Structural damage detection using sparse sensors installation by optimization procedure based on the modal flexibility matrix

This paper is aimed at presenting a novel and effective method to detect and estimate structural damage by introducing an efficient objective function which is based on Modal Assurance Criterion (MAC) and modal flexibility matrix. The main strategy in the proposed objective function relies on searching a geometrical correlation between two vectors. Democratic Particle Swarm Optimization (DPSO) algorithm, a modified version of original PSO approach, is used to minimize the objective function resulting in the assessment of damage in different structure types. Finally, the presented method is generalized for a condition in which a limited number of sensors are installed on the structure using Neumann Series Expansion-based Model Reduction (NSEMR) approach. To evaluate the efficiency of the proposed method, different damage patterns in three numerical examples of engineering structures are simulated and the proposed method is employed for damage identification. Moreover, the stability of the method is investigated by considering the effects of a number of important challenges such as effects of different locations for sensor installation, prevalent modeling errors and presence of random noises in the input data. It is followed by different comparative studies to evaluate not only the robustness of the proposed method, but also the necessity of using introduced techniques for problem solution. Finally, the applicability of the presented method in real conditions is also verified by an experimental study of a five-story shear frame on a shaking table utilizing only three sensors. All of the obtained results demonstrate that the proposed method precisely identifies damages by using only the first several modes’ data, even when incomplete noisy modal data are considered as input data.