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© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
"optiSLang inside ANSYS Workbench" - efficient, easy, and safe to use
Robust Design Optimization (RDO)
- second: part: Design Robustness and Design Reliability
Johannes Will, CEO Dynardo GmbH
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© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
Agenda
• Introduction to Robust Design Optimization
• Robustness analysis
• Reliability Analysis
• Robust Design Optimization
• Life demonstration
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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
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Premium Consultancy and Software Company for CAE-based Robustness Evaluation, Reliability
Analysis and Robust Design Optimization using Stochastic Analysis
Dynardo is the consulting company which successfully introduced stochastic analysis into complex CAE-based virtual product development processes. Recently, it is applied in the power generation industry, automotive industry and high-level consumer goods industry
DYNARDO Field of Excellence
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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• Virtual prototyping is necessary for cost efficiency • Test cycles are reduced and placed late in the product development • CAE-based optimization and CAE-based robustness evaluation becomes
more and more important in virtual prototyping
– Optimization is introduced into virtual prototyping – Robustness evaluation is the key methodology for safe, reliable and
robust products – The combination of optimizations and robustness evaluation will lead
to robust design optimization strategies
Challenges in Virtual Prototyping
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Design for Six Sigma
• Six Sigma is a concept to optimize the manufacturing processes such that automatically parts conforming to six sigma quality are produced
• Design for Six Sigma is a concept to optimize the design such that the parts conform to six sigma quality, i.e. quality and reliability are explicit optimization goals
• Because not only 6 Sigma values have to be used as measurement for a robust design, we use the more general classification Robust Design Optimization
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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)
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
Example: Analytical nonlinear function
• Additive linear and nonlinear terms and one coupling term
• Contribution to the output variance (reference values): X1: 18.0%, X2: 30.6%, X3: 64.3%, X4: 0.7%, X5: 0.2%
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Robustness Design Optimization
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robust Design Optimization Robust Design Optimization (RDO) optimize the design performance
with consideration of scatter of design (optimization) variables as well as other tolerances or uncertainties.
As a consequence of uncertainties the location of the optima as well as the contour lines of constraints scatters.
To measure Design Robustness stochastic analysis become
necessary.
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
• When material, geometry, process or environmental scatter is significantly affecting the performance of important response values
• When significant scatter of performance is seen in reality and there is doubt that safety distances may be to small or safety distances should be minimized for economical reasons than stochastic analysis needs to be implemented.
When and How to apply RDO?
• Iterative RDO strategies using optimization steps with safety margins in the design space and checks of robustness in the space of scattering variables
or • Automatic RDO strategies estimating variance based or probability
based measurements of variation for every candidate in the optimization space
are possible RDO strategies.
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Which Robustness measurements? Robustness in terms
of constraints • Safety margin (sigma level) of one
or more responses y:
• Reliability (failure probability) with respect to given limit state:
“Taguchi” = 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):
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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What is necessary for successful implementation? 1. Introduction of realistic scatter definitions Distribution function Correlations Random fields
2. Using of reliable stochastic methodology Variance-based robustness evaluation using optimized LHS
3. Development of reliable robustness measurements Standardized post processing Significance filter Measurements of forecast quality Reliable variation and correlation measurements
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Definition of Uncertainties
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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• Design variables • Material, geometry, loads,
constrains,… • Manufacturing • Operating processes (misuse) • Resulting from Deterioration • …
Uncertainties and Tolerances Property SD/Mean
% Metallic materiales, yield 15 Carbon fiber rupture 17
Metallic shells, buckling strength
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Bond insert, axial load 12
Honeycomb, tension 16
Honeycomb, shear, compression 10
Honeycomb, face wrinkling 8
Launch vehicle , thrust 5
Transient loads 50 Thermal loads 7.5
Deployment shock 10
Acoustic loads 40 Vibration loads 20
Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace. Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris 1994
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Optimal translation of scattering variables - measurement of scattering variables can be easily imported and optimal statistic translation (distribution function and correlation) can be fitted using Excel and optiSLang
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Random Field Parametric • Introduction of scatter of spatially correlated scatters need parametric of
scatter shapes using random field theory.
The correlation function represents the measure of “waviness” of random fields. The infinite correlation length reduced the random field to a simple random variable. Usually, there exist multiple scatter shapes representing different scatter sources.
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Implementation of Random Field Parametric
4. Running Robustness Evaluation including Random Field effects
3. Generation of multiple imperfect structures using Random Field parametric
Introduction of spatial correlated scatter to CAE-Parameter (geometry, thickness, plastic values)
1. Input: multiple process simulation or measurements
2. Generation of scatter shapes using Random field parametric, quantify scatter shape importance
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Variance-based Robustness Analysis
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness = Sensitivity of Uncertainties
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness check of optimized designs • With the availability of parametric modeling environments like
ANSYS workbench an robustness check becomes very easy! • Menck see hammer for oil and gas exploration (up to 400m deep) • Robustness evaluation against tolerances, material scatter and working
and environmental conditions • 60 scattering parameter
Design Evaluations: 100 Process chain: ProE-ANSYS workbench- optiSLang
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness Evaluation of NVH Performance
• Consideration of scatter of body in
white, suspension system • Prognosis of response value scatter • Identify correlations due to the input
scatter • Up-to-date robustness evaluation
of body in white have 300 .. 600 scattering variables
• Using filter technology to optimize the number of samples
How does body and suspension system scatter influence the NVH performance?
by courtesy of
Start in 2002, since 2003 used for Production Level
Will, J.; Möller, J-St.; Bauer, E.: Robustness evaluations of the NVH comfort using full vehicle models by means of stochastic analysis, VDI-Berichte Nr.1846, 2004, S.505-527, www.dynardo.de
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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RDO procedure of consumer goods Goal: Check and improve Robustness of
a mobile phone against drop test conditions!
Using sensitivity analysis the worst case drop test position as well as optimization potential out of 51 design variables was identified
Robustness evaluation against production tolerances and material scatter (209 scattering parameter) shows need for improvements
Safety margins are calculated with Robustness evaluation after design improvements
Design Evaluations: Sensitivity 100, Robustness 150
by courtesy of
Sensi2 ANGLE_X = 3 °
CoD lin adj
CoD quad adj
CoD lin adj
Spearman
CoP
48 48 46 58
Ptchelintsev, A.; Grewolls, G.; Will, J.; Theman, M.: Applying Sensitivity Analysis and Robustness Evaluation in Virtual Prototyping on Product Level using optiSLang; Proceeding SIMULIA Customer Conference 2010 , www.dynardo.de
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness evaluation as early as possible Goal: Tolerance check before any
hardware exist! Classical tolerance analysis tend to be very
conservative Robustness evaluation against production
tolerances and material scatter (43 scattering parameter) shows:
- Press fit scatter is o.k. - only single tolerances are important (high
cost saving potentials) Production shows good agreement!
Design Evaluations: 150 solver: ANSYS/optiSLang
by courtesy of
Suchanek, J.; Will, J.: Stochastik analysis as a method to evaluate the robustness of light truck wheel pack; Proceedings WOSD 6.0, 2009, Weimar, Germany, www.dynardo.de
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness Evaluation
Minimum required user input: definition of input variation /scatter definition of robustness criteria number of samples for ALHS
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Reliability Analysis
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Reliability Analysis • Robustness can verify relatively high probabilities only
(±2σ, like 1% of failure) • Reliability analysis verify rare event probabilities (≥3σ,
smaller then 1 out of 1000)
• First order reliability method (FORM), ≥2σ, gradient based • Importance sampling using design point (ISPUD), Sigma level ≥ 2, n ≤ 50 • Monte-Carlo-Simulation, independent of n, but very high effort for ≥2σ • Latin Hypercube sampling, independent of n, still very high effort for ≥2..3σ • Asymptotic Sampling, ≥2σ, n ≥ 10 • Adaptive importance sampling, ≥2σ, n ≤ 10 • Directional sampling, ≥2σ, n ≤ 10 • Directional Sampling using global adaptive response surface method, ≥2σ,
n ≤ 5..10
There is no one magic algorithm to estimate probabilities with “minimal” sample size.
It is recommended to use two different algorithms to verify rare event probabilities
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robustness & Reliability Algorithms
How choosing the right algorithm? Robustness Analysis provide the
knowledge to choose the appropriate algorithm
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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sig
ma
= +
/-1
0kN
si
gm
a =
+/
-5kN
Application Example ARSM for Reliability • Fatigue life analysis of Pinion shaft • Random variables
• Surface roughness • Boundary residual stress • Prestress of the shaft nut
• Target: calculate the probability of failure
• Probability of Failure: • Prestress I: P(f)=2.3 10-4 (230
ppm) • Prestress II: P(f)=1.3 10-7 (0.13
ppm)
Solver: Permas Method: ARSM 75 Solver evaluations
by courtesy of
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robust Design Optimization
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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Robust Design Optimization
Pareto Optimization
Adaptive Response Surface
Evolutionary Algorithm
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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1) From the 31 optimization parameter the most effective one are selected with optiSLang Sensitivity analysis.
3) From optiSLang Robustness Evaluation safety margins are derived. 4) Three steps of optimization using optiSLang ARSM and EA optimizer improve the design to an optiSLang Six sigma design.
2) The DX Six Sigma design was checked in the space of 36 scattering variables using optiSLang Robustness evaluation. Some Criteria show high failure probabilities!
5) Reliability proof using ARSM to account the failure probability did proof six sigma quality.
Start: Optimization using 5 Parameter using DX Six Sigma, then customer asked: How save is the design?
by courtesy of
Iterative RDO Application Connector
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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RDO Centrifugal Compressor Parameterization Parametric geometry definition using ANSYS BladeModeler (17 geometric parameter) Model completion and meshing using ANSYS Workbench
by courtesy of
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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
by courtesy of
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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
by courtesy of
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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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
by courtesy of
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
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optiSlang inside ANSYS workbench What‘s the Difference?
Ease and safe of use • Minimized input, easy to use and safe to use Innovative Methodology • Sensitivity analysis and optimization for large (number of variables)
non-linear problems • Optimization with robust defaults (ARSM, EA, GA, PARETO) • Complete methodology suite to run robust design optimization Key applications • Sensitivity analysis, MOP generation, Optimization • Robustness evaluation and Robust Design Optimization • Calibration, Model update and parameter identification
© Dynardo GmbH • Confidence by Design • June 20th 2012, Houston
contact: Johannes Will, [email protected] Tel +49 3643 9008 35 Further information: www.dynardo.com