Vibration-based structural damage identification through optimization techniques has become an interesting research topic in recent years. Dynamic characteristics such as frequencies and mode shapes are used to construct the objective function. The objective functions based on only frequencies are not very sensitive to damage in large structures. However, objective functions based on both mode shapes and frequencies are very effective. In real measurement condition, the number of installed sensors is limited, and there are no economic reasons for measuring the mode shapes at all degrees of freedom. In this kind of circumstances, mode expansion methods are used to address the incompleteness of mode shapes. In this article, the system equivalent reduction and expansion process is applied to determine the unmeasured mode shapes. Two experimental examples including a cantilever beam and a truss tower are investigated to show system equivalent reduction and expansion process’ efficiency in estimating unmeasured mode shapes. The results show that the technique used for expansion is influential. Damage identification is formulated as an optimization problem, and the residual force vector based on expanded mode shapes is considered as an objective function. In order to minimize the objective function, grey wolf optimization and Harris hawks optimization are used. Numerical studies on a 56-bar dome space truss and experimental validation on a steel frame are performed to demonstrate the efficiency of the developed approach. Both numerical and experimental results indicate that the combination of the grey wolf optimization and expanded mode shapes with system equivalent reduction and expansion process can provide a reliable approach for determining the severities and locations of damage of skeletal structures when it compares with those obtained by Harris hawks optimization.

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New optimization algorithms have been increasingly developed in the course of the recent years. The accuracy of identified results in optimization-based damage detection methods depends on the objective function and optimization algorithm. This paper employs multiverse Optimizer (MVO) to solve the optimization-based damage identification problem. Statistical results obtained by MVO are compared with those of sine cosine algorithm (SCA) and Harris hawks optimization (HHO) in order to perform a comparative study. Two objective functions are used in this optimization problem. The first one is based on the modal assurance criterion (MAC) and the second one on modified total modal assurance criterion (MTMAC). Numerical and experimental examples indicate that the combination of objective function based on MTMAC and MVO algorithm can provide accurate and reliable results in structural damage detection process. MAC is also rejected in competition with MTMAC. While using SCA-MTMAC, the accuracy of the results is acceptable in some cases. However, HHO-MTMAC gives weak results in most cases. MVO and SSA are the lowest, and HHO spends significantly more time in terms of computational cost.

Incomplete sensed data in structures have made exact structural damage detection a serious challenge. In this paper, an effective method is presented for damage detection and estimation in structures based on incomplete modal data of a damaged structure via a pattern search algorithm. An objective function based on the condensed mass and stiffness matrices is formulated. The proposed method determines the damage to structural elements using optimization of the objective function by using pattern search algorithm. The performance of the presented method has been verified through two numerical examples, namely, a two-span continuous beam and a three-story plane frame with and without noise in the modal data containing several damages. Also, the effect of the discrepancy in mass and stiffness between the finite-element model and the actual tested dynamic system has been investigated. Furthermore, the experimental data from the vibration test of a mass–stiffness system are used for verification of the proposed approach. The results show that the presented method is sensitive to the location and severity of structural damage in spite of the incomplete modal data.

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