A flexibility-based method via the iterated improved reduction system and the cuckoo optimization algorithm for damage quantification with limited sensors

In this paper, a novel and effective damage diagnosis algorithm is proposed to localize and quantify structural damage using incomplete modal data, considering the existence of some limitations in the number of attached sensors on structures. The damage detection problem is formulated as an optimization problem by computing static displacements in the reduced model of a structure subjected to a unique static load. The static responses are computed through the flexibility matrix of the damaged structure obtained based on the incomplete modal data of the structure. In the algorithm, an iterated improved reduction system method is applied to prepare an accurate reduced model of a structure. The optimization problem is solved via a new evolutionary optimization algorithm called the cuckoo optimization algorithm. The efficiency and robustness of the presented method are demonstrated through three numerical examples. Moreover, the efficiency of the method is verified by an experimental study of a five-story shear building structure on a shaking table considering only two sensors. The obtained damage identification results for the numerical and experimental studies show the suitable and stable performance of the proposed damage identification method for structures with limited sensors.