Robust Design - Dynardo GmbH

DYNARDO • © Dynardo GmbH 2012
Robustness & Reliability Analysis
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DYNARDO • © Dynardo GmbH 2012
Robust Design Optimization
Robust Design
Variance based
Robustness Evaluation
Probability based
Robustness Evaluation,
(Reliability analysis)
Optimization
Sensitivity Study
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization Methodology
Start
Single & Multi objective
(Pareto) optimization
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DYNARDO • © Dynardo GmbH 2012
How to define Robustness of a Design
• 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
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DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation / Reliability Analysis
• Variance-based robustness evaluation
measure product serviceability
– Safety and reliability for 1 & 2 (3)
Sigma levels and identifies the most
sensitive stochastic variables
– Possible with high number of
stochastic variables
• Probability-based robustness evaluation
(reliability analysis) measure product
serviceability
– Safety and reliability for high
reliability levels (3,4,5,6-Sigma) with
small number of variables
– Possible with a limited number of
stochastic variables
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DYNARDO • © Dynardo GmbH 2012
Definition of Uncertainties
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DYNARDO • © Dynardo GmbH 2012
Uncertainties and Tolerances
• Design variables
• Material, geometry, loads,
constrains,…
• Manufacturing
• Operating processes (misuse)
• Resulting from Deterioration
• …
Property SD/Mean
%
Metallic materiales, yield 15
Carbon fiber rupture 17
Metallic shells, buckling
strength
6
14
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 • ECCOMAS 2012 congress• © Dynardo GmbH 2012
Definition of Uncertainties
Translate know how about uncertainties into proper scatter definition
Distribution functions define
variable scatter
Correlation is an important
characteristic of stochastic
variables.
Yield stress
Tensile strength
Correlation of single uncertain values
spatial correlated
thickness distribution
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DYNARDO • © Dynardo GmbH 2012
Design “single” scatter shapes
• Use of CAD-parameter or mesh morphing functions to
design “single” scatter shapes
Measured ed imperf imperfection modelled imperfection
Imperfection of cylindricity of truck wheel component
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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DYNARDO • © Dynardo GmbH 2012
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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DYNARDO • RDO forming simulation • © Dynardo GmbH 2012
Use forming simulation to generate scatter fields
4. Mapping to crash mesh
3. Generation of n-imperfect formed
parts using scatter field parametric
2. Identification of most important
scatter fields for scattering forming
result values (thickness,
hardening)
5. Run Robustness Evaluation of
assembly including scatter from forming
1. Running Robustness
evaluation of forming simulation
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DYNARDO • © Dynardo GmbH 2012
Use measurements to generate Random Fields
3. Identification of most
important random fields for
measured quantity (geometry)
4. Generate imperfect geometries using
Random Field parametric
2. Trimming of initial FE-mesh regarding
measurement or realization
5. Run Robustness Evaluation to identify
the most sensitive random fields
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1. Multiple Measurements
from Manufacturing
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DYNARDO • © Dynardo GmbH 2012
Implementation of Random Field Parametric
Introduction of spatial correlated scatter to CAE-Parameter (geometry,
thickness, plastic astic values)
3. Generation of multiple imperfect
structures using Random Field parametric
2. Generation of scatter shapes using
Random field parametric, quantify scatter
shape importance
4. Running Robustness Evaluation
including Random Field effects
1. Input: process simulation or
measurements
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DYNARDO • © Dynardo GmbH 2012
Variance-based Robustness Analysis
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DYNARDO • © Dynardo GmbH 2012
Which Robustness do You Mean?
Robustness evaluation due to naturally given scatter
Goal: measurement of variation and correlation
Methodology: variance-based robustness evaluation
Positive side effect of robustness evaluation: The measurement of
prognosis quality of the response variation answer the question - Does
numerical scatter significantly influence the results?
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DYNARDO • © Dynardo GmbH 2012
Statistic Measurements
• Evaluation of robustness with statistical
measurements
– Variation analysis (histogram,
coefficient of variation, standard
variation, distribution fit,
probabilities)
– Correlation analysis (linear,
quadratic, nonlinear) including
principal component analysis
– Forecast quality: Evaluation of
Coefficient of Prognosis (CoP)
including coefficients of
determination (CoD)and coefficient
of importance (CoI)
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DYNARDO • © Dynardo GmbH 2012
Advanced Statistic Measurements
• Advanced histogram options
– PDF fit (automatic/manual)
– Number of histogram classes
– PDF values ready for optiSLang
input
– Limits with probabilities
– Probabilities with limit
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DYNARDO • © Dynardo GmbH 2012
Standardized and Automated Post Processing
Example how the post
processing is
automated for passive
safety at BMW
The maximum from
the time signal was
taken.
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DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation using optiSLang
1) Define the robustness space using
scatter range, distribution and
correlation
5) Identify the most
important scattering
variables
4) Check the CoI/CoP CoI
2) Scan the robustness space by
producing and evaluating n
(100) Designs
3) 3) Check the variation interval
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DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation of NVH Performance
Start in 2002, since 2003 used for Production Level
How does body and suspension system scatter influence the NVH
performance?
• Consideration of scatter of body in
white, suspension system
• Prognosis of response value scatter
• Identify correlations due to the input
scatter
• CAE-Solver: NASTRAN
• Up-to-date robustness evaluation of
body in white have 300 .. 600
scattering variables
• Using filter technology to optimize the
number of samples
by courtesy of
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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DYNARDO • ECCOMAS 2012 congress• © Dynardo GmbH 2012
Robustness Evaluation of break systems
Start in 2007, since 2008 used for Production Level
How does material and geometric scatter influence the break noise
performance ?
• Consideration of material
and geometry scatter
• Break noise is a instability
problem
• Identify correlations due to
the input scatter
• CAE-Solver: NASTRAN,
ABAQUS, ANSYS
• Up-to-date robustness
evaluation have 20 ..30
scattering variables
• Integration of geometric
scatter via random fields
1. Define the
Uncertainties
4. Post
processing
2. Simulate random m parameters
p
3. Generate set of random
specimen, replace in FE assembly
to compute
by courtesy of
Will, J.; Nunes, R.: Robustness evaluations of the break system concerning squeal noise
problem, Weimarer Optimierungs- und Stochastiktage 2009, www.dynardo.de
X2
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X1

DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation of Forming Simulations
• Consideration of process
and material scatter
• Determination of process
robustness based on 3-
Sigma-values of quality
criteria
• Projection and
determination of
statistical values on
FE-structure
necessary
CAE-Solver: LS-DYNA,
AUTOFORM and others
Start in 2004 - since 2006 used for production level
1. Variation der Eingangsstreuungen
mittels geeigneter
Samplingverfahren
3. statistische Auswertung
und Robustheitsbewertung
Will, J.; Bucher, C.; Ganser, M.; Grossenbacher, K.: Computation and visualization of
statistical measures on Finite Element structures for forming simulations; Proceedings
Weimarer Optimierung- und Stochastiktage 2.0, 2005, Weimar, Germany
2. Simulation inkl.
Mapping
auf einheitliches
Netz
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Why SoS and What is SoS ?
Why: Engineers need to evaluate statistical Das Bild kann zurzeit nicht angezeigt werden. data on the structure to locate
„hot spots“ of variation as well as investigate correlations
What: A post processor for Statistics on finite element Structures
• Visualization of descriptive statistics on the structure
• Visualization of correlations between random input
and structural results
• Visualization of quality performance (QCS)
• Identification of scatter shapes using Random Fields
Key features:
• locale „hot spots“ of variation
• Data reduction and smoothing by mesh coarsening
• Identification of relevant scatter shapes
• Vizualisation statistics of eroded (failed) elements
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DYNARDO • © Dynardo GmbH 2012
Statistical post-processing on FE-meshes
Motivation: - Visualization of statistical measurements
- Identification of hot spots,
- Identification of correlation structure (random fields)
1. Import data
(multiple simulation on runs
or measurements) ments)
3. Export local statistics
and imperfection
amplitudes to
optiSLang for further ther
post-processing
2. Visualize variation, v correlation,
identify ify random fi field shapes
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DYNARDO • © Dynardo GmbH 2012
Statistical post-processing on FE-meshes
SoS is the tool to answer the questions:
Where? Locate hot spots of highest variation and/or extreme values, which
may cause lack of performance or quality.
Why? Find the input parameters which cause scatter of the results, by
analysing correlation/CoD between random inputs and spatially distributed
results, export to optiSLang p g for MoP/CoP / analysis. y
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DYNARDO • © Dynardo GmbH 2012
SoS application crash simulation
• Stringer in a car body subject to crash simulation
• 55 random inputs: sheet thickness and material parameters (also of
other parts), load parameters (velocity, barrier angle etc.)
• Observed result: remaining effective plastic strain
[Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts.
SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.]
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DYNARDO • © Dynardo GmbH 2012
SoS application crash simulation
• Analysis of a car structure subject to
random crash load case
• Decomposition of plastic strain
random field
• Analysis of largest influence by
MoP/CoP in optiSLang
[Bayer, V.; Will, J.: Random Fields in Robustness and Reliability Assessment of Structural Parts.
SIMVEC, Verein Deutscher Ingenieure VDI, Baden-Baden 2010.]
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DYNARDO • © Dynardo GmbH 2012
SoS - Eroding elements
General eroding information.
Green area: no elements eroded.
Red area: there were eroded elements.
Eroding percent plot shows the
percentage of eroded elements.
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DYNARDO • © Dynardo GmbH 2012
SoS – Validated Global and Local Statistics
Variation, mean value, correlation, Histogram, linear & quadratic
QCS using SoS on FE-structure correlation, CoD, CoI, CoP and
Anthill plots using optiSLang at local
nodal or element values
Selection of nodal/element results in
SoS and export to optiSLang *.bin
CoD linear base
Correlation
R-value
Cotrrelation
Y-tolerance
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DYNARDO • © Dynardo GmbH 2012
SoS - Applications
- use SoS for robustness evaluation of forming processes
- use SoS for visualization and hot spot investigation at robustness
evaluations in crashworthiness or drop test applications
- use SoS for the identification of random fields from simulation or
measurements
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Standardized and Automated Post Processing
Productive Level needs standardized and automated post processing!
1. Check variation of
plasticity, failure,
intrusions.
3. Summarize variation
and correlation
2. Identify the beginning of the
phenomena in time and use SoS to
identify the source of variation
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DYNARDO • © Dynardo GmbH 2012
Summary SoS – Statistic on Structure
The post processor for Statistics on finite element Structures
- Statistic Measurements
- Single Designs
- Differences between Designs
- Variation interval
- Minimum/Maximum
- Mean Value
- Standard deviation
- Coefficient of variation
- Quantile (± ����
- Correlation & CoD
- Linear correlation & CoD
- At nodal/element level
- Process quality criteria Cp, Cpk
process indices
- Random field generation
- Scatter shape extraction and
visualisation
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DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation of Passive Safety
• Consideration of scatter of material
and load parameters as well as test
conditions
• Prognosis of response value
variation = is the design robust!
• Identify correlations due to the input
scatter
• Quantify the amount of numerical
noise
• CAE-Solver: MADYMO, ABAQUS
Start in 2004, since 2005 used
for productive level
Goal: Ensuring Consumer
Ratings and Regulations &
Improving the Robustness of a
System
Will, J.; Baldauf, H.: Integration of Computational Robustness Evaluations in Virtual
Dimensioning of Passive Passenger Safety at the BMW AG , VDI-Berichte Nr. 1976, 2006,
Seite 851-873, www.dynardo.de
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Robustness Evaluation Crashworthiness
Start in 2004 – since 2007 use for Production Level
• Consideration of scatter of thickness,
strength, geometry, friction and test
condition
• CAE-Solver: LS-DYNA, Abaqus
• Prognosis of intrusions, failure and
plastic behavior
• Identify Coefficient of Prognosis and
nonlinear correlations
• Check model robustness
• 100 .. 200 scattering variables
• Introduction of forming scatter via
Random Fields
by courtesy of the Daimler AG
In comparison to robustness evaluations for NVH, forming or passive
safety, crashworthiness has very high demands on methodology and
software!
by courtesy of
Will, J.; Frank, T.: Robustness Evaluation of crashworthiness load cases at Daimler AG;
Proceedings Weimarer Optimierung- und Stochastiktage 5.0, 2008, Weimar, Germany,
www.dynardo.de
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DYNARDO • © Dynardo GmbH 2012
Summary Robustness Evaluation
• optiSLang + SoS have completed the necessary methodology to run
robustness evaluation for NVH, passive safety, forming simulation or
crashworthiness
Success Key:
• Necessary distribution types and correlation definitions
available
• Optimized LHS sampling
• Reliable measurements of variation, correlation and determination
including filter technology
• Projection of statistic onto the FE-structure
Main customer benefit:
• Identification of problems early in the virtual prototyping stage
• Measure, verify and finally significantly improve the modeling quality
(reduce numerical scatter and modeling errors)
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DYNARDO • © Dynardo GmbH 2012
What is necessary for successful implementation?
1. Introduction of realistic
scatter definitions
� Distribution function
� Correlations
� Random fields
2. Using of reliable stochastic methodology
methodology
� Variance-based robustness
evaluation using optimized LHS
3. Development of reliable robustness
measurements
� Standardized post processing
� Significance filter
� Reliable variation and correlation
measurements
Acceptance of method/result documentation/communication!
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DYNARDO • © Dynardo GmbH 2012
Robustness and Stability of the Model
Which quantity of „numerical noise“ is acceptable?
� Quantification via coefficients of prognosis (CoP)
� Estimation of numerical noise: 100% - CoP
Experience in passive safety, CFD or
crashworthiness tells that result values
with lower CoP than 80% show:
- High amount of numerical noise
resulting from numerical approximation
method (meshing, material, contact,..)
- Problems of result extractions
- Physically instable behavior
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DYNARDO • © Dynardo GmbH 2012
Robustness Insurance Crash Loading
Response CoV
CoD
lin[%]
CoD lin
adj [%]
CoD
quad [%]
CoD
quad adj
[%]
max_int_energy 0.036 99.0 99.0 100.0 99.0
max_hourglass_energy 0.066 91.0 87.0 98.0 94.0
x_1129403_1129404 0.217 54.0 31.0 93.0 79.0
x_4000558_1129403 1.383 86.0 79.0 93.0 80.0
x_4139132 0.123 89.0 83.0 97.0 91.0
x_4144932 0.131 88.0 82.0 97.0 90.0
y_4139132 0.224 92.0 89.0 98.0 93.0
y_4144932 0.252 95.0 93.0 98.0 95.0
z_4139132 0.348 33.0 0.015 90.0 71.0
z_4144932 1.035 49.0 24.0 91.0 74.0
max_sec29_rforce 0.032 87.0 80.0 96.0 88.0
max_sec29_xforce 0.032 86.0 78.0 96.0 87.0
max_sec33_rforce 0.034 89.0 84.0 97.0 90.0
max_sec33_xforce 0.034 90.0 84.0 97.0 90.0
max_plast 0.211 88.0 82.0 95.0 86.0
summ_plast 0.26 91.0 87.0 97.0 92.0
In qualified FE-models numerical scatter is not
dominating important response values!
Model guidelines, model verification and robustness
evaluation ensure a reasonable model quality.
LS-DYNA low speed structural
crash case
Robustness evaluation against
structure and loading scatter
show coefficients between 71
and 99 %
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DYNARDO • © Dynardo GmbH 2012
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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DYNARDO • © Dynardo GmbH 2012
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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DYNARDO • © Dynardo GmbH 2012
Reliability Analysis
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© Dynardo GmbH 2012
Reliability analysis
• Limit state function g(x) divides random variable space X
in safe domain g(x)>0 and failure domain g(x) ��
• Multiple failure criteria (limit state functions) are possible
• Failure probability is the probability that at least one failure criteria is
violated (at least one limit state function is negative)
• Integration of joint probability density function over failure domain
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DYNARDO • © Dynardo GmbH 2012
Definition of limit state functions
Dynardo • optiSlang Seminar
Example damped oscillator
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DYNARDO • © Dynardo GmbH 2012
Reliability Analysis Algorithms
Gradient-based
algorithms = First
Order Reliability
algorithm (FORM)
ISPUD Importance
Sampling using Design
Point
Adaptive Response
Surface Method
Monte Carlo Sampling Latin Hypercube Sampling Directional Sampling
X2
X1
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DYNARDO • © Dynardo GmbH 2012
How choosing the right algorithm?
Robustness Analysis provide the
knowledge to choose the
appropriate algorithm
Robustness & Reliability Algorithms
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DYNARDO • © Dynardo GmbH 2012
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)
by courtesy of
Solver: Permas
Method: ARSM
75 Solver evaluations
sigma = +/-5kN
sigma = +/-10kN
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DYNARDO • © Dynardo GmbH 2012
Probability Assessment of Railways
• Goal: investigate the crosswind stability of Railway
systems
• Sensitivity analysis against stochastic loading
parameters followed by probability analysis
• Random variables
• crosswind amplitude, duration
• aerodynamic coefficients
Solver: ADAMS + Matlab
Methods: LHS, FORM, ISPUD
Proppe, C.Wetzel, C.; Probabilitic Assessment of the Crossswind Stability of Railway
Systems; Proceedings Weimarer Optimierung- und Stochastiktage 4.0, 2007, Weimar,
Germany, www.dynardo.de
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DYNARDO • © Dynardo GmbH 2012
Robust Design Optimization
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DYNARDO • © Dynardo GmbH 2012
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
48

© Dynardo GmbH 2012
© Dynardo GmbH
Sigma level vs. failure probability
• The sigma level can be used to calculate the probability of exceeding
a certain response value
• Since the distribution type is often unknown, this estimate may be
very inaccurate for small probabilities
• The sigma level deals with single limit values, whereas the failure
probability quantifies the event, that any of several limits is exceeded
� Reliability analysis should be applied to proof the required safety level
Distribution Required sigma level (CV=20%)
p F = 10 -2 p F = 10 -3 p F = 10 -6
Normal 2.32 3.09 4.75
Log-normal 2.77 4.04 7.57
Rayleigh 2.72 3.76 6.11
Weibull 2.03 2.54 3.49
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DYNARDO • © Dynardo GmbH 2012
Robust Design Optimization
Robust Design
Variance based
Robustness Evaluation
Probability based
Robustness Evaluation,
(Reliability analysis)
Optimization
Sensitivity Study
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization Methodology
Start
Single & Multi objective
(Pareto) optimization
50

Robust Design
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 proof Robust Designs safety distances are quantified with variance
or probability measurements using stochastic analysis.
51

Methods for Robust Design Optimization
Variance-based RDO
• Safety margins of all critical responses
are larger than a specified sigma level
(e.g. Design for Six Sigma)
Reliability-based RDO
• Failure probability with respect to given
limit states is smaller as required value
Taguchi-based RDO
• Taguchi loss functions
• Modified objective function
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DYNARDO • © Dynardo GmbH 2012
Robust Design Optimization - RDO
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.
Robustness Robustne evaluation
SSensitivity it analysis
Define safety factors
Robust design optimization
Robustness proof!
53

DYNARDO • © Dynardo GmbH 2012
Iterative RDO Application Connector
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!
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 optimizer improve the design to
an optiSLang Six sigma design.
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
54

Robust Design Optimization of a rubber seal
Using DesignModeler parametric
was rebuild with 11 Parameter.
Using optiSLang sensitivity
analysis 7 effective parameter
are identified. Using ARSM
design was optimized to have
minimal volume and sufficient
pressure at all contact points.
Initial design
Including Uncertainty of
loading and material 6
Sigma quality was violated.
Therefore iterative RDO
increasing safety margins
was performed to reach 3
Sigma design level.
Robust design
Using optiSLang Reliability
Analysis 3 sigma quality was
proven.
Customer started optimization with two parameter and found minimal improvement
potential.
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DYNARDO • NAFEMS conference 2012 • © Dynardo GmbH 2012
Summary
• Stochastic analysis needs a balance between input definitions,
stochastic analysis method and post processing
• Use specific/concrete robustness/reliability measurements
• RDO using one global response surface approximation for
optimization and robustness space usually underrepresents the
influence of scattering variables
• Because all RDO strategies will try to minimize solver runs for
robustness measures, a final proof of robustness/reliability is
mandatory
• Carefully translation and introduction of material scatter is crucial
• Start with robustness evaluation of start/optimal candidate design
• Continue with iterative RDO approach using safety distances
• If safety distances in optimization space vary significant automatic
RDO is necessary
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DYNARDO • © Dynardo GmbH 2012
Part 7
Applications
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DYNARDO • © Dynardo GmbH 2012
Application Crashworthiness
AZT Insurance Crash Load Case
• Scatter definition (40..60 scattering
parameter)
– Velocity, barrier angle and position
– Friction (Road to Car, Car to
Barrier)
– Yield strength
– Spatially correlated sheet metal
thickness
• Main result: Prognosis of plastic
behavior
• CAE-Solver: LS-DYNA
Deterministic analysis show no problems with an AZT load case. Tests
frequently show plastic phenomena which Daimler would like to minimize.
Motivation for the robustness evaluation was to find the test phenomena
in the scatter bands of robustness evaluations, to understand the sources
and to improve the robustness of the design.
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DYNARDO • © Dynardo GmbH 2012
Did You Include All Important Scatter?
Scatter of uniform sheet
thickness thickness (cov=0.05),
yield strength, friction, test est
conditions
We could not find
or explain the test
results!
Introduction of sheet metal
thickness scatter per part
- 100 LS-DYNA simulation
- Extraction via LS-PREPOST
SoS - post processing
Statistics_on_Structure
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DYNARDO • © Dynardo GmbH 2012
Definition of Scatter is the Essential Input!
Which degree of forming scatter discretization is becomes necessary?
Level 1 - No distribution information: - increase uniform coil thickness
scatter cov=0.02 to cov=0.03..0.05
Level 2 - Use deterministic distribution information: - use thickness
reduction shape from deterministic forming simulation and superpose coil
(cov=0.02) and forming process scatter (cov=0.01..0.03)
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DYNARDO • © Dynardo GmbH 2012
Did You Include All Important Scatter?
Scatter of sheet
thickness, forming
process scatter
covmax=0.05
yield strength, friction,
n,
test conditions
We could find and
explain the test results!
+
Introduction of spatial correlated
forming process scatter
- 100 LS-DYNA simulation
- Extraction via LS-PREPOST
SoS
- post prozessing
Statistics_on_Structure
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DYNARDO • © Dynardo GmbH 2012
Iterative Robust Design Optimization
• Design optimization task
• 4 continuous, 2 binary design
variables
• Single objective formulations
(maximal removal power)
• 2 optimization restrictions
• Robustness of performance should
be preserved
by courtesy of
Könning, M; Plotzitza, A.: Optimierung und Robustheitsbewertung mit optiSLang bei der
Robert Bosch GmbH, Proceeding Weimarer Optimierung- und Stochastiktage 1.0, 2004,
www.dynardo.de
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DYNARDO • © Dynardo GmbH 2012
Iterative Robust Design Optimization
• With help of the sensitivity analysis,
the optimization task was
formulated.
• With help of genetic algorithms, the
optimization was performed.
• With robustness evaluation,
robustness and reliability were
checked.
• The performance was increased by
25 %!
• The results of the digital product
development were proven by
testing!
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DYNARDO • © Dynardo GmbH 2012
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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DYNARDO • © Dynardo GmbH 2012
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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DYNARDO • © Dynardo GmbH 2012
RDO Centrifugal Compressor
Optimization goal: increase efficiency
Constraints: 2 pressure ratio’s, 66 frequency constraints, Robustness
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
Input Parameter 21
Output Parameter 43
Constraints 68
Tolerance
limit
1.34

DYNARDO • © Dynardo GmbH 2012
RDO Centrifugal Compressor
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.
Robustness evaluation
Sensi + first optimization step
by courtesy of
RDO optimization
Robustness proof using Reliability
Analysis
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Robust Design Optimization of a rubber seal
Parametric model and Sensitivity Study
• Customer investigated Seal optimization using only 2 parameter
• Using DesignModeler parametric was rebuild with 11 parameter
Initial design
Sensitivity study
• Using optiSLang sensitivity approach 7 effective optimization
parameter are identified
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Robust Design Optimization of a rubber seal
Deterministic optimization
Using optiSLang ARSM algorithm
design was optimized to have minimal
volume and sufficient pressure at all
contact points.
Initial design
Including Uncertainty of loading and
material 6 Sigma quality was violated.
Therefore iterative RDO increasing safety
margins of contact forces was performed
to reach 3 Sigma design level.
Optimal design
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Robust Design Optimization of a rubber seal
Iterative Robust Design Optimization
• Required sigma level = 3 sigma
• 4 iterations of sequential optimization and robustness analysis
• Deterministic optimum (140 design evaluations): 14% failure
• Robust optimum (540 design evaluations): 0.3% failure
• Young’s modulus is most important scattering variable
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Robust Design Optimization of a rubber seal
Iterative RDO – Reliability proof
• 7 geometry + 2 material =9 important parameters detected
from robustness analysis
Directional Sampling on ARSM
• FORM failed
• ARSM: 116 design evaluations
• Failure probability
= 0.07%, 3.2 sigma
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RDO on global response surface
• Approximation of model responses in
mixed optimization/stochastic space
• Simultaneous RDO is performed on
a global response surface
• Applicable to variance-, reliabilityand
Taguchi-based RDO
• Approximation quality significantly
influences RDO results
� Final robustness/reliability proof
is required
• Pure stochastic variables have small
influence compared to design variables
� Important local effects in the stochastic
space may be not represented
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Robust Design Optimization of a rubber seal
RDO on global response surface
• Optimization variables are varied in optimization space
• Pure stochastic variables are varied +/- 4 sigma
• 200 LHS samples generated with uniform distribution
• Approximation quality between 93% and 97%
• Young’s modulus is in RDO space
minor important but in robustness
space most important
� Pure stochastic variables
are unimportant
� Poor local approximation quality
for robustness analysis
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Robust Design Optimization of a rubber seal
RDO on global response surface
• Evolutionary algorithm (444 designs) + 50 Robustness samples for
each optimization design
• Mean values and standard deviation of contact pressures as
robustness measures
• RDO-Optimization with constraints for all contacts: 3.5 sigma
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Robust Design Optimization of a rubber seal
RDO on global response surface – Robustness proof
Small approximation error Large approximation error
Failure probability:
• Upper left contact pressure 2.2% (2.0 sigma)
• Lower left contact pressure 1.4% (2.2 Sigma)
� Optimal design is not robust!
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DYNARDO • © Dynardo GmbH 2012
Iterative RDO Application Connector
Goal: high safety level of connector
by courtesy of
10 contact forces have to be checked,
failure may happen if N< 1 N
The failure probability of single contact should
be lower than 10%
The failure probability of 5 contacts should be
less than 1 out 4.300.000. (6 Sigma
Design)
� Status quo: pre optimized design
using ANSYS DX and 5 optimization
parameter
Question:
how optimal and robust is the design
Solver: ANSYS Workbench
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DYNARDO • © Dynardo GmbH 2012
Step 1 - Sensitivity analysis
The Sensitivity Analysis id done in the design
space of 31 potential CAD (ProE) design
parameters
by courtesy of
Identification of n=15
most important
design parameters
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DYNARDO • © Dynardo GmbH 2012
Step 2 - Robustness analysis
The failure probability of
single contact failure
is checked with
Robustness
evaluation.
The Robustness Analysis
is done in the
Robustness space of
36 CAD tolerances
• Global variancebased
robustness
analysis using
Advanced Latin
hypercube sampling
with 90 design
evaluations
by courtesy of
Performance
critical contact
force F3o_v
With failure
probability of
89 %!
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DYNARDO • © Dynardo GmbH 2012
Step 3 - Optimization
• n=15 most important CAD design
parameters
• Objective: minimal failure distance
of every contact
by courtesy of
Step 1: ARSM
- Stagnation after 5 Iterations (126
Design evaluations), contact force
F3o_v still violating criteria
Step 2: introducing of additions constraints
Restart of Evolutionary Optimization using
best Design_ARSM, stop after 390
Design evaluations with feasible
design, but now other contact forces
become critical
Step 3: modifying the design space range
and introducing additional constraints
Restart using ARSM with best Design_EA,
stop after 172 Design evaluations
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DYNARDO • © Dynardo GmbH 2012
Step 4 Robustness Analysis • 36 scattering CAD tolerances
by courtesy of
• Global variance-based robustness
analysis using Advanced Latin
hypercube sampling with N=50 design
Failure probabilities of two forces higher
than 1%
Performance critical contact force F3o_v
with failure probability 9 %!
Contact force F2o_h with failure
probability 1 %!
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DYNARDO • © Dynardo GmbH 2012
Step 5 - Reliability analysis
Identification of n=12 most important random parameters using coefficients of
importance
Defining the limit state condition for violation more than 50% of the contact
forces are lesser than 1N
by courtesy of
Reliability analysis using ARSM with
N=137 D-optimal design of
experiment
Adaptive sampling on the MLS
surrogate model without samples
in the unsafe domain
Probability of failure is near zero,
assumption: normal distributed
random parameters
Optimized design is an Six Sigma
Design
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DYNARDO • © Dynardo GmbH 2012
Results
� Variance and probability-based robust design optimization with 31
optimization parameters and 36 scattering parameters
� Increasing the performance critical contact force F3o_v according
failure probability 89% -> 9%
� Failure probabilities of the other contact forces lesser than 1%
� System failure probability (more than 50% of the contact forces are
lesser than 1) is near zero! (Six Sigma Design)
� N=950 parallel finite element calculations
� Total calculation time 1 week
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Robustness Analysis drop test of mobile phone
A robustness evaluation is a so called global variance-based stochastic
analysis which addresses the question how much the response values
scatter under the consideration of input parameter scatter.
• 209 scattering variables (drop position, material (E,
ro, yield), geometry (thickness, radius), environment
(friction)
• 150 Latin Hypercube Samples
Statistical Post Processing include:
• The variation of the responses
• Coefficient of Determination/Importance, checking
linear and non-linear correlation
• Coefficient of Prognosis
• Statistics on Structure for critical part
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Process automation – drop test
Run the robustness
analysis in optiSLang.
209 scattering inputs
by courtesy of
Run ABAQUS which creates *.csv
files containing the results.
150 designs
Run the robusteval script
after the robustness analysis
is finished. All the designs
will be processed and *.rpt
files are created.
Post processing in
optiSLang.
- 36 responses
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DYNARDO • © Dynardo GmbH 2012
Post Processing Robustness - drop test
CoD lin
adj
CoD quad
adj
CoD lin
Adj
Spearman
• The Histogram shows a variation between 45.35
and 121.1
• Probability of violating the limit is 9.33 %
(1-0.9067=0.0933)
CoP
48 48 46 66
• Maximum Cop is 66 %, Inputs ANGLE_Y and
ANLGE_X have the most significant influence
by courtesy of
• Reference
• Maximum
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DYNARDO • © Dynardo GmbH 2012
Statistics on Structure (SoS)
• Based on Robustness analysis results (optiSLang)
• Visualization of statistics (Maxima, Minima, Mean value, Coefficient of
variation, …) to locate „hot spots“ of variation at the FE Structure
• Benefits:
• Visualization of Min/Max and scatter range on FE Structure
• Visualization of spatial Distribution of Variation and Correlation on FE-
Structure
• Selecting and visualizing important regions and their correlations
We have to select one time
frame for every design
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Combining SoS and optiSLang
• The picture above shows the maximum of S11 (positive - tension)
• In SoS it is possible to select elements at hot spots and generate optiSLang
*.bin file (see black circles)
• Use the result_monotoring in optiSLang to identify local variation and
correlation, The CoP plots below show that ANGLE_X and ANGLE_Y have
strongest strong influence nfluence on S11 2to:Histogram for the to selected check elements
variation
Structure in
ABAQUS viewer
Element El sets – all glass element sets
by courtesy of
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DYNARDO • © Dynardo GmbH 2012
Part 8
Costumers
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DYNARDO • © Dynardo GmbH 2012
Our Costumers agree
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DYNARDO • © Dynardo GmbH 2012
What‘s the Difference to Others?
Methodology
• Sensitivity analysis and optimization for large (number of variables)
non-linear problems
• COP/MOP to minimize the number of solver calls
• Optimization with robust defaults (ARSM, EA,GA,PARETO)
• Complete methodology suite to run robustness evaluation, reliability
analysis and robust design optimization
Key applications
• Optimization with large number of parameter (>10) having non
linear effects, noise, design failure
• Model update and parameter identification using sensitivity study
and optimization
• oS (+SOS) have completed the functionality for robustness
evaluation and reliability analysis and robust design optimization to
be used in production
We do not just offer a tool, we deliver a process.
We are the ones who implemented robustness evaluation at
different industries.
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WOSD 2012 • © Dynardo GmbH 2012
optiSLang goes International
DYNARDO, CADFEM (Germany, Austria, Swiss)
SVSFEM (Czech Republic, Slovakia, Hungary)
Pera Global (China, Shanghai)
CADFEM India (India, Hyderabad)
CAE Technology Inc. (Korea, Seoul)
TaeSung S&E Inc. (Korea, Seoul)
CADFEM CIS (Russia, Moscow)
CADFEM US (USA)
Tecosim Japan (Japan, Saitama)
Introduction Weimar Optimization and Stochastic days 2012
91