Structural Damage Identification Based on Quadratic Optimization of Objective Functions with Modal Residual Force and Weighting Strategy

Structural damage identification (SDI), an important issue in the field of structural health monitoring (SHM), is usually converted into a constrained optimization problem. However, the conventional objective functions defined by natural frequencies and mode shapes are insensitive enough to structural damage. To tackle this problem, this study proposed a new SDI method based on quadratic optimization of objective functions with both modal residual force and weighting strategy. First, a new structural damage index was constructed by Taylor expansion and sensitive matrix analysis about the modal residual force with respect to damage factor, and then the new index was introduced into a new objective function together with the frequency and mode shape. Then, to balance the magnitude effects of each term in objective functions, a weighting strategy was introduced to define the second new objective function for higher SDI accuracy and robustness to noise. The two proposed objective functions were further solved for SDI with a novel metaheuristic optimization technique, the whale optimization algorithm (WOA). To evaluate the effectiveness of the proposed SDI method, numerical simulations on a simply supported beam and a truss structure, as well as various experimental verifications on a simply supported beam in the laboratory, were carried out. The results show that the proposed SDI method outperforms the traditional method with a higher SDI accuracy and robustness to noise, and the second objective function is more suitable for multiple damage identification in complex structures.