Experimental Verification of the Damage Locating Vector Method

In recent years, numerous approaches have been proposed for detecting damage in structures, in which the flexibility-based Damage Locating Vector (DLV) method is one of the promising techniques. By computing a set of load vectors from the change of the flexibility matrix before and after damage and then applying them as static forces to analytical model for static computation, the DLV method is able to locate damage in structures. The main purpose of this paper is to experimentally verify this method. Following a brief overview of the DLV method and construction of the flexibility matrix from experimental data, the experimental setup is described. The test structure is a 15 ft long three-dimensional truss structure. To simulate damage in the structure, the original truss member is replaced by one with reduced stiffness. Results show that the DLV method can successfully detect the damage using limited number of sensors and truncated modes. INTRODUCTION The condition of civil infrastructure is in a the state of decline due to daily use, corrosion, natural hazards, etc., and thus monitoring its condition becomes a very important issue. By continuously monitoring the condition of the structure, necessary measures can be carried out at an early stage, which could substantially Y. Gao, Doctoral Candidate, Univ. of Illinois at Urbana-Champaign, 205 North Mathews Ave. B207, Urbana, IL 61821, U.S.A. B.F. Spencer, Jr., Nathan M. Newmark Professor, Univ. of Illinois at Urbana-Champaign, 205 North Mathews Ave. 2113, Urbana, IL 61821, U.S.A. D. Bernal, Associate Professor, Northeastern University, 427 Snell Engineering Center, Boston, MA 02115, U.S.A. reduce the maintenance costs and reduce the likelihood of future collapse of the structure. The first implementations of structural health monitoring (SHM) appear to have taken place in offshore structures and bridges. One class of damage identification methods employed for SHM measures the change in frequencies to determine structural damage. Vandiver [1] examined the change in resonant frequencies due to the damage in structural elements. Cha and Tuck-lee [2] examined the change in frequency response data and used this information for structural parameter updating. Changes in a structure’s mode shapes have also been utilized. West [3] was perhaps the first to systematically use mode shape information for localization of structural damage without employing a prior finite element model. Another such technique takes advantage of the change in the flexibility matrix. Pandey and Biswas [4][5] presented a damage detection and localization method based on the flexibility changes in the structure. Recently, Bernal [6] proposed a promising new flexibilitybased method, the Damage Locating Vector (DLV) method, for damage localization. In this paper, following a brief overview of the DLV method, an approach to construct the flexibility matrix with inputs measured is presented. The DLV method is then verified through test of a 15 ft long, three-dimensional truss structure. Experimental results for two damage cases are presented. PROBLEM FORMULATION AND SOLUTION Health monitoring methods based on the flexibility matrix have recently been shown to be quite promising. Because an inverse relationship exists between the flexibility matrix and the square of the modal frequencies, the flexibility matrix is not sensitive to higher frequency modes. This unique characteristic allows the use of a small number of truncated modes to construct a reasonably accurate representation of the flexibility matrix. The DLV Method Bernal [6] proposed a flexibility-based damage localization method, the DLV method. This technique is based upon the determination of a special set of vectors, the so-called damage locating vectors (DLVs). The DLVs have the property that when they are applied to the structure as static forces at the sensor locations, no stress will be induced in the damaged elements. This unique characteristic can be employed to localize structural damage. First, let’s look at how to obtain the DLVs. For a linear structure, the flexibility matrices at sensor locations can be constructed from measured data before and after damage and denoted as and , respectively. Assume that we have a set of linear-independent load vectors , which satisfy the following relationship