Processing of Structural Responses via Wavelet Transform for Detecting Damages under Earthquake Excitation

Structural damage identification can be considered as the main step in Structural Health Monitoring (SHM). We can find many different methods which use structural dynamic responses for damage prognosis. Although some of them are concentrated on solving an inverse problem for damage identification, others suggest a direct procedure for defect detection. Despite the good performance of these methods in damage identification, researchers are attempting to find efficient and simple methods for damage identification with high level of accuracy. This paper presents a reference-free method for structural damage identification under earthquake excitation. Damages are defined as some changes in the special instants during an earthquake occurrence and structural time history responses are used as an input signal for discrete wavelet analysis. Finally the “detail coefficients” are inspected for determining the damage characteristics, such as the appearance, the time sequence, and the location of damage(s). Although the peak values in the detail coefficients can show the existence and time sequence of damage, for determining damage location we should inspect these peaks for finding the maximum value. As a result, the associated element with a signal which has maximum peak, can be considered as the damaged element. The applicability of the presented method is demonstrated by studying three numerical examples. First example is devoted for damage identification in a four-story shear frame. It is assumed that we have equipped all of the stories by sensors for recording structural responses. Three different damage scenarios with single and multiple damage cases under two samples of earthquake records, namely El-Centro (1940), and Northridge (1994) earthquakes, are studied. In addition, we study the effect of using different wavelet mother functions and different input signals, such as displacement and velocity responses. All of the obtained results emphasize the applicability of the presented method in damage identification. In second example, we consider a concrete simple beam with ten elements by simulating two different damage scenarios. In this case, we inspect the applicability of the method by considering only the transitional degrees of freedom (DOF) as the equipped DOFs by sensors. This can be interpreted as using limited number of sensors. In addition we use the displacement time histories for damage identification. For having a clear strategy in damage localization, we propose two rules for judging about elements’ health which are based on seeking maximum values of the wavelet coefficients in the damaged instants. Obtained results show the good performance of the presented method in finding time sequence of damage occurrence and damage location. In the third example, we investigate the applicability of the presented method in the presence of complex models of damages by defining bilinear stiffness reduction. In this case, although damage can cause some reduction in the effective stiffness of damaged structure, this reduction is different in positive and negative displacements. Two different damage scenarios are simulated on a single DOF structure under different excitations, namely earthquake excitations and generated White Noise excitation. Obtained results reveal the robustness of the presented method in damage prognosis in the presence of complex damage models.