svm@student.ethz.ch

Possible System Identification Approaches

PhD Student, Seyed Vahid Moosavi

Professor Ludger Hovestadt14 June 2012

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What is System Identification?

Predict the “Smoke Amount” based on “the building features”

Bridge Displacement

Wind Flow

Stock Market

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Why System Identification?

• System-State Space Modeling• Sensitivity analysis • What-if analysis• System Design Optimization

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System Identification In a Symbolic Form

System(black-Box??)

OrWhite 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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Classic System Identification(We can easily measure any variable of interest)

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And If we can’t measure enough or we want to Design a new system….

We Build a Simulation Model

7Goulet, 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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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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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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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=9,765,625Total required

time(Nmodels) X

(time_per_model)

3125 X 10= 31250 mins

=520 Hours21 Days

162,7604 H67,816 Days

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What can we do? What is the State of the art?

(Generalize It!!)Surrogate Models

Meta-modelingResponse 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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First step results… ( A sample case: Data and explanation by James A. Gulet)

Parameters:1. Plymouth-side support longitudinal stiffness 1E [4, 11] kN/mm2. Saltash-side support longitudinal stiffness 1E [4, 11] kN/mm3. Deck expansion joint longitudinal stiffness 1E [4, 11] kN/mm4. 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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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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Map interpretation

Normalized Values of each parameter

Each map is representing the value of one parameter in our FE modelEach dot in the map shows one possible modelThe labels of each dot is either 0 (rejected) or 1 (accepted)

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The effect of first Parameter

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The effect of second Parameter

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The effect of third Parameter

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The effect of fourth Parameter

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The effect of fifth Parameter

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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 stepsFocusing on Surrogate Models for fast Statistical Models

And Applications in Design-Optimization

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Thanks!