Introduction to Parametric Optimization and Robustness ...

1

Introduction to Parametric

Optimization and Robustness

Evaluation with optiSLang

Dynardo GmbH

2Introduction to the parametric optimization and robustness evaluation with

optiSLang

© Dynardo GmbH

1. Introduction to optiSLang


2. Process integration


3. Sensitivity analysis


5. Robustness analysis


6. Training6. Training

4. Parametric Optimization



optiSLang

© Dynardo GmbH













optiSLang

© Dynardo GmbH© 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

Dynardo is engineering specialist for

CAE-based sensitivity analysis,

optimization, robustness evaluation

and robust design optimization

• Mechanical engineering

• Civil engineering &

Geomechanics

• Automotive industry

• Consumer goods industry

• Power generation

CAE-Consulting


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


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


optiSLang

© Dynardo GmbH

2ndMultidisciplinary

Optimization

Adaptive Response Surface, Evolutionary

Algorithm, Pareto Optimization

Robust Design Optimization with optiSLang


optiSLang

© Dynardo GmbH













optiSLang

© Dynardo GmbH

Process Integration

Parametric model as base for

• User defined optimization (design) space

• Naturally given robustness (random) space

Design variablesEntities that define the design space

Response variablesOutputs from the system

The CAE processGenerates the results according to the inputs

Scattering variablesEntities that define the robustness space


optiSLang

© Dynardo GmbH

optiSLang Integrations & Interfaces

Direct integrations� ANSYS Workbench� MATLAB� Excel� Python� SimulationX

Supported connections� ANSYS APDL� Abaqus� Adams� AMESim� …

Arbitary connection ofASCII file based solvers

© Dynardo GmbH


optiSLang

© Dynardo GmbH

Full Integration of optiSLang in ANSYS Workbench

• optiSLang modules Sensitivity, Optimization and

Robustness are directly available in ANSYS Workbench


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)


optiSLang

© Dynardo GmbH

Example: Simulation Model in ANSYS Mechanical


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


optiSLang

© Dynardo GmbH













optiSLang

© Dynardo GmbH

Solver

SensitivityEvaluation

• Correlations• Reduced regression• Variance-based

Regression Methods

• 1D regression• nD polynomials• Sophisticatedmetamodels

•

Design of Experiments

• Deterministic• (Quasi)Random

© Dynardo GmbH

Flowchart of Sensitivity Analysis

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


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

© Dynardo GmbH


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

© Dynardo GmbH


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


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%)


optiSLang

© Dynardo GmbH

• Both responses show slightly nonlinear and monotonic behavior and can

be explained with a prognosis quality of 99%

� Optimization should be straight forward

Example: Results of the Sensitivity Analysis


optiSLang

© Dynardo GmbH













optiSLang

© Dynardo GmbH

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

DOE

Solver

Optimizer• Gradient• EA/GA

Sensitivity analysis

Optimization

Solver

MOP

SolverMOP

Optimizer• Gradient• ARSM• EA/GA


optiSLang


optiSLang Optimization Algorithms

Gradient-based Methods

• Most efficient method if gradients are accurate enough

• Consider its restrictions like local optima, only continuous variablesand noise

Adaptive Response Surface Method

• Attractive method for a small set of continuous variables (<20)

• Adaptive RSM with default settings is the method of choice

Nature inspired Optimization

• GA/EA/PSO imitate mechanisms of nature to improve individuals

• Method of choice if gradient or ARSM fails

• Very robust against numerical noise, non-linearity, number of variables,…

Start


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


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


optiSLang

© Dynardo GmbH

Example: Initial vs. Optimal Design

Initial Design Optimal Design

Mass = 790g Mass = 588g

Equivalent Stress = 439MPa Equivalent Stress = 200MPa


optiSLang

© Dynardo GmbH













optiSLang

© Dynardo GmbH© Dynardo GmbH© Dynardo GmbH

Robustness in terms of constraints

• Safety margin (sigma level) of one or more responses y:

• Reliability (failure probability) with respect to given limit state:

Robustness in terms of the objective

• Performance (objective) of robust optimum is less sensitive to input uncertainties

• Minimization of statistical evaluation of objective function f (e.g. minimize mean and/or standard deviation):


optiSLang


Robustness Analysis

1) Define the robustness space using scatter range, distribution and correlation

2) Scan the robustness space by producing and evaluating ndesigns

3) Check the variation 4) Check the

explainability of the model

5) Identify the most important scattering variables


optiSLang

© Dynardo GmbH

Definition of the Parameter Uncertainties

• The definition of different distribution types is possible

(Normal, Uniform, Truncated-Normal, Log-normal, Gumbel, Weibull, …)

• Mean value, Standard deviation or Coefficient of Variation

have to be specified

• Correlations between the random variables can be considered as well


optiSLang


Robustness Postprocessing

Traffic light plotHistogram & Statistical Data

MOP/CoP

Sensitivities


optiSLang

© Dynardo GmbH

• Statistical Evaluation of the Maximum Stress:

• Safety distance to failure stress of 300MPa is estimated

with a sigma level of only 3.18

� Attention: Requirement of a 4.5 sigma level is not fulfilled

Example: Results of the Robustness Evaluation


optiSLang

© Dynardo GmbH

• Force in main direction is the most important input

parameter for the maximum stress

� Attention: Scatter of this uncertainty is difficult to be reduced

� Therefore design has to be changed to reduce

mean value of maximum stress

and to fulfill the robustness requirement

� Safety factor is increased and

deterministic optimization

is performed again

Example: Results of the Robustness Evaluation


optiSLang

© Dynardo GmbH

Iterative Robustness Design Optimization

• Adapt the constraint condition to move the mean away from the limit

• Robustness evaluation is performed again for new optimal design

• Only 2 to 3 iterations steps are necessary to obtain robust design


optiSLang

© Dynardo GmbH

Example: Robustness of Second Optimum

• Stress: Safety margin to failure limit of 300MPa is estimated

with a sigma level of 4.82 (would fulfill the robustness requirement)

• The sigma level of 4.82 corresponds to a failure probability of 7.1*10-7

if the response is perfect normally distributed


optiSLang

© Dynardo GmbH

Initial Design Deterministic Optimum

Robust Optimum

Mass 790 g 588 g 666 g

Stress 439 MPa 200 MPa 176 MPa

Sigma Level - 3.3 4.8

Failure Probability >0.5 10^-3 10^-6

© Dynardo GmbH

ExampleSummary:


optiSLang


Further Training

optiSLang 4 Basics 3 day introduction to process integration, sensitivity,

optimization, calibration and robustness analysis

optiSLang inside ANSYS Workbench 2 day introduction seminar to

parameterization in ANSYS Workbench, sensitivity analysis and

optimization

optiSLang 4 and ANSYS Workbench 1 day introduction to the integration

of ANSYS Workbench projects in a optiSLang 4 solver chain,

parameterization of signals via APDL output

Parameter Identification 1 day seminar on basics of model calibration,

application of sensitivity analysis and optimization to calibration problems

Robust Design and Reliability Analysis 1 day seminar on basics of

probability, robustness and reliability analysis, robust design optimization

See our website: http://www.dynardo.de/en/trainings.html

© Dynardo GmbH

12th Weimar

Optimization and

Stochastic Days 2015

November 5-6

cc neue weimarhalle

Conference for CAE-based

parametric optimization,

stochastic analysis and

Robust Design Optimization

Registration and Info: www.dynardo.de/en/wost

Introduction to Parametric Optimization and Robustness ...

Documents

Transcript of Introduction to Parametric Optimization and Robustness ...