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
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
3Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
4Introduction to the parametric optimization and robustness evaluation with
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
5Introduction to the parametric optimization and robustness evaluation with
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
6Introduction to the parametric optimization and robustness evaluation with
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
7Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
2ndMultidisciplinary
Optimization
Adaptive Response Surface, Evolutionary
Algorithm, Pareto Optimization
Robust Design Optimization with optiSLang
8Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
9Introduction to the parametric optimization and robustness evaluation with
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
10Introduction to the parametric optimization and robustness evaluation with
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
11Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
Full Integration of optiSLang in ANSYS Workbench
• optiSLang modules Sensitivity, Optimization and
Robustness are directly available in ANSYS Workbench
12Introduction to the parametric optimization and robustness evaluation with
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)
13Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
Example: Simulation Model in ANSYS Mechanical
14Introduction to the parametric optimization and robustness evaluation with
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
15Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
16Introduction to the parametric optimization and robustness evaluation with
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
17Introduction to the parametric optimization and robustness evaluation with
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
18Introduction to the parametric optimization and robustness evaluation with
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
19Introduction to the parametric optimization and robustness evaluation with
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
20Introduction to the parametric optimization and robustness evaluation with
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%)
21Introduction to the parametric optimization and robustness evaluation with
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
22Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
23Introduction to the parametric optimization and robustness evaluation with
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
24Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH© Dynardo GmbH
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
25Introduction to the parametric optimization and robustness evaluation with
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
26Introduction to the parametric optimization and robustness evaluation with
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
27Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
Example: Initial vs. Optimal Design
Initial Design Optimal Design
Mass = 790g Mass = 588g
Equivalent Stress = 439MPa Equivalent Stress = 200MPa
28Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
29Introduction to the parametric optimization and robustness evaluation with
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):
30Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH© Dynardo GmbH© Dynardo GmbH
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
31Introduction to the parametric optimization and robustness evaluation with
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
32Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH© Dynardo GmbH© Dynardo GmbH
Robustness Postprocessing
Traffic light plotHistogram & Statistical Data
MOP/CoP
Sensitivities
33Introduction to the parametric optimization and robustness evaluation with
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
34Introduction to the parametric optimization and robustness evaluation with
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
35Introduction to the parametric optimization and robustness evaluation with
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
36Introduction to the parametric optimization and robustness evaluation with
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
37Introduction to the parametric optimization and robustness evaluation with
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:
38Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
1. Introduction to optiSLang
1. Introduction to optiSLang
2. Process integration
2. Process integration
3. Sensitivity analysis
3. Sensitivity analysis
5. Robustness analysis
5. Robustness analysis
6. Training6. Training
4. Parametric Optimization
4. Parametric Optimization
39Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH© Dynardo GmbH
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
41Introduction to the parametric optimization and robustness evaluation with
optiSLang
© Dynardo GmbH
Thanks for your attention!