June-2012 final

1. svm@student.ethz.ch
Possible System Identification Approaches
PhD Student, Seyed Vahid Moosavi
Professor Ludger Hovestadt
14 June 2012
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2. What is System Identification?
Predict the “Smoke Amount”
based on “the building features”
Bridge Displacement
Wind Flow
Stock Market
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3. Why System Identification?
• System-State Space Modeling
• Sensitivity analysis
• What-if analysis
• System Design Optimization
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4. System Identification In a Symbolic Form
System
(black-Box??)
Or
White box
Model Input
(e.g. load cases)
Some real
Phenomenon
(Model Parameters or
structure)
(e.g. strain or tension
parameters)
Some real observations
(e.g. test cases)
Model Output
(predicted)
(e.g. vertical
displacement of the
bridge)
Error
Threshold
(or confidence interval)
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5. Classic System Identification
(We can easily measure any variable of interest)
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6. And If we can’t measure enough or we want to Design a new
system….
We Build a Simulation Model
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7. Goulet, J.-A., Kripakaran, P., and Smith, I.F.C. (2010). Multimodel structural performance monitoring. Journal of Structural Engineering,
136(10):13091318.
An Example
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8. So…
A set Partial
Differential
Equations
(All possible instances of
comprehensive models)
Finite Element Analysis
Approximated
by
A
software
e.g. Ansys
We have
AND considerable Amount
of Parameters as INPUTs for
FEA
Through
Exhaustive
search
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9. A sample result
Goulet, J.-A., Kripakaran, P., and Smith, I.F.C. (2010). Multimodel structural performance monitoring. Journal of Structural Engineering,
136(10):13091318.
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10. But…
• Normally these simulations are time consuming.
no. of Parameters Np 5 10
No. of possible
values for each
parameter
Nc 5 5
Possible models Nmodels= Nc^Np 5^5=3125 5^10=9,765,625
Total required
time
(Nmodels) X
(time_per_model
)
3125 X 10= 31250
mins
=520 Hours
21 Days
162,7604 H
67,816 Days
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11. What can we do?
What is the State of the art?
(Generalize It!!)
Surrogate Models
Meta-modeling
Response Surface Method
• Approximate the input-output of Comprehensive Model (e.g. FE)
with a faster approximation using “Statistical approaches”.
Toward a Black-Box Method
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12. First step results… ( A sample case: Data and explanation by James A. Gulet)
Parameters:
1. Plymouth-side support longitudinal stiffness 1E [4, 11] kN/mm
2. Saltash-side support longitudinal stiffness 1E [4, 11] kN/mm
3. Deck expansion joint longitudinal stiffness 1E [4, 11] kN/mm
4. Main-cable initial strain [5E-4, 3E-3] mm/mm
5. Sidespan cable initial strains [5E-4, 3E-3] mm/mm.
The interval of each parameter value is discretized in five
parts to generate a hyper-grid containing 3125 (5^5)
combination of parameters. The result of this process is
an initial model set containing the predicted frequencies
and mode shapes for all 3125 model instances.
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13. Sample data
Candidate
Rejected
• Classic approach is “Time Consuming” even for simplified models
• We used a sample of models from FE simulation with their final results.
• We trained a Self Organizing Map (SOM) to see the relation bet.
Different parameters values and the result of the FE model
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14. Map interpretation
Normalized
Values of each
parameter
Each map is representing the value of one parameter in our FE model
Each dot in the map shows one possible model
The labels of each dot is either 0 (rejected) or 1 (accepted)
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15. The effect of first Parameter
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16. The effect of second Parameter
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17. The effect of third Parameter
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18. The effect of fourth Parameter
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19. The effect of fifth Parameter
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20. What we got so far
• Faster Model Tuning and sensitivity analysis
• Finding the most important parameters (so lower required
time for model generation)
• We somehow generalized the behavior of FE models
• We can conduct modified sampling method
And Next possible steps
Focusing on Surrogate Models for fast Statistical Models
And Applications in Design-Optimization
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21. Thanks!
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