probabilistic design systems (pds) chapter seven

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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… 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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ANSYS PDSANSYS PDSANSYS PDSANSYS PDS


… 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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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• …


… Introduction

• The goal is to design more reliable products by estimating a component's lifetime.

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… 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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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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… 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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… 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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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 Results

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Mean Value Sample Plot



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Standard Deviation Sample Plot:



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Histogram Plot:



For random input variables For random output parameters

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Cumulative Distribution Function:



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Sensitivities:



Note:Sensitivity plot for• Spearman rank

order correlation coefficient

• Linear correlation coefficient

• Single parameter Sensitivity study

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Scatter Plot:



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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

probabilistic design systems (pds) chapter seven

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