Sensitivity Analysis, Multidisciplinary Optimization, Robustness Evaluation, and Robust Design Optimization with optiSLang 3.2

Outline Introduction Process Integration Parametrize editor Interfaces to common solvers Post processing Sensitivity analysis Design of experiments Coefficient of correlation Simple regression, quadratic & rank order correlation Multiple regression, Coefficient of Determination (CoD) Coefficient of Importance (CoI) Significance filter Moving Least Squares approximation Coefficient of Prognosis (CoP) Meta-model of Optimal Prognosis (MOP) Applications Accompanying example: Sensitivity analysis of an analytical function (Tutorial 1) 1.Tag Vormittags Intro, Prozesintegration, Parametrisierung Nachmittags Sensi Outline & Flowcharts

Outline Multidisciplinary Optimization Single objective, constraint optimization Gradient based optimization Global and adaptive response surface methods Evolutionary algorithm (EA) Particle swarm optimization (PSO) Multi objective optimization Pareto optimization with evolutionary algorithm Applications Accompanying example: Optimization of a damped oscillator (Tutorial 2, Part 1) Model calibration/identification Parametrization of characteristic curves as signals Sensitivity analysis Definition of objective functions Dependent parameters Accompanying example: Calibration of a damped oscillator (Tutorial 2, Part 2) 2. Tag Optimierung bis ca. 15 Uhr Abschließend Identifikation ca 2h Outline & Flowcharts

Outline Robustness analysis Definition of robustness Random variables Definition of uncertainties Variance-based robustness analysis Statistical measures Applications Reliability analysis Accompanying example: Robust design optimization of a damped oscillator (Tutorial 2, Part 3) Robust design optimization Definition of robust design optimization (RDO) Design for Six-Sigma Iterative RDO procedure Simultaneous RDO procedure 3. Tag Reliability optional, je nach Zeit und Bedarf Outline & Flowcharts

Standard optimization Optimizer Gradient ARSM EA/GA Sensitivity analysis DOE MOP Solver Solver Full design variable space X for sensitivity analysis Scanning the design space with DOE by direct solver calls Generating MOP on DOE samples Sensitivity analysis gives reduced design variable space Xred Optimization requires start value x0, objective function f(x) and constraint conditions gj(x) Optimizer determines optimal design xopt by direct solver calls oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Outline & Flowcharts

Optimization with MOP pre-search Optimizer Gradient ARSM EA/GA Optimizer Gradient ARSM EA/GA Sensitivity analysis DOE MOP Solver MOP 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 Good approximation quality of MOP is necessary for objective and constraints (CoP ≥ 90%) oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Outline & Flowcharts

Optimization with MOP using external DOE Sensitivity analysis Optimizer Gradient ARSM EA/GA External DOE Excel plugin MOP MOP External DOE exists from experiments or other sources Excel plugin is used to generate optiSLang binary file MOP uses external DOE scheme to generate approximation and to perform sensitivity analysis Optimization is performed on MOP to obtain approximate optimum oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Outline & Flowcharts

Optimization + Robustness evaluation Optimizer Gradient ARSM EA/GA Robustness Variance Sigma-level Reliability Sensitivity analysis DOE MOP Solver Solver Solver oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Full optimization variable space X for sensitivity analysis Sensitivity analysis gives reduced optimization variable space Xred Optimizer determines optimal design xopt by direct solver calls Robustness evaluation (varianced-based or reliability-based) in the random variable space Xrob at optimal design xopt Outline & Flowcharts

Iterative Robust Design Optimization Robustness Optimizer Gradient ARSM EA/GA Robustness Variance Sigma-level Reliability Sensitivity analysis DOE MOP Solver Solver Solver No Yes Update constraints End oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Sensitivity analysis gives reduced optimization variable space Xred Optimizer determines optimal design xopt by direct solver calls Robustness evaluation Robust optimum – end of iteration Non-robust optimum - update constraints and repeat optimization + robustness evaluation Outline & Flowcharts

Simultaneous Robust Design Optimization Sensitivity analysis Optimizer DOE MOP Solver Solver Robustness Solver oS sensitivity studies scan the design space and evaluate the sensitivities with statistical measurements. That is in contrast to traditional (mathematical) sensitivity analysis using functional analysis (gradient, differentiation,..). The advantage of oS sensitivity analysis is that we can handle a large number of variables and all kind of non linearity's or other ugly things. Some customers gain more advantage from verifying and understanding their design space then from optimizing the parameter sets. Sensitivity analysis gives reduced optimization variable space Xred Optimizer determines optimal design xopt by direct solver calls with simultaneous robustness evaluation for every design Each robustness evaluation determines robustness values by direct solver calls Outline & Flowcharts