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Ph.D. candidate: Giuseppe Abbiati
Advisor: Prof. Oreste S. Bursi
“Dynamic substructuring of complex hybrid systems based on time-integration, model reduction and
model identification techniques”
Doctoral School in:“Engineering of Civil and Mechanical Structural Systems”
26th cycle
Department of Civil, Environment and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123, Trento, Italy.
7/10/2014Page 1
NU
ME
RIC
AL
SID
E
Delay compensator
Transfer system:Actuators, controllers etc..
Filters
Sensors:Load cells etc..
Physical Substructure (PS)
Numerical Substructure (NS)
EX
PE
RIM
EN
TAL
SID
Enf
7/10/2014Page 2
Hybrid system/Hardware-in-the-loop simulator
[ ]nd m[ ]nr N
TIM
E IN
TE
GR
AT
ION
LO
OP
for
n=1:
1:st
epsExternal loading
- The remaining structure is computed analytically
- Critical non-linear parts are tested in laboratory
Physical piers-CRITICAL PARTS-
Numerical deck and piers
Civil eng. application of hybrid simul.: a RC bridge
Hybridsystem
NS
PS
7/10/2014Page 4
Mech. eng. application of hybrid simul.: a piping system
Physical pipingbranch
-CRITICAL PARTS-
Numerical piping branch
Hybridsystem
NS
PS
7/10/2014Page 5
State of the art limitations in hybrid simulation
• PARTITIONED TIME INTEGRATION APPROACH APPLIED TO A REALISTIC CASE STUDY WITH COMPLEX NSs;
• MODEL UPDATING OF THE NS BASED ON THE RESPONSE OF A DIFFERENT PS SUBJECTED TO DIFFERENT LOADING;
• SIMULATION OF A HYBRID SYSTEM CHARACTERIZED BY A DISTRIBUTED PARAMETER PSs WITH DISTRIBUTED LOADING;
State of the art limit.: time integration
Experimental time [s]
Monolithic time integration
= testing time scale= integration time step, = controller time step,
NS response
PARTITIONED TIME INTEGRATION APPROACH APPLIED TO A REALISTIC CASE STUDY WITH COMPLEX NSs
Experimental time [s]
Partitioned time integration
NS response
7/10/2014Page 7
On-line model updating, Bouc-Wen model, Unscented Kalman filter
State of the art limit.: model updating of NSs
MODEL UPDATING OF THE NS BASED ON THE RESPONSE OF A DIFFERENT PS SUBJECTED TO DIFFERENT LOADING
NSPS
7/10/2014Page 8
State of the art limit.: distributed parameters PSs
SIMULATION OF A HYBRID SYSTEM CHARACTERIZED BY A DISTRIBUTED PARAMETER PSs WITH DISTRIBUTED LOADING
PS
= inertial seismic loading
• HYBRID SIMULATION OF THE RIO TORTO BRIDGE
• HYBRID SIMULATION OF AN INDUSTRIAL PIPING SYSTEM
Outline
7/10/2014Page 9
7/10/2014Page 10
Rio Torto Bridge: innovative contributions
• Application of the partitioned time integration approach, which allowed for the simulation of nonlinear NSs;
• model updating of NSs -numerical piers- based on the response of PSs -physical piers-.
7/10/2014Page 11
• Application of model reduction techniques to handle the PS and to simulate a distributed seismic loading.
The piping system: innovative contributions
PS
HYBRID SIMULATION OF THE RIO TORTO BRIDGE
7/10/2014Page 12
RC bridge with plain rebars, structural assessment, seismic retrofitting, hybrid simulation
THE RIO TORTO BRIDGE CASE STUDY
7/10/2014Page 13
7/10/2014Page 14
MAIN DIMENSIONS OF THE BRIDGE
• Total span = 412 m
• Single span = 33 m
• Taller pier height = 41.50 m, Pier #7
• Shorter pier height = 14.00 m, Pier #12
7/10/2014Page 15
2 x 12 Friction Pendulum Bearing (FPB) isolation device
TRANSVERSAL SEISMIC LOADING
PROPOSED SEISMIC RETROFITTING SCHEME
PHYSICAL SUBSTRUCTURES
(2 Piers + FPB isolation devices)
NUMERICAL SUBSTRUCTURES
7/10/2014Page 16
SUBSTRUCTURING SCHEME FOR TESTING PURPOSES
Gerber saddles (removed in the isolated case)
Bologna Firenze
About 900 Degrees-of-Freedom (DoFs)
Element types:
• nonlinearBeamColumn for piers
• elasticBeamColumn for the deck
7/10/2014Page 17
THE OPENSEES REFERENCE MODEL (RM) OF THE BRIDGE
Bologna Firenze
Materials:
• Kent-Scott-Park model for concrete (Concrete01)
• Menegotto-Pinto model for rebars (Steel02)
• Nonlinear shear behaviour of transverse beam (hysteretic)
singleFPBearing elements with a
Coulomb frictionModel.
Gerber saddles (removed in the isolated case)
7/10/2014Page 18
THE OPENSEES REFERENCE MODEL (RM) OF THE BRIDGE
Hysteretic loops of Pier #11 in the non-isolated case
7/10/2014Page 19
HYSTERETIC RESPONSES OF OPENSEES PIERS
NONLINEAR NUMERICAL PIERS WERE NEEDED !!!
SLS ULS
-0.06 +0.06 -0.20 +0.20
PHYSICAL SUBSTRUCTURES
(2 Piers + FPB isolation devices)
NUMERICAL SUBSTRUCTURES
SUBSTRUCTURING REQUIREMENTS
7/10/2014Page 20
7/10/2014Page 21
OPENSEES FIBER-BASED FE MODEL:
- CONVERGENCE IS NOT ENSURED;
- HIGH VARIANCE OF SINGLE STEP SOLVING TIME (NON-
DETERMINISTIC).
FROM THE HYBRID SIMULATION PERSPECTIVE:
- TEST CAN FAIL;
- ACTUATORS CAN STOP UNTIL THE NUMERICAL PART IS
SOLVED (MATERIAL RELAXATION IN THE PS)
SUBSTRUCTURING REQUIREMENTS
REDUCED NONLINEAR NUMERICAL PIERS WERE NEEDED !!!
7/10/2014Page 22
DYNAMIC SUBSTRUCTURING OF OPENSEES MODELS
Substructuring scheme and subparts
DECK: LINEAR
PIERS: LINEAR/NONLINEAR
ISOLATORS: NONLINEAR
Pier #9CONSTRAINT MODE
CONSTRAINT MODES: static deformation shapesowing to unit displacements applied to boundaryDoFs, one by one, whilst the others retained
7/10/2014Page 23
, ,T T Tk m f= = =Τ KT T MT T ML
RR
L
= = ⋅
xx T x
x
DYNAMIC SUBSTRUCTURING OF OPENSEES PIERS
GUYAN static condensation:
XR
XL
XL
7/10/2014Page 24
( ) ( )( )2/ 1 ( ( ) ) | |
g
n
r c x m x f u t p t
r k x sgn x r r xρ α β γ
+ ⋅ + ⋅ = − ⋅ + = ⋅ + ⋅ − ⋅ ⋅ + ⋅
ɺ ɺɺ ɺɺ
ɺ ɺ ɺ
�(�)= transversal force history from OpenSEES;
���(�)= input accelerogram;
�, ,�, � = linear parameters;
,α, �, γ, �= nonlinear parameters.
PIER REDUCED TO A S-DOF NONLINEAR HYSTERETIC SYSTEM
7/10/2014Page 25
( )( )
( ) ( )
2
, ,1
1
,max min
m
i red i OSi
red OSOS OS
x xm
NRMSE =
−=
−
∑x x
x x
{ } ( )( ), ,
ˆˆ ˆ, , min , , ,
ˆˆ 1, 0
red OSNRMSE
n
ρ α βρ α β ρ α β
γ
= = =
x x
XOS = displacement responses of the OpenSEES pier
Xred = displacement responses of the S-DOF reduced pier
PARAMETER IDENTIFICATION FOR THE S-DOF NONLINEAR REDUCED PIER
7/10/2014Page 26
Forc
e [
kN
]
Displacement [mm]
Bilinear hysteretic model
ISOLATOR REDUCTION TO A S-DOF NONLINEAR SYSTEM
7/10/2014Page 27
Bilinear hysteretic model
( ) ( )( ) ( ) ( ) ( )( )
1m x c x kx ku p t
u x N x M u M x N u
α α
δ δ
⋅ + ⋅ + + − =
= − + +
ɺɺ ɺ
ɺ ɺ ɺ ɺ
ISOLATOR REDUCTION TO A S-DOF NONLINEAR SYSTEM
7/10/2014Page 28
{ } ( )( ), ,
ˆ ˆˆ, , min , , ,red OSk
k NRMSE kα δ
α δ α δ= r r
( )
( ) ( ) ( ) ( ), ,
, OS, OS,1
1red i OS i i
i
i OS j j j j jj
r k x k u
u N x M u M x N u x t
α α
δ δ=
= ⋅ ⋅ + − ⋅ ⋅ = − + + ⋅ ∆
∑ ɺ ɺ ɺ
0.0046, 2.0278 8, 5.0000 4k eeα δ= = = −
XOS = displacement responses of the OpenSEES isolator
Xred = displacement responses of the S-DOF reduced isolator
PARAMETER IDENTIFICATION FOR THE S-DOF REDUCED ISOLATOR
7/10/2014Page 29
Validation of reduced NSs at ULS
VALIDATION OF SUBSTRUCTURED NUMERICAL PARTS
Iso. of Piers #9Piers #9
Dis
pla
cem
ent
[m]
Displacement [m]Forc
e [
N]
Time [s]
7/10/2014Page 30
HYBRID MODEL OF THE NON-ISOLATED BRIDGE
88-DoFs << ~900-DoFs
(Hybrid model) (OpenSEES RM)
UNIFORM TRANSVERSAL SEISMIC LOADING
7/10/2014Page 31
88-DoFs << ~900-DoFs
(Hybrid model) (OpenSEES RM)
UNIFORM TRANSVERSAL SEISMIC LOADING
HYBRID MODEL OF THE ISOLATED BRIDGE
Page 32 10-Jul-14
4 200400
2Atss
t
λ ⋅∆ ⋅= = =∆
PARTITIONED TIME INTEGRATION
NS
PS
λ = extended testing time scale = 200
4At ms∆ =
2t ms∆ =
200 4 800At msλ ⋅∆ = ⋅ =Sim. time step: Exp. time step:
Contr. time step: Subcycling:
Page 33 10-Jul-14
NS
PS
RESPONSE OF THE NS
PARTITIONED TIME INTEGRATION
4 200400
2Atss
t
λ ⋅∆ ⋅= = =∆
λ = extended testing time scale = 200
4At ms∆ =
2t ms∆ =
200 4 800At msλ ⋅∆ = ⋅ =Sim. time step: Exp. time step:
Contr. time step: Subcycling:
( )( ) ( ) ( ) ( )1 1
1 1
1 1 1
1
1 1
m n nn n n
n n n n
n m n m n f n f
n n n
t t
α α α
γ γ
α α α α
+ + +
+ +
+ +
+ + +
+ =
⇓
= + ∆ − + ∆
− + = − +
⇓
+ =
My Ky f
y y v v
v v y y
My Ky f
ɺ
ɺ ɺ
ɺ
• FIRST ORDER
SYSTEMS
• USER CONTROLLED
ALGORITHMIC
DAMPING
• SELF STARTING
• ENERGY PRESERVING
7/10/2014Page 34
THE GCbis-MG-α PARALLEL PARTITIONED TIME INTEGRATORS
7/10/2014Page 35
0 0.05 0.1-0.01
0
0.01
Dis
p. [m
]
0.01
λ = 128, ∆t = 1/1024, ∆tA = 1/1024, ss = 128
2 0.01u =Free decay response to:
PSDoF #1
PSDoF #2
Time [s]
-- exp.-- num.
EXPERIMENTAL VALIDATION OF THE GCbis-MG-α METHOD
7/10/2014Page 36
EXPERIMENTAL SET-UP AT THE ELSA LAB. OF THE JRC OF ISPRA (VA)
1:2.5 SCALE MOCK-UP PIERS
7/10/2014Page 37
HV
F LF
B∆ =
EXPERIMENTAL SET-UP OF PIERS
PHOTOGRAMMETRIC MEASUREMENTS
7/10/2014Page 38
1:2.5 SCALE MOCK-UP ISOLATORS
EXPERIMENTAL SET-UP OF ISOLATORS
G ± ∆FV
7/10/2014Page 39
EXPERIMENTAL EQUIPMENT
PIE
R #
9P
IE
R #
11
ISO
#9
IS
O #
11
: Vertical actuator (12x) in force control mode;
: Horizontal actuator (6x) in displacement control mode;
Plan view of the experimental set-up
PID-based control architecture
PHYSICAL PIERS
NUMERICAL PIERS
NEED FOR AN UPDATING STRATEGY FOR NUMERICAL PIERS
7/10/2014Page 40
DAMAGE MUST ACCUMULATE ON BOTH PSs AND NSs TEST BY TEST
7/10/2014Page 41
PROPOSED MODEL UPDATING TESTING PROCEDURE
Disp. [mm]
7/10/2014Page 42
MODEL UPDATING OF OPENSEES FE MODEL OF PHYSICAL PIERS
{ } ( )( )expˆ min ,
pcpc OS pc
ff NRMSE f= r r
OpenSEES FEM of Pier #11
ULS RESPONSETest k09
Maximum compressive strength of concrete01
fpc
-- OpenSEES.-- experimentalF
orc
e [
N]
7/10/2014Page 43
MODEL UPDATING OF THE OPENSEES RM OF THE BRIDGE
Pier #9
Pier #11
Hollow piers
Solid piers
7/10/2014Page 44
( ) ( )( )2/ 1 ( ( ) ) | |
g
n
r c x m x f u t p t
r k x sgn x r r xρ α β γ
+ ⋅ + ⋅ = − ⋅ + = ⋅ + ⋅ − ⋅ ⋅ + ⋅
ɺ ɺɺ ɺɺ
ɺ ɺ ɺ
{ } ( )( ), ,
ˆˆ ˆ, , min , , ,
ˆˆ 1, 0
red OSNRMSE
n
ρ α βρ α β ρ α β
γ
= = =
x x
XOS = displacement responses of the UPDATED OpenSEES RM
Xred = displacement responses of the reduced pier
DYNAMIC IDENTIFICATION OF NONLINEAR REDUCED PIERS
7/10/2014Page 45
1) Test k06: non-isolated bridge at SLS (10% PGA)
2) Test k07: non-isolated bridge at SLS
3) Test l01: isolated bridge at SLS
4) Test l02: isolated bridge at ULS
5) Test k09: non-isolated bridge at ULS
6) Test k11: non-isolated bridge at ULS (after shock)
7) Test k12: non-isolated bridge at ULS (200% PGA)
LIST OF MAIN HYBRID SIMULATIONS
7/10/2014Page 46
NON-ISOLATED BRIDGE AT SLS
EVOLUTIONS OF CONCRETE COMPRESSIVE STRENGTHS IDENTIFIED ON PHYSICAL PIERS
7/10/2014Page 47
Pier #9, SLS Pier #9, ULS
Pier #11, SLS Pier #11, ULS
HYSTERETIC LOOPS OF PHYSICAL PIERS
isolated configurationnon-isolated configuration
7/10/2014Page 48
DAMAGE PATTERN AFTER ULS TESTS
Column ends uplifting, expulsion of concrete covers
Diffuse crack patterns
7/10/2014Page 49
EVOLUTIONS OF MAIN BRIDGE EIGENFREQUENCIES
Eigenvalues of linearized non-isolated models
7/10/2014Page 50
COMPARISON OF NUMERICAL RESPONSES TO PHYSICAL MEASUREMENTS
Hysteretic loops and dissipated energies of Piers #9 and #11
Pier #9, ULS
Pier #11, ULSPier #9, ULS
Pier #11, ULS
7/10/2014Page 51
HYBRID SIMULATION OF AN INDUSTRIAL PIPING SYSTEM
Table Characteristics of the piping system
Pipe Size MaterialLiquid/Internal
Pressure
8” and 6” Schedule 40
API 5L Gr. X52fy= 418 Mpa; fu = 554 Mpa;
Elongation = 35.77%
Water/3.2 MPa
A 3D model of the piping+support Dimensions and specifications of the piping
7/10/2014Page 52
THE INDUSTRIAL PIPING SYSTEM CASE STUDY
7/10/2014Page 53
#1
#2
, , N P N P N Px x y y z zθ θ θ θ θ θ≠ ≠ ≠
ANSYS REFERENCE MODEL (RM) OF THE PIPING
X
Positions of minimum bending moments were chosen as coupling nodes.
The seismic action was applied the x direction.
SEISMIC LOADING
7/10/2014Page 54
EXPERIMENTAL SET-UP OF THE PS
A pair of hydraulic actuators imposed displacements to coupling DoFs
X
Numerical-DoFs
Boundary-DoFs
Physical-DoFs
DOFS PARTITIONING
7/10/2014Page 55
( )
T
T
T
TT
T
T
T
T
T
T
B P
P
P
N
Ng
T
N P
B
B u
= = = = − + ⋅ ⋅
u
r
f
u
r
f M M I
u u
f
r
f
0
ɺɺ
Displacement vector
Restoring force vector
External load vector
Challenge: to reduce P-DoFs to B-DoFs and perform tests with two actuators only
A reduction basis T reflects a kinematic assumption:
N
NB
BP
= ⋅
uu
u Tu
u
T
T
T
P P
P P
P Pgu
=
= = − ⋅
M T M T
K T K T
f T M I
ɶ
ɶ
ɶ ɺɺ
Reduced matrices of the PS:
REDUCTION BASIS REQUIREMENTS
7/10/2014Page 56
X: time history responses of the PS, i.e. B- and P-DoFs, arranged in row-wise.
U: orthonormal matrix of eigenvectors of XXT.
V: orthonormal matrix of eigenvectors of XTX.
Σ: diagonal matrix of the singular values of X, sorted in descending order.
X1
X2
X3
X4
XM
XM-1
1
... T
M
= =
X
X UΣV
X
The Principal Component Analysis (PCA) was applied to the dynamic
response of the PS predicted by ANSYS RM.
REDUCTION BASIS REQUIREMENTS
7/10/2014Page 57
Σ11 > Σ22 > … > Σii: singular values of X in descending order
� = ∑ Σ������ : total data energy
�� =∑ Σ�� �⁄���� : normalized cumulative data energy
• rank two;
• span principal component subspace;
• entail consistent kinematic assumptions.
REDUCTION BASIS REQUIREMENTS
7/10/2014Page 58
N N
B BCB
P q
= ⋅
u u
u T u
u u
S
I
Φ D
0
Φ
CB
S D
=
I 0 0
T 0 I 0
0 Φ Φ
Constraint modes: static deformation shapes owing to unit displacements applied to B-DoFs, one by one, whilst the other retained
Fixed interface vibration modes: eigenmodes of the PS constrained at its B-DoFs
Additional modal coordinates
THE CRAIG-BAMPTON METHOD APPLIED TO THE PSEUDODYNAMIC CASE
7/10/2014Page 59
,
,
N
B P r B PBB
q P r qqq
= ⋅ = ⋅
0 0 0 0 u
r 0 K 0 u K u
r 0 0 K u
ɶ ɶ
u=1
u=1
STATIC AND DYNAMIC CONTRIBUTIONSARE PLEASANTLY UN-COUPLED !!!
Constraint mode contributionExperimentally measured
Fixed interface vibration mode contributionNumerically modelled
7/10/2014Page 60
THE CRAIG-BAMPTON METHOD APPLIED TO THE PSEUDODYNAMIC CASE
Errors between time history responses of the
Reduced Model (NS + Reduced PS) and Reference Model
Error Coupling DoF #1 Coupling DoF #2NRMSE 0.003 0.001
NEE 0.006 0.001
7/10/2014Page 61
RM 2 2
CM 2
NEE CM−=
x x
x( ) ( )RM CM 2
CM CM
NRMSEmax min
N−=
−x x
x x
X: response signal
N: length of response signal in sample
Sensitive to frequency mismatching
Sensitive to amplitude mismatching
THE CRAIG-BAMPTON METHOD APPLIED TO THE PSEUDODYNAMIC CASE
[ ]RN LN
R L RB LB
RP LP
= =
Φ Φ
Φ Φ Φ Φ Φ
Φ Φ
1SERP RB
−
=
IT
Φ Φ
where:
Φ : mass normalized eigenvectors of the global system (column-wise)ΦR : retained eigenmodes ΦL : truncated eigenmodes
With relevant N-DoFs, B-DoFs and P-DoFs components (row-wise)
N
NB
SE BP
= ⋅
uu
u Tu
u
7/10/2014Page 62
THE SEREP METHOD APPLIED TO REAL-TIME HYBRID SIMULATION
Errors between time history responses of the
Reduced Model (NS + Reduced PS) and Reference Model
Error Coupling DoF #1 Coupling DoF #2NRMSE 0.015 0.0016
NEE 0.069 0.0003
7/10/2014Page 63
RM 2 2
CM 2
NEE CM−=
x x
x( ) ( )RM CM 2
CM CM
NRMSEmax min
N−=
−x x
x x
X: response signalN: length of response signal in sample
THE SEREP METHOD APPLIED TO REAL-TIME HYBRID SIMULATION
Sensitive to frequency mismatching
Sensitive to amplitude mismatching
Test Case PGA (g)
Identification test of the PS, IDT Hammer Test -
Real time tests 1 RTDS 0.020
Real time tests 2 RTDS 0.020
Elastic test, ET PDDS 0.042
Operational limit state test, SLOT PDDS 0.079
Damage limit state test, SLDT PDDS 0.112
Safe life limit state test, SLVT PDDS 0.421
Collapse limit state test, SLCT PDDS 0.599
EXPERIMENTAL PROGRAM
7/10/2014Page 64
• Identified damping = 0.5%;
• Time scale factor λ = 50;
• Water pressure = 3.2MPa.
LSRT-2 time integration algorithm available on the Network for Earthquake EngineeringSimulation (NEES) repository as simlsrt2 -id #209 tool.
7/10/2014Page 65
EXPERIMENTAL SET-UP
Piping system
7/10/2014Page 66 MOOG hydraulic actuator pair
EXPERIMENTAL SET-UP
0 2 4 6 8 10-6
-4
-2
0
2
4
6x 10
-3 node 114 dir 1
time [s]
disp
. [m
]
expnum
Displacement responses at the Coupling DoF #1 and relevant errors w.r.t. numerical simulations.
Pseudodynamic caseSLCT, PGA = 0.599g
Error Coupling DoF #1 Coupling DoF #2
NRMSE 0.038 0.066NEE 0.112 0.396
EXPERIMENTAL VALIDATION OF THE CRAIG-BAMPTON-BASED APPROACH APPLIED TO THE PSEUDODYNAMIC CASE
7/10/2014Page 67
X d
ispla
cem
ent
[m]
Time [s] ANSYS Reference Model
2 3 4 5 6 7 8 9 10 11 12-8
-4
0
4
8x 10
-3
time [s]
disp
. [m
]
numexp
Displacement responses at the Coupling DoF #1 and relevant errors w.r.t. numerical simulations.
Real-time caseET, PGA = 0.020g
Error Coupling DoF #1 Coupling DoF #2
NRMSE 0.083 0.239NENERR 0.289 0.379
7/10/2014Page 68
EXPERIMENTAL VALIDATION OF THE SEREP-BASED APPROACHAPPLIED TO THE REAL-TIME CASE
ANSYS Reference Model
X d
ispla
cem
ent
[m]
Time [s]
7/10/2014Page 69
CONCLUSIONS
• THE PARTITIONED TIME INTEGRATION APPROACH WAS APPLIED FOR THE FIRST TIME TO A COMPLEX BRIDGE PROVIDED WITH NONLINEAR NSs IN BOTH ISOLATED AND NON-ISOLATED CONFIGURATIONS;
• NSs -NUMERICAL PIERS- WERE UPDATED OFFLINE ACCORDING TO RESPONSES OF PSs -PHYSICAL PIERS- CHARACTERIZED BY DIFFFERENT SHAPES AND LOADING;
• HYBRID SIMULATION WAS APPLIED FOR THE FIRST TIME TO AN INDUSTRIAL PIPING SYSTEM CHARACTERIZED BY A DISTRIBUTED PARAMETER PS.
• BOTH THE CRAIG-BAMPTON AND THE SEREP METHODS WERE SUCCESSFULLY APPLIED IN THE CASE OF SEISMIC LOADING.
• STATE SPACE APPROACH FACILITATES THE INTEROPERATION OF TIME INTEGRATION, SYSTEM IDENTIFICATION AND MODEL REDUCTION TOOLS.
7/10/2014Page 70
On the NS side:
- Development of state space modeling environments.
- Possible application of on-line model updating techniques.
FUTURE PERSPECTIVES
( ( ) ) | |nr A sgn x r r xβ γ = − ⋅ ⋅ + ⋅ ɺ ɺ ɺ
7/10/2014Page 71
On the PS side:
- Experimental validation of alternative reduction bases in the linear range (balanced truncation, proper orthogonal decomposition, etc.);
- Extension of the proposed approach to nonlinear PSs.
FUTURE PERSPECTIVES
YIELDING OF ELBOWS
7/10/2014Page 72
Publications on international journals(accepted, submitted and in preparation):
1. Ceravolo R., Abbiati G., 2012. Time Domain Identification Of Structures: AComparative Analysis Of Output-Only Methods - International Journal ofEngineering Mechanics, 139(4):537-544.
2. Bursi O.S., Abbiati G., Reza Md.S., 2013. A Novel Hybrid Testing Approach forPiping Systems of Industrial Plants. Special Issue of Smart Structures andSystems on ''Recent Advances in Real-time Hybrid Simulation'' (RTHS) - In print.
3. Reza Md.S., Abbiati G., Bursi O.S., Paolacci F., 2013. Seismic performanceevaluation of a full-scale industrial piping system at serviceability and ultimatelimit states. Journal of Loss Prevention - Under review.
4. Abbiati G., Ceravolo R., Surace C., 2013. Unbiased time-dependent estimators foron-line monitoring of full-scale structures under ambient excitation. MechanicalSystems and Signal Processing - Under review.
5. Bursi O.S., Paolacci F., Di Sarno L., Abbiati G., 2014. Hybrid simulation andassessment of a multi-span RC bridge with plain bars. Earthquake Engineering &Structural Dynamics - In preparation.
7/10/2014Page 73
Additional SCOPUS indexed publications:
1. Reza M.S, Abbiati G., Bonelli A., Bursi O.S., 2013. ''Pseudo-dynamic testing of apiping system based on model reduction techniques''. SERIES ConcludingWorkshop joint with NEES-US Earthquake Engineering Research Infrastructures.JRC Ispra, May 28-30.
2. Abbiati G., Bursi O.S., Cazzador E., Mei Z., Paolacci F., Pegon P., 2013. ''Pseudo-dynamic testing with non-linear substructuring of a reinforced concrete bridge''.SERIES Concluding Workshop joint with NEES-US Earthquake EngineeringResearch Infrastructures JRC Ispra, May 28-30.
3. Paolacci F., Di Sarno L., Pegon P., Molina F. J., Poljansek M., Bursi O.S., Abbiati G.,Ceravolo R., Erdik M., Deisi R., Mohamad A, 2013. ''Assessment of the seismicbehaviour of a retrofitted old R.C. highway bridge through PsD testing''. SERIESConcluding Workshop joint with NEES-US Earthquake Engineering ResearchInfrastructures JRC Ispra, May 28-30.
4. Paolacci F., Di Sarno L., De Risi R., Abbiati G., Mohamad A., Malena M., CorritoreD. 2013. ''Refined and simplified numerical models of an isolated old highwaybridge for PsD testing''. SERIES Concluding Workshop joint with NEES-USEarthquake Engineering Research Infrastructures JRC Ispra, May 28-30.
7/10/2014Page 74
Thank you for your attention.
Any question?
