UC San Diego
UC San Diego Previously Published Works
Title
Modal Identification Study of Vincent Thomas Bridge Using Simulated Wind-Induced Ambient
Vibration Data
Permalink
https://escholarship.org/uc/item/0pr116xc
Journal
Computer-Aided Civil and Infrastructure Engineering, 23(5)
ISSN
1467-8667
Authors
He, Xianfei
Moaveni, Babak
Conte, Joel P
et al.
Publication Date
2008-07-01
DOI
10.1111/j.1467-8667.2008.00544.x
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Computer-Aided Civil and Infrastructure Engineering, Revised version, August 2007
Modal Identification Study of Vincent Thomas Bridge Using
Simulated Wind-Induced Ambient Vibration Data
Xianfei He, Babak Moaveni, Joel P. Conte
& Ahmed Elgamal
Department of Structural Engineering, University of California at San Diego, USA
&
Sami F. Masri
Department of Civil and Environmental Engineering, University of Southern California, USA
Abstract
In this paper, wind-induced vibration response of Vincent Thomas Bridge, a suspension bridge located in
San Pedro near Los Angeles, California, is simulated using a detailed three-dimensional finite element
model of the bridge and a state-of-the-art stochastic wind excitation model. Based on the simulated wind-
induced vibration data, the modal parameters (natural frequencies, damping ratios, and mode shapes) of
the bridge are identified using the data-driven stochastic subspace identification method. The identified
modal parameters are verified by the computed eigenproperties of the bridge model. Finally, effects of
measurement noise on the system identification results are studied by adding zero-mean Gaussian white
noise processes to the simulated response data. Statistical properties of the identified modal parameters
are investigated under increasing level of measurement noise. The framework presented in this paper will
allow to investigate the effects of various realistic damage scenarios in long-span cable-supported
(suspension and cable-stayed) bridges on changes in modal identification results. Such studies are
required in order to develop robust and reliable vibration-based structural health monitoring methods for
this type of bridges, which is a long-term research objective of the authors.
To whom correspondence should be addressed. Department of Structural Engineering, University of California at
San Diego, 9500 Gilman Drive, La Jolla, California 92093-0085, USA; E-mail: jpconte@ucsd.edu
; Tel: 858-822-
4545; Fax: 858-822-2260
-1-
Computer-Aided Civil and Infrastructure Engineering, Revised version, August 2007
1 INTRODUCTION
Vibration-based structural health monitoring has been the subject of significant research in structural
engineering in recent years. The basic premise of vibration-based structural health monitoring is that
changes in structural characteristics such as mass, stiffness, and energy dissipation mechanisms influence
the vibration response characteristics of structures. Therefore, changes in dynamic features such as modal
parameters and quantities derived thereof are often used as damage indicators in structural damage
identification and health monitoring. Salawu (1997) presented a review on the use of natural frequency
changes for damage detection. It is however challenging if not impossible to localize the detected damage
(e.g., to obtain spatial information on the damage) from changes in natural frequencies only. Pandey et al.
(1991) introduced the concept of mode shape curvature for damage localization. In their study, both a
cantilever and a simply supported beam model were used to demonstrate the effectiveness of using
changes in modal curvature as damage indicator to detect and localize damage. As another mode shape
based damage indicator, Pandey and Biswas (1994) proposed the use of changes in the dynamically
measured flexibility matrix to detect and localize damage. They showed that the flexibility matrix of a
structure can be easily and accurately estimated from a few low frequency vibration modes of the
structure. Methods based on changes in identified modal parameters to detect and localize damage in
structures have also been further developed for the purpose of damage quantification (i.e., estimation of
the extent of damage). Among these methods are strain-energy based methods (Shi et al., 2002), the direct
stiffness calculation method (Maeck and De Roeck, 1999), and sensitivity-based finite element (FE)
model updating methods (Friswell and Mottershead, 1995; Teughels and De Roeck, 2004). A
comprehensive literature survey on vibration-based structural health monitoring methods can be found in
a number of recent publications (Doebling et al., 1996; Farrar and Jauregui, 1998; Sohn et al., 2003).
In order to develop a robust and reliable structural health monitoring methodology, it is essential to
investigate the effects of realistic damage scenarios on structural modal properties. Since it is
inconvenient or impossible to study the changes in structural modal parameters caused by various damage
scenarios and damage levels through actual tests on a real structure during its service life, dynamic
-2-
Computer-Aided Civil and Infrastructure Engineering, Revised version, August 2007
response simulation of the structure based on a well calibrated and validated FE model thereof provides
an essential tool in structural health monitoring research. In this paper, a simulation platform is presented
to simulate the wind-induced (ambient) vibration response of Vincent Thomas Bridge (VTB) using a
detailed three-dimensional (3D) FE model of the bridge and a state-of-the-art stochastic wind excitation
model. The VTB is a suspension bridge that crosses over the main channel of Los Angeles Harbor in San
Pedro, California. The bridge was constructed in the early 1960’s with an overall length of approximately
1850 m, comprising the main span of 457 m and 154 m spans on either side. Generally, traffic, wind,
micro-tremors and their combinations are the main sources of ambient excitation for bridges. This paper
focuses on realistic simulation of the wind-induced response of VTB and system identification of the
bridge based on its simulated wind response data.
Wind loads, including self-excited (caused by the interaction between wind and structural motion) and
buffeting forces (caused by the fluctuating wind velocity field), are dependent on the geometric
configuration of the bridge deck section, the reduced frequency of the bridge, and the incoming wind
velocity fluctuations. In the simulation, the self-excited forces are represented in the time domain by
means of convolution integrals involving aerodynamic impulse functions and structural motions. In order
to simulate properly the stochastic characteristics of buffeting forces, the longitudinal (along-wind
direction) and vertical spatially discrete wind velocity fields along the bridge axis are simulated as two
independent stochastic vector processes according to their prescribed power spectral density matrices.
The spectra of the longitudinal and vertical wind velocity fields are assumed to remain constant along the
bridge axis and the coherence function of the wind velocity fluctuations at two different positions along
the bridge is taken as the model proposed by Davenport (1968).
In the second part of the paper, the dynamic properties of the bridge are identified using the data-
driven stochastic subspace identification method (Van Overschee and De Moor, 1996) based on low-
amplitude simulated wind-induced response of VTB. The system identification results are verified by the
computed eigenproperties of the bridge FE model, which allows to assess the performance of the above
output-only system identification method when applied to wind-excited long-span suspension bridges. In
-3-
Computer-Aided Civil and Infrastructure Engineering, Revised version, August 2007
order to study the effects of measurement noise on the system identification results, zero-mean Gaussian
white noise processes are added to the simulated output signals. Statistical properties (bias and
coefficient-of-variation) of the identified modal parameters are investigated under increasing level of
measurement noise.
The framework presented in this paper will allow to investigate systematically the effects of various
realistic damage scenarios in long-span cable-supported bridges on changes in modal identification results
obtained from ambient vibration data. Such studies are required in order to develop robust and reliable
vibration-based structural health monitoring methods for this type of bridges, which is a long-term
research objective of the authors.
2 AERODYNAMIC FORCES
2.1 Self-excited forces
The differential equations of motion of a bridge subjected to aerodynamic forces with respect to the static
equilibrium position can be expressed as
() () () () () ()
se b
tttttMx Cx Kx F F F
++ ==+t (1)
where , , and = nodal displacement, velocity, and acceleration response vectors,
respectively
;
M, C, and K = structural mass, damping, and stiffness matrices, respectively; F = nodal
load vector, and the subscripts se and b denote the s
()tx ()tx
()tx
elf-excited and buffeting aerodynamic force
components, respectively.
For harmonic structural motion, the self-excited forces such as lift
s
e
L , drag
s
e
D , and pitching moment
s
e
M
(see Figure 1) per unit span of the bridge are typically expressed as (Scanlan, 1978a; Simiu and
Scanlan, 1996; Chen et al., 2000a, b)
2* * 2*2* * 2*
12 345 6
1
()
2
se
hB hp
L t U B KH KH K H K H KH K H
UU BU
a
ra
éù
êú
=+++++
êú
ëû
p
B
(2a)
2* * 2* 2* * 2*
12 345 6
1
()
2
se
p
Bph
D t U B KP KP K P K P KP K P
UU BU
a
ra
éù
êú
=+++++
êú
ëû
h
B
(2b)
-4-
