optislang inside ansys efficient, easy, and safe to use robust design optimization (rdo) ·...

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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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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


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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


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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


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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


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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)


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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


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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.


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• 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):


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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


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Definition of Uncertainties


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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


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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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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


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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.


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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


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Variance-based Robustness Analysis


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Robustness = Sensitivity of Uncertainties


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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


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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


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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


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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


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Robustness Evaluation

Minimum required user input: definition of input variation /scatter definition of robustness criteria number of samples for ALHS


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Reliability Analysis


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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


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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


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Robustness & Reliability Algorithms

How choosing the right algorithm? Robustness Analysis provide the

knowledge to choose the appropriate algorithm


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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


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Pareto Optimization

Adaptive Response Surface

Evolutionary Algorithm


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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


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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


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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


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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


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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


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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


contact: Johannes Will, [email protected] Tel +49 3643 9008 35 Further information: www.dynardo.com

mailto:[email protected]

optislang inside ansys efficient, easy, and safe to use robust design optimization (rdo) ·...

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