Outline

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

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) Outline & Flowcharts

3. 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) Outline & Flowcharts

4. 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 • Applications • Simultaneous RDO procedure • Accompanying example: Robust design optimization of a damped oscillator (Tutorial 2, Part 3) Outline & Flowcharts

5. Standard optimization • 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 Optimization • Optimizer • Gradient • ARSM • EA/GA Sensitivity analysis MOP DOE Solver Solver Outline & Flowcharts

6. Optimization with MOP pre-search • 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%) Optimization • Optimizer • Gradient • ARSM • EA/GA • Optimizer • Gradient • ARSM • EA/GA Sensitivity analysis MOP DOE MOP Solver Solver Outline & Flowcharts

7. Optimization with MOP using external DOE • 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 Optimization • Optimizer • Gradient • ARSM • EA/GA Sensitivity analysis External DOE Excel plugin MOP MOP Outline & Flowcharts

8. Optimization + Robustness evaluation • 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 Optimization Robustness • Optimizer • Gradient • ARSM • EA/GA • Robustness • Variance • Sigma-level • Reliability Sensitivity analysis MOP DOE Solver Solver Solver Outline & Flowcharts

9. Iterative Robust Design Optimization • 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 Optimization Robustness • Optimizer • Gradient • ARSM • EA/GA • Robustness • Variance • Sigma-level • Reliability Sensitivity analysis MOP DOE Solver Solver Solver No Yes Update constraints End Outline & Flowcharts

10. Simultaneous Robust Design Optimization • 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 Robust Design Optimization Sensitivity analysis Optimizer MOP DOE Solver Solver Robustness Solver Outline & Flowcharts