Reliability analysis and robust design optimization … · Reliability analysis and robust design...
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Reliability analysis and robust design optimization using ANSYS and optiSLang Dr.-Ing. Johannes Will, Dynardo GmbH, Weimar, Germany Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Transcript of Reliability analysis and robust design optimization … · Reliability analysis and robust design...
Reliability analysis and robust design optimization
using ANSYS and optiSLang
Dr.-Ing. Johannes Will, Dynardo GmbH, Weimar, Germany
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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CAE-Consulting
Our expertise: • Mechanical engineering • Civil engineering & Geomechanics • Automotive industry • Consumer goods industry • Power generation
Software Development Dynardo is your engineering specialist for CAE-based sensitivity analysis, optimization, robustness evaluation and robust design optimization.
Founded: 2001 (Will, Bucher, CADFEM International)
More than 35 employees, offices at Weimar and Vienna
Leading technology companies Daimler, Bosch, Eon, Nokia, Siemens, BMW, are supported by us
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Excellence of optiSLang optiSLang is an algorithmic toolbox for sensitivity analysis, optimization, robustness evaluation, reliability analysis and robust design optimization.
optiSLang is the commercial tool that has completed the necessary functionality of stochastic analysis to run real world industrial applications in CAE-based robust design optimizations. optiSLang development priority: safe of use and ease of use!
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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Start
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Optimization
Sensitivity Study
Single & Multi objective (Pareto) optimization
Robust Design Variance based Robustness
Evaluation
Probability based Robustness Evaluation,
(Reliability analysis)
Robust Design Methodology Definition
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Sensitivity Analysis
© 2010 ANSYS, Inc. All rights reserved. Borrowed by with courtesy of ANSYS, Inc.
Gradient-based algorithms
Meta model of optimal Prognosis(MOP)
Natural Inspired Optimization
Genetic algorithms, Evolutionary strategies & Particle Swarm Optimization Start
Optimization Algorithms
Multi objective (Pareto) Optimization
Local adaptive RSM
Global adaptive RSM
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
How choosing the right algorithm?
Gradient-Based
Algorithms
Evolutionary Algorithm
Pareto Optimization
Adaptive Response Surface
global Response Surface
Optimization Algorithms:
Sensitivity Analysis allows
best choice!
Which one is the best?
© 2010 ANSYS, Inc. All rights reserved. Borrowed by with courtesy of ANSYS, Inc.
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Start
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Optimization
Sensitivity Study
Single & Multi objective (Pareto) optimization
Robust Design Variance based
Robustness Evaluation
Probability based Robustness Evaluation,
(Reliability analysis)
Robust Design Methodology Definition
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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Definition of Uncertainties
Correlation is an important characteristic of stochastic variables.
Distribution functions define variable scatter
Correlation of single uncertain values
Spatial Correlation = random fields
1) Translate know how about uncertainties into proper scatter definition
Tensile strength
Yiel
d st
ress
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• Intuitively: The performance of a robust design is largely unaffected by random perturbations
• Variance indicator: The coefficient of variation (CV)
of the objective function and/or constraint values is smaller than the CV of the input variables
• Sigma level: The interval mean+/- sigma level does not reach an undesired performance (e.g. design for six-sigma)
• Probability indicator: The probability of reaching undesired performance is smaller than an acceptable value
How to Define Robustness of a Design
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Sensitivity of Uncertainties
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Gradient-based algorithms = First Order Reliability algorithm (FORM)
Adaptive Response Surface Method
Latin Hypercube Sampling
Reliability Analysis Algorithms ISPUD Importance Sampling using Design Point
Monte Carlo Sampling Directional Sampling
X1
X2
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Robustness & Reliability Algorithms
How choosing the right algorithm?
Robustness Analysis provide the knowledge to choose the
appropriate algorithm
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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Start
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Robust Design Optimization
Optimization
Sensitivity Study
Single & Multi objective (Pareto) optimization
Robust Design Variance based
Robustness Evaluation
Probability based Robustness Evaluation,
(Reliability analysis)
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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Robust Design Optimization 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):
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Robust Design Optimization
Pareto Optimization
Adaptive Response Surface
Evolutionary Algorithm
© 2010 ANSYS, Inc. All rights reserved. Borrowed by with courtesy of ANSYS, Inc.
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• With improvements in parametric modeling, CAE (software) and CPU (hardware) there seems to be no problem to establish RDO (DfSS) product development strategies by using stochastic analysis
• There are many research paper or marketing talks about RDO/DfSS. • But why industrial papers about successful applications are so rare? Where is the problem with RDO?
Challenges of RDO in Virtual Prototyping
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Challenge of RDO – reliable input
Successful RDO needs a balance between three main pillars • Reliable input = know how and definition of input uncertainties • Reliable analysis = reliable stochastic analysis methodology • Reliable post processing = use of stochastic/statistic results in
the design process Let’s derive the functionality of an RDO process/package to support
real world industrial RDO tasks Reliable input scatter definition • all possible important input scatter sources have to be included to
be able to estimate output scatter and input scatter importance ⇒ many scattering variables (in the beginning) of an RDO task ⇒ not only optimization parameter scatter! ⇒ for best translation of input scatter a suitable variety of
distribution functions are necessary ⇒ correlations between scattering inputs needs to be considered
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Challenge of RDO - reliable analysis Reliable CAE-based stochastic analysis • if single design evaluation needs significant CPU it is a challenge to
balance between number of solver runs spend on Robustness Estimation and Reliability Analysis and the reliability of the scatter measurements itself ⇒ Efficient and reliable methodology to sort out
important/unimportant input scatter and estimate variance based output scatter ranges (mean values, standard deviation)= Robustness Evaluation
⇒ Efficient and reliable methodology to estimate probabilities = Reliability Analysis
⇒ Efficient and reliable methodology to combine optimization and Robustness/Reliability analysis
⇒ Because all RDO algorithms will estimate robustness/reliability
measurements with minimized number of solver runs the proof of the reliability of the final RDO design is absolutely mandatory!
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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Challenge of RDO - reliable post processing Reliable post processing • Stochastic Analysis and statistical post processing estimates
variation of response values ⇒ Reliable quantification of input scatter variable importance ⇒ Reliable estimation of variation using fit of distribution
functions ⇒ Provide error estimation of reliability measurements
(probabilities) ⇒ Filter of insignificant/unreliable results ⇒ Easy and safe to use
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
Robust Design Optimization - RDO
Sensitivity analysis
Robustness evaluation
Define safety factors
Robustness proof!
Robust Design Optimization combines optimization and Robustness Evaluation . From our experience it is often necessary to investigate both domains separately to be able to formulate a RDO problem. optiSLang offers you either iterative or automatic RDO flows.
Robust design optimization
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RDO Centrifugal Compressor Parameterization Parametric geometry definition using ANSYS BladeModeler (17 geometric parameter) Model completion and meshing using ANSYS Workbench
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RDO Centrifugal Compressor Fluid Structure Interaction (FSI) coupling Parametric fluid simulation setup using ANSYS CFX Parametric mechanical setup using ANSYS Workbench
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Optimization goal: increase efficiency Constraints: 2 pressure ratio’s, 66 frequency constraints, Robustness
Tolerance limit 1.34<ΠT<1.36 ~13% outside
RDO Centrifugal Compressor
Input Parameter 21 Output Parameter 43 Constraints 68
Initial SA ARSM I EA I ARSM II ARSM III
Total Pressure Ratio 1.3456 1.3497 1.3479 1.3485 1.356 1.351
Efficiency [%] 86.72 89.15 90.62 90.67 90.76 90.73
#Designs - 100 105 84 62 40
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Robustness evaluation
Robustness proof using Reliability Analysis Sensi + first optimization step
RDO optimization
Robust Design Optimization with respect to 21 design parameters and 20 random geometry parameters, including manufacturing tolerances. Robust Design was reached after 400+250=650 design evaluations consuming.
RDO Centrifugal Compressor
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Parameter Manager
Parameter & Responses
optiPlug - ANSYS Workbench optiSLang Interface
OptiSLang-Plugin:
just click to integrate workbench in
optiSLang
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
The Workbench Effect – easier to use
Easy parametric set up of complex simulations
easy use of best praxis automated flows inside ANSYS
optiSLang inside ANSYS Workbench
Fully parametric
Robust Design Optimization, ANSYS UGM Houston September 1th 2011
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