Hybrid Simulation with On-line Updating of Numerical Model based on Measured Experimental Behavior

M.J. Hashemi, Armin Masroor, and Gilberto MosquedaUniversity at Buffalo

International Mini-Workshop on Hybrid SimulationHarbin Institute of Technology

May 18, 2012

Acknowledgements• Research funding

– NSF: CAREER Award CMMI-0748111– NEESR CMMI-0936633 (PI Eduardo Miranda, Stanford)– NSF Award CMS 0402490 for shared use access of nees@buffalo

• Collaborators– Eduardo Miranda, Helmut Krawinkler, Stanford University– Dimitrios Lignos, McGill University– Ricardo Medina, University of New Hampshire

Introduction

• In hybrid simulation, it is often assumed that a reliable model of numerical substructure exists– Nonlinear behavior can be distributed throughout structural model

• During a hybrid simulation, experimental data is gathered from experimental structural components – other similar components may be present throughout numerical structure

Objective:• Use on-line measurements of experimental substructure to

update numerical models of similar components (Elnashai et al. 2008)– Could experience similar stress/strain demands– Could experience very different demands, but likely at lower

amplitudes (Test component experiencing largest demands)

Introduction

Algorithm

Numerical Substructure may contain models to be updated

Auxiliary model of experiment to calibrate model parameters

Other tasks focus on when and what to update

Online Updating Challenges

Experimental Issues:1. The on-line identification process should instantaneously and

automatically track the critical characteristics of the system and their variations as time proceeds, without requiring any major action by the researcher during the test.

2. Measurement data are usually contaminated by errors (noise) that can substantially influence the accuracy of the identification result.

3. In online schemes, it is difficult to manipulate the input–output data as can be done for offline applications.

Online Updating Issues

Numerical Issues:1. Lack of understanding of nonlinear structural behavior and selection

of models/parameters for numerical simulation.2. For effective on-line identification schemes, it is necessary to develop

a reasonable non-linear model that is able to provide a good representation of the system behavior.

3. Problems related to under- and over-parameterization exists that can be overcome by setting boundaries on the parameters.

4. Independent of the system to be identified, online identification algorithm must be adaptable to capture parameter changes as time progresses (ex., if a fracture occurs).

5. Parameters should converge smoothly and rapidly to the proper parameter values.

Hysteretic Model

• Modified Bouc-Wen Model:1. Baber and Noori (1985) extension of the Bouc-Wen model to

include degrading behavior. 2. Has been used by several researchers for simulating and

identifying hysteretic system response3. Model is high nonlinear and has nine control parameters including

stiffness and strength degradation.

Parameter Identification

• System Identification - The parameters of a system model is sought given the excitation and output

• In this application, the system excitation and output are only known to the current simulation time

• Early identification of some parameters is difficult – cannot calibrate yield force until structure actually yields

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

For

ce (

kips

)

Displacement (in)

Experimental HysteresisBilinear ModelYeild Force

alpha = 0.027K = 5.525Fy = 2.256

Example: Extracting Initial Stiffness, Yield Force and Post Elastic Stiffness Ratio From

Experimental Response

Parameter Identification • Objective:Find the best-fit parameters to minimize the

error function E defined as:

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Displacement[in.]

For

ce [

Kip

s]

Curve Fitting

Experimental ElementCalibration of Numerical Model

Note:Auxiliary Numerical Model and Experimental Model have identical deformation demands

Parameter Identification TechniquesDownhill Simplex :1. The Downhill Simplex method is a multidimensional optimization

method which uses geometric relationships to aid in finding function minimums

2. The Simplex method is not sensitive to small measurement noise and does not tend to divergence

Unscented Kalman Filter:3. UKF is a recursive algorithm for estimating the optimal state of a

nonlinear system from noise-corrupted data4. To identify the unknown parameters of a system, these

parameters should be added to the states of the system to be estimated using experimental substructure response.

Structural Model

NumericalExperimental

• One Bay Frame Structure – Element 1: Experimental substructure– Element 2: Numerical substructure similar to Element 1– Element 3: Spring that varies demands between Element 1 and Element 2

Experimental Substructure

One Bay Frame Structural Properties

Experimental Control xPCtarget Values

Period (sec) 0.5182

Elastic Stiffness (kips/in) 5.88

Mass for Each DoF (kips/g) 0.04

Integration Scheme Newmark Explicit

Integration Time Step (sec) 0.005

Ground Motion Time Step (sec) 0.02

Simulation Time Step (sec) 0.25

El Centro

Test Protocol

• Test Series 1:Verification of Parameter Identification Techniques:– Mass 1 and 2 are equivalent and Element 3 is rigid: – Deformation demands in Element 1 and 2 are identical. – Online calibration of the Element 2 using parameter identification techniques,

ideally, should produce a hysteresis identical to Element 1.

Test Series 2: Implementation in General Condition:• Element 3 is flexible, Mass 1

and 2 are different: • Deformation demands in

Element 1 and 2 different. • Although elements may have

similar properties, they experience different deformation demands and damage at different times

Test Series 1 [Identical Deformation Demands]

• Reference Model:

Reference Model: Response of Element 2 is replaced by measured behavior for Element 1 since both have the same

demands

-3 -2 -1 0 1 2-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5Fo

rce

(kip

)

Displacement (in)

Element 1Element 2

Test Series 1 [Identical Deformation Demands]

Calibration of the Experimental Response

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Displacement[in.]

For

ce [

Kip

s]

Experimental Element

Calibrated Numerical Model

Calibration:

Test Series 1 [Identical Deformation Demands]

Initial Values For Updating Test

Initial Values:No stiffness or strength degradation assigned to the numerical model

No updating is implemented

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-3

-2

-1

0

1

2

3

p elem

[ki

p]

Displacement [in.]

Experimental ElementCalibrated Numerical Model [No Stiffness and StrengthDegradation]

Test Series 1 [Identical Deformation Demands]

• Results for updating in real time:

• Auxiliary model is numerical model in this case

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-3

-2

-1

0

1

2

3

p elem

[kip

]

Displacement [in.]

Element 1Element 2

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-3

-2

-1

0

1

2

3

p elem

[ki

p]

Displacement [in.]

Element 1Element 2

Downhill Simplex Unscented Kalman Filter

Test Series 2 [Different Deformation Demands]

• Reference Model:

-2 -1.5 -1 -0.5 0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

p elem

[kip

]

Displacement [in.]

Element 1Element 2

Reference Model: Response of Element 2 is Based on the Calibration of Experimental Element Response without

degradation

Test Series 2 [Different Deformation Demands]

• Updating Tests:• Simplex Downhill:

• Unscented Kalman Filter:

Initial values for numerical model parameters used in the Downhill Simplex Method are the same as the calibrated numerical model with no strength and stiffness degradation; these are the Updating Parameters :

Initial values for the updating parameters for the UKF Method were chosen the same as the test with “no updating”.Updating Parameters :

Test Series 2 [Different Deformation Demands]

• Results:

-2 -1.5 -1 -0.5 0 0.5 1-3

-2

-1

0

1

2

3

Fo

rce

[kip

]

Displacement [in.]

Exp-Spring-Exp [Calibrated]Exp-Spring-NumExp-Spring-Num-Updt-SimplexExp-Spring-Num-Updt-Kalman

Comparison of Element 2 Hysteresis For Different Tests

Test Series 2 [Different Deformation Demands]

• Results:

0 1000 2000 3000 4000 5000 6000 7000-3

-2

-1

0

1

2

3

For

ce [

kip]

Step Number

Exp-Spring-Exp [Calibrated]Exp-Spring-NumExp-Spring-Num-Updt-SimplexExp-Spring-Num-Updt-Kalman

Comparison of Element 2 Forces History for Different Tests

Test Series 2 [Different Deformation Demands]

• Results:

0 1000 2000 3000 4000 5000 6000 7000-2

-1.5

-1

-0.5

0

0.5

1

Dis

plac

emen

t [in

.]

Step Number

Exp-Spring-Exp [Calibrated]Exp-Spring-NumExp-Spring-Num-Updt-SimplexExp-Spring-Num-Updt-Kalman

Comparison of Element 2 (=DOF2) Displacement History For Different Tests

Test Series 2 [Different Deformation Demands]

• Parameter Calibration:

0 2000 4000 6000 80004

4.5

5

5.5

6

6.5

Time

Pa

ram

ete

r V

alu

e

KoNote: Initial values for the updating parameters for the UKF Method were obtained from test with “no updating”.

Updated Parameter Values In UKF Identification Technique

Updating Parameters:

Test Series 2 [Different Deformation Demands]

• Parameter Calibration:

0 2000 4000 6000 80004

5

6

7

8

9

10

11x 10

-3

Time

Pa

ram

ete

r V

alu

e

0 2000 4000 6000 80001

1.5

2

2.5

3

3.5

Time

Pa

ram

ete

r V

alu

e

n

Updated Parameter Values In UKF Identification Technique

Test Series 2 [Different Deformation Demands]

• Parameter Calibration:

0 2000 4000 6000 80001.5

2

2.5

3

3.5

Time

Pa

ram

ete

r V

alu

e

0 2000 4000 6000 80001

1.5

2

2.5

3

Time

Pa

ram

ete

r V

alu

e

Updated Parameter Values In UKF Identification Technique

Test Series 2 [Different Deformation Demands]

• Results:

0 2000 4000 6000 80000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time

Pa

ram

ete

r V

alu

e

0 2000 4000 6000 80000

0.01

0.02

0.03

0.04

0.05

0.06

Time

Pa

ram

ete

r V

alu

e

Updated Parameter Values In UKF Identification Technique

Test Series 2 [Different Deformation Demands]

• Parameter Calibration:

0 1000 2000 3000 4000 5000 60000

0.05

0.1

analysis stepsde

ltaN

u

0 1000 2000 3000 4000 5000 60000

0.005

0.01

0.015

0.02

analysis steps

delt

aEta

Updated Parameter Values for Downhill Simplex Technique

Note: Initial values for the updating parameters for the Downhill Simplex Method were chosen the same as the calibrated numerical model with “no strength and stiffness degradation”.

Updating Parameters:

Upcoming Tests:) Reproduce NEES earthquake simulator collapse tests (NEES Project, PI H. Krawinkler) using hybrid simulation (PI E. Miranda) to examine substructuring and updating techniques

Experimental Substructure

Numerical Substructure

Upcoming Tests: Substructuring on Four Story Steel Moment Frame

• Substructuring Techniques– Techniques to reduce

number of actuators for boundary conditions

• Updating of numerical model

Upcoming Tests

Conclusion

1. A basic objective is to implement and advance the methodology of hybrid simulation with updating of the numerical substructure model(s) during the test and thereby better predict the response of inelastic structures more accurately.

2. An auxiliary numerical model was implemented to calibrate numerical model parameters. Different optimization techniques were examined to minimize the objective function, defined as the error between numerical and experimental substructure response. Both methods give relatively accurate estimates.

3. Hybrid simulation with updating can be implemented using common software such as OpenSEES and MATLAB®. Algorithms for updating process, time of implementing the updated parameters in numerical model and others can be coded by the researcher and used in the proposed framework.

4. The procedure was implemented here for a simple structural model, with more complex applications expected in the near future

Thank You!

Questions?