Transcript PDS - ANSYS presentation

Probabilistic Design
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Introduction
An Example
Motivation
Features
Benefits
Probabilistic Methods
Probabilistic Results/Interpretation
Summary
Introduction
Purpose of a Probabilistic Design System (PDS)
ANSYS
Input
Material Properties
Geometry
Boundary Conditions
Output
Deformation
Stresses / Strains
Fatigue, Creep,...
It’s a reality that input
parameters are subjected to
scatter => automatically the
output parameters are
uncertain as well!!
Introduction
Purpose of Probabilistic Design System (PDS)
ANSYS PDS
Questions answered with probabilistic design:
• How large is the scatter of the output parameters?
• What is the probability that output parameters do not fulfill design
criteria (failure probability)?
• How much does the scatter of the input parameters contribute to the
scatter of the output (sensitivities)?
An Example
Example: Lifetime of Components !!!
Random input
variables
Material
• Strength
• Material
Properties
Loads
• Thermal
• Structural
Geometry/
Tolerances
Boundary
Conditions
• Gaps
• Fixity
Finite-Element
Model
Random output
parameters
• LCF lifetime
• Creep lifetime
• Corrosion lifetime
• Fracture mechanical lifetime
•…
Evaluate reliability of products !
Evaluate quality of products !
Evaluate warranty costs !
To evaluate is the first step
to improvement !
Motivation
Influence of Young’s Modulus and Thermal Expansion Coefficient on
thermal stresses:
thermal = E ·  ·T
Deterministic Approach:
Emean and mean => evaluate expected value:  expect
Probabilistic Approach:
‘E’ scatters
±5%
‘E’ and ‘ ‘ scatter ±5%
P( thermal > 1.05  expect)
16% (~1 out of 6)
22% (~1 out of 5)
P( thermal > 1.10  expect)
2.3% (~1 out of 40)
8% (~1 out of 12)
Scatter in material properties and loads
Property
SD/Mean %
Metallic materiales, yield
15
Carbon fiber composites, rupture
17
Metallic shells, buckling strength
14
Junction by screws, rivet, welding
8
Bond insert, axial load
12
Honeycomb, tension
16
Honeycomb, shear, compression
10
Honeycomb, face wrinkling
8
Launch vehicle , thrust
5
Transient loads
50
Thermal loads
7.5
Deployment shock
10
Acoustic loads
40
Vibration loads
20
Source: Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace.
Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris 1994
Motivation
±5-100%
Materials,
Bound.Cond.,
Loads, ...
Thermal
Analysis
CAD
Geometry
FEM
CFD
± 0.1-10%
Materials,
Bound.Cond., ...
±5-50%
LCF
Structural
Analysis
FEM
Materials,
Bound.Cond.,
±5-100% Loads, ...
Materials
±30-60%
±??%
PDS Benefits
Deterministic Analysis:
• Only provides a YES/NO answer
• Safety margins are piled up
“blindly” (worst material,
maximum load, … worst case)
1 worst case assumption =10-2
2 worst case assumptions =10-4
3 worst case assumptions =10-6
4 worst case assumptions =10-8
...
Probabilistic Analysis:
• Provides a probability and
reliability (design for reliability)
• Takes uncertainties into account in
a realistic fashion => This is closer
to reality => Over-design is
avoided
=> Leads to costly over-design
• Only “as planned“, “as is” or
the worst design
• “Tolerance stack-up” is included
(design for manufacturability)
PDS Benefits
Deterministic Analysis:
Probabilistic Analysis:
• Sensitivities do not take range
of scatter or possibilities into
account
• Range/width of scatter is “built-in”
into probabilistic sensitivities
• Sensitivities do not take
interactions between input
variables into account (second
order cross terms)
• Interactions between input
variables are inherently taken care
of
• Quality is “indirectly” affected
• Quality becomes a measurable,
quantifiable and controllable
quantity
PDS Benefits
Illustration of the Benefits of
Probabilistic Analysis over Deterministic Analysis
Probabilistic Analysis
Deterministic Analysis
Features of the ANSYS/Probabilistic Design System
• Free for ANSYS users (included in ANSYS since rel. 5.7)
• Works with any ANSYS analysis model
• Static, dynamic, linear, non-linear, thermal, structural, electromagnetic, CFD ..
• Allows large number random input and output parameters
• 10 statistical distributions for random input parameters
• Random input parameters can be correlated
• Probabilistic methods:
• Monte Carlo - Direct & Latin Hypercube Sampling
• Response Surface - Central Composite & Box-Behnken Designs
Features of the ANSYS/Probabilistic Design System
• Use of distributed, parallel computing techniques for
drastically reduced wall clock time
• Comprehensive probabilistic results
• Convergence plots, histogram, probabilities, scatter
plots, sensitivities, ...
• State-of-the art statistical procedures to address the
accuracy of the output data
• Confidence intervals
Features of the ANSYS/Probabilistic Design System
ANSYS Customer Base
• All “Top 10” Fortune 100
Industrial companies
• 73 of the Fortune 100
Industrial companies
• Over 5,700 commercial
companies
• Over 40,000 commercial
customer seats
• Over 100,000 university
licenses
Probabilistic Design
• Available since ANSYS
5.7 and after
• Used by well over 100
companies in production
Probabilistic Methods
Monte Carlo Simulation:
Perform numerous analysis runs based on sets
of random samples, and then evaluate statistics
of derived responses.
• Direct (Crude) Sampling Monte Carlo
(DIR)
• Latin Hypercube Sampling Monte Carlo
(LHS)
• User defined
(USR)
Probabilistic Methods
Monte Carlo Simulation Method Scheme:
Simulation of input
parameters at
random locations
X1
X2
Statistical analysis of
output parameters
X3
Repetitions = Simulations
ANSYS
Probabilistic Methods
Finite Element Runs for Monte Carlo
For Monte Carlo Simulation the number of simulations does not
depend on the number of random input variables, but on the
probabilistic result you are looking for:
• For assessment of the statistics of output parameters (Mean, sigma)
Nsim  30 … 100
• For histogram and cumulative distribution function
Nsim  50 … 200
• For assessment of low probabilities P (tails of the distribution)
Nsim  30/P … 100/P
Probabilistic Methods
– Response Surface Methods:
Select specific observation points for each
random variable, run analyses, establish
response surface for each response parameter,
perform Monte Carlo Analysis on Response
Surface.
• Central Composite Design
(CCD)
• Box-Behnken Matrix
(BBM)
• User defined
(USR)
Probabilistic Methods
Response Surface Methods Scheme:
Simulation of input parameters
at specific locations
X1
Statistical analysis of
output parameters
X2
X3
Evaluate input
parameter values
DOE
Monte Carlo Simulations
on Response Surface
Repetitions = Simulations
ANSYS
Response Surface Fit
Probabilistic Methods
Finite Element Runs for Response Surface
For Response Surface Methods the number of simulations depends on the
number of random input variables only :
No. of random
input variables
1
2
3
4
5
6
7
8
9
10
...
Coefficients
of equation
3
6
10
15
21
28
36
45
55
66
Central
Compos.
BoxBehnken
9
15
25
27
45
79
81
147
149
13
25
41
49
57
65
121
161
Parallel Distributed Processing
Model file
+ Input
variables
Result
output
parameters
Client
Run analysis 1,4, …
Server 2
Build the Model
Identify Machines
Click “Run…”
Post-process Results
PC
PC
UNIX
UNIX
Server 1
Run analysis 2,5,6, ...
to PC
to UNIX
to PC
to UNIX
Server 3
Run analysis 3,7
PDS Tight Integration into ANSYS
Main Menu
•Enter the PDS
module from ANSYS
Main Menu
•Generate a loop file
representing any
type of analysis
•Pre-processing
•Define Methods and
Run options
•Fit Response
Surfaces
•Post-processing
•Database handling
Probabilistic Results
Post-processing of simulations results:
The results should be displayed such that the user can
graphically and intuitively answer the questions:
1 How large is the scatter of the output parameters?
 Plot: Statistics (sigma), Histogram, Sample Diagrams
2 What is the probability that output parameters do not fulfil design criteria
(failure probability)?
 Plot: Cumulative Distribution Function, Probabilities
3 How much does the scatter of the input parameters contribute to the scatter
of the output?
 Plot: Sensitivities, Scatter Diagram, Response Surface
Probabilistic Results
Simulation Value Sample Plot:
Probabilistic Results
Mean Value Sample Plot:
Probabilistic Results
Standard Deviation Sample Plot:
Probabilistic Results
Histogram Plot:
Histogram for
random input variables
Histogram for
random output parameters
Probabilistic Results
Cumulative Distribution Function:
Show probabilities as
empirical cumulative
distribution function
Probabilistic Results
Cumulative Distribution Function:
Show probabilities as:
- normal plot
- log-normal plot
- Weibull plot
Probabilistic Results
Sensitivities:
Show sensitivities as:
• Spearman rank
order sensitivity plot
• Linear correlation
sensitivity plot
Probabilistic Results
Scatter Plot:
Probabilistic Results
Response Surface Plot:
Response Surface Types:
• Linear
• Quadratic w/o X-terms
• Quadratic with X-terms
Regression Analysis:
• Full Regression
• Forward-StepwiseRegression
Transformations:
• Logarithmic Y*=log(Y)
• Square root Y*=sqrt(Y)
• Power
Y*=Y^a
• Box-Cox (automatic!)
• ...
Probabilistic Results Sharing
HTML Report:
Note:
•Report is
automatically
generated (pushbutton)
•It includes all
pictures according to
user
preferences/options
•It includes
explanations as text
Click to see Report
Summary
• Deterministic engineering design practices have matured
and do not yield significant performance gains.
• Future design improvements will require accounting for
variations.
• Probabilistic approach enables Design for Quality,
Reliability and Robustness
• Reduced warranty costs
• Better resale value
• Increased market size, market share, and margin on
sales
• Distributed computing allows faster simulation turn-around