Introduction to Parametric Optimization and Robustness Evaluation with optiSLang Dynardo GmbH 1 © Dynardo GmbH 1. Introduction 2. Process to optiSLang integration 6. Training 3. Sensitivity analysis 5. Robustness 4. Parametric analysis Optimization Introduction to the parametric optimization and robustness evaluation with 2 optiSLang © Dynardo GmbH 1. Introduction 2. Process to optiSLang integration 6. Training 3. Sensitivity analysis 5. Robustness 4. Parametric analysis Optimization Introduction to the parametric optimization and robustness evaluation with 3 optiSLang © Dynardo GmbH Dynardo • Founded: 2001 (Will, Bucher, CADFEM International) • More than 50 employees, offices at Weimar and Vienna • Leading technology companies Daimler, Bosch, E.ON, Nokia, Siemens, BMW are supported Software Development CAE-Consulting • Mechanical engineering • Civil engineering & Dynardo is engineering specialist for Geomechanics CAE-based sensitivity analysis, • Automotive industry optimization, robustness evaluation • Consumer goods industry and robust design optimization • Power generation Introduction to the parametric optimization and robustness evaluation with 4 optiSLang © Dynardo GmbH Robust Design Optimization (RDO) in virtual product development optiSLang enables you to: • Identify optimization potentials • Improve product performance • Secure resource efficiency • Adjust safety margins without limitation of input parameters • Quantify risks • Save time to market Introduction to the parametric optimization and robustness evaluation with 5 optiSLang © Dynardo GmbH Excellence of optiSLang • optiSLang is an algorithmic toolbox for • sensitivity analysis, • optimization, • robustness evaluation, • reliability analysis • robust design optimization (RDO) • functionality of stochastic analysis to run real world industrial applications • advantages: • predefined workflows, • algorithmic wizards and • robust default settings Introduction to the parametric optimization and robustness evaluation with 6 optiSLang © Dynardo GmbH Robust Design Optimization with optiSLang 2nd Multidisciplinary Optimization Adaptive Response Surface, Evolutionary Algorithm, Pareto Optimization Introduction to the parametric optimization and robustness evaluation with 7 optiSLang © Dynardo GmbH 1. Introduction 2. Process to optiSLang integration 6. Training 3. Sensitivity analysis 5. Robustness 4. Parametric analysis Optimization Introduction to the parametric optimization and robustness evaluation with 8 optiSLang © Dynardo GmbH Process Integration Parametric model as base for • User defined optimization (design) space • Naturally given robustness (random) space Design variables Entities that define the design space Response variables The CAE process Outputs from the Generates the system Scattering variables results according Entities that define the to the inputs robustness space Introduction to the parametric optimization and robustness evaluation with 9 optiSLang © Dynardo GmbH optiSLang Integrations & Interfaces Direct integrations ANSYS Workbench MATLAB Excel Python SimulationX Supported connections ANSYS APDL Abaqus Adams AMESim … Arbitary connection of ASCII file based solvers Introduction to the parametric optimization and robustness evaluation with 10 optiSLang © Dynardo GmbH Full Integration of optiSLang in ANSYS Workbench • optiSLang modules Sensitivity , Optimization and Robustness are directly available in ANSYS Workbench Introduction to the parametric optimization and robustness evaluation with 11 optiSLang © Dynardo GmbH Example: Optimization of a Steel Hook Deterministic Optimization • Minimize the mass • The maximum stress should not exceed 300MPa • Initially a safety factor of 1.5 is defined • 10 geometry parameters are used for the design variation Robustness requirement • Proof for the optimal design that the failure stress limit is not exceeded with a 4.5 sigma safety margin • 16 scattering parameters are considered (geometry and material properties and the load components) Introduction to the parametric optimization and robustness evaluation with 12 optiSLang © Dynardo GmbH Example: Simulation Model in ANSYS Mechanical Introduction to the parametric optimization and robustness evaluation with 13 optiSLang © Dynardo GmbH Example: The Design Parameters A Outer_Diameter 25-35 mm B Connection_Length 20-40 mm C Opening_Angle 10-30 ° D Upper_Blend_Radius 18-22 mm E Lower_Blend_Radius 18-22 mm F Connection_Angle 120-150 ° G Lower_Radius 45-55 mm H Fillet_Radius 2-4 mm I Thickness 15-25 mm Depth 15-25 mm Introduction to the parametric optimization and robustness evaluation with 14 optiSLang © Dynardo GmbH 1. Introduction 2. Process to optiSLang integration 6. Training 3. Sensitivity analysis 5. Robustness 4. Parametric analysis Optimization Introduction to the parametric optimization and robustness evaluation with 15 optiSLang © Dynardo GmbH Flowchart of Sensitivity Analysis Design of Regression Sensitivity Experiments Methods Evaluation • Deterministic • 1D regression • Correlations • (Quasi)Random • nD polynomials • Reduced regression • Sophisticated • Variance-based metamodels Solver 1. Design of Experiments generates a specific number of designs, which are all evaluated by the solver 2. Regression methods approximate the solver responses to understand and to assess its behavior 3. The variable influence is quantified using the regression functions Introduction to the parametric optimization and robustness evaluation with 16 optiSLang © Dynardo GmbH Response Surface Method • Approximation of response variables as explicit function of all input variables • Approximation function can be used for sensitivity analysis and/or optimization • Global methods ( Polynomial regression , Neural Networks, …) • Local methods (Spline interpolation, Moving Least Squares , Radial Basis Functions, Kriging, …) • Approximation quality decreases with increasing input dimension • Successful application requires objective measures of the prognosis quality Introduction to the parametric optimization and robustness evaluation with 17 optiSLang © Dynardo GmbH Metamodel of Optimal Prognosis (MOP) • Approximation of solver output by fast surrogate model • Reduction of input space to get best compromise between available information (samples) and model representation (number of inputs) • Determination of optimal approximation model • Assessment of approximation quality • Evaluation of variable sensitivities Introduction to the parametric optimization and robustness evaluation with 18 optiSLang © Dynardo GmbH Definition of the Design Parameter Bounds • Specify the ranges of the design parameters • You may choose continuous and discrete/binary optimization variables Introduction to the parametric optimization and robustness evaluation with 19 optiSLang © Dynardo GmbH Example: Results of the Sensitivity Analysis • For the mass 6 important inputs are detected by the MOP • For the maximum stress only 3 inputs are important • Thickness, depth and lower radius are important for both responses • Prognosis quality of both response values is very good (99%) Introduction to the parametric optimization and robustness evaluation with 20 optiSLang © Dynardo GmbH Example: Results of the Sensitivity Analysis • Both responses show slightly nonlinear and monotonic behavior and can be explained with a prognosis quality of 99% Optimization should be straight forward Introduction to the parametric optimization and robustness evaluation with 21 optiSLang © Dynardo GmbH 1. Introduction 2. Process to optiSLang integration 6. Training 3. Sensitivity analysis 5. Robustness 4. Parametric analysis Optimization Introduction to the parametric optimization and robustness evaluation with 22 optiSLang © Dynardo GmbH Optimization with MOP pre-search Optimization Optimizer Optimizer Sensitivity analysis • Gradient • Gradient • EA/GA • ARSM DOE MOP • EA/GA Solver SolverMOP Solver • Full optimization is performed on MOP by approximating the solver response • Optimal design on MOP can be used as – final design (verification with solver is required!) – as start value for second optimization step with direct solver Introduction to the parametric optimization and robustness evaluation with 23 optiSLang © Dynardo GmbH optiSLang Optimization Algorithms Gradient-based Adaptive Response Nature inspired Methods Surface Method Optimization • Most efficient method if • Attractive method for • GA/EA/PSO imitate gradients are accurate a small set of mechanisms of nature to enough continuous variables improve individuals (<20) • Consider its restrictions • Method of choice if like local optima, only • Adaptive RSM with gradient or ARSM fails continuous variables default settings is the • Very robust against and noise method of choice numerical noise, non- linearity, number of variables,… Start Introduction to the parametric optimization and robustness evaluation with 24 optiSLang © Dynardo GmbH Definition of the Objective and Constraints • All design parameters, responses and help variables can be used within mathematical formulations for objectives and constraints • Minimization and maximization tasks with constraints are possible Introduction to the parametric optimization and robustness evaluation with 25 optiSLang © Dynardo GmbH Optimization Wizard • Previous Sensitivity study may provide required information • By a few settings, optiSLang suggests the most promising algorithm • All algorithms come with robust default settings Introduction to the parametric optimization and robustness evaluation with 26