Simultaneous identification of impact force and structural local damage under pre-segmentation of structural elements

Abstract

Identifying dynamic force and structural damage is often mathematically treated as an optimization problem. The number of optimization variables is closely related to the complexity and calculation amount of the identified problem. To reduce the number of optimization variables during the solution process and emphasize the localized characteristics of structural damage, a novel output-only method is proposed to address the problem of simultaneous identification under a pre-assumption of structural damage locations. The main idea is to decompose the identified problem into a series of subtasks. For each task, only part of a structure rather than the whole will be updated to reduce the discrepancy between the calculated responses and the measured ones. To realize this idea, the structure is simulated via a finite element (FE) model, and then the structural elements are divided into several groups. Each group is used to generate one identified task, in which the identified problem is formulated as a constrained optimization problem. Stiffness reduction coefficients of the elements, which are contained in the corresponding element group, are regarded as the optimization variables, while the impact force reconstructed via sparse regularization is mathematically formulated as a constraint for the optimization problem. The gradient descent method combined with a greedy strategy is introduced for solving the optimization problem of each task. The identified results obtained from all the tasks are regarded as candidates for a final one. To comprehensively consider the residual errors of structural responses and the sparsity of identified results, the Bayesian information criterion (BIC) is introduced for determining the final identified result. Numerical simulations and experimental studies are carried out. The illustrated results demonstrate that the proposed method is capable of simultaneously identifying the impact force and structural local damage, even though it still has shortcomings such as relatively poor robustness of identified damage and great subjectivity of group division for structural elements. Some relative issues are discussed as well.