Chinmoy Kolay

Research Engineer

Thomas Marullo

IT System Administrator

NHERI Lehigh EF

1

Large-scale nonlinear viscous damper

characterization test

RTHS implementation challenges and

NHERI Lehigh solutions

RTHS of a RC building with nonlinear

viscous damper

2

Outline

Groups

3

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Large-scale nonlinear viscous damper

characterization test

RTHS challenges and NHERI Lehigh

solutions

RTHS of a RC building with nonlinear

viscous damper

4

Outline

Damper Characterization Test

5

Nonlinear fluid viscous damper

Make: Taylor Devices Inc.

Nominal force capacity 600 kN

Max stroke 125 mm

Theoretical force-velocity:

=

Manufacturer provided

= 773 .

and = 0.4

Operating temperature:

6.7 to +54.4 (+20 to + 130

Procedure for Damper Characterization

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Develop a damper

model

Assign model

parameters

Predict model

response

Calculate error

between model

and measured

experimental data

Revis

e p

ara

mete

rs

to m

inim

ize e

rro

r Predefined

displacement tests

Input Displacement and Test Matrix

7

Amplitude

mm (in.)

Frequency (Hz)

0.25 0.50 1.0 1.5

76.2 (3.0) 119.7 (4.7) 239.4 (9.4) 478.8 (18.9) 718.2 (28.3)

Numbers in the cells are max velocities in mm/s (in/s)

Actuator Power Curve

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0 500 1000 15000

0.5

1

1.5

1 valve

2 valves

3 valves

Max demand

Power curve for 1700 kN actuators at 3000 psi

Force (kN)

Vel

oci

ty (

m/s

)

Damper Characterization Test Data

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Nonlinear Maxwell Damper Model

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Damper shows strong frequency dependent behavior

Usually modeled using a nonlinear Maxwell model

,

,

,

,

Total damper deformation: = +

Total damper velocity: = +

Damper force:

= = =

= = =

1

Model parameters: , , and

Governing equation (nonlinear ODE)

+

1

=

||

1

||

1 ||1

=||

1

Solution of nonlinear ODEGoverning equation (nonlinear ODE): +

1

=

Solver: variable-step Dormand-Prince solver (ode45) which belongs to 5th order

Runga-Kutta familty

Simulink model for solution of the nonlinear ODE

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Identify , , and so that the error between the model prediction and experimental data are minimized

We use particle swarm optimization (PSO) algorithm

(Kennedy and Eberhart, 1995; Ye and Wang, 2007;

Chae, 2011)

The algorithm in Matlab script is available for users

Objective function: Normalized root mean square error

, , ==1

2

=1

2

and

are experimental and predicted damper forces,

respectively

is the total number of samples

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Determination of Model Parameters

Measured vs Model Prediction

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Large-scale nonlinear viscous damper

characterization test

RTHS implementation challenges and

NHERI Lehigh solutions

RTHS of a RC building with nonlinear

viscous damper

14

Outline

Nonlinear damper

Experimental substructure

Introduction: RTHS

Nonlinear

damper

Linear

damper

Real time response

Effective force +1Ground acceleration

Integration of equations of motion

+1 + +1 + +1 + +1

= +1

Simulation coordinator

+1

+1

Force

transformation

+1

FE model

Linear

damper

Analytical

substructure

Ramp generator and

kinematic transformation

for each actuator DOF

ATS

compensator

Servo

controller

+1 , +1

+1

+1

+1

+1

Servo-hydraulic actuator control

and experimental substructure

15Kolay, C. Parametrically Dissipative Explicit Direct Integration Algorithms for Computational and Experimental Structural Dynamics.

Ph.D. Dissertation. Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, USA, 2016

RTHS: Implementation issues and challenges

Analytical substructure

Fast and accurate state

determination procedure for

complex structures

Experimental substructure

Large capacity hydraulic

system and dynamic actuators

required

Actuator kinematic

compensation

Robust control of dynamic

actuators for large-scale

structures

Numerical integration algorithm

Accurate

Explicit

Unconditionally stable

Dissipative

Fast communication

Simulation coordinator

Preferred

16

RTHS: Implementation issues and challenges

NHERI Lehigh

Solutions

Numerical integration algorithm

Accurate

Explicit

Unconditionally stable

Dissipative

Fast communication

Simulation coordinator

Various explicit model-based algorithms

RTMD real-time integrated control architecture

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Model-based explicit algorithms for RTHSNHERI Lehigh Solutions to RTHS Challenges

Single-parameter families of

Algorithms with numerical dissipation

Model-Based Algorithms

Semi-Explicit- (SE-) Method Explicit- (E-) Method

Single-Parameter Semi-Explicit-(SSE-) Method

Kolay-Ricles-(KR-) Method(Kolay & Ricles, 2014)

Chen-Ricles (CR) Algorithm(Chen & Ricles, 2008)

Families of

algorithms

Kolay, C., & Ricles, J. M. (2015). Assessment of explicit and semi-explicit classes of model-based algorithms for direct integration in

structural dynamics. International Journal for Numerical Methods in Engineering. doi:10.1002/nme.5153

Modified Kolay-Ricles-(MKR-) Method

(Kolay & Ricles, 2016)

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19

Simulink Block Diagram for E- Method

Block 1 & 5 runs at =1

1024sec

Others run at = =4

1024sec (say)

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Timing

RTHS: Implementation issues and challenges

HybridFEM

Multi-grid real-time hybrid simulation

NHERI Lehigh

Solutions

Analytical substructure

Fast and accurate state

determination procedure

21

Lehigh HybridFEM

MATLAB and SIMULINK based computational modeling

and simulation coordinator software

Run Modes

MATLAB script for numerical simulation

SIMULINK modeling for Real-Time Hybrid simulation with

experimental elements via xPCs, and hydraulics-off for training

and validation of user algorithms.

Users Manual for training

Karavasilis, T. L., Seo, C.-Y., & Ricles, J. M. (2012). HybridFEM: A program for dynamic time history analysis and

real-time hybrid simulation (ATLSS Report). ATLSS Report (Vol. 0809). Bethlehem, PA.

NHERI Lehigh Solutions to RTHS Challenges

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Lehigh HybridFEM

Configuration Options:

Coordinate system of nodes

Boundary, constraint and restraint conditions

Elements

Elastic beam-column

Elastic spring

Inelastic beam-column stress resultant element

Non-linear spring

Displacement-based NL beam-column fiber element

Force-based beam NL column fiber element

Zero-length

2D NL planar panel zone

Elastic beam-column element with geometric stiffness

Geometric nonlinearities

Steel wide flange sections (link to AISC shapes Database)

Reinforced concrete sections

Structural mass & inherent damping properties

Adaptable integration methods

Materials

Elastic

Bilinear elasto-plastic

Hysteretic

Bouc-Wen

Trilinear

Stiffness degrading

Concrete

Steel

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RTHS: Implementation issues and challenges

Large hydraulic power supply system

5 large capacity dynamic actuators

Development of actuator kinematic compensation

Servo hydraulic actuator control: Adaptive Time Series Compensator (ATS)

NHERI Lehigh

Solutions

Experimental substructure

Large capacity hydraulic system and dynamic actuators required

Actuator kinematic compensation

Robust control of dynamic actuators for large-scale structures

24

25

Servo Hydraulic Actuator Control

Nonlinear servo-valve dynamics

Nonlinear actuator fluid dynamics

Test specimen material and

geometric nonlinearities

Slop, misalignment, deformations

in test setup

Variable amplitude

error and time delay in

measured specimen

displacement

Inaccurate structural response

Delayed restoring force adds energy into

the system (negative damping)

Can cause instability

It is important to compensate

Servo Hydraulic Actuator Control

Actuator delay compensation

Inverse compensation (Chen 2007)

Adaptive inverse compensation (AIC, Chen

and Ricles 2010)

Adaptive time series (ATS) compensator

(Chae et al. 2013)

Chae, Y., Kazemibidokhti, K., and Ricles, J.M. (2013). Adaptive time series compensator for delay

compensation of servo-hydraulic actuator systems for real-time hybrid simulation, Earthquake

Engineering and Structural Dynamics, DOI: 10.1002/ eqe.2294..

Chen C. Development and numerical simulation of hybrid effective force testing method. Ph.D.

Dissertation, Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA

2007.

Chen, C. and Ricles, J.M. Tracking error-based servohydraulic actuator adaptive compensation for

real-time hybrid simulation. ASCE Journal of Structural Engineering, 2010; 136(4):432-440.

26

= 0

+ + 2

Adaptive Time Series (ATS) Compensator

: compensated input displacement into actuator

: adaptive coefficients

Adaptive coefficients are optimally updated to minimize the error between

the specimen target and measured displacements using the least squares

method

A = a0k a1k ank[ ]T

Xm = xmxm d

n

dtnxm( )

T

xm = xk-1m xk-2

m xk-qm

T

Uc = uk-1c uk-2

c uk-qm

T

(Output (measured) specimen displacement history)

(Input actuator displacement history)

A = XmTXm( )

-1

XmTUc

2nd order ATS compensator

Chae, Y., Kazemibidokhti, K., and Ricles, J.M. (2013). Adaptive time series compensator for delay compensation of servo-hydraulic

actuator systems for real-time hybrid simulation, Earthquake Engineering and Structural Dynamics, DOI: 10.1002/ eqe.2294.

: target specimen displacement

Large-scale nonlinear viscous damper

characterization test

RTHS implementation challenges and

NHERI Lehigh solutions

RTHS of a RC building with nonlinear

viscous damper

28

Outline

29

RTHS configuration

1999 Chi-Chi EQ record scaled to MCE hazard level

Time step: =3

1024s

Prototype floor plan

RTHS configuration

Analytical substructure modeled using force-based elements with fixed number of iterations and linear elastic elements

Mass, tangent, and initial stiffness proportional inherent damping

Time step: =3

1024s

MKR- method (parameter )

Model-based integration parameters (, , ) determined from characterization test data

ATS Compensator for adaptive time delay and amplitude compensation

30

31

Explicit Modified KR- (MKR-) Method

Velocity update: +1 = +

Displacement update: +1 = + + 2

Weighted equations of motion: +1 + +1 + +1 = +1

where,

+1 = +1 +

+1 = 1 +1 +

+1 = 1 +1 +

+1 = 1 +1 +

Initial acceleration: 0 = [ 0 0]

Kolay, C., & Ricles, J. M. (2014). Development of a family of unconditionally stable explicit direct integration algorithms

with controllable numerical energy dissipation. Earthquake Engineering and Structural Dynamics, 43(9), 13611380.

http://doi.org/10.1002/eqe.2401

, , and : model-based integration parameters

Integration Parameters

Parameter controlling numerical energy dissipation

= spectral radius when =

varies in the range 0 1

= 1: No numerical energy dissipation

= 0: Asymptotic annihilation

Scalar integration parameters:

=2

3 +2 1

3 +

2 ++1; =

+1; =

1

2 + ; =

1

2

1

2+

Model-based integration parameter matrices:

= + + 2

1; =1

2+

= + + 2

1 + + t2

IP stands for integration parameters

, , and need to be formed based on the hybrid system

32Kolay, C., & Ricles, J. M. (2016). Improved explicit integration algorithms for structural dynamic analysis with unconditional

stability and numerical dissipation. Submitted to Journal of Earthquake Engineering.

RTHS: Model-Based Integration Parameters

Model-based integration parameters (, , and ) require , , and

For the present study

= =analytically modeled mass matrix

Experimental substructure mass is small

= 0 + 1 +

= initial stiffness matrix of analytical substructure

=equivalent damping matrix of experimental substructure

0 and 1 are Rayleigh damping coefficients

= +

=equivalent stiffness matrix of experimental substructure

How can we determine and

?

33

34

Model-based integration parametersLinearization of nonlinear Maxwell model at a small velocity (0.5 in/s) and determination

of frequency dependent equivalent Kelvin-Voigt model parameters

What is the value of ?

, ,

,

Linearized Maxwell model

=

=

= 1

Linearized

Linearization

,

=

2

1 + 2

=

1 + 2

Equivalent Kelvin-Voigt model

,

,

,

,

35

RTHS Test Matrix

Test No.

1 1 0 0.75

2 2 0 0.75

3 212

0.75

4 2 1 0

36

RTHS Test Data

References Chae, Y. (2011). Seismic Hazard Mitigation of Building Structures Using Magneto-Rheological Dampers. Ph.D. dissertation, Department

of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA.

Chae, Y., Kazemibidokhti, K., & Ricles, J. M. (2013). Adaptive time series compensator for delay compensation of servo-hydraulicactuator systems for real-time hybrid simulation. Earthquake Engineering & Structural Dynamics, 42(11), 16971715. doi:10.1002/eqe

Chen, C., & Ricles, J. M. (2008). Development of direct integration algorithms for structural dynamics using discrete control theory. Journal of Engineering Mechanics, 134(8), 676683. http://doi.org/10.1061/(ASCE)0733-9399(2008)134:8(676)

Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ, 19421948.

Kolay, C. Parametrically Dissipative Explicit Direct Integration Algorithms for Computational and Experimental Structural Dynamics. Ph.D. Dissertation. Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, USA, 2016

Kolay, C., & Ricles, J. M. (2014). Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation. Earthquake Engineering and Structural Dynamics, 43(9), 13611380. http://doi.org/10.1002/eqe.2401

Kolay, C., & Ricles, J. M. (2016). Force-based frame element implementation for real-time hybrid simulation using explicit direct integration algorithms. Submitted to Journal of Structural Engineering.

Kolay, C., & Ricles, J. M. (2016). Improved explicit integration algorithms for structural dynamic analysis with unconditional stability and numerical dissipation. Submitted to Journal of Earthquake Engineering.

Kolay, C., Ricles, J. M., Marullo, T. M., Mahvashmohammadi, A., & Sause, R. (2015). Implementation and application of the unconditionally stable explicit parametrically dissipative KR- method for real-time hybrid simulation. Earthquake Engineering & Structural Dynamics, 44(5), 735755. http://doi.org/10.1002/eqe.2484

Ye, M. and Wang, X. (2007). Parameter estimation of the Bouc-Wen hysteresis model using particle swarm optimization. Smart Materials and Structures, 16(6), 23412349.

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Thank you

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