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UNIVERSITY OF OXFORDDEPARTMENT OF ENGINEERING SCIENCE
Hybrid TestingSimulating Dynamic Structures in the Laboratory
Tony Blakeborough and Martin Williams
SECED Evening Meeting
28 January 2009
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Outline
Introduction Dynamic test methods – why do we need new ones?
The real-time hybrid method Displacement-controlled tests Testing strategy and equipment Numerical integration schemes Compensation for transfer system dynamics
Recent developments and applications Tests under force control Crowd-structure interaction Distributed hybrid testing in the UK-NEES project
Conclusions
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Acknowledgements
Numerous colleagues contributed to the work described here, particularly:
Current researchers: Mobin Ojaghi, Ignacio Lamata Past researchers: Antony Darby, Paul Bonnet, Kashif Saleem, Javier
Parra Collaborators at Bristol, Cambridge, Berkeley, JRC Ispra
We have received financial support from: EPSRC The Leverhulme Trust The European Commission Royal Academy of Engineering Instron
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Testing methods in earthquake engineering
Shaking tables – apply prescribed base motion to models Can accurately reproduce earthquake input Normally limited to small-scale models – expensive at large scale Scaling problems (physical and time) Control problems
SUNY Buffalo Bristol University
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Testing methods (cont.)
Pseudo-dynamic test facilities: Slow test, with inertia and damping components modelled
numerically, stiffness forces fed back from test specimen Can be conducted at large scale Best suited to flexible structures with concentrated masses Expanded timescale can’t capture rate effects Feedback loop can cause errors to accumulate
JRC Ispra
Lehigh University
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Future trends
Major upgrading initiatives, e.g. NEES (USA), E-Defense (Japan)
Very large shaking tables
Enhancements to pseudo-dynamic methods: Effective force testing
Real-time hybrid testing
Distributed hybrid testing
San Diego outdoor shaking table
Minnesota EFT facility
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E-Defense, Japan
1200 tonne payload amax = 1.5 g, vmax = 2 m/s, umax = 1 m
24 x 450 tonne actuators 15,000 l/min oil flow rates
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Real-time hybrid testing
d0(t)
d1(t)
d1(t) – d0(t)
dg(t)
FL(t) FR(t)
FD(t)
dg(t)
Emulated system:
Numerical substructure:
Physical substructure:
Ground displacement
Forces fed back from physical substructure
Computed displacements
Displacement applied by actuator
Displacements
Forces
Dissipator
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Real-time hybrid testing
Advantages: Avoids physical scaling problems Avoids time scaling problems Ideal for testing rate-dependent systems Economical – only the key parts need to be modelled physically Now being strongly pursued by NSF NEES programme
Needs: High-performance hardware and communications Fast solution of numerical substructure Compensation of transfer system dynamics
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Typical test set-up
Real-time PC
dSpaceboard Proprietary
controller
Monitoring PC
Actuator 1 Actuator 2
Command GPIB interface
Command
Feedback
FeedbackCommand
Feedback
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Structural Dynamics Lab
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Structural Dynamics Lab @ Oxford
Hydraulic installation
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The Flight Deck
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Typical real-time control loop
Dual time-stepping implementation: Numerical model runs at main steps ~ 10 ms Controller runs at sub-steps ~ 0.2 ms
Imperfect transfer system dynamics cause: Errors in timing and amplitude of applied loads Inaccuracy and/or instability of test
Numerical substructure
Outer-loop compensation
Inner-loop (proprietary)
controller
Servo-hydraulic actuator
Physical substructure
Force feedback
Displacement feedback
Transfer system
Input load
dcom dactddes
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Typical test strategy
1. Solve numerical substructure to give desired actuator displacement at the next main step,
2. Curve fit to the current and the past few displacement points.
3. Use curve fit to extrapolate forward by a time equal to the estimated actuator delay, to give the command displacement,
4. Use same curve fit to interpolate dcom values at sub-steps.
Send to the inner loop controller, together with the current actuator position dact
5. Repeat step 4 at sub-steps, until the next main step.
1des
nd
1com
nd
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Numerical integration schemes
We require: Very fast solution of numerical substructure (~10 ms) Accuracy, stability, ability to model non-linear response
Explicit integration (e.g. Newmark’s method) All required data known at start of timestep Quick, sufficiently accurate Need short timestep for stability
Implicit integration (e.g. constant average acceleration method) Requires knowledge of states at end of timestep, therefore iteration (or sub-
step feedback) Unconditionally stable
Two-step methods (e.g. operator-splitting) Explicit predictor step, implicit corrector
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Test system
Simple mass-spring system
All springs in numerical model have bi-linear properties
Increase DOFs in numerical model to test algorithms
Physical substructure Numerical substructure – n-DOF
Base motion
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10-DOF numerical substructure
Sine sweep input through several resonances
5 ms main-step
0.2 ms sub-step
Red = numerical simulation
Blue = hybrid test
Exp
licit
Tw
o-st
ep m
etho
dsIm
plic
it
Results
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In frequency domain
10-DOF numerical substructure
Sine sweep input through several resonances
5 ms main-step
0.2 ms sub-step
Red = numerical simulation
Blue = hybrid test
Exp
licit
Tw
o-st
ep m
etho
dsIm
plic
it
Results
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50-DOF numerical substructure
Sine sweep input through several resonances
25 ms main-step (15 ms Newmark)
0.2 ms sub-step
Implicit schemes unable to compute in real time
Red = numerical simulation
Blue = hybrid test
Exp
licit
Tw
o-st
ep m
etho
ds
Results
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50-DOF numerical substructure
Sine sweep input through several resonances
25 ms main-step (15 ms Newmark)
0.2 ms sub-step
Implicit schemes unable to compute in real time
Red = numerical simulation
Blue = hybrid test
Exp
licit
Tw
o-st
ep m
etho
ds
Results
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Actuator dynamics
Both timing and amplitude errors exist, and may vary during test
Delay of the order of 5 ms is unavoidable
Delay has an effect similar to negative damping instability
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Compensation schemes
Two components:
Forward prediction scheme Aims to compensate for known or estimated errors through scaling
and extrapolation Exact polynomial extrapolation Least squares polynomial extrapolation Linearly extrapolated acceleration Laguerre extrapolator
Delay estimation Delay and amplitude error estimates are updated as test proceeds
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Validation experiments – Test A
Linear, 2DOF system, single actuator
m2 m1
Base motion
m2 m1Feedback force Actuator
Emulated system
Numerical: Physical:
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Test B
Non-linear, 2DOF system, single actuator
m2 m1
Base motion
m2 m1F
Emulated system
Numerical: Physical:
Gapnon-linearity
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Test C
Linear, 3DOF system, two actuators
Asynchronous input motions, stiff coupling
m3 m2g2
m3
m2
F2
Emulated system
Numerical:
Physical:
m1g1
g2 m1F1
Numerical:
g1
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Effect of forward prediction
Test A, with fixed delay estimate, exact polynomial extrapolation
Hybrid test
Analytical response
Synchronization plots:
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Comparison of forward prediction schemes
RMS errors (%) over a test with constant delay and amplitude error estimates
Test A Test B Test C Test C
Act#1 Act#2
No compensation unstable unstable unstable unstable
Exact extrapolation 1.8 1.5 2.9 2.5
Least squares extrapolator 1.9 2.0 - -
Linear acceleration 1.9 1.6 3.4 2.7
Laguerre extrapolator 1.8 1.7 unstable unstable
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Delay updating results
Delay estimates produced by updating scheme in Test C:
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Effect of delay updating
RMS errors (%) over a test with with third order exact extrapolation
Tests A and B used 0.5 ms sub-steps
Test C used 0.2 ms sub-steps
Test A Test B Test C Test C
Act#1 Act#2
No update 1.8 1.5 2.9 2.5
With updating scheme 0.9 1.1 2.3 1.8
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Developments and applications
Tests under force control Dorka and Jarret Damper Crowd-structure interaction Grandstand simulation rig Distributed hybrid testing Oxford-Bristol-Cambridge
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EU NEFOREE project comparison of testing methods
8630kg mass
3m
3m
Single storey test building designed by Prof Bursi at Trento
Parallel tests on shaking table, reaction wall and real time hybrid substructuring
Two dissipative devices to be tested - Dorka shear device and Jarret dampers
Natural frequency Unbraced 2.6Hz 2% damping Braced 8.6Hz 5% damping (Dorka)
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Seismic testing of dampers
NEFOREE – EU study
Shaking table set-up (elevation)
Hybrid test of device
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Dorka and Jarret devices
Dorka shear panel: shear diaphragm in SHS - hysteretic damping
Jarret dampers: Non-linear visco-elastic devices
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Control problems
Two actuators – equal but opposite forces Dorka cell - very stiff specimen Significant rig/specimen interaction LVDT noise 30m rms produced significant forces Not possible to run under displacement control
Run test in force-control Two MCS controllers – one for magnitude and other
for force imbalance Displacement feedback into numerical model
Solution
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Force control loop
Physical substructure
Measure deformation of test specimen
Numerical substructure
Apply measured displacements to
numerical substructure
External earthquake loads
Command actuators to apply forces to
physical substructure
Calculate forcesat interface between physical and numerical substructures
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Numerical substructure
Massm
Columns - kc
x
Damper -
Braces - kb
F
gx
g
ubbb
xx
xc
x
x
00
1
01
2 222
g
ubub
xm
x
xm
x
F
00
0
10
0 2222
8630kg mass
3m
3m
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Earthquake records
0 2 4 6 8 10 12 14 16 18 20-1
-0.5
0
0.5
1
Time(s)N
orm
alis
ed a
ccel
erat
ion
0 1 2 3 4 5 6 7 8 9 10-1
-0.5
0
0.5
1
Time(s)
Nor
mal
ised
acc
eler
atio
n
El Centro
Synthesised
EC8 record
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Response of Dorka device (El Centro 0.2g)
0 5 10 15 20 25-12
-10
-8
-6
-4
-2
0
2
4
6
8
Time (s)
Forc
e (k
N)
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Detail - EC8 synthesised earthquake tests
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8-15
-10
-5
0
5
10
Time (s)
For
ce (
kN)
Force demand
Measured force
Error
3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
-60
-40
-20
0
20
40
60
Time (s)
For
ce (
kN)
Force demand
Measured force
Error
0.2g pga
1.2g pga
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Specimen hysteresis curves
-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-15
-10
-5
0
5
10
15
Specimen displacement (mm)
Spe
cim
en f
orce
(kN
)
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-40
-30
-20
-10
0
10
20
30
40
50
Specimen displacement (mm)S
peci
men
for
ce (
kN)
EC8 0.2g EC8 0.6g
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Large hysteresis loops
-1.5 -1 -0.5 0 0.5 1 1.5 2-60
-40
-20
0
20
40
60
Specimen displacement (mm)
Spe
cim
en f
orce
(kN
)
-3 -2 -1 0 1 2 3 4-80
-60
-40
-20
0
20
40
60
80
Specimen displacement (mm)
Spe
cim
en f
orce
(kN
)
EC8 0.9g EC8 1.2g
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Conclusions – Dorka device
Real time hybrid tests successful Simulated behaviour in 8Hz frame with 5% damping Stiff specimen required force feedback loop Device robust enough for use
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Jarret devices
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Response to square wave input
1.8 2 2.2 2.4 2.6 2.8
-4
-2
0
2
4
6
8
Time (s)
For
ce (
kN)
Brace demand
Measured force
Error
-2 -1 0 1-10
-5
0
5
10
Specimen displacement (mm)
Spe
cim
en f
orce
(kN
)
-100 -50 0 50 100-10
-5
0
5
10
Specimen velocity (mm/s)
Spe
cim
en f
orce
(kN
)
0.15g alternating sign (square wave) ground acceleration of period 2s
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Response of Jarret devices
3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8
-5
0
5
Time (s)
For
ce (
kN)
Force demand
Measured force
ErrorEl Centro record with a pga of 0.2g around the peak at 3.3s
21 21.5 22 22.5 23
-2
-1
0
1
2
Time (s)
For
ce (
kN)
Force demand
Measured force
Error
.... and at end of record
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Response of Jarret devices
0 5 10 15
-20
-10
0
10
20
Time (s)
Forc
e (
kN
)
Force demand
Measured force
Error
0 5 10 15-6
-4
-2
0
2
4
6
Time (s)
Dis
pla
cem
ent
(mm
)
Force & displacement response of to the EC8 record with a pga of 0.6g
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Response of Jarret devices
-10
0
10-200 -150 -100 -50 0 50 100 150 200
-15
-10
-5
0
5
10
15
20
Displacement (mm)
Velocity (mm/s)
For
ce (
kN)
Force against displacement and velocity for the EC8 record with a pga of 0.6g
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Response of Jarret devices
-10
-5
0
5
10-200 -150 -100 -50 0 50 100 150 200
-15
-10
-5
0
5
10
15
20
Velocity (mm/s)
Displacement (mm)
For
ce (
kN)
-6 -4 -2 0 2 4 6
-200
0
200
-15
-10
-5
0
5
10
15
20
Velocity (mm/s)Displacement (mm)
For
ce (
kN)
EC8 record with a pga of 0.6g
Velocity projection Displacement projection
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Conclusions – Jarret device
Tests successfully completed Realistic tests at low velocities Problems at higher velocities due to extreme non-linear
response in velocity Student just starting work on this – possibly use
velocity feedback with improved displacement measurements
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Human-structure interaction in grandstands
EPSRC funded studyRA – Anthony Comer
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Grandstand rig
15-seater grandstand rig
Standard design – typical rake & seat distances
Test crowd coordination
Effect of grandstand movement on coordination
Simulate various natural frequencies and mass ratios
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Grandstand rig design
Aluminium alloy fabricated rakers and stretchers
Light & stiff – lowest internal natural frequency >30Hz
Air spring at each corner to take out mean load
Electro-mechanical actuator at each corner to control rig
Load cell under each spectator
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Control problems
Force feedback from load cells at actuators suffered large levels of interference from e/m fields emitted by motors
Filtering would introduce too much lag for stability
Digital displacement feedback available from linear encoders (resolution 3μm) immune from e-m interference
Use force control with displacement feedback
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Control strategy
Three significant degrees of freedom Heave (vertical displacement) Roll Pitch
Feedforward Measure loads applied by ‘spectators’ Resolve into resultant vertical load and roll & pitch moments Apply equivalent forces at actuators to balance force resultants and
keep rig stationary
Numerical model Simulate vertical and rotational damped springs numerically to
control dynamics of grandstand Apply a proportion of vertical resultant load to excite the rig
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Response to 130kg male jumping
40 45 50 55-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Time (s)
Forc
e r
esultant
Vertical force (N)
Pitch moment (Nm)
Roll moment (Nm)
40 45 50 55-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time (s)
Equiv
ale
nt
dis
pla
cem
ent
(mm
)
Vertical
Pitch
Roll
Vertical response only
Rotations successfully tared off
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Conclusions – grandstand simulation
Controlled tests possible on grandstand with spectators jumping and bobbing
Can also be used to wobble seated and standing spectators to assess the acceptability of motion (main dynamic use in project)
Can be used to simulate human-structure interaction
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Split-site testing – hybrid testing over the internet
Numerical and physical substructures at separate locations
Possibility of testing very large components
Possible only over the internet
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Network architecture
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JANET internet route
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Communication interruptions
JANET delays
~10ms - OK
Inconsistency causes problems
Solution Use UK-light –
a dedicated link
0 1 2 3 4 5 6 7 8 9 10-6
-4
-2
0
2
4
6sine 5mm command to bristol rig from oxford
time (s)
disp
lace
men
t (m
m)
achieved bristol (measured ox)
command oxford
0 1 2 3 4 5 6 7 8 9 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35network "delay" sine 5mm command to bristol rig from oxford
time (s)
Del
ay (
s)
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Oxford-Bristol test
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Results of test on Monday
0 5 10 15 20 25
-15
-10
-5
0
5
10
15
time s
disp
lace
men
t m
m
Achieved displacements
achieved bris(ox)floor 1
achieved oxford floor 2achieved oxford floor 3
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Limitations
Physical substructure Limits set by equipment Response times of actuators Control problems at limits of actuator capacity Stiffness of frames
Reduce uncertainty Proof testing (strength/performance guarantee) Check individual items Assess design under realistic loading Validate computer models used in design
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Architecture of 3 site test – radial model
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State of work in split site testing
Ethernet not a problem provided use a dedicated link
Tests possible and seem to work
Future work Increase natural frequencies of systems – currently “3Hz but up to 10
should be possible Investigate different interconnection links
At moment there is a central numerical model with physical sites as servers at end of radial spokes – other arrangements are possible
Investigate force control Extend to the rest of the world – planning links with EU in FP7
research
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Conclusions
Simulation of real time behaviour It works for ‘stiffness’ and ‘rate dependent’ components Reproduces rate/time dependent effects Useful for more realistic component testing Allows devices to be checked in much more arduous circumstances Copes with non-linear behaviour in both physical and numerical
substructures
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General conclusions
What test at all? Reduce uncertainty
Proof testing (strength/performance guarantee) Check individual items Assess design under more realistic loading Validate computer models used in design
Challenging activity
Push current control techniques and test equipment to limits Trickle down effect – improved techniques help standard testing