conventional hybrid and real-time hybrid testing brian phillips 브라이언 필립스 university of...
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Conventional Hybrid and
Real-Time Hybrid Testing
Brian Phillips브라이언 필립스
University of Illinois at Urbana-Champaign일리노이 대학교 - 어바나 샴페인
For 2008 Asia-Pacific Summer School in Smart Structures Technology at KAIST
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Experimental Testing Experimental evaluation of components required
when Response not well understood Difficult to model numerically Model development stage
Outcomes help improve Understanding of dynamic response Computational models and constitutive relationships Design methods and codes
Seismic Evaluation of Structures
Quasi-static
Shaking Table Hybrid
Hybrid versus Quasi-Static
Shore Western Series 92 Actuator
Quasi-Static Predefined loading path
Hybrid Loading path depends on structural response
Similar Qualities Provide structural capacity Hardware
Controller
Hybrid versus Shake Table Shake Table
Dynamic loading rate Directly account for rate dependent behavior Model entire structure, usually scaled Predefined loading path
Conventional Hybrid Quasi-static loading rate Rate dependent behavior included numerically Continual observation and monitoring of experiment Pause and resume test Substructuring Loading path depends
on structural response
gx
Ramp Ramp
Hold Hold t
x
Hybrid Test Method Combination of
Experimental testing Analytical simulation
Concept proposed in late 1960’s (Hakuno et al., 1969) Developed in the mid 1970’s (Takanashi et al. 1975)
Incorporated digital computers Discrete systems quasi-static loading
Also known as Hybrid Simulation Pseudodynamic test method (PsD) Computer-actuator on-line test Virtual prototyping
Basis of Method Equation of Motion
MN = mass (numerical) CN = viscous damping (numerical) F = effective external force RN = restoring force (numerical) RE = restoring force (experimental)
Represents stiffness, damping, and inertial forces in experimental structure
tFxxxRxRtxCtxM ENNN ,,
RE in Conventional Hybrid Testing RE(x)
RE = K∙x(t) for linear elastic Rate dependent behavior included numerically Experiment conducted arbitrarily slowly
Actuator dynamics become insignificant Larger actuators can be easily accommodated Full scale specimens
Hybrid Testing Components System inputs
Earthquake record Analytical model of structure (MN, CN, KN)
Numerical integration scheme Calculate displacements (x) at discrete points in time
Experimental setup Apply displacements (x) to specimen Usually applied at 100 to 1000 time scale Measure specimen restoring force (RE)
Numerical integration of next time step
Required Equipment (Shopping List) Servo-hydraulic system
Servo-controller Servo-valve Hydraulic actuators
Instrumentation Displacement transducer Load cell
Strong floor and reaction wall On-line computer
Numerical integration Generate command signal (D/A conversion) Read restoring force (A/D conversion)
Hybrid Test Flow of Information
D/A
A/D
PID
ServoController
Control Loop
Hybrid Testing Loop
LVDT
Load Cell
SpecimenActuator
Servovalvexc xc
xm
xm
Rm
Rm
i
Δt
1111 iiii FRxCxM
m
c, kgx
x = displacementR = forcei = current□c = commanded□m = measured
δt
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Numerical Integration Discrete representation of equation of
motion
ti = iΔt, i = 1, …, n Smaller Δt increases accuracy as well as
computational demand
1111 iiii FxRxCxM
ti ti+1
xi xi+1
x
t
xi-1
ti-1
Numerical Integration Schemes Explicit
Displacement solution at ti +1 is based on previous steps (ti, ti-1, etc.)
Computationally efficient Conditionally stable solution
Related to natural frequencies of structure and Δt
Implicit Displacement solution at ti+1 is based on previous and current
steps (ti+1, ti, ti-1, etc.) Iterative procedure for nonlinear behavior Some implicit methods are unconditionally stable
Beneficial to stiff and MDOF structures
Central Difference Method Explicit method Low computational cost Easily fits into hybrid testing framework Stability condition ωΔt ≤ 2
t
xxx iii
211
211 2
t
xxxx iiii
ti ti+1
xi xi+1
x
tti-1
xi-1
2Δt
CDM in Hybrid Testing Framework
Initial Conditions
NNN KCM ,,
Compute Velocity and Acceleration
11, ii xx
External Force
1iF
Impose Command on Actuator
1ix
Measure Restoring Force1, iER
Conditions at Step i
ixixix
Update
1ii
Compute Displacement
1ixiiii xtxtxx 2
1 2
1
11 2
1 iiii xxtxx
11,1,11 iiEiNiNiN FRRxCxM
Newmark Beta Method(Newmark, 1959) β and γ determine the stability and accuracy of method
Popular variations β = 0 and γ = 1/2 Central Difference Method (explicit) β = 1/4 and γ = 1/2 Constant Average Acceleration (implicit) β = 1/6 and γ = 1/2 Linear Acceleration Method (implicit)
γ controls numerical damping γ = 1/2 No numerical damping (second order accurate) γ < 1/2 Negative numerical damping (first order accurate) γ > 1/2 Positive numerical damping (first order accurate)
1
21 2
1iiiii xxtxtxx 11 1 iiii xxtxx
Alpha Method (α-HHT)(Hibler et al., 1977) Modification of the Newmark method
Properties Unconditionally stable α alters numerical damping α = 0 Constant average acceleration method Maintains second-order accuracy for any γ Favorable dissipation in higher modes (potentially
spurious) with little affect on lower modes
iiiiiii FFRxRxxCxCxM 1111 111
214
1 2212
1 031
Operator Splitting (OS) Method(Nakashima 1990) Predictor components
Based on previous steps only (explicit)
Corrector components Includes next step in formulation (implicit)
1
21 2
1iiiii xxtxtxx 11 1 iiii xxtxx
1~
ix 1~
ix
12
11~
iii xtxx 111
~ iii xtxx
Operator Splitting (OS) Method No iteration of command on specimen
Explicit formulation for inelastic portion Implicit formulation for elastic portion
1
~iR
R
x
0K
1ix1~
ix
11011~~
iiii xxKRR
FxxRxxRxCxM iiE
iiI
ii 111111~,~,
Unconditionally stable for softening type stiffness
Predictor Step
Corrector Step
Obtain restoring force at end of time step with no iteration
α-OS Method (Combescure and Pegon, 1997) Combination of α-HHT and OS Methods Allows alpha method to be implemented without
iterating commands on the specimen Unconditionally stable for softening
nonlinearities Accuracy of higher modes affected by severe
stiffness degradation, lower modes remain accurate
α-OS Method in Action
Compute Acceleration
11ˆˆ
ii FxM
External Force
1iF
Impose Command on Actuator
1~
ix
Compute Pseudo-Force1
ˆiF
Conditions at Step i
ixixix
Compute Correctors
1ix 1ixCompute Predictors
1~
ix 1~
ix
02 11ˆ KtCtMM
iiii xt
xtxx 212
~2
1
iii xtxx 1~1
iiiiii xCRRFFF ~~1
~1ˆ
111
12
11~
iii xtxx
111~
iii xtxx
Initial Conditions
0K M̂C
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Errors in Hybrid Testing
xc
xm
Rm
Modeling Errors Numerical Integration Errors
1111 iiii FRxCxM
ti ti+1
xi xi+1
x
t
Experimental Errors
Experimental Error Sources
Flexibility of reaction frame Displacement control ofhydraulic actuators
x
t
Commanded
Measured
Intrinsic Noise
x
t
Instrumentation errors•Calibration errors•Noise
Precision errors•Range of instruments•Properties of specimen
Experimental Errors in Hybrid Testing Method is sensitive to experimental errors Closed loop experiment
Errors accumulate throughout entire test System instability Undesired damage to specimen
Quasi-static and shake table test methods are less sensitive to experimental error Predefined command history
Experimental Error Types Systematic errors
Actuator overshooting and undershooting Actuator lag Can lead to system instabilities
Random errors High frequency noise in instrumentation Less severe than systematic errors Can be controlled using dissipative integration algorithms
Relaxation of restoring forces Can be reduced by minimizing or eliminating hold period
Rate effects Can increase speed to fast or real-time hybrid testing
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Variations of Hybrid (Pseudodynamic, PsD) Testing
Conventional PsD Testing
Takanashi, et al., 1975
SubstructurePsD Testing
Dermitzakis and Mahin, 1985
ContinuousPsD Testing
Takanashi and Ohi, 1983
Real-TimeHybrid Testing
Nakashima, et al., 1992
Effective ForceTesting
Mahin, et al., 1985, 1989
DistributedSubstructure PsD
TestingWatanabe, et al., 2001
Distributed Continuous PsD
TestingMosqueda, et al., 2004
1
2
3 45
(Carrion, 2007)
Substructure PsD Testing
Experimental SubstructureNumerical Substructure
Structure of Interest
Distributed Substructure PsD Testing
Continuous PsD Testing Provides continuous actuator movement
No hold phase Avoids force relaxation Can be conducted for both slow and fast rates
Prediction and correction phases
Ramp Ramp
Hold Hold t
xPrediction Prediction
Correction Correction
Effective Force Testing Convert earthquake ground motion into
equivalent inertial forces at each DOF Independent of stiffness and damping Force controlled actuators
Force commands known prior to experiment No substructuring Full mass and damping must be included in specimen
Control-structure interaction limits ability to apply force control around natural frequencies (Dyke et al., 1995) Must apply accurate compensation (challenging)
m
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Real-Time Hybrid Testing (RTHT) 1:1 time scaling Accurately test rate dependent components (i.e.
dampers, friction devices, and base isolation) Cycles must be performed very quickly
System dynamics become important Time delays: computation and communication Time lags: lag in response of actuator to command
NumericalCalculations
Apply Displacement
Measure RestoringForces
Δt = 10 – 20 msec
RTHT Hardware Restrictions Dynamically rated actuators
Double ended
Fast, dedicated computers xPC Target (Mathworks) dSpace (dSpace) CompactRIO (NI)
Shore WesternSeries 91 Actuator
Real Time
RTHT Restrictions on Explicit Numerical Integration Controller sampling rate δt smaller than
typical Δt of numerical integration Separate signal generation (δt) and response
analysis (Δt), (Nakashima and Masaoka, 1999) Signal generation based on polynomial
extrapolation and interpolation
x
tΔt Δt
extrapolation interpolation
δtδt
PIDδt
ServoController
x
tΔtNumericalIntegration
RTHT Restrictions on Implicit Numerical Integration Actuators must move with smooth velocity Iteration of implicit schemes unpredictable
Fix number of iterations n Interpolate commands (δt) between time steps (Δt) based on
each subsequent iteration (Jung and Shing 2007)
Δt Δt
x
t
ni
i
i
d
d
d
1
21
11
...
ti-1 ti ti+1
δtδt = Δt / n
Quadratic Curves
Actual Commands
δt δt δt
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Time Delays Data acquisition and communication
D/A conversion of command signal A/D conversion of measured signals Communication delays
Computer, controller, DAQ system
Computation time Numerical integration strategy Complexity of numerical model
Constant throughout test
0 0.5 1 1.5 2
-1
-0.5
0
0.5
1
Time (sec)
Digital - Analog Conversion
Digital SignalAnalog Signal
Time Lags Finite response time of actuators Control-structure interaction (Dyke et al., 1995)
Dynamic coupling of actuator and specimen
Frequency dependent
Actuator FRF
0 10 20 30 40 500
0.5
1
1.5
Frequency (Hz)
Ma
gn
itud
e
0 10 20 30 40 50
-250
-200
-150
-100
-50
0
Frequency (Hz)
Ph
ase
(d
eg
)
0 10 20 30 40 50-14
-13
-12
-11
-10
Frequency (Hz)
Tim
e la
g (
ms)
Effects of Time Delays and Time Lags
Td
Imposedxm
Commandedxc
MeasuredResponse
ActualResponse
Inaccuracies that propagate throughout experiment Introduces negative damping into system
ceq = -kTd for SDOF Problems arise with
structures with low damping experiments with large hydraulic actuators
t
x
x
R
xcxm
Rm
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
System Modeling in theFrequency Domain Measure frequency response function (FRF) from
command (xc) to measured response (xm) Determine number of poles and zeros based on
theoretical models Create system model to match experimental data
0 10 20 30 40 500
0.5
1
1.5
Ma
gn
itud
e
Frequency (Hz)
ExperimentalModel
0 10 20 30 40 500
0.5
1
1.5
Frequency (Hz)
ExperimentalModel
0 10 20 30 40 500
0.5
1
1.5
Frequency (Hz)
ExperimentalModel
3-Pole Model 4-Pole Model 5-Pole Model
Effect of Actuator Dynamics on RTHT Exact system FRF for SDOF has 2 poles, no zeros
RTHT system FRF includes additional number of poles and zeros equal to the order of the actuator FRF
pexnumpexnumdF KKsCCMssG
2
1
sG
snSS
sdKsCMs
sdsG
xfxu
L
Fxunumnum
xudF 12
Actuator Dynamics
sd
snsG
xu
xuxu
FdKKdCCdM pexnumpexnum
sG
sG
S
SKsCMs
sG
xf
xu
L
Fnumnum
dF
2
1
pexpex
xf kscmssG
2
1Experimental Component
Effect of Actuator Dynamics on RTHT Examine using numerical simulation
SDOF model, 1 Hz natural frequency Exact system: 2 poles
4 pole model of actuator dynamics RTHT system: 6 poles and 4 zeros
Actuator dynamics add negative damping Characterize stability based on structural
damping ζ ζth = 3.54% stability threshold
Structure
k2
m1
k1 c1
FRFζ = 5%
0 1 2 3 4 5 6 7 8 9 1010
-5
10-4
10-3
10-2
10-1
100
Frequency (Hz)
Mag
nitu
de
Exact
RTHT
0 1 2 3 4 5 6 7 8 9 10-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Frequency (Hz)
Pha
se ( )
Exact
RTHT
FRF Magnitude FRF Phase
Negative DampingNegative Damping
ζ = 5% > ζth = 3.54%
Pole-Zero Map ζ = 5%
-250 -200 -150 -100 -50 0-400
-300
-200
-100
0
100
200
300
4000.050.110.180.250.340.48
0.64
0.86
0.050.110.180.250.340.48
0.64
0.86
50
100
150
200
250
300
350
400
50
100
150
200
250
300
350
400
Pole-Zero Map
Real Axis
Imag
inar
y A
xis
Exact
RTHT Pole
RTHT Zero
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0-8
-6
-4
-2
0
2
4
6
80.0040.0090.0140.0210.030.042
0.065
0.14
0.0040.0090.0140.0210.030.042
0.065
0.14
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Pole-Zero Map
Real Axis
Imag
inar
y A
xis
Exact
RTHT Pole
Pole-Zero Map Pole-Zero Map Zoom
Additional RTHT Poles and Zeros
Dominant Poles
ζ = 5% > ζth = 3.54%
Impulse Response ζ = 5%
0 1 2 3 4 5 6 7 8 9 10-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Time (sec)
Dis
p (in
)
Exact
RTHT
Negative Damping
ζ = 5% > ζth = 3.54%
Structure
k2
m1
k1 c1
0 1 2 3 4 5 6 7 8 9 1010
-5
10-4
10-3
10-2
10-1
100
Frequency (Hz)
Mag
nitu
de
Exact
RTHT
0 1 2 3 4 5 6 7 8 9 10-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Frequency (Hz)
Pha
se ( )
Exact
RTHT
FRFζ = 3%
FRF Magnitude FRF Phase
Negative DampingNegative Damping
ζ = 3% < ζth = 3.54%
-250 -200 -150 -100 -50 0 50-400
-300
-200
-100
0
100
200
300
4000.060.130.210.30.40.54
0.7
0.9
0.060.130.210.30.40.54
0.7
0.9
50
100
150
200
250
300
350
400
50
100
150
200
250
300
350
400
Pole-Zero Map
Real Axis
Imag
inar
y A
xis
Exact
RTHT Pole
RTHT Zero
-0.4 -0.2 0 0.2-8
-6
-4
-2
0
2
4
6
80.0060.0130.0210.0320.044
0.065
0.1
0.2
0.0060.0130.0210.0320.044
0.065
0.1
0.2
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Pole-Zero Map
Real Axis
Imag
inar
y A
xis
Exact
RTHT Pole
Pole-Zero Map ζ = 3%
Pole-Zero Map Pole-Zero Map Zoom
Additional RTHT Poles and Zeros
Dominant Poles
ζ = 3% < ζth = 3.54%
0
Impulse Response ζ = 3%
0 1 2 3 4 5 6 7 8 9 10-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Time (sec)
Dis
p (in
)
Exact
RTHT
Negative DampingUnstable Response
ζ = 3% < ζth = 3.54%
Structure
k2
m1
k1 c1
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Delay/Lag Compensation
Td
ti+1 ti+1+Td
x(ti)
x(ti+1)
xm(ti+1)
imposed
current
calculated
Td
ti+1 ti+1+Td
x(ti)
x(ti+1)
xm(ti+1)
imposedxp(ti+1+Td)
current
calculated
predicted
x(ti+1) ≠ xm(ti+1) x(ti+1) ≈ xm(ti+1)
t
x
Uncompensated
t
x
Compensated
Delay/lag compensation is a critical component of RTHT
Traditional Delay/Lag Compensation Delays and lags are combined to create a total
time delay Actuator lags are actually frequency dependent Single delay may be inadequate for MDOF
Actuator FRF with time delay model
0 10 20 30 40 500
0.5
1
1.5
Frequency (Hz)
Ma
gn
itud
e
0 10 20 30 40 50
-250
-200
-150
-100
-50
0
Frequency (Hz)
Ph
ase
(d
eg
)
0 10 20 30 40 50-14
-13
-12
-11
-10
Frequency (Hz)
Tim
e la
g (
ms)
Td
1
Td ≈ 12.5 msec
Response PredictionPolynomial Extrapolation (Horiuchi 1996) Most widely used method Send command based on command desired after Td Predicted displacement based on current and previous
time steps 3rd order provides balance of speed and accuracy Accuracy and stability concern when Td is large
compared to smallest period of structure
xc
Td
x0x1x2x3
x
t
Response PredictionModel Based Can estimate response of system after Td(ω)
based on available system information M, C, K, F Known prior to testing or at onset of experiment
Model may be updated as necessary
Td
1ix1ˆ ix
Δt
1
1
1
i
i
i
R
F
x
1ˆ ixModel-Based
PredictorM, C, K
uncompensated target displacement(initial condition)
restoring forceCompensated target
displacement(send to controller)
ix
ΔtΔtt
input force
Model BasedFeedforward Compensation Open loop compensation Sends a command to test setup that is a best
guess to produce the desired response Ideally completely cancels actuator dynamics No added stability issues
GFF(s) Gxu(s)
Feedforward Experimental Setup
d u x
d≈x
Feedforward Compensation
K
pssG
n
iixu
FF
1
,
n
iixu
n
iixu
nFF
ps
pssG
1,
1,
0 5 10 15 20 25 30 35 40 45 500
0.5
1
1.5
Mag
nitu
de
Experimental
Model
0 5 10 15 20 25 30 35 40 45 50
-200
-100
0
Pha
se (
deg)
0 5 10 15 20 25 30 35 40 45 50-14
-12
-10
Frequency (Hz)
Tim
e la
g (m
s)
Actuator FRF with 3 Pole Model Feedforward FRF
n
iixu
xu
ps
KsG
1,
Not proper system, unstable
Modified inverse dynamics
Proper system, stable, α > 1
Feedforward Numerical Simulation
3 Pole Model of Actuator FRFResponse to Unit
Step Displacement Input
0 20 40 60 80 1000.94
0.96
0.98
1
1.02
1.04
1.06
Frequency (Hz)
Ma
gn
itud
e
Gxu
GFF
GxFFu
0 0.01 0.02 0.03 0.04 0.05 0.060
0.2
0.4
0.6
0.8
1
1.2
Time (sec)
Dis
pla
cem
en
t (in
)
Without FFWith FF
Feedback Compensation Closed loop compensation Error between desired and measured displacement used
to modify command Minimize e = d - x
Example controller is GFB(s) = KFB
Slower than feedforward compensation Not effective at reducing actuator lag
GFB(s) Gxu(s)
Feedback Experimental System
xd uFB
+-
+
+e u
d
x
d≈x
Combined Feedfoward and Feedback Compensation Feedforward controller ideally cancels actuator dynamics Feedback controller eliminates errors due to
Inaccuracies in modeling of feedforward controller Added dynamics to make feedforward controller stable Changes in specimen during experiment
GFB(s) Gxu(s)
GFF(s)
Feedforward
Feedback Experimental System
xd
uFF
uFB
+-
+
+e u
x
d≈x
Experimental Comparison of Delay Compensation Methods
0.00
0.25
0.50
0 5 10 15
Frequency (Hz)
Err
or
no
rm
No Delay Comp.Pol. ExtrapolationModel Based 0.00
0.25
0.50
0 5 10 15 20
Frequency (Hz)
Err
or
no
rm
Pol. Extrapolation
Model Based
(Carrion, 2007)
Linear Ky/Ke = 1.0 Nonlinear Ky/Ke = 0.02
SDOF System ζ = 2%, CDM, 2δt = Δt = 0.0062 sec
Model based approach allows testing of structure with twice the natural frequency as polynomial extraction
Structure
k2
m1
k1 c1
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Real-Time Hybrid Testing Applications
Experimental Substructure
DamperActuator
Dampers
Base Isolation Devices
m2
m1
k1
k2
Numerical Substructure
Numerical Substructure
m2
m1
k1
k2
gx
Structure
k1
k2
m1
m2
gx
Structure
k1
k2
m1
m2
gx
Actuator
Gravity load
Base Isolation Device
Experimental Substructure
Presentation Outline Introduction and Motivation Numerical Integration Schemes Errors in Hybrid Testing Variations of Hybrid Testing Real-Time Hybrid Testing
Basics Time Delays and Time Lags System Modeling Compensation Techniques Applications
Conclusions
Conclusions Hybrid testing is an appealing structural testing method
Similar equipment as quasi-static testing Time scale may be extended
Substructuring Facilitates full-scale testing
Real-Time Hybrid Testing Accurately test rate dependent components Time delays and lags can undermine experiment Model based compensation techniques are a powerful
alternative
Acknowledgements Dr. B.F. Spencer and Dr. J. Carrion for their
advice and support Dr. C.B. Yun for his invitation to provide a lecture
for the APSS program. 감사합니다 !
This material is based upon work supported under a National Science Foundation Graduate Research Fellowship.Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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