Damage Identification of a Composite Beam Using Finite Element Model Updating

TLDR: The damage identification study presented in this paper leveraged a full-scale sub-component experiment conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego to identify damage in the beam through a finite element model updating procedure.

Abstract: The damage identification study presented in this paper leveraged a full-scale sub-component experiment conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego. As payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set of low-amplitude vibration response data was acquired from the beam at various damage levels. The Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse responses recorded in its undamaged and various damaged states using accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage in the beam through a finite element model updating procedure. The identified damage is consistent with the observed damage in the composite beam.

Figures

Fig. 24. Composite shell failure at location of stirrup holes: (a) near accelerometer a3, and (b) near accelerometer a7

Fig. 25. Concrete core at north side of the splice (see Figures 2 and 4)

Table 4. Natural frequencies [Hz] and damping ratios [%] identified using ERA based on acceleration data at states S0 to S6 (all 12 impact tests considered in a single identification)

Table 3. Mean [%] / coefficient-of-variation [%] of the damping ratios identified using ERA based on acceleration data for states S0 to S6 (sets of 12 impact tests)

Table 5. Mean [Hz] / coefficient-of-variation [%] of the natural frequencies identified using ERA based on FBG sensor macro-strain data at states S1 to S5 (sets of 12 impact tests)

Fig. 16. Modal decomposition of impulse response measured by FBG strain sensors 1 to 4 at state S1

Full text

UC San Diego
UC San Diego Previously Published Works
Title
Damage Identification of a Composite Beam Using Finite Element Model Updating
Permalink
https://escholarship.org/uc/item/05w071fw
Journal
Computer-Aided Civil and Infrastructure Engineering, 23(5)
ISSN
1467-8667
Authors
Moaveni, Babak
He, Xianfei
Conte, Joel P
et al.
Publication Date
2008-07-01
DOI
10.1111/j.1467-8667.2008.00542.x
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

Computer-Aided Civil and Infrastructure Engineering, Accepted, August 2007
Damage Identification of a Composite Beam Using
Finite Element Model Updating
Babak Moaveni, Xianfei He, & Joel P. Conte
∗
Department of Structural Engineering, University of California at San Diego, USA
&
Raymond A. de Callafon
Department of Mechanical and Aerospace Engineering, University of California at San Diego, USA
Abstract
The damage identification study presented in this paper leveraged a full-scale sub-component experiment
conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San
Diego. As payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set
of low-amplitude vibration response data was acquired from the beam at various damage levels. The
Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies,
damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse
responses recorded in its undamaged and various damaged states using accelerometers and long-gage
fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage
in the beam through a finite element model updating procedure. The identified damage is consistent with
the observed damage in the composite beam.
1
INTRODUCTION
In recent years, structural health monitoring has received increased attention in the civil engineering
research community with the objective to identify structural damage at the earliest possible stage and
evaluate the remaining useful life (damage prognosis) of structures. Vibration-based, non-destructive
∗
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
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Computer-Aided Civil and Infrastructure Engineering, Accepted, August 2007
damage identification is based on changes in dynamic characteristics (e.g., modal parameters) of a
structure as a basis for identifying structural damage. Experimental modal analysis (EMA) has been used
as a technology for identifying modal parameters of a structure based on its measured vibration data. It
should be emphasized that the success of damage identification based on EMA depends strongly on the
accuracy and completeness of the identified structural dynamic properties. Extensive literature reviews on
vibration-based damage identification were provided by Doebling et al. (1996, 1998) and Sohn et al.
(2003).
Damage identification consists of detecting the occurrence of damage, localizing the damage zones, and
estimating the extent of damage. Numerous vibration-based methods have been proposed to achieve these
goals. Salawu (1997) presented a review on the use of changes in natural frequencies for damage
detection only. However, it is in general impossible to localize damage (i.e., obtain spatial information on
the structural damage) from changes in natural frequencies only. Pandey et al. (1991) introduced the
concept of using curvature mode shapes for damage localization. In their study, by using a cantilever and
a simply supported analytical beam model, they demonstrated the effectiveness of employing changes in
curvature mode shapes as damage indicator for detecting and localizing damage. Bernal and Gunes
(2004) have incorporated changes in modal flexibility matrices (or flexibility proportional matrices) into
the damage locating vector (DLV) technique to localize damage. Recently, Adeli and Jiang (2006a)
presented a novel multi-paradigm dynamic time-delay fuzzy wavelet neural network (WNN) model for
non-parametric identification of structures using the nonlinear auto-regressive moving average with
exogenous inputs (NARMAX) approach. Jiang and Adeli (2005, 2006b) applied this WNN model to
high-rise building structures, for both nonlinear system and damage identification. Methods based on
changes in identified modal parameters to detect and localize damage have also been further developed
for the purpose of damage quantification. Among these methods are strain-energy based methods (Shi et
al., 2002) and the direct stiffness calculation method (Maeck and De Roeck, 1999). Another class of
sophisticated methods consists of applying sensitivity-based finite element (FE) model updating for
damage identification (Friswell and Mottershead, 1995). These methods update the physical parameter of
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Computer-Aided Civil and Infrastructure Engineering, Accepted, August 2007
a FE model of the structure by minimizing an objective function expressing the discrepancy between
analytically predicted and experimentally identified features that are sensitive to damage such as natural
frequencies and mode shapes. Optimum solutions of the problem are reached through sensitivity-based
optimization algorithms. In recent years, sensitivity-based FE model updating techniques have been
applied successfully for condition assessment of structures (Teughels and De Roeck, 2004).
The study presented in this paper, which is an extension of an already published conference paper
(Moaveni et al., 2006), leveraged a full-scale sub-component experiment conducted in the Charles Lee
Powell Structural Research Laboratories at the University of California, San Diego (UCSD). As payload
project attached to a quasi-static test of a full-scale composite beam, the authors acquired a high-quality
set of low-amplitude vibration response data from the beam at various damage levels. The Eigensystem
Realization Algorithm (ERA) (Juang and Pappa, 1985) was applied to identify the modal parameters
(natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam
based on its impulse responses recorded in its undamaged and various damaged states using
accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are
presented and compared at different levels of damage. They are then used to identify damage in the beam
using a sensitivity-based finite element model updating procedure.
2 COMPOSITE BEAM EXPERIMENT
The designed I-5/Gilman Advanced Technology Bridge is a 137m (450ft) long cable-stayed bridge sup-
ported by a 59m (193ft) high A-frame pylon, and utilizing fiber reinforced polymer (FRP) composite
materials. The bridge system is a dual plane, asymmetric cable-stayed design as shown in Figure 1.
Before the I-5/Gilman Advanced Technology Bridge can be constructed, a Validation Test Program to
evaluate the performance of the bridge was performed. The prototype test program, which was conducted
at the Charles Lee Powell Structural Research Laboratories at UCSD, evaluated the manufactured FRP
components at the material level, through coupon testing and other non-destructive techniques on the
members, and at the element level on full-scale sub-component, connection and system tests (Brestel et
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Computer-Aided Civil and Infrastructure Engineering, Accepted, August 2007
al., 2003). The test leveraged in this study was conducted on a full-scale sub-component longitudinal
girder of the bridge (Test L2). The objective of this experiment was to validate the design of a concrete-
filled composite beam component of the planned I-5/Gilman Advanced Technology Bridge (Seible et al.,
1996). For this purpose, uni-directional quasi-static cyclic load tests (i.e., load-unload cycles) of
increasing amplitude were applied to the beam, gradually introducing damage. After each of several
sequences of loading-unloading cycles, a set of low-amplitude dynamic tests was performed in order to
investigate the changes in dynamic characteristics (extracted from the vibration response data) as a
function of increasing structural damage. For this purpose, two different sources of dynamic excitation
were used, namely (1) a computer-controlled electro-dynamic shaker, and (2) an impact hammer. The
vibration data obtained from the impact tests revealed to be the most informative to identify the beam
modal parameters at different levels of damage. The small-strain vibration response data was measured at
several damage levels using a set of four long-gage (1m) fiber Bragg grating (FBG) strain sensors and a
set of eight single channel piezoelectric accelerometers.
2.1 Test Setup
The longitudinal girders for the I-5/Gilman Advanced Technology Bridge consist of prefabricated carbon/
epoxy shells filled with concrete. In the second phase of the longitudinal girder test program, which is
considered in this study, a girder shell specimen (L2) of diameter 0.91m (3ft) and length 9.75m (32ft) was
cut into two equal halves, spliced together at mid-span with mild steel reinforcement, and filled with
concrete (see Figures 2 and 3). The splice using longitudinal steel reinforcement allows a ductile behavior
of the connection. In the FRP shell, two rows of 51mm (2in) diameter holes were drilled along the top
edge of the girder and shear stirrups were embedded in the concrete core to provide interfacial shear
resistance between the girder and the deck.
A uni-directional quasi-static cyclic loading was applied to the girder using four 1335kN (300kips) dis-
placement-controlled hydraulic actuators in a four-point bending test (see Figure 3). Initially, the girder
was loaded to a total of 1000kN (225kips) to establish a well-lubricated pin connection at the supports of
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Frequently asked questions

Q1. What have the authors contributed in "Damage identification of a composite beam using finite element model updating" ?

In this paper, the authors presented the application of a two-stage damage identification method to a fullscale composite beam ( sub-component ) based on its measured vibration response. 

Q2. Why is the mode identified as non-classically damped?

It should be noted that due to low signal-to-noise ratio and/or identification or modeling errors, a truly classically-damped mode could be identified as non-classically damped. 

Q3. Why are the modes of the beam-support system generally not zero?

It should be noted that, due to flexibility of the support structures relative to the beam, the mode shapes of the beam-support system are generally not zero at the support-8-locations. 

Q4. How many accelerometers were attached to the girder specimen?

In addition to the FBG strain sensors, eight accelerometers were attached to the girder specimen to measure vertical acceleration. 

Q5. What is the modal assurance criterion for the beam?

Based on the identified modal parameters of the composite beam, an element-by-element sensitivitybased finite element (FE) model updating approach (Conte and Liu, 2001; Teughels and De Roeck, 2004) was used to identify (detect, localize and quantify) the damage in the beam at various damage levels. 

Q6. What is the effect of the moduli of elasticity of elements 2 and 9?

since there were no sensors between nodes 3 and 12 (foot of left support) as well as between nodes 9 and 13 (foot of right support), the use of the moduli of elasticity of all four elements 2, 9, 11, 12 as updating parameters would result in compensation effects between elements 2 and 11 as well as between elements 9 and 12. 

Q7. How many vertical impact tests were performed on the beam?

A total of 12 vertical impact tests were performed on the beam at each of the 7 states S0 to S6, with states S0 and S1 representing the beam in its undamaged condition. 

Q8. How many physical modes of vibration were extracted from the girder?

after per-forming a singular value decomposition, a system of order n = 16 was realized based on the natural frequency stabilization diagram (Peeters and De Roeck, 2001), from which a maximum of 8 physical modes of vibration could be extracted. 

Q9. What is the MAC value for the undamaged and damaged modes?

MAC values are bounded between 0 and 1 and measure the degree of correlation between corresponding mode shapes in the undamaged and damaged states (MAC value of 1 for unchanged mode shapes). 

Q10. what is the objective function for damage identification based on FE model updating?

The objective (cost) function used in this study for damage identification based on FE model updating is given byT1 2 f = r Wr (3)where r denotes the residual vector, expressing the discrepancy between experimentally identified modal parameters and their analytically predicted (using the FE model) counterparts, and W is a diagonal weighting matrix with each diagonal component inversely proportional to the standard deviation of the natural frequency of the corresponding vibration mode based on the 12 identifications at each damage state (see Table 2). 

Q11. Why was it more convenient to use ERA to the two types of measurements separately?

Since two separate data acquisition systems, not time-synchronized and with different sampling rates, were used to collect-6-the acceleration and macro-strain data, it was more convenient to apply ERA to the two types of measurements separately. 

Q12. What was the sequence of dynamic tests performed on the beam?

The repeated sequence of dynamic tests consisted of a set of forced vibration tests using a 0.22kN (50lbs) force electrodynamic shaker followed by a set of impact (free vibration) tests using an impact hammer with integrated load cell recording the applied force. 

Q13. What is the reason for the large damage factor in element 12?

it is worth noting that the large damage factor identified in element 12 (representing the north support) is likely due to the initial friction in the support pin, i.e., the pin was not well lubricated initially and broke free during the first set of quasi-static tests leading to state S2. 

Q14. What was the frequency range of the forced vibration tests performed using the shaker?

The forced vibration tests performed using the shaker consist of a set of sixteen (Gaussian) white noise excitations followed by three (linear) sine sweeps across the frequency ranges 12-22Hz, 38-48Hz, and 93-103Hz, respectively. 

Q15. What is the advanced method of detecting damage?

Another class of sophisticated methods consists of applying sensitivity-based finite element (FE) model updating for damage identification (Friswell and Mottershead, 1995). 

Q16. What is the reason why the modal frequency is not consistent with the others?

The few cases when an identified modal frequency is not consistent with the others could be explained by a low participation of the corresponding vibration mode (e.g., impact applied near a modal node) resulting in a low signal-to-noise ratio. 

Q17. What is the effect of the effective moduli of elasticity on the beam elements?

From the results presented in Table 8 and Figure 20, it is observed that the effective moduli of elasticity display an overall decreasing trend with increasing level of damage.