A new two-stage method for damage identification in linear-shaped structures via Grey System Theory and optimization algorithm

The main objective of this paper is concentrated on presenting a new two-stage method for damage localization and quantification in the linear-shaped structures. A linear-shaped structure is defined as a structure in which all elements are arranged only in a straight line. At the first stage, by employing Grey System Theory (GST) and diagonal members of the Generalized Flexibility Matrix (GFM), a new damage index is suggested for damage localization using only the first several modes’ data. It is followed by the second stage which is devoted to damage quantification in the damaged elements by proposing an optimization-based procedure to formulate fault prognosis problem as an inverse problem, and it is solved by the Pattern Search Algorithm (PSA) to reach the optimal solution. The applicability of the presented method is demonstrated by studying different damage patterns on three numerical examples of linear-shaped structures. In addition, the stability of the presented method in the presence of random noises is evaluated. The obtained results reveal good and acceptable performance of the proposed method for detecting damage in linear-shaped structures.