2.5 Probabilistic Design
Exploring randomness and scatter reveals a simple truth: It’s a
part of reality - everywhere!
Y
Monte Carlo
X
Response Surface
NEW FEATURES 5.7
Z
Probabilistic Design: Bringing FEA closer to REALITY!
Training Manual 001419
15 Aug 2000
2.5-1
Probabilistic Design
Introduction
– Recognises the fact that input parameters do vary despite
the best intentions.
– Predicts variation in design performance.
– Allows design for reliability.
NEW FEATURES 5.7
• Probabilistic Design takes into account
uncertainties (scatter) in input data and performs
multiple runs to calculate scatter in output data.
Training Manual 001419
15 Aug 2000
2.5-2
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,...
NEW FEATURES 5.7
Input
Training Manual 001419
15 Aug 2000
2.5-3
Probabilistic Design
… Introduction
• Typical questions answered with probabilistic
design:
– 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)?
NEW FEATURES 5.7
– How large is the scatter of the output parameters?
ANSYS PDS
Training Manual 001419
15 Aug 2000
2.5-4
Probabilistic Design
… Introduction
• The goal is to design more reliable products by estimating a
component's lifetime.
Material
• Strength
• Material
Properties
Loads
• Thermal
• Structural
Finite-Element
Model
Random Output
Parameters
• LCF lifetime
• Creep lifetime
• Corrosion lifetime
• Fracture mechanical lifetime
•…
NEW FEATURES 5.7
Random Input
Variables
Geometry/
Tolerances
BC's
• Gaps
• Fixation
Training Manual 001419
15 Aug 2000
2.5-5
Probabilistic Design
… Introduction
• Probabilistic Design System (PDS) is useful in
several industries and applications, e.g:
– Gas Turbines (Rotating Machinery)
– Automotive (Power Train)
NEW FEATURES 5.7
– Aerospace
Training Manual 001419
15 Aug 2000
2.5-6
Probabilistic Design
… Introduction
Deterministic Analysis
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 “builtin” into probabilistic
sensitivities.
•
Inherently takes into account
interactions between input
variables.
– Closer to reality
– Over-design is avoided
NEW FEATURES 5.7
•
Training Manual 001419
15 Aug 2000
2.5-7
Probabilistic Design
PDS Features
• Works with any ANSYS model.
• 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:
NEW FEATURES 5.7
– Static, dynamic, linear, non-linear, thermal, Structural,
Electro-magnetic, CFD …
– Monte Carlo - Direct & Latin Hypercube Sampling
– Response Surface - Central Composite & Box-Behnken
Designs
Training Manual 001419
15 Aug 2000
2.5-8
Probabilistic Design
… PDS Features
• Comprehensive probabilistic results, e.g:
– Convergence plots
– Probabilities
– Scatter plots
– Sensitivities
• State-of-the art statistical procedures to analyze and
visualize probabilistic results
NEW FEATURES 5.7
– Histogram
• Use of distributed, parallel computing techniques
for drastically reduced wall clock time of the
analysis
Training Manual 001419
15 Aug 2000
2.5-9
Probabilistic Design
GUI for PDS
– Start by creating a loop file
of any analysis
– Define the problem
– Specify methods and run
options
– Fit response surfaces
– Postprocessing
NEW FEATURES 5.7
• PDS menus are organized
according to sequence of
use, similar to design
optimization menu:
– Database handling
Training Manual 001419
15 Aug 2000
2.5-10
Probabilistic Design
PDS Results
• Different types of results displays are available to
answer typical PDS questions:
• 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?"
NEW FEATURES 5.7
– Statistics, histogram, sample diagrams
Training Manual 001419
15 Aug 2000
2.5-11
Probabilistic Design
Probabilistic Results
Simulation Value Sample Plot:
NEW FEATURES 5.7
Training Manual 001419
15 Aug 2000
2.5-12
Probabilistic Design
Probabilistic Results
Mean Value Sample Plot
NEW FEATURES 5.7
Training Manual 001419
15 Aug 2000
2.5-13
Probabilistic Design
Probabilistic Results
Standard Deviation Sample Plot:
NEW FEATURES 5.7
Training Manual 001419
15 Aug 2000
2.5-14
Probabilistic Design
Probabilistic Results
Histogram Plot:
NEW FEATURES 5.7
For random input variables
For random output parameters
Training Manual 001419
15 Aug 2000
2.5-15
Probabilistic Design
Probabilistic Results
Cumulative Distribution Function:
NEW FEATURES 5.7
Training Manual 001419
15 Aug 2000
2.5-16
Probabilistic Design
Probabilistic Results
Sensitivities:
NEW FEATURES 5.7
Note:
Sensitivity plot for
• Spearman rank
order correlation
coefficient
• Linear correlation
coefficient
• Single parameter
Sensitivity study
Training Manual 001419
15 Aug 2000
2.5-17
Probabilistic Design
Probabilistic Results
Scatter Plot:
NEW FEATURES 5.7
Training Manual 001419
15 Aug 2000
2.5-18
Probabilistic Design
Summary
• Probabilistic Design is a new feature at ANSYS 5.7
• Based on widely accepted Monte Carlo simulation
technique and Response Surface methods
• Allows for parallel / distributed processing of jobs
NEW FEATURES 5.7
• An easy-to-use tool for realistic prediction of
reliability
Training Manual 001419
15 Aug 2000
2.5-19