Sensitivity Analysis, Multidisciplinary Optimization, Robustness Evaluation,

and Robust Design Optimization with optiSLang 3.2

2 Outline & Flowcharts

• 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

3 Outline & Flowcharts

• 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

4 Outline & Flowcharts

• 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

5 Outline & Flowcharts

• 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

Standard optimization

DOE

Solver

Optimizer• Gradient• ARSM• EA/GA

Sensitivity analysis

Optimization

Solver

MOP

6 Outline & Flowcharts

Optimization with MOP pre-search

DOE

Solver

Optimizer• Gradient• ARSM• EA/GA

Sensitivity analysis

Optimization

SolverMOP

MOP

• 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%)

Optimizer• Gradient• ARSM• EA/GA

7 Outline & Flowcharts

Optimization with MOP using external DOE

ExternalDOE

Optimizer• Gradient• ARSM• EA/GA

Sensitivity analysis

Optimization

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

Excel plugin

8 Outline & Flowcharts

• 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 evaluation

DOE

Solver

Optimizer• Gradient• ARSM• EA/GA

Sensitivity analysis

Optimization

Solver

MOP

Robustness• Variance• Sigma-level• Reliability

Robustness

Solver

9 Outline & Flowcharts

• 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

Iterative Robust Design Optimization

DOE

Solver

Optimizer• Gradient• ARSM• EA/GA

Sensitivity analysis

Optimization

Solver

MOP

Robustness• Variance• Sigma-level• Reliability

Robustness

Solver

Update constraints

No Yes

End

10 Outline & Flowcharts

• 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

Simultaneous Robust Design Optimization

DOE

Solver

OptimizerSensitivity analysis

Robust Design Optimization

Solver

MOP

Robustness

Solver