Training Manual 00141915 Aug 2000

2.5-1

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Y

Z

XMonte Carlo

Response Surface

Probabilistic Design: Bringing FEA closer to REALITY!

2.5 Probabilistic Design

Exploring randomness and scatter reveals a simple truth: It’s a part of reality - everywhere!

Training Manual 00141915 Aug 2000

2.5-2

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

Introduction

• Probabilistic Design takes into account uncertainties (scatter) in input data and performs multiple runs to calculate scatter in output data.

– Recognises the fact that input parameters do vary despite the best intentions.

– Predicts variation in design performance.

– Allows design for reliability.

Training Manual 00141915 Aug 2000

2.5-3

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic 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!!

Training Manual 00141915 Aug 2000

2.5-4

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

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)?

Training Manual 00141915 Aug 2000

2.5-5

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

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.

Training Manual 00141915 Aug 2000

2.5-6

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

… Introduction

• Probabilistic Design System (PDS) is useful in several industries and applications, e.g:

– Aerospace

– Gas Turbines (Rotating Machinery)

– Automotive (Power Train)

Training Manual 00141915 Aug 2000

2.5-7

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic 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.

Training Manual 00141915 Aug 2000

2.5-8

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

PDS 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

Training Manual 00141915 Aug 2000

2.5-9

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

… PDS 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

Training Manual 00141915 Aug 2000

2.5-10

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

GUI for PDS

• 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

Training Manual 00141915 Aug 2000

2.5-11

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

PDS 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?"

Training Manual 00141915 Aug 2000

2.5-12

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Simulation Value Sample Plot:

Probabilistic Design

Probabilistic Results

Training Manual 00141915 Aug 2000

2.5-13

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Mean Value Sample Plot

Probabilistic Design

Probabilistic Results

Training Manual 00141915 Aug 2000

2.5-14

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Standard Deviation Sample Plot:

Probabilistic Design

Probabilistic Results

Training Manual 00141915 Aug 2000

2.5-15

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Histogram Plot:

Probabilistic Design

Probabilistic Results

For random input variables For random output parameters

Training Manual 00141915 Aug 2000

2.5-16

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Cumulative Distribution Function:

Probabilistic Design

Probabilistic Results

Training Manual 00141915 Aug 2000

2.5-17

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Sensitivities:

Probabilistic Design

Probabilistic Results

Note:Sensitivity plot for• Spearman rank

order correlation coefficient

• Linear correlation coefficient

• Single parameter Sensitivity study

Training Manual 00141915 Aug 2000

2.5-18

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7

Scatter Plot:

Probabilistic Design

Probabilistic Results

Training Manual 00141915 Aug 2000

2.5-19

NEW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7N

EW

FEA

TU

RES 5

.7Probabilistic Design

Summary

• Probabilistic Design is a new feature at ANSYS 5.7

• An easy-to-use tool for realistic prediction of reliability

• Based on widely accepted Monte Carlo simulation technique and Response Surface methods

• Allows for parallel / distributed processing of jobs