Shock and Vibration

Volume 2015, Article ID 906062, 8 pages

http://dx.doi.org/10.1155/2015/906062

## Identification of Structural Damage in Bridges Using High-Frequency Vibrational Responses

Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia

Received 28 November 2014; Revised 30 March 2015; Accepted 1 April 2015

Academic Editor: Maosen Cao

Copyright © 2015 Ivana Mekjavić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The present research aims to develop an effective and applicable structural damage detection method. A damage identification approach using only the changes of measured natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. The computational technique used to identify the damage from the measured data is described. The performance of the proposed technique on numerically simulated real concrete girder bridge is evaluated using imposed damage scenarios. To demonstrate the applicability of the proposed method by employing experimental measured natural frequencies this technique is applied for the first time to a simply supported reinforced concrete beam statically loaded incrementally to failure. The results of the damage identification procedure show that the proposed method can accurately locate the damage and predict the extent of the damage using high-frequency (here beyond the 4th order) vibrational responses.

#### 1. Introduction

Damage or fault detection, as determined by changes in the dynamic properties or response of structures, is a subject that has received considerable attention in the literature. Since the changes in the stiffness of the structure, whether local or distributed, will cause changes in the modal parameters (notably natural frequencies, mode shapes, etc.), the location and the severity of damage in structure can be determined by changes in the modal characteristics [1–5]. Furthermore, since the natural frequencies are rather easy to measure with a relatively high level of accuracy, the methods based on the measurements of natural frequencies are potentially attractive [6–10]. For applications to large civil engineering structures the somewhat low sensitivity of frequency shifts to damage requires either very precise measurements of frequency change or large levels of damage. An exception to this limitation occurs at higher modal frequencies, where the modes are associated with local responses. However, over recent decades, the practical limitations involved with the excitation and identification of the resonant frequencies associated with these local modes, caused in part by high modal density and low participation factors, made them difficult to identify [11]. Raghavendrachar and Aktan [12] performed impact tests on a three-span reinforced concrete bridge with a goal of detecting local or obscure damage, as opposed to severe, global damage. The authors concluded that modal parameters may not be reliable as damage indicators if only the first few modes are measured. For this type of damage, modal information for higher modes would be required. Farrar and Cone [13] presented the results of damage–detection experiment performed on the I-40 bridge over the Rio Grande river. They identify the modal properties from the ambient test, when the bridge was undamaged, and from the forced-excitation tests for each of the damage cases. The results indicate that modal frequencies, modal damping ratios, and mode shapes may not be sensitive enough indicators to detect damage at an early enough stage to be practical. The destructive tests performed on the I-40 bridge highlight the fact that damage typically is a local phenomenon. Local response is captured by higher frequency modes whereas lower frequency modes tend to capture the global response of the structure and are less sensitive to local changes in a structure [11]. Consequently, the low-frequency vibrational responses are insensitive to small damage and moreover, small damage is more easily accommodated by higher-frequency vibrational responses. Currently, new advanced instrumentation typified by the scanning laser vibrometer (SLV) preserves a high level of accuracy in high-frequency vibration measurements providing the detection of small levels of damage [14].

Ideally, a robust damage identification method should be able to identify that damage has occurred at a very early stage, locate the damage within sensor resolution being used, provide some estimate of the severity of the damage, and predict the remaining useful life of the structure. Several frequency-change sensitivity analysis methods presented in [6–8] can be used to detect and locate damage in structures; however they cannot correctly quantify damage in general cases. In order to avoid the insufficiency of the first-order sensitivity analysis neglecting second-order terms, Bicanic and Chen [9] presented a novel perturbation-based approach using the exact relationship between the changes of structural parameters and the changes of modal parameters.

Here, based on the nonlinear perturbation theory, an efficient iterative computational procedure is presented in order to identify damage in framed structures for which high-order (beyond the 4th order) measured natural frequencies are available. The efficiency of the proposed technique is evaluated through an example of the real concrete girder bridge with simulated damage and through laboratory testing of a simply supported reinforced concrete beam subjected to various levels of static load.

#### 2. Direct Iteration Technique

The computational procedure for the direct iteration technique has been developed to solve the element scalar damage parameters as well as the mode participation factors [9]. The procedure consists of calculating the damage parameters, for example, crack location, from the frequency changes.

The iterative solution procedure is described in the following section. Depending on the number of available natural frequencies NF (number of equations) and the number of structural damage parameters NXE (number of unknowns), the eigenmode-stiffness sensitivity matrix may not be square. When the number of the measured natural frequencies for the damaged structure NF is much fewer than the number of structural damage parameters NXE (finite-elements) (), the system of equations is significantly underdetermined and the pseudoinverse solution can become ill-conditioned. In order to find a solution for what is in general an ill-conditioned system, the singular value decomposition (SVD) technique [15] is applied.

A FORTRAN computer program for structural damage identification has been developed based on the knowledge of the computational procedure presented next [16].

##### 2.1. Computational Procedure

*Step 1. *Assume the initial mode participation factors to be zero, that is, no changes in eigenvectors. Establish the initial values for and fromwhere and are the eigenmode-stiffness sensitivity matrix and vector, respectively, which are defined aswhere , , and can be defined in general form asand , , and are the eigenmode-stiffness sensitivity coefficients, which can be defined in a general form aswhere is the th original eigenvector, is the contribution of the th element to the global stiffness matrix, is the change in the th eigenvalue, is the th original eigenvalue, and a superscript refers to the damaged structure.

*Step 2. *Evaluate current estimate for fromwhere

*Step 3. *Evaluate new modal participation factors fromwhereand return to Step 2 if solution has not converged.

Once the mode participation factor is found, the eigenvectors for the damaged structure can be calculated as where the pairing of the eigenvalues for the original structure and the damaged structure can be checked using the MAC factors (Modal Assurance Criterion) [17], defined asThe highest factors indicate the most possible pairings of the original mode and the damaged mode .

#### 3. Numerical Example

A model of the real concrete girder bridge comprising 39 elements, 40 nodes, and 116 degrees of freedom (DOFs), shown in Figure 1, is used to investigate the effect of the number of original eigenvectors available and the natural frequencies of the damaged structure adopted in the calculation.