Chapter Seven
Probabilistic Design
Systems (PDS)
7. Probabilistic Design
Training Manual
• The scope covered as part of this seminar is limited to
highlighting the basic concepts of probabilistic design:
A. Introduction – define probabilistic design and compare
deterministic vs. probabilistic analysis
B. Features – using ANSYS for probabilistic design
C. Probabilistic Results – sample results displays
DESIGN OPTIMIZATION 5.7
• This module focuses on quantifying the quality and reliability
of a design using Probabilistic Design Systems (PDS).
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Probabilistic Design
A. Introduction
Training Manual
– Recognizes the fact that input parameters do vary despite the
best intentions.
– Predicts variation in design performance.
– Allows design for reliability.
DESIGN OPTIMIZATION 5.7
• Probabilistic Design takes into account uncertainties (scatter)
in input data and performs multiple runs to calculate scatter
in output data.
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Probabilistic Design
… Introduction
•
•
•
ANSYS
Output
•
•
•
Material properties
Geometry
Boundary Conditions
It’s a reality that input
parameters are subjected to
scatter => automatically the
output parameters are uncertain
as well!!
Deformation
Stresses, strains
Fatigue, creep,...
DESIGN OPTIMIZATION 5.7
Input
Training Manual
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Probabilistic Design
… Introduction
Training Manual
– How large is the scatter of the output parameters?
– What is the probability that output parameters do not fulfil
design criteria (failure probability)?
– How much does the scatter of the input parameters contribute to
the scatter of the output (sensitivities)?
DESIGN OPTIMIZATION 5.7
• Typical questions answered with probabilistic design:
ANSYS PDS
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Probabilistic Design
… Introduction
The goal is to design more reliable products by estimating a
component's lifetime.
Random Input
Variables
Material
• Strength
• Material
Properties
Loads
• Thermal
• Structural
Finite-Element
Model
Random Output
Parameters
• LCF lifetime
• Creep lifetime
• Corrosion lifetime
• Fracture mechanical lifetime
•…
DESIGN OPTIMIZATION 5.7
•
Training Manual
Geometry/
Tolerances
BC's
• Gaps
• Fixation
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Probabilistic Design
… Introduction
Training Manual
Probabilistic Analysis
•
Only provides a YES/NO
answer.
•
•
Provides a probability and
reliability (design for
reliability).
Safety margins are piled up
“blindly” (worst material,
maximum load, … worst case).
Leads to costly over-design.
•
Takes uncertainties into
account in a realistic fashion.
•
Only “as planned”, “as is,” or
the worst design.
•
“Tolerance stack-up” taken
into account
•
Sensitivities do not take
interactions between input
variables into account (second
order cross terms).
•
Range/width of scatter is
“built-in” into probabilistic
sensitivities.
•
Inherently takes into account
interactions between input
variables.
– Closer to reality
– Over-design is avoided
DESIGN OPTIMIZATION 5.7
Deterministic Analysis
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Probabilistic Design
B. Features
Training Manual
– Static, dynamic, linear, non-linear, thermal, Structural, Electromagnetic, CFD …
• Allows large number random input and output parameters
(max. total = input plus output is 5000).
• Ten statistical distributions for input parameters.
• Random input parameters can be correlated.
• Probabilistic methods:
DESIGN OPTIMIZATION 5.7
• Works with any ANSYS model.
– Monte Carlo - Direct & Latin Hypercube Sampling
– Response Surface - Central Composite & Box-Behnken Designs
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Probabilistic Design
… Features
Training Manual
– Convergence plots
– Histogram
– Probabilities
– Scatter plots
– Sensitivities
• State-of-the art statistical procedures to analyze and visualize
probabilistic results
• Use of distributed, parallel computing techniques for
drastically reduced wall clock time of the analysis
DESIGN OPTIMIZATION 5.7
• Comprehensive probabilistic results, e.g:
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Probabilistic Design
… Features
PDS menus are organized
according to sequence of
use, similar to design
optimization menu:
– Start by creating a loop file
of any analysis
– Define the problem
– Specify methods and run
options
– Fit response surfaces
– Postprocessing
DESIGN OPTIMIZATION 5.7
•
Training Manual
– Database handling
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Probabilistic Design
C. Probabilistic Results
Training Manual
– Statistics, histogram, sample diagrams
• These plots can be used to answer the question "How large
is the scatter of the output parameters?"
– Cumulative distribution function, probabilities
• "What is the probability that output parameters do not fulfil
design criteria (failure probability)?"
– Sensitivities, scatter diagram, response surface
• "How much does the scatter of the input parameters
contribute to the scatter of the output?"
DESIGN OPTIMIZATION 5.7
• Different types of results displays are available to answer
typical PDS questions:
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Probabilistic Design
… Probabilistic Results
DESIGN OPTIMIZATION 5.7
Simulation Value Sample Plot:
Training Manual
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Probabilistic Design
… Probabilistic Results
DESIGN OPTIMIZATION 5.7
Mean Value Sample Plot
Training Manual
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Probabilistic Design
… Probabilistic Results
DESIGN OPTIMIZATION 5.7
Standard Deviation Sample Plot:
Training Manual
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Probabilistic Design
… Probabilistic Results
Training Manual
DESIGN OPTIMIZATION 5.7
Histogram Plot:
For random input variables
For random output parameters
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Probabilistic Design
… Probabilistic Results
DESIGN OPTIMIZATION 5.7
Cumulative Distribution Function:
Training Manual
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Probabilistic Design
… Probabilistic Results
Training Manual
Note:
Sensitivity plot for
• Spearman rank
order correlation
coefficient
• Linear correlation
coefficient
• Single parameter
Sensitivity study
DESIGN OPTIMIZATION 5.7
Sensitivities:
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Probabilistic Design
… Probabilistic Results
DESIGN OPTIMIZATION 5.7
Scatter Plot:
Training Manual
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Probabilistic Design
D. Summary
Training Manual
• Randomness and uncertainty is taken into account as it
appears in real life
• Based on widely accepted Monte Carlo simulation technique
and Response Surface methods
• Ideal for parallel / distributed processing of jobs
DESIGN OPTIMIZATION 5.7
• Probabilistic Design helps to design for reliability and quality
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