of prognosis quality (CoP) of meta-models • Further optimization of the parameter sets with the most
• Generation of the Metamodel of Optimal Prognosis (MOP) appropriate algorithms (Best-Practice-Management)
A R I A SENSITIVITY V T I O E R N OPTIMIZATION T E ANALYSIS M A R A P
L CAE-Data A
M I Optimal Design
N I
M
L
E
S
S
S
O
L
Measurement V
Data E
R -
MODEL CALIBRATION R • Effi cient methods of stochastic analysis for the U
N determination of failure probabilities
• Find the best fi t for simulation and measurement S
• Evaluation of result value variation
• Identifi cation of the relevant scatter input parameter
(CoP + MOP) Coeffi cient of Prognosis (CoP)
The CoP quantifi es the forecast quality of a meta-model (re-
gression model) for the prognosis of a result value.
ROBUSTNESS EVALUATION
Metamodel of Optimal Prognosis (MOP)
The MoP represents the meta-model with the best progno- with the help of meta-models. Thus, a No Run Too Much- sis quality of the result value. For the determination of the strategy will be implemented with a maximum of progno- MOP, subspaces of important input variables are evaluated sis quality for correlations in regard to design evaluations.
5 www.dynardo.de 6 S Process Integration and Automation S E C O ITIVIT R S Y N A O P E N Virtual product development - S A P E L T Y I A S M C I I S Z A T IO N
Understand
Input 1 Parameter reduction by Improve Output 1
sensitivity analysis Wizard based
optimization
ESS
TN E S VA U L B U Input 2 Output 1 O A R T I O
N
Analyze Input n Check of robustness Output n and reliability
PROCESS INTEGRATION AND AUTOMATION Statistics on Extraction Tool Kit Process integration Structures (SoS) (ETK) easy setup supported by wizard-based user interface Interactive process automation and integration as well as constant access to design parameters are the Analysis and generation Extraction of e.g. CAD, MBS, FEM, CFD, EM, Matlab, Excel, in-house solver ... key for successful CAE - based parametric studies. In optiSLang, this procedure is guided and supported of fi eld data simulation results by wizards and default settings.
Process integration optiSLang inside ANSYS Workbench Interfaces and automation optiSLang supports the interfacing to almost any software are displayed at the same time. This enables full access and optiSLang inside ANSYS Workbench provides the user with optiSLang provides several interfaces. The provided Python, tool which is used in virtual product development. The inter- traceability of the complete workfl ow. The user can connect any a direct integration into the parametric modeling environ- C++ and command line interfaces allow the automatic cre- faces are mainly used “inside optiSLang”. Thus, in optiSLang complex simulation processes of CAE solvers, pre- and postpro- ment of this standard CAE software. Thus, it can be ac- ation, modifi cation and execution of projects. As a conse- context, they are called “tool integrations”. Nowadays, more cessors in heterogeneous networks or clusters. They are autom- cessed through a minimized user input. The Workbench quence, the usage within custom applications is secured than 100 different CAx software solutions are coupled with atized either in a single solver process chain or in very complex functionality is also broadened by optiSLang’s signal pro- and optiSLang projects can be integrated into customized optiSLang. The new generation of optiSLang gives access to: multidisciplinary / multidomain fl ows. Even performance maps cessing integration. Users are able to implement responses platforms. Repetitive and exhausting tasks can be stan- and their appraisal can be part of standardized projects. not yet extractable or integrated in ANSYS Workbench, e.g. dardized and automatized. • CAD (Catia, Nx, Creo, Solidworks …) non-scalar responses like load displacement curves. Alter- • CAE (ANSYS, Abaqus, AMESim …) natively, for integration of ANSYS Workbench projects in • MS Excel, Matlab, Python … COSTS optiSLang, an integration node is available. Extensibility • In-house solver The openness of Dynardo’s premium software also enables users to plug-in their own: Different parametric environments can be collected and CFD combined to one automatized parametric workfl ow for • Algorithms for DOE, Optimization, Robustness etc. modern product development. • Meta-models (CAD-) FEM I • Tool integrations Modell REPORT Defi nition of CAx Workfl ows Current requirements for fl exibility and upcoming requests PARAMETERS The graphical user interface supports the workfl ow approach FEM II for extensibility are satisfi ed by those interfaces. Therefore, visually by single building blocks and algorithms which are optiSLang is the platform to address future needs of virtual graphically coupled in order to show dependencies and schedul- product development. ing. The relationships can be determined and controlled in one MBS, EM ... context. Easily understandable charts as well as control panels Graphical user interface of ANSYS Workbench with optiSLang integration
5 www.dynardo.de 6 Sensitivity Analysis
Latin Hypercube Sampling (LHS) Minimization of solver runs by using advanced LHS with minimal input correlation error T S U L A E F A D U T Parameter Bounds L O A M M Defi nition of the design space I A T T P E with variation ranges of O D
optimization parameter M
O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S
A Important variables and
S
M
I S
O
N best meta model
I
L
V
SENSITIVITY ANALYSIS M
E
R
-
R • Identifi cation of the most impor-
U
N
S
By means of a global sensitivity analysis and the automatic generation of the Metamodel of Optimal tant variables fi ltered by auto- Prognosis (MOP), optimization potential and the corresponding important variables are identifi ed. With matic workfl ows this previous knowledge, task-related objective functions and constraints can be defi ned as well as Variable Contribution and Prognosis Quality • Automatic selection of the meta suitable algorithms can be selected. • Verifi cation of prognosis quality for response variation model with the best possible • Verifi cation of optimization parameter contribution forecast quality (MOP)
Practical Application Design variables are defi ned by their lower and upper bounds • Quantifi cation of the forecast quality of a meta-model x1 x2 x3 x4 x5 y or by several possible discrete values. In industrial optimization (regression model) for the prognosis of result value 0.189507 0.423225 0.647602 0.0261494 0.0613115 tasks, the number of design variables can often be very large. variation by the Coeffi cient of Prognosis (CoP) With the help of a sensitivity analysis, engineers can accurately • Identifi cation of the most important input variables 0.00129613 0.00655266 -0.00150015 0.00972097 identify those variables which effectively contribute to a possi- related to each result value, constraint and objective ble improvement of the optimization goal. Based on this iden- • Minimization of solver runs by MOP/CoP workfl ow tifi cation, the number of design variables is decisively reduced -0.00219622 0.00136814 -0.00880888 and an effi cient optimization can be conducted. Additionally, a sensitivity analysis helps to formulate the optimization task Methods 0.00518452 0.0070207 appropriately concerning the choice and number of objectives, • Defi nition of optimization variables with upper and their weighting or possible constraints. Furthermore, it is used lower bounds -0.0105491 to estimate the numerical noise of the CAE solver as well as the • Defi nition of the Design of Experiments (full factorial, proper physical formulation of the design problem. central composite, D-optimal) • Latin Hypercube Sampling for optimal scanning of x1 x2 x3 x4 x5 y multi-dimensional parameter spaces Best Practice • Automated generation of the MOP • Coverage of the entire design space by optimized Latin • Quantifi cation of the prognosis quality by the CoP 3D plot of single response with respect to the most important variables Extended linear correlation matrix Hypercube Sampling (LHS) and minimization of correla- tion errors among input variables • Identifi cation of optimization potential and confl icting Postprocessing & Visualization objectives • Histograms • Identifi cation of the meta-model with the best progno- • Correlation matrix / Parallel Coordinate Plots sis quality of the result value variation in the most fi t- • 2D and 3D anthill plots / 2D and 3D plots of the MOP ting sub space of important variables by MOP workfl ow • Principal Component Analysis
7 www.dynardo.de 8 Multidisciplinary Optimization
Sensitivity analysis Understand the design • Defi nition of the design space • Selection of the most important design
with optimization variables T S variables with the help of CoP/MOP U L A • Scan of the design space with E F A • Verifi cation of parameter ranges, D U T L O advanced LHS A M response extraction, constraints M I A • Identifi cation of Metamodels of T T and objectives P E Optimal Prognosis (MOP) by O D
CoP/MOP workfl ow M
O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S A
S
M
Pre-optimization using the MOP
I S
O
N
I
L
V
M
Optimization of the design with
E
R
-
R
U
N
S
MULTIDISCIPLINARY OPTIMIZATION
Final optimization based on knowledge only one additional CAE solver call from the sensitivity and pre-optimization step by using the MOP optiSLang provides powerful optimization algorithms and automated workfl ows for an effi cient • Selection of the most appropriate optimizer determination of optimal design parameters regarding various multidisciplinary, nonlinear and and start design multicriteria optimization tasks. • Exploring the limits of the design
Practical Application Methods Structures and sub-systems need to often be designed • Gradient-based methods (NLPQL) to withstand multidisciplinary load cases. For example, • Nature-inspired Optimization Algorithms (NOA) incl. 1. Iteration vehicle body structures are exposed to crash (non-linear Genetic Algorithms (GA), Evolutionary Strategies (ES) transient), Noise Vibration Harshness (frequency domain), and Particle Swarm Optimization (PSO) stiffness (linear static), durability (linear static) and aerody- • Automatic Adaptive Response Surface Method (ARSM) in namics (CFD). The structural requirements to meet loads in case of less than 20 important optimization variables objective 3. Iteration one discipline are very often different to requirements for loads in other disciplines. Unless loads from all disciplines are considered simultaneously during the optimization Postprocessing & Visualization process, the resulting design will not be well balanced for • Interactive post processing adapted to the optimization objective 5. Iteration structural performance. Multi-disciplinary optimization is algorithm Adaptation scheme of the ARSM algorithm essential to achieve this objective. • Fast investigation of optimization performance using different visualization options objective • Selection of individual designs Best Practice • Identifi cation of the most relevant input parameters and response values with the help of a sensitivity analysis and CoP/MOP Adaptation scheme of the ARSM algorithm Evolutionary Algorithm solving constraint optimization problem with noisy • Pre-optimization of parameter sets using the MOP with only objective function one additional solver call • Optimization wizard for automatic selection of the most fi tting algorithms for design optimization • Easy defi nition of parameter range, objectives and con- straints
9 www.dynardo.de 10 Multiobjective Optimization
Understand the design Sensitivity analysis • Selection of the most important design • Defi nition of the design space variables by using CoP/MOP
with optimization variables T S U L • Verifi cation of parameter ranges, response A • Scan of the design space with E F A D U extraction and constraints T L O advanced LHS A M M • Verifi cation of the confl icting I A • Identifi cation of Metamodels of T T P E character of objectives Optimal Prognosis (MOP) by O D
CoP/MOP workfl ow M
O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S A
S
M
I S Pre-optimization using the MOP
O
N
I
L
V
M
E
• Investigation of the Pareto Frontier by
R
-
R
U
N
S
MULTIOBJECTIVE OPTIMIZATION
Final optimization based on knowledge using the MOP from the sensitivity and pre-optimization step • Verifi cation of important designs with Multiobjective optimization is applied when several confl icting objectives occur. Considering these additional CAE solver calls objectives simultaneously leads to a set of Pareto optimal solutions which can be used for choosing the • Selection of the most appropriate optimizer and start designs best production design. • Derivation of the Pareto Frontier
Practical Application Methods Optimization, robustness and reliability studies have an • Use of evolutionary algorithms and Particle Swarm increasing importance in industrial engineering. Often, Optimizations there are confl icting objectives in the optimization task, • Fitness assignment using dominance-based ranking for example minimum mass versus maximum stiffness of • Dominance based constraint handling the product. A sensitivity study is performed in order to • Verifi cation of diversity by density estimation identify the most relevant parameters for confl icting objec- tives and to formulate the objective functions properly. As a result, the frontier of Pareto optimal solutions allow to Postprocessing & Visualization quantify the trade-offs in satisfying confl icting objectives • Visualization of the objective space and to choose an optimal design which represents the best • Selection of 2D or 3D subspace visualizations compromise between the objectives for the particular de- • Parallel coordinate plots and cluster analysis for best sign application. Finally, this design can be evaluated in a design selection subsequent robustness analysis.
Best Practice • Detection and evaluation of confl icting objectives • Verifi cation of confl icting objectives by single optimiza- Pareto frontier of two objective functions Three-dimensional Pareto frontier tions with weighted objective functions • Integration of the previous knowledge obtained from sensitivity analyses and weighted optimizations into the initial function of Pareto optimization
11 www.dynardo.de 12 Parameter Identifi cation
Verifi cation of the response variation window Verifi cation that the variation window of the
T S results to be identifi ed include the Sensitivity analysis U L A E F A experimental results • Defi nition of the calibration D U T L O design space by using continuous A M M I A T T varying parameter P E O D
• Scan of the calibration
design space M O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S A
S
M
I S Formulation of the identifi cation task
O
N
I
L
V
M
E
• Identifi cation of sensitive input parameter
R
-
R
U
N
S
PARAMETER IDENTIFICATION
• Selection of best measures to compare Best possible fi t simulation with experimental results The parameter identifi cation, also named model update, identifi es parameters of CAE models suitable Identifi cation of the best possible fi t with the • Extraction of start values for the best possible calibration with test results. Methods of parameter identifi cation can also identify appropriate optimizer depending on the dimension values that are not directly measurable, such as material parameters. and/or type of sensitive optimization parameter
Practical Application Methods Coefficients of Prognosis (using MoP) Coefficients of Prognosis (using MoP) Measurement data represents characteristic system responses • Consideration of scalar response values full model: CoP = 97 % full model: CoP = 95 %
that are critical to validate and to improve the physical model • Defi nition of multi-channel signals, e.g. time-displace- r r 4 4 INPUT: m INPUT: Ekin of the system. In the context of parameter identifi cation, model ment curves 7 % 16 % 3 update means using fi eld observations and simulation runs to • Extensive library of functions, e.g. local values as maximum 3 INPUT: D INPUT: m 9 % 23 % approximate simulation model parameters. By means of sen- and minimum amplitudes, global values as integrals of 2 2 INPUT paramete INPUT paramete INPUT: k INPUT: k sitivity analyses, it is fi rst detected which parameters actually certain properties and more complex signal calculations 41 % 28 % 1 1 INPUT: Ekin INPUT: D have an infl uence on the simulation results and the calibration • Defi nition of individual objective functions 47 % 35 % procedure. Furthermore, the analysis helps to defi ne suitable • Metamodel of Optimal Prognosis (MOP) for sensitivity 0 20 40 60 80 100 0 200 40 60 80 CoP [%] of OUTPUT: max2 CoP [%] of OUTPUT: max8 measures to quantify the difference between measurement analysis of different signal properties and pre-evaluation and simulation. Finally, it can be analyzed whether the inverse • Several optimization algorithms (e.g. gradient-based or 1.5
problem can be solved non-ambiguously, which means there is nature-inspired) 1 a unique parameter combination that allows optimal match- 0.5 0
ing between measurement and simulation. disp_ref[m] -0.5
Postprocessing & Visualization -1
• Histograms -1.5 0 2 4 6 8 10 Best Practice • Illustration of statistical evaluations time [s] • Sensitivity analysis to check unknown parameters for • Visualization of signal functions and the corresponding signifi cant infl uence on the model response with reference value for each design evaluation Sensitivity analysis at different signal values Experimental setup of a wedge splitting test [Trunk 1999] (top left) | 2D simula- • CoP identifi es the best possible result extraction by com- tion model (top right) | simulated curves from the sensitvity analysis (bottom) paring model and measured values • CoP verifi es the uniqueness of the best possible correla- tion model between parameter and result variation • Check for non-unique (multiple) parameter sets due to coupling of parameters which need to be identifi ed
13 www.dynardo.de 14 Robustness Evaluation
Scan the Robustness Space • Creation and calculation of a small set (100) of
possible design scenarios by using LHS T S Input Parameter Variation U L A • First estimation of probabilities using the E F A Defi nition of the robustness space D U T L O histogram with the best possible translation A M M I A of expected input scatter T T P E O D into stochastic variables
M
O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S
A
S Investigation of response variation M
I S
O
N
I
L
V Investigation of the response
ROBUSTNESS EVALUATION M
E
R
-
R
U
N
variation by using coeffi cients S
optiSLang quantifi es the robustness of designs by generating a set of possible design realizations on the of variation, standard deviation, basis of scattering input variables. Optimized Latin Hypercube Sampling and the quantifi cation of the Verifi cation of responses variation sigma levels and probability of limit prognosis quality of the result variation by the Coeffi cient of Prognosis (CoP) ensure the reliability of the • Identifi cation of the causes of responses variations violation variation and correlation values with a minimum of design calculations. and the related scattering of in/out variables • Identifi cation of the best strategy to improve robustness
Practical Application Often, highly optimized designs are pushed to the boundaries • Quantifi cation of robustness by the histogram of result of their feasible performance. For this reason, it is necessary values including fi tting of distribution function and ap- to investigate how these designs are affected by scattering in- proximation of violation probability put variables, which could be geometry, material parameters, boundary conditions or loads. In order to cope with the un- avoidable uncertainties in operating conditions as well as in Methods manufacturing process, it is essential to introduce appropriate • Stochastic input variables with distribution types and robustness measures based on uncertainty analysis. A pos- input correlation sible fi rst measure is the variance indicator where the relative • Optimized Latin Hypercube Sampling variations of the critical model responses are compared to the • Fitting of distribution function in the histogram of result relative variation of the input variables. values • Approximation of Sigma margins • Approximation of violation probability Best Practice • Defi nition of uncertainties as the crucial input of a robustness analysis Postprocessing & Visualization • Predefi ned distribution function types and an input • Histograms to illustrate scatter of result values correlation matrix to support the defi nition of scattering • Correlation matrix, MOP-based CoPs for statistical evalu- Extended matrix of correlations Histogram with probability of violation and Sigma margins input variables ation • Automated generation of optimized Latin Hypercube • Distribution fi tting, Sigma values, violation probabilities Samples (LHS) to scan the robustness space • Traffi c light plot to check the violation of limit values of • Identifi cation of the most affecting input scatter using critical responses the MOP/CoP workfl ow
15 www.dynardo.de 16 Reliability Analysis
Scan the Robustness Space • Creation and calculation of a small set (100) of
possible design scenarios by using LHS T S Input Parameter Variation U L A • First estimation of probabilities by using E F A Defi nition of the robustness space D U T L O the histogram with the best possible translation A M M I A of expected input scatter T T P E O D into stochastic variables
M
O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S A
S
M
Verifi cation of probabilities
I S
O
N
I
L
V
RELIABILITY ANALYSIS M
Verifi cation of the estimation of
E
R
-
R
U
N
S
rare event probabilities by using The reliability analysis in optiSLang provides powerful numerical algorithms for the determination of appropriate reliability analysis small violation probabilities (less than 1 out of 1000). Thus, a reliability analysis allows the necessary fi nal Verifi cation of responses variation verifi cation of small probabilities of failure after the conduction of a robustness evaluation or Robust • Identifi cation of the causes of responses variations Design Optimizations (RDO). and the related scattering of in/out variables • Identifi cation of the best strategy to improve robustness
Practical Application Methods In many cases, optimized designs need to meet high safety • First Order Reliability Method (FORM) and Importance or quality requirements that have to correspond with low Sampling Using Design Point (ISPUD) for continuously failure probabilities (less than 1 out of 1000). Here, a reli- differentiable limit state functions ability analysis is necessary to investigate how these de- • Directional Sampling and Adaptive Sampling (AS) for a signs are affected by scattering input variables, e.g. geom- moderate number of random variables, multiple failure etry, material parameters, boundary conditions or loads. As mechanisms and small probabilities of failure an alternative to the estimation of safety distances by using • Adaptive Response Surface Method (ARSM) as most ef- standard deviations in robustness evaluations, a reliability fi cient method for less than 20 random variables analysis calculates the probability whether a certain limit will be exceeded by using stochastic analysis algorithms. With a reliability analysis, the rare event of violation can be Postprocessing & Visualization quantifi ed and proven to be less than an acceptable value. • Histograms • 2D/3D anthill plots • History plots Best Practice • Violation probabilities • Robustness evaluation for the approximation of viola- tion probabilities and for the identifi cation of important random variables as the basis for an appropriate selec- Reliability analysis using Adaptive Response Surface Method Application of directional sampling procedure tion of methods regarding a reliability analysis • Defi nition of one or various failure mechanisms using limit state functions • Recommendation of verifying low probabilities of failure with two alternative algorithms of reliability analysis
17 www.dynardo.de 18 Robust Design Optimization (RDO)
Scan of the design and robustness space • Identifi cation of important optimization variables
S • Identifi cation of the response variation and U L T Sensitivity Analysis F A D E safety margins for design robustness L A • Defi nition of the design space by A U T I M O using optimization variables T M P A O • Defi nition of the robustness T E
D space given by all relevant
scattering variables M O
D
U
L
A
R
N
O
I
T
C
A
R
E
T
N
I
R
E
S
U
L
E
L
S A
S
M
I S Robust Design Optimization
O
N
I
L
V
ROBUST DESIGN OPTIMIZATION (RDO) M
E
• Searching the design space for
R
-
R
U
N
S
optimal designs The Robust Design Optimization (RDO) combines CAE-based optimization with robustness evaluation • Robustness evaluation of all or and allows a product optimization with a synchronized assurance of robustness. optiSLang provides Final proof of design reliability selected optimization candidates iterative as well as simultaneous methods for variance-based and reliability-based RDO including tasks Prove of the design reliability in terms of sigma levels by using sequential or simultaneous conforming to Design For Six Sigma (DFSS). or probabilities of violation by using a reliability analysis RDO strategies
Practical Application Postprocessing & Visualization The main idea behind RDO is the consideration of uncertain- • Reliability-based RDO for tasks with high sigma level • Histograms ties in the design process. There are different sources of un- • Simultaneous RDO in case of sharply varying safety margins • Anthill plots to visualize deterministic response values certainties like loading conditions, tolerances of geometrical • Sequential RDO with deterministic optimization and • Additional illustration of statistical evaluation of the dimensions or material properties caused by production or de- stepwise adjusted safety factors as best practice method robustness measures terioration. Some can have a signifi cant impact to the design in the majority of cases • Violation probabilities and sensitivity indices of robust- performance which has to be considered in the design optimi- • Recommendation of fi nal reliability proof for tasks with ness measures zation procedure. This can be done by an iterative RDO. It com- a sigma level higher than three bines deterministic optimization with variance or probability based robustness analysis at certain points during the optimi- zation process. If necessary safety distances vary strongly in the Methods design space, a simultaneous RDO has to be run. In this case, the robustness measures of every design on the optimization Variance-based RDO loop have to be estimated by using a stochastic analysis. • Evolutionary Algorithm (EA), Genetic Algorithms, ARSM • EA combined with robustness evaluation Best Practice • Adaptive response surfaces in combination with robust- • Defi nition of the design space of optimization variables ness evaluation as well as the robustness space of all scattering variables • Initial sensitivity analysis within the design space as well Reliability-based RDO as initial robustness evaluation within the space of scat- • Evolutionary algorithm, genetic algorithms, ARSM tering variables in order to identify important parame- • Evolutionary algorithm combined with First Order Reli- ters, optimization potential, initial violation probabilities ability Method (FORM)
and safety margins • Adaptive response surfaces for optimization and reli- Varying location of the optima and contour lines of constraints as a conse- Variance-based Robust Design Optimization samples using ARSM in combi- • Variance-based RDO for tasks with low sigma level ability analysis quence of uncertainties nation with Advanced Latin Hypercube Sampling
19 www.dynardo.de 20 Statistics on Structures
STATISTICS ON STRUCTURES
The software solution for the analysis and simulation of data being distributed in space or time. Statistics on Structures (SoS) provides you with pre- and post- processing tools for spatially distributed 3D data and Hot spot detection example: In a deep drawing simulation (metal forming production process) the plastic strain must not exceed a certain threshold by a given can be applied to sensitivity analysis, optimization, robustness evaluation and RDO. probability. On the left: Visualization of critical zones (in yellow and red) for the non-exceedance probability of the threshold on the FEM mesh and statistical identifi cation of the most likely failure point. Right: Detailed robustness evaluation at the hot spot in optiSLang: Distribution fi tting, evaluation of thresholds and sensitivity analysis with variable ranking.
Background Hot spot detection Benefi ts SoS enhances optiSLang’s capabilities of parametric studies to One major diffi culty when analyzing fi eld data is that posi- • Reliable and simple detection of hot spots, e.g. potential • Realistic description of random effects on FE structures fi eld data. Examples of fi eld data are tions of maxima and minima may change in space or time. failure locations by statistical measures • Detection of hot spots and potential failure locations By taking the whole fi eld variation into account, the identi- • Reduction of numerical complexity by separation of loca- • Analysis of causes and effects of production tolerances • Time histories (e.g. signal processing, parameter calibra- fi cation of hot spots can be simplifi ed, leading to increased tion and response, increases accuracy of further analysis and natural scatter tion, loading curves) accuracy of numerical results in robustness evaluations, • Supporting the mitigation of quality problems • Geometric deviations (e.g. geometric boundary, shell meta-modeling and sensitivity analyses. Correlation analysis of variations • Application of robust design optimizations thickness, thickness of composite layers) • Identifi cation and ranking of input parameters that • Material properties (e.g. distribution of mortar and The 3D visualization provides further confi dence in statisti- infl uence the variation of the model response admixtures in concrete, porosity in ceramics, friction cal results of FEM data and helps to understand variations • Spatially local sensitivity analysis at hot spots using Extension of optiSLang to signals and spatially parameters on surfaces) in numerical CAE models. Random fi eld models allow a pa- optiSLang’s Metamodel of Optimal Prognosis (MOP) to distributed data using SoS • Damages (e.g. distribution of cracks, residual strains after rameterization of fi eld data through scatter shapes. Thus, identify and rank important input parameters optiSLang SoS forming), pre-stress distribution and loading conditions SoS is also able to generate imperfect designs, allowing the • Spatially global sensitivity analysis using spatial correla- consideration of spatially and temporally distributed per- tions and noise pre-fi ltering (F-MOP) to visualize the in- Optimization turbations as inputs in robustness studies. fl uence of individual input parameters on the FEM mesh Hot spot detection signals 3D fi eld
• Improved accuracy for small number of design evaluations Sensitivity analysis scalar 3D fi eld, signals
Optimization on meta model scalar 3D fi eld, signals Highlights Random fi eld models • Simulation of imperfect designs (e.g. random geom- Robustness evaluation Visualization of statistical properties on FEM meshes etries, pre-damage, time signals … ) Generation of random designs scalar 3D fi eld, signals
• Intuitive GUI with many statistical functions • Predict variation of fi eld data using nonlinear fi eld meta Compute robustness measures scalar, signals 3D fi eld • Extensive 3D data visualization models (F-MOP) in optimization Hot spot detection signals 3D fi eld • Easy integration into custom CAE processes • Identifi cation of coupled mechanisms through scatter shapes (e.g. buckling) Sensitivity analysis scalar 3D fi eld, signals Extensive GUI for MOP-Postprocessing
21 www.dynardo.de 22 Customization & Pilot Projects
CUSTOMIZATION & PILOT PROJECTS
Dynardo provides computational services and customized solutions for your FE analyses and CAE optimi- zation tasks in virtual product development of all engineering disciplines. Due to the company‘s combi- Fully automatized optimization workfl ow in optiSLang considering structural costs and metric of performance map, running several solvers and using HPC nation of being a CAE service provider and software developer, Dynardo is your competent and fl exible partner for complex tasks in the CAE fi eld.
Pilot Projects RDO Consulting Service Especially for the introduction of CAE-based Robust Design In cases, customers would like to investigate the potentials In the uncomplicated and fl exible cooperation with Dynardo, In the framework of the virtual product development pro- Optimization in product development processes, a pilot of CAE-based optimization for their product lines but have it is a great advantage that the company is not only a soft- cess of the Daimler AG, parametric CAE-models are em- project as an initial cooperation based on the customer‘s not implemented a CAE-based development process yet, ware developer but also an engineering service provider. Di- ployed for the evaluation and optimization of different product knowledge and our consulting experience would we offer to generate and verify a virtual model of a product rect communication with the programers and individual li- functional requirements like driving comfort or crashwor- be a perfect start. Dynardo has expertise in various indus- and conduct a CAE-based optimization. The fi nal result will cense agreements ensure a rapid adaptation and extension thiness behavior. Robust dimensioning means to design a trial fi elds and will help you to conduct realistic safety and show possible optimized product confi guration and how in- of the software optiSLang to specifi c technical requirements vehicle which is as insensitive as possible in regard to exist- reliability analysis, proper assessment of material behavior, put variation affects the design responses using the MOP/ of Robert Bosch GmbH. ing scatter in material or production properties. In order to prediction of failure evolution, design optimization or simu- CoP methodology. Roland Schirrmacher (Robert Bosch GmbH) ensure robustness within the virtual prototyping, in 2002, lation of FEM based limit load analysis. Corporate Sector Research and Advance Engineering Daimler started implementing optiSLang for NVH analysis Future Mechanical and Fluid Components (CR/ARF1) of driving comfort. Since then, applications have been ex- tended to crashworthiness, brake squeal load cases as well Customization as forming simulation. You want to make your virtual product development more effi cient? Dynardo develops customized solutions based on For high end consumer goods, the robustness is a key func- optiSLang and SoS. We integrate your in-house software tion. In 2008, Nokia implemented sensitivity analyses into into optiSLang or make optiSLang be a part of your company the virtual prototyping to identify critical drop directions of SPDM (Simulation Process & Data Management) solution. load cases as well as robustness evaluations of the drop test Even fully automatized RDO workfl ows can be generated. regarding production tolerances and material scatter. With We help you to establish a company-wide standard work- the help of optiSLang, the robust product performance of fl ow and make your products benefi t from consistent and mobile phones could be increased concerning critical drop effi cient CAE processes. conditions. Detection of geometric deviations between two incompatible meshes of a car cowling (copyright/courtesy of DAIMLER AG)
23 www.dynardo.de 24 WELCOME TO
SUPPORT & TRAININGS
In training courses for beginners, advanced users or experts, we provide information about our software products and the methods of CAE-based Robust Design Optimization as well as practical applications in various industries.
Support The main interest of our support team is a successful cus- multidisciplinary optimization and robustness evaluation. tomer. We provide technical support by phone, e-mail or The trainings are not only for engineers, but are also per- online. All requests regarding our software products optiS- fectly suited for decision makers in the CAE-based simula- Lang, multiPlas, SoS and ETK will be processed thoroughly tion fi eld. For all trainings there is a discount of 50% for stu- and answered immediately. Our support team will also dents and 30% for university members/PHDs. You can fi nd help you to implement effi cient RDO applications and its an overview of the current training program at our homep- various methods to solve CAE-challenges in your particular age www.dynardo.de. fi eld of business. ANNUAL WEIMAR Internet Library Info days and webinars Our internet library is the perfect source for your research OPTIMIZATION AND STOCHASTIC DAYS During our info days and webinars, you will receive an intro- on CAE-topics and applications of CAE-based RDO. There duction to performing complex, non-linear FE-calculations you will fi nd practical references and state-of-the-art case Your conference for CAE-based parametric optimization, stochastic analysis and Robust Design Optimization using optiSLang, multiPlas, SoS and ETK. At regular webi- studies matched to the different fi elds of methods and ap- in virtual product development. nars, you can easily get information about all relevant is- plications. sues of CAE-based optimization and stochastic analysis. During an information day, you will additionally have the opportunity to discuss your specifi c optimization task with Infos our experts and develop fi rst approaches to solutions. www.dynardo.de/en/consulting The annual conference aims at promoting successful appli- Take the opportunity to obtain and exchange knowledge www.dynardo.de/en/trainings cations of parametric optimization and CAE-based stochas- with recognized experts from science and industry. www.dynardo.de/en/library tic analysis in virtual product design. The conference offers Trainings focused information and training in practical seminars and You will fi nd more information and current dates at: For a competent and customized introduction to our soft- interdisciplinary lectures. Users can talk about their experi- www.dynardo.de/en/wost. ware products, visit our basic or expert trainings clearly ences in parametric optimization, service providers present explaining theory and application of a sensitivity analysis, their new developments and scientifi c research institutions We are looking forward to welcoming you at the next Weimar inform about state-of-the-art RDO methodology. Optimization and Stochastic Days.
25 Contact & Distributors
Germany & worldwide Sweden, Denmark, Finland, Norway USA EDR & Medeso AB Dynardo GmbH Lysgränd 1 CADFEM Americas, Inc. Steubenstraße 25 SE-721 30 Västerås 27600 Farmington Road, Suite 203 B 99423 Weimar www.medeso.se Farmington Hills, MI 48334 Phone: +49 (0)3643 9008-30 www.cadfem-americas.com Fax.: +49 (0)3643 9008-39 United Kingdom of Great Britain and www.dynardo.de Northern Ireland Ozen Engineering Inc. [email protected] IDAC Ltd 1210 E Arques Ave 207 Airport House Business Centre Sunnyvale, CA 94085 Dynardo Austria GmbH Purley Way www.ozeninc.com Offi ce Vienna Croydon, Surrey, CR0 0XZ Wagenseilgasse 14 www.idac.co.uk USA/Canada 1120 Vienna SimuTech Group Inc. www.dynardo.at Ireland 1800 Brighton Henrietta Town Line Rd. [email protected] CADFEM Ireland Ltd Rochester, NY 14623 18 Windsor Place www.simutechgroup.com Germany Lower Pembroke Street Dublin 2 Japan CADFEM GmbH www.cadfemireland.com TECOSIM Japan Limited Marktplatz 2 4F Mimura K2 Bldg. 1-10-17 85567 Grafi ng b. München Turkey Kami-kizaki, Urawa-ku, Saitama-shi www.cadfem.de FIGES A.S. Saitama 330-0071 Teknopark Istanbul www.tecosim.co.jp science + computing ag Teknopark Bulvari 1 / 5A-101-102 Hagellocher Weg 73 34912 Pendik-Istanbul Korea 72070 Tübingen www.fi ges.com.tr TaeSung S&E Inc. www.science-computing.de Kolon Digital Tower 2 North Africa 10F, Seongsu-dong 2 ga Austria CADFEM Afrique du Nord s.a.r.l. Seongdong-gu CADFEM (Austria) GmbH Technopôle de Sousse Seoul 333-140 Wagenseilgasse 14 TUN-4002 Sousse www.tsne.co.kr 1120 Wien www.cadfem-an.com www.cadfem.at China Russia PERA-CADFEM Consulting Inc. Switzerland CADFEM CIS Bldg CN08, LEGEND-TOWN CADFEM (Suisse) AG Suzdalskaya 46, Offi ce 203 Advanced Business Park, Wittenwilerstrasse 25 111672 Moscow No. 1 BalizhuangDongli, 8355 Aadorf www.cadfem-cis.ru Chaoyang District, www.cadfem.ch Beijing 100025 India www.peraglobal.com Czech Republic, Slovakia, Hungary CADFEM Engineering Services India SVS FEM s.r.o. 6-3-902/A, 2nd Floor, Right Wing Škrochova 3886/42 Rajbhawan Road, Somajiguda 615 00 Brno-Židenice Hyderabad 500 082 www.svsfem.cz www.cadfem.in
Publication details
Publisher Dynardo GmbH Steubenstraße 25 99423 Weimar www.dynardo.de [email protected]
Executive Editor & Layout Henning Schwarz [email protected] Publication worldwide Registration Local court Jena: HRB 111784 Copyright © Dynardo GmbH. All rights reserved VAT Registration Number The Dynardo GmbH does not guarantee or warrant accuracy or DE 214626029 completeness of the material contained in this publication.