Hybrid Simulation with On-line Updating of Numerical

Model Based on

Measured Experimental Behavior

M. Javad Hashemi, Armin Masroor, and Gilberto Mosqueda

University at Buffalo

Quake Summit 2012

July 12 , 2012

Introduction

-2 -1.5 -1 -0.5 0 0.5 1-4

-3

-2

-1

0

1

2

3

4

p elem

[ki

p]

Displacement [in.]

Experimental ObservationBilinear Model with Initial Values

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

-2

-1

0

1

2

3

p elem

[ki

p]

Displacement [in.]

Experimental ObservationUpdated Bilinear Model

1 2 3 4 5 6 7 8 91.5

2

2.5

3

updating steps

Yei

ld F

orce

1 2 3 4 5 6 7 8 94.5

5

5.5

6

updating steps

Ela

stic

Sti

ffne

ss

1 2 3 4 5 6 7 8 90.06

0.08

0.1

updating steps

Post

Ela

stic

Sti

ffne

ss R

atio

System Identification – Determine system parameters given the input and output

In this application, the system output is 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

Introduction

In hybrid simulation, it is often assumed that a reliable model of numerical substructure exists

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

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)

Updating in Hybrid Simulation

Updating in Hybrid Simulation

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: 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.

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

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

Online Updating Challenges

Numerical Issues: 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.

Independent of the system to be identified, online identification algorithm must be adaptable to capture parameter changes as time progresses (such as sudden fracture).

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

Hysteretic Model

Smooth Hysteretic Model: Has been used by several researchers for simulating

and identifying hysteretic system response Model is highly nonlinear and has nine control

parameters including stiffness and strength degradation.

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 Techniques

Downhill Simplex : The Downhill Simplex method is a multidimensional

optimization method which uses geometric relationships to aid in finding function minimums

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

The code is ready as a function in Matlab and with some slight modification it is ready to use

Actuators are on hold while finding the updated parameters

Limited number of updating which sometimes causes non-uniform hysteresis

Parameter Identification Techniques

Unscented Kalman Filter: UKF is a recursive algorithm for estimating the

optimal state of a nonlinear system from noise-corrupted data

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.

The updating is instantaneously (each step) Converges smoothly and rapidly Actuators work continuously

Structural ModelOne 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

NumericalExperimental

Experimental Substructure

Hybrid Simulation Architecture

One Bay Frame Structural Properties

Experimental Control xPCtarget

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 ProtocolTest 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 are different• Although elements 1 and 2 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 -2.5 -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

2.5p el

em [

kip]

Displacement [in.]

Element 1Element 2

Test Series 1 [Identical Deformation Demands]

Calibration of the Experimental Response

Calibration:

-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.]

Forc

e [K

ips]

Experimental ElementCalibration of Numerical Model

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

-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.]

Experimental Element Initial

Test Series 1 [Identical Deformation Demands]

Results for updating in real time:

Downhill Simplex Unscented Kalman Filter

-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.]

Experimental ElementUpdated Numerical Model

-3 -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.]

Experimental ElementUpdated Numerical Model

Test Series 2 [Different Deformation Demands]

Reference Model:

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

-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

[ki

p]

Displacement [in.]

Element 1Element 2

Test Series 2 [Different Deformation Demands] Results:

Comparison of Element 2 Hysteresis For Different Tests

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

-2

-1

0

1

2

3

Forc

e [k

ip]

Displacement [in.]

Element 2-Experimental[Calibrated]Element 2-InitialElement 2-Updated(SD)Element2-Updated(UKF)

Test Series 2 [Different Deformation Demands]

Results:

0 1000 2000 3000 4000 5000 6000 7000-3

-2

-1

0

1

2

3

Forc

e [k

ip]

Analysis Steps

Element 2-Experimental [Calibrated]Element 2-InitialElement 2-Updated(SD)Element 2-Updated(UKF)

1400 1600 1800 2000 2200 2400 2600 2800 3000 3200

-2

-1

0

1

2

3

Forc

e [k

ip]

Analysis Steps

Element 2-Experimental [Calibrated]Element 2-InitialElement 2-Updated(SD)Element 2-Updated(UKF)

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

Test Series 2 [Different Deformation Demands]

Results:

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

0 1000 2000 3000 4000 5000 6000 7000-2

-1.5

-1

-0.5

0

0.5

1

Dis

plac

emen

t [in

.]

Analysis Steps

Element 2-Experimental [Calibrated]Element 2-InitialElement 2-Updated(SD)Element 2-Updated(UKF)

1800 2000 2200 2400 2600 2800 3000 3200 3400 3600

-1

-0.5

0

0.5

1

1.5

Dis

plac

emen

t [in

.]

Analysis Steps

Element 2-Experimental [Calibrated]Element 2-InitialElement 2-Updated(SD)Element 2-Updated(UKF)

Test Series 2 [Different Deformation Demands]

Online 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]

Online 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]

Online 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]

Online Parameter Calibration:

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

Reproduce NEES earthquake simulator collapse tests (NEES Project, PI H. Krawinkler) using hybrid simulation (PI E. Miranda) to examine

substructuring and updating techniques

Upcoming Tests

Upcoming Tests

Conclusion1. 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

Acknowledgements Research funding

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

Thank You!

Questions?