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Model-based identification of damage from sparse sensor measurements using Neumann series expansion

Abstract This paper presents a novel and effective modal data-based methodology for structural damage localization and quantification when the structure is equipped with a limited number of sensors. Damage detection problem is defined as an inverse model-based problem and a new damage-sensitive cost function is introduced using calculated Generalised Flexibility Matrix and Modal Assurance Criterion. The second-order approximation of Neumann Series Expansion-based Model Reduction approach is employed for numerically simulation of sparse sensor installation. Finally, a hybrid version of two different evolutionary optimization algorithms, named Particle Swarm Optimization–Colonial Competitive Algorithm (PSO–CCA), is suggested and utilized for solving optimization problem. This hybridization, not only can pick the positive points of the PSO and CCA for searching complex solution domain, but also can lead to achieving a powerful, fast speed optimization strategy. The efficiency of the presented method is demonstrated by studying three numerical examples under different damage patterns. Various challenges, such as the robustness of the method in the presence of random noises in the input data, are investigated. The obtained results introduce the presented method as a viable and practical strategy for structural damage identification, especially when a limited number of sensors are installed on the structure.