Transcript DYNAMIC TESTING TECHNIQUES IN STRUCTURAL ENGINEERING

CIE 616
FALL 2004
ADVANCED DYNAMIC TESTING
TECHNIQUES
IN STRUCTURAL ENGINEERING
by
Andrei M Reinhorn
Xiaoyun Shao
Contents
– Introduction of dynamic testing methods
– Effective force testing
– Pseudo dynamic testing
– Real time hybrid dynamic testing
INTRODUCTION
– Quasi-static loading test method (QST)
– Shaking table testing method (STT)
– Effective force method (EFT)
– Pseudo-dynamic testing method (PDT)
– Real time pseudo-dynamic testing method (RTPDT)
– Real time dynamic hybrid testing method (RTDHT)
Quasi-static loading test method (QST)

a test specimen is subjected to slowly changing prescribed
forces or deformations by means of hydraulic actuators

inertial forces within the structures are not considered in
this method.

purpose is to observe the material behavior of structural
elements, components, or junctions when they are subjected
to cycles of loading and unloading.

dynamic nature of earthquakes are not captured
Shaking table testing method (STT)

test structures may be subjected to actual earthquake
acceleration records to investigate dynamic effects

inertial effects and structure assembly issues are well
represented

the size of the structures are limited or scaled by the size
and capacity of the shake table
Other testing methods (STT)
• Effective Force Method
• Pseudo-dynamic testing
• Real Time Dynamic Hybrid Testing
(new developement)
:
m5x5a
:
m4x4a
Fi
:
m3x3a
F
i
:
m2x2a
:
m1x1a
F2
F1
Effective force testing method (EFT)
m4x4a
:
m3x3a
:
m2x2a
:
m1x1a
:
– Real-Time PseudoDynamic Hybrid
Testing System
– Real-Time
“Dynamic” Hybrid
Testing System
m5x5a
:
• Effective Force
Technique
• Hybrid Testing &
Computing
Applies the inertial ground motion generated forces through synchronized actuators - NEW
Effective force testing method (EFT)

applying dynamic forces to a test specimen that is anchored
rigidly to an immobile ground; perform real-time earthquake
simulation

these forces are proportional to the prescribed ground
acceleration and the local structural masses.
:
m5x5a
:
m4x4a
based on a force control algorithm
m3x3a
:

:
m2x2a
:
m1x1a
• Effective Force
Technique
• Hybrid Testing &
Computing
– Pseudo-Dynamic
Hybrid Testing
System
– Real-Time
“Dynamic” Hybrid
Testing System
Fi
F2
F1
Applies forces in substructure through actuators only – real time operation is a benefit but not a must
Pseudo-dynamic testing method (PSD)

applying slowly varying forces to a structural model

motions and deformations observed in the test specimens are
used to infer the inertial forces that the model would have
been exposed to during the actual earthquake

Substructure techniques
Real time pseudo-dynamic testing method
(RTPDT)

same as the PSD test except that it is conducted in the real
time

Introduce problem in control, such as delay caused by
numerical simulation and actuator
• Effective Force
Technique
• Hybrid Testing &
Computing
– Real-Time PseudoDynamic Hybrid Testing
System
– Real-Time “Dynamic”
Hybrid Testing System
Fi
Applies forces in substructure through shake table and actuators – real time operation is a must
Real-Time Seismic Hybrid Testing
INTERFACE FORCES
ACTIVE FEEDBACK FROM
SIMULATED STRUCTURE
APPLIED BY ACTUATORS
AGAINST REACTION WALL
REACTION
WALL
SIMULATED
STRUCTURE
SHAKING TABLES
(100 ton)
FULL OR NEAR
FULL SCALE TESTED
SUBSTRUCTURE
Fig.1. Real-Time Hybrid Seismic Testing System
(Substructure Dynamic Testing)
Real time dynamic hybrid testing method
(RTDHT)

based on shaking table test combined with substructure
techniques.

part of the structure (the physical model) is constructed and
tested on the shaking table

The rest part of the structure (the numerical model) is
numerically modeled in the compute

the earthquake effect on the superstructure was calculated
as a interface force and applied to the substructure by the
actuators (force control based)
Block Diagrams of Various Testing Methods
Excitation
Specimen
Response
Open Loop Test
> Quasi-Static Loading:
Cyclic Loading
Specimen
> Shaking Table:
Ground Motion
Quasit-static; Shaking Table Test
Response
Open Loop Control (in concept)
Mass Multiplier &
Actuator Application
Effective Force
Excitation
Specimen
Effective Force Test
Response
Closed Loop Test
Solution of Models
Equation of Motion
force
measured
applied
displacement
Excitation
Specimen
Pseudo-dynamic Test Method
Response
Closed Loop Test
RESPONSE ANALYSIS
(Superstructure)
SUPERSTRUCTURE
RESPONSE
CONTROL IMPLEMENTATION
dislacment
command
measured
force (q)
STRUCTURE
RESPONSE
EXCITATION
Specimen
(SUBSTRUCTURE)
SUBSTRUCTURE
RESPONSE
Pseudo-dynamic Test with Substructure
Closed Loop Test
Simulator/Controller
>RESPONSE ANALYSIS
(Superstructure)
>DELAY COMPENSATION
SUPERSTRUCTURE
RESPONSE
STRUCTURE
RESPONSE
external
force (p)
EXCITATION
Shake Table
force
command
Specimen
(SUBSTRUCTURE)
measured
displacement
SUBSTRUCTURE
RESPONSE
Real-time Hybrid Dynamic Test
Summary of dynamic test methods
Advantages

Size of the specimen can be large or very large
Disadvantages


Inertial forces are not true forces and distorted by discrete
parameter model, actuators and computers
Rate effects are neglected because of quasi-static loading
PDT

Size of the specimen can be large or very large


Inertial forces are not true forces and distorted by discrete
parameter model, actuators and computers
Actuator time delay is introduced
RTPDT

True inertia forces in assembly

Size of the specimen is limited


True inertia forces on the specimen
Specimen can be large or very large

Part of the inertia forces are simulated with errors (same as
PDT)
Actuator time delay is introduced
STT
RTDHT

Effective Force Testing
Equation of motion
Mxa  Cx  Kx  0
Subscript refers to motion relative to a fixed reference frame
(absolute displacement)
x  x  Ix
a
g
x  x  Ix
a
g
Mx  Cx  Kx  Mx  P  t 
g
eff
Open Loop Control (in concept)
Mass Multiplier &
Actuator Application
Effective Force
Excitation
Specimen
Effective Force Test
Response
Effective Force Test – Hardware Components
• Servo-Hydraulic Actuators
• Servo-Hydraulic Control System
• Elastic Spring
• Measurement Instrumentation (DAQ)
• Computer
– Simulator
– Controller
Effective Force Test – Hardware Configuration
`
`
STS
CONTROLLER
DAQ
xPc Software
SCRAMNet
DSP Read/
Write
xPC Software
SCRAMNet
Analog I/O
DSP
Signal
Generation
Analog I/O
SCRAMNet to
Analog I/O
Bridge
Test Software
Control
ServoController
Servo-Hydraulic
Control
Structure
DAQ Hardware
Signal
Conditioners
SCRAMNet
Effective Force Test -Dynamic force control
Series elasticity and displacement feedback
Effective Force Test -Dynamic force control
Series elasticity and displacement feedback
Actuator
Displacement
Feedback
Desired
Force
1/K LC
+

C
+
1
G Actuator
G Actuator
Actuator
Displacement
+
Actuator in
Closed-loop
Displacement Control
Compensation
Structure
Displacement

-
K LC
Series Spring
1
ms 2  cs  k
Structure
Achieved Force
Desired Force
 CG
ms 2  cs  k
ms 2  cs  k  K LC 1  CG 
Ideal: C = 1/G
Achieved
Force
Effective Force Test -Dynamic force control
The advantages of using the series spring
• the actuator can be well tuned and operated in displacement
control
• it provides for one more parameter than can be altered in the
control design (the oil stiffness cannot be)
• the term KLC(1-CG) in the transfer function indicates that the
smaller the value of KLC the less sensitive is the transfer
function to deviations of C from 1/G
Effective Force Test – Effect of Time Delay
The dynamic characteristics of hydraulic actuators inevitably
include a response delay , which is equivalent to negative
damping
Experimental
2.0
1.8
1.6
Numerical
Magnitude
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0
2.0
4.0
6.0
Frequency (Hz)
8.0
10.0
Effective Force Test – Predictive Control
1/K LC
+

+
+
+
Corrective
Displcement

+

-
T = e-s
Predictive
Displcement
T0
1
m0 s  c0 s  k 0  K LC 0
Delay
Model
Model of StructureSpring System
Actuator
+

-
K LC
Series Spring
2
1
ms 2  cs  k
Structure
Smith Predictor
Effective Force Test – Predictive Control
2.0
1.8
1.6
Without compensation
Magnitude
1.4
1.2
1.0
With compensation
0.8
0.6
0.4
0.2
0.0
0.0
2.0
4.0
6.0
Frequency (Hz)
8.0
10.0
Effective Force Test – Software
•Simulink®
•Realtime Workshop®5
•XPC Target
Pseudo dynamic testing
Define a model of the structure system
Define the desired excitation – usually base
acceleration
Calculate the expected response of structure –
displacement
Use an actuator to apply the desired displacement in
the structure
Measure the resistance force in the structure (or
estimate it from measurements)
Repeat the above steps – start from second
Mdi  Cdi  Ri  fi
Pseudo-dynamic testing
Input excitation fi (desired)
-1
Δt  
Δt 

ai+1 =  m+ c   fi+1 -ri+1 -cvi - ca i 
2  
2


vi+1 =vi +
Δt
 a +a 
2 i i+1
Δt 2
di+2 =di+1 +Δtvi+1 +
a
2 i+1
Impose di+1 on the structure
Measure ri+1
Set i - 1 = I
Pseudo dynamic testing
Solution of Models
Equation of Motion
force
measured
applied
displacement
Excitation
Specimen
Pseudo-dynamic Test Method
Response
Pseudo-dynamic testing – Hardware
Components
•
Servo-Hydraulic Actuators
•
Servo-Hydraulic Control Systems
•
Measurement Instrumentation
•
On-line computer
Pseudo-dynamic testing – Hardware
Configuration (Local)
`
`
`
SIMULATOR
CONTROLLER
DAQ
Flex Test
Matlab
Software
Integration
Algorithm
xPc Software
SCRAMNet
DSP Read/
Write
xPC Software
SCRAMNet
Analog I/O
Test Software
Control
Simulation
Interface
SCRAMNet
DSP
Signal
Generation
Analog I/O
SCRAMNet to
Analog I/O
Bridge
ServoController
Servo-Hydraulic
Control
SV
DAQ Hardware
Signal
Conditioners
SCRAMNet
Pseudo dynamic testing
Discretized equation of motion of the structure at time
intervals
ti  it
for
, i  1toN
Mdi  Cdi  Ri  fi
Equation solved in computer step by step, with Ri as the
reaction force measured from the specimen under test.
Result is the displacement command of next step that will be
applied to the specimen at each node of mass by actuators.
Pseudo dynamic test—integration algorithm
– Both explicit and implicit time-stepping integration algorithm
can be applied for solving equation of motion in Pseudodynamic tests.
– Explicit methods compute the response of the structure at
the end of current step based on the state of the structure
at the beginning of the step.
•
•
•
•
•
Central difference method (Takanashi et al. 1975),
Newmark- Beta method (1959),
Modified Newmark’s method (1986),
The γ-function pseudodynamic algorithm (Chang et al. 1997)
Unconditionally stable explicit method(Chang, 2002)
(continued on next)
Pseudo dynamic test—integration algorithm
(continued)
– Implicit methods require knowledge of the structural
response at the target displacement in order to compute the
response.
– the displacement is dependent on other response parameters
at the end of the step
,
– iteration is required in the algorithm to satisfy both the
imposed kinematic conditions and the equilibrium conditions
at the end of the time step
• Newmark – Alpha method (Hilber et al. 1977)
• Hybrid implicit algorithm (Thewalt and Mahin, 1987)
• Newton iteration (Shing, 1991)
Pseudo dynamic test—integration algorithm
(continued)
– implicit iteration algorithm provide improved
stability characteristics and permit the used of
larger integration time steps
– iteration on experimental model is not practical
since structure materials are path dependent
– explicit methods are easier to implement
– Explicit integration methods are preferred for
PSD simulation when stability limits are satisfied
for the structural model under investigation
Pseudo dynamic test—integration algorithm
(continued)
Example: Modified Newmark’s Method
 
Md
i 1
d i 1

t
2
M (d i 1  d i )  (1   )R i 1  R i  f i 1
2

t

 d i  td i 
d
i
2
t  
d i 1  d i  (d
i  d i 1 )
2
Substitute into and solve for
 
d
i 1
 2 
2  
di 
d i  M 1 f i 1  R i  (1   )R i 1 
(2   )t
2 
Pseudo-dynamic testing –
substructuring principle
• may fabricate only part of the structure whose hysteretic
behavior is complex and apply the test to this part
• remaining part treated in the computer
Pseudo-dynamic testing –
substructuring principle
 M ee
M T
 ea
   Cee
M ea  d
e
    T

M aa  d a  Cea
Cea  d e  R e  f e 
       

Caa  d a  R a  f a 
subscripts a and e denote the degrees of freedom within the
analytical and experimental substructures.
  C d  K d  f  M d


Meed
e
ee e
ee e
e
ea a  Cead a  K ead a
  C d  K d  f  M Td
  C Td  K Td
Maa d
a
aa a
aa a
a
ea
e
ea
e
ez
Deede  fe  Deada
Daada  fa  DeaTde
 Tested part. Calculate displacement command for next step.
 Interface force: Deada
 Analytical part. Calculate interface state used in interface
force.
Pseudo-dynamic testing – Hardware
Configuration (Internet)
Pseudo-dynamic testing –Software
•
Response analysis – Matlab Simulink
•
Controller implementation – Matlab Stateflow
Dynamic hybrid testing - I
• Combined use of earthquake simulators, actuators and
computational engines for simulation
• Details later in the presentation
Response Feedback
Computational
Substructure
Physical
Substructure
Physical
Substructure
Shake Table
Computational
Substructure
Ground/Shake Table
Structural Actuator
Dynamic hybrid testing - II
Well understood
Structural
Actuator
Foundatio
n
Laminar
Soil Box
Shake Table
Focus of
interest
Real-time dynamic hybrid testing - II
Response
Feedback
Structural
Actuator
Has to operate in
Force Control
Distributed
mass
Foundatio
n
Laminar
Soil Box
Shake Table
Acceleration input:
Table introduces
inertia forces
Substructure Testing – Unified Approach
Response Feedback
Computation
al
Substructure
Physical
Substructur
e
Physical
Substructur
e
Structural
Actuator
Shake Table
Computation
al
Substructure
Ground/Shake
Table
Shake table acceleration, ut 
1  s  u1
 3
First story contribution
to shake table acceleration
Actuator Force, Fa   
1  1
 s   m2 u1
First story contribution
to actuator force
s
k3
m2
 x3
 x2
Third story contribution
to shake table acceleration

1   3
 s   k3  x3
 x2
Third story contribution
to actuator force


1  s   0 and 3  s   0
Unified approach to substructure testing
• If   s   0 and   s   0 , then the control requires a shake table and
an actuator to implement the substructure testing.
1
3
• If   s   0 and   s   0 , then the controller require just an actuator
to implement the substructure testing as pseudo-dynamic
testing:
1
3
• Note:
– In pseudo-dynamic testing, inertia effects are computed.
– In dynamic hybrid testing (   s   0 or   s   0 ), the actuator
should operate in force control.
1
3
Hybrid Controller Implementation (UB-NEES)
• Flexible architecture using parallel processing
Design done jointly between MTS and UB
Implementation of RTDHT
Actuator
Structure
Shake
Table
Substructure response
Second
(simulated)
floor
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.0
2.0
4.0
6.0
8.0
10.0
First
(physical)
floor
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0.0
2.0
4.0
6.0
Hybrid test
8.0
10.0
Shake table
Actuator
Structure
Shake
Table