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.
In this paper, the structural mode shapes extracted from the finite element model of a simply supported reinforced concrete beam are employed for damage identification using different types of wavelets. To start with, the parity of signals, wavelets, and their convolution, that is, wavelet transform properties, are verified. In light of the mathematical modeling complexity of modal frequency, which relates to the localization and quantification of damage in the reinforced concrete beam, the maximum curves based on multiresolution wavelet transform coefficient differences and the corresponding theoretical assumptions are described and analyzed. It is concluded that the maximum curve reaches a peak value at a specific scale for a specific case, based upon which, a new mode shape based algorithm and damage index are proposed for damage identification. The accuracy of localization as well as the sensitivity of quantification is further discussed.
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