Probabilistic Design Systems (PDS)
Chapter Seven
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Training Manual7. Probabilistic Design
• This module focuses on quantifying the quality and reliability of a design using Probabilistic Design Systems (PDS).
• 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
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Probabilistic Design
A. Introduction
• Probabilistic Design takes into account uncertainties (scatter) in input data and performs multiple runs to calculate scatter in output data.
– Recognizes the fact that input parameters do vary despite the best intentions.
– Predicts variation in design performance.
– Allows design for reliability.
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Training Manual
Probabilistic Design
… Introduction
InputInputInputInput ANSYSANSYSANSYSANSYS OutputOutputOutputOutput
• Material properties• Geometry• Boundary Conditions
• Deformation• Stresses, strains• Fatigue, creep,...
It’s a reality that input parameters are subjected to scatter => automatically the
output parameters are uncertain as well!!
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Training Manual
ANSYS PDSANSYS PDSANSYS PDSANSYS PDS
Probabilistic Design
… Introduction
• Typical questions answered with probabilistic design:
– 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)?
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Training Manual
Random InputVariables
Random OutputParameters
Finite-ElementModel
Material• Strength• Material
Properties
BC's• Gaps• Fixation
Geometry/Tolerances
Loads• Thermal• Structural
• LCF lifetime• Creep lifetime• Corrosion lifetime• Fracture mechanical lifetime• …
Probabilistic Design
… Introduction
• The goal is to design more reliable products by estimating a component's lifetime.
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Training Manual
Probabilistic Design
… Introduction
Deterministic Analysis
• Only provides a YES/NO answer.
• Safety margins are piled up “blindly” (worst material, maximum load, … worst case). Leads to costly over-design.
• Only “as planned”, “as is,” or the worst design.
• Sensitivities do not take interactions between input variables into account (second order cross terms).
Probabilistic Analysis
• Provides a probability and reliability (design for reliability).
• Takes uncertainties into account in a realistic fashion.
– Closer to reality– Over-design is avoided
• “Tolerance stack-up” taken into account
• Range/width of scatter is “built-in” into probabilistic sensitivities.
• Inherently takes into account interactions between input variables.
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Training Manual
Probabilistic Design
B. Features
• Works with any ANSYS model.
– Static, dynamic, linear, non-linear, thermal, Structural, Electro-magnetic, 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:
– Monte Carlo - Direct & Latin Hypercube Sampling
– Response Surface - Central Composite & Box-Behnken Designs
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Probabilistic Design
… Features
• Comprehensive probabilistic results, e.g:
– 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
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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
– Database handling
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Probabilistic Design
C. Probabilistic Results
• Different types of results displays are available to answer typical PDS questions:
– 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?"
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Simulation Value Sample Plot:
Probabilistic Design
… Probabilistic Results
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Training Manual
Mean Value Sample Plot
Probabilistic Design
… Probabilistic Results
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Training Manual
Standard Deviation Sample Plot:
Probabilistic Design
… Probabilistic Results
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Histogram Plot:
Probabilistic Design
… Probabilistic Results
For random input variables For random output parameters
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Cumulative Distribution Function:
Probabilistic Design
… Probabilistic Results
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Sensitivities:
Probabilistic Design
… Probabilistic Results
Note:Sensitivity plot for• Spearman rank
order correlation coefficient
• Linear correlation coefficient
• Single parameter Sensitivity study
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Scatter Plot:
Probabilistic Design
… Probabilistic Results
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Training Manual
Probabilistic Design
D. Summary
• Probabilistic Design helps to design for reliability and quality
• 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
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