COMMISSION OF THE EUROPEAN COMMUNITIES
FP7- INFRASTRUCTURES-2008-1
SP4-Capacities
SERIES
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES
FOR EUROPEAN SYNERGIES
Geographically distributed continuous hybrid
simulation tests using shaking tables
Ferran Obón Santacana
Uwe E. Dorka
Universität Kassel (UNIKA)
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
Overview
1. Dorka’s substructure algorithm
2. Adapting the algorithm
3. Test set-up and numerical models.
4. Evaluation of the control of the actuators
5. Tests using OpenFresco.
6. Tests using NSEP protocol.
7. Comparison of protocols.
8. Numerical tests with Celestina
9. Large numerical models
10. Conclusions
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s substructure algorithm
Basics of substructure testing:
•Substructure testing is a numerical time integration
process including restoring forces measured as response
from one or several substructures.
•No iterative solver can be used in this process.
•A method is required with unconditional numerical
stability and high accuracy.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s substructure algorithm
Any time integration scheme can be derived from time discretisation:
Dynamic equilibrium:
With
M
d2
dt 2
u(t )  C dtd u(t )  Ku (t )  f l (t )  f r (t )  f c (t )
fr: vector of numerical nonlinear restoring forces
fc : vector of restoring forces measured at the interface between
numerical model and tested substructure
Shape functions to discretise the displacements over 3 steps in time:
N i 1   1    / 2
N i  1   1   
N i 1   1    / 2
with:
  t / t
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s substructure algorithm
and using a weighted residual approach:
weighting function W:



 d
 M u i 1 d 2 N i 1  u i d 2 N i  u i 1 d 2 N i 1
dt
dt
dt

1
 C u i 1 dtd N i 1  u i dtd N i  u i 1 dtd N i 1
1W  K u i 1 N  u i N  u i 1 N

i 1
n
i 1

i 1
i
i 1
 f* N i 1  f* N i  f* N i 1
2
2



f*  f l  f c  f r
1
   W   12 d
1
1
  W
1
2
1
 Wd ;
1
1
1
2
1   d  Wd ;
1




SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s substructure algorithm
leads to a 3-point recurrence scheme:

u i 1  M  tC   t 2 K


1

 2 M  1  2 tC   12  2    t 2 K u i 


2
i 1
1

 M  1   tC   2     t K u 



2 i 1
2 i
1
  t f*   2  2    t f*

 1

2 i 1








t
f


*
 2




with:
u0

i 1

 M  tC   t K
2

1
u i 1  u0i 1  G f ri 1  f ci 1


 2 M  1  2 tC   12  2    t 2 K u i 


2
i 1
1

 M  1   tC   2     t K u 



2 i 1
2 i
1
  t f l   2  2    t f*

 1

2 i 1








t
f


*
 2


Every time integration
algorithm is a linear control
equation within each time step
that has an initial value u0 and a
constant gain G:


G  t 2 M  tC  t 2 K

1

SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s Substructure Algorithm
Performance of various time integration schemes:
Period elongation
Numerical damping
Any of those can be used in Dorka algorithm but the unconditionally stable
Newmark scheme without numerical damping yields the best results!
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
1. Dorka’s substructure algorithm
•
•
Sub-stepping avoids iteration within the
time step and allows the actuators to run
continuously.
If any equilibrium error occurs at the
end of the time step it can be
compensated.

u i 1  u0i 1  G f ri 1  f c
i 1
new load and error compensation:
f*i  f l i  f ei  f ri  f ci
initialization with new u0
i 1
j =1
apply displacement at each sub-step:
j
i
i 1 j
u  u0 (1  )  u0 ( )  G f r  f c 
k
k

calculate
fr
measure f s
i=i+1
yes: j = j + 1
j<k
error force
compensation
no
time derivatives of shape functions give:
i 1
d
i 1
d2
; dt
2 u
dt
u
error force:
fu
i 1
 (M
 fl
d2
dt 2
i 1
 f ri 1  f ci 1
u i 1  C
d
dt
u i 1  Ku i 1 )
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
2. Adapting the algorithm
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
2. Adapting the algorithm
•

u i 1  u0i 1  G f ri 1  f c
i 1

•
•
•
•
Only a portion of the G matrix has to be
exchanged between facilities.
The communication is performed at the
step level.
If there are multiple facilities with
several sub-structures the
communication must be done at the
sub-step level if there is a strong
influence between the coupling nodes.
The network speed is unreliable.
Special treatment of the actuators has
been considered:
•
•
The actuators will continue with the
ramp function at the end of the sub-step.
The actuators will stop in case data is not
received for several steps.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
3. Test set-up and numerical modelling
•
Experiments performed:
•
•
•
Protocols:
•
•
Model used as a benchmark of a
steel frame.
Evaluation of the control of the
actuators. Purely numerical with
empty cylinders.
Sub-structure test with a single Degree
of Freedom (DOF) and the UHYDEfbr device.
OpenFresco.
Platform for Networked Structural
Experiment (PNSE).
Model used for testing.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
3. Test set-up and numerical modelling
Fixed TMD.
The friction device was active and
with the springs they provided the
necessary force to stabilise the test.
There were no velocity dependant
forces.
•
•
•
Coupling Force. Pressure drop (0.25 bar to 0.1 bar)
2000
1500
Shaking table with UHYDE-fbr and fixed TMD.
•
The UHYDE-fbr operates through
solid friction.
The hysteresis loops can be varied by
changing the air pressure.
Coupling Force [N]
•
UHYDE-fbr
[9]
1000
500
0
-500
-1000
-1500
-2000
-2500
-0.03
-0.02
-0.01
0
Displacement [m]
0.01
0.02
0.03
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
4. Evaluation of the control of the actuators
Accuracy of the actuators
20
Control value
Measured
15
Continuous tests performed
with HYSTEC using
OpenFresco and an empty
cylinder. Scale factor of 200.
10
0
-5
-10
-15
-20
Accuracy of the actuators
2
-25
-30
0
2000
4000
6000
8000
10000
1
Number of substeps
Due to reduced P the
actuators present error
in the positioning.
Phase lag is important
Displacement [mm]
Displacement [mm]
5
12000
14000
Control value
Measured
16000
0
-1
-2
-3
1
1.1
1.2
1.3
Number of substeps
1.4
1.5
1.6
4
x 10
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
5. Tests using OpenFresco
•
•
•
•
•
Adwin Pro II
Another
experimental
control
facility was designed by Andreas
Schellenberg as a request from
UNIKA.
It does not assume any controller
and bridges the communication
between OpenFresco and the
control hardware using predefined
messages over TCP/IP.
The speed limit with University of
Oxford was 200 ms/step (scale
factor of 20, RTT = 0.036 s).
The speed limit with U. California,
Berkeley, was 1 s/step (scale factor
of 100, RTT = 0.2 s)
Although
the
communication
stopped at one point, there were no
effects on the test.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
5. Tests using OpenFresco
Displacement of the cylinder. Constant Pressure 0.25 bar.
Displacement of the cylinder. Pressure drop (0.25 bar to 0.1 bar)
0.03
0.03
Measured displacement
Control displacement
(Numerical value)
0.02
0.02
0.01
0.01
Displacement [m]
Displacement [m]
Measured displacement
Control displacement
(Numerical value)
0
0
-0.01
-0.01
-0.02
-0.02
-0.03
0
1000
2000
3000
4000
Number of substeps
5000
6000
-0.03
7000
0
1000
1500
1500
1000
1000
500
500
Coupling Force [N]
Coupling force [N]
2000
0
-500
-1500
-1500
-2000
-2000
0
Displacement [m]
0.01
6000
7000
-500
-1000
-0.01
5000
0
-1000
-0.02
3000
4000
Number of substeps
Coupling Force. Pressure drop (0.25 bar to 0.1 bar)
Coupling force. Constant pressure 0.25 bar.
2000
-2500
-0.03
2000
0.02
0.03
-2500
-0.03
-0.02
-0.01
0
Displacement [m]
0.01
0.02
0.03
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
6. Tests using NSEP protocol
• The
same
test
was
performed for comparison.
• The new version of the
NSEP protocol (NSEPv2)
was used.
• It required single-precision
for exchanging data.
• The time step was always 2s
without considering the
proximity of the facility.
• This could be due to
limitations in the NSEP
server
running
under
Windows 7.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
6. Tests using NSEP protocol
Displacement of the cylinder. Pressure drop (0.25 bar to 0.1 bar)
Displacement offf the cylinder. Constant pressure 0.25 bar.
0.03
0.03
Measured displacement
Control displacement
(Numerical value)
0.02
0.02
0.01
0.01
Displacement [m]
Displacement [m]
Measured displacement
Control displacement
(Numerical value)
0
0
-0.01
-0.01
-0.02
-0.02
-0.03
-0.03
0
1000
2000
3000
4000
Number of substeps
5000
6000
7000
0
1000
2000
1500
1500
1000
1000
500
500
0
-500
-1500
-1500
-0.01
0
Displacement [m]
0.01
6000
7000
-500
-1000
-0.02
5000
0
-1000
-2000
-0.03
3000
4000
Number of substeps
Couplint Force. Pressure drop (0.25 bar to 0.1 bar)
2000
Coupling Force [N]
Coupling Force [N]
Coupling Force. Constant pressure 0.25 bar.
2000
0.02
0.03
-2000
-0.03
-0.02
-0.01
0
Displacement [m]
0.01
0.02
0.03
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
7. Comparison of the protocols:
OpenFresco vs. NSEPv2
Comparison of protocols
0.03
OpenFresco
NSEPv2
0.02
Displacement [m]
0.01
0
-0.01
-0.02
-0.03
0
1000
2000
3000
4000
Number of substeps
5000
6000
7000
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
8. Numerical tests with Celestina
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
9. Large numerical models
•
•
•
•
Large numerical models where tested.
The UHYDE-fbr was used as a non-linear
substructure.
256 cores where used in the Linux Cluster. Intel
MKL libraries
4 cores where used in the regular desktop (Core
i5). OpenBLAS libraries / With optimizations.
Size
Complex models
(METU)
1000 DOFs
Time per iteration
Regular Desktop
Linux Cluster
0.7 ms
-
10000 DOFs
200 ms /43 ms
87 ms
50000 DOFs
Not possible
450 ms
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
10. Conclusions
Dorka’s sub-structure algorithm allows performing geographically continuous
distributed testing with different protools:
•
The tests could be performed with a time scale factor of 100 with U. California, Berkeley
(USA), 20 with U. Oxford (UK) and 200 with HYSTEC (S. Korea) using OpenFresco
A time scale factor of 200 using PNSE with NCREE (Taiwan) and U. Oxford (UK).
Celestina (Purely numerical)
•
•
•
Since the actuators run continuously updating must be performed between no-more
than three sub-steps.
As a rule of thumb, the speed of the test (step time) can be set to:
•
•
Step Time 
•
0.8
Special attention has to be paid when considering multiple sub-structures that are not
located at the same laboratory.
•
•
•
nSubsteps * Average Round Trip Time
The communication has to be performed at the sub-step level when there is a strong
influence between the sub-structures.
Multi-protocol, multi-site testing. This is the next step.
The algorithm allows performing sub-structure tests with large numerical models in
combination of supercomputers/regular desktop computers (10.000 DOF in 0.087
s/step or 43 ms/step with optimizations).
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
Acknowledgements
Special thanks go to:
1. University of California, Berkeley: Stephen A. Mahin, Andreas Schellenberg and
Selim Gunay.
2. HYSTEC: Chul-Young Kim and Dae-Sung Jung.
3. NCREE: Keh-Chyuan Tsai and Kung-Juin Wang.
4. University of Oxford: Tony Blakeborough and Ignacio Lamata.
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
Thank you
for your attention!