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)
1.Tag
Vormittags Intro, Prozesintegration, Parametrisierung
Nachmittags Sensi
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)
2. Tag
Optimierung bis ca. 15 Uhr
Abschließend Identifikation ca 2h
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
Simultaneous RDO procedure
3. Tag
Reliability optional, je nach Zeit und Bedarf
Outline & Flowcharts

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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