A Hilbert transform sensitivity-based model-updating method for damage detection of structures with closely-spaced eigenvalues

In this paper, a novel method is proposed for damage detection of structures with closely-spaced eigenvalues. The proposed method uses a transformed form of the condensed frequency response function matrix each of whose columns is obtained as the sum of the unwrapped instantaneous Hilbert phase of the corresponding decomposed column of the original matrix using Empirical Mode Decomposition (EMD) algorithm. A new sensitivity-based model updating equation is then developed, which uses the constructed new matrix as input. The constructed sensitivity-based equation is solved via the least squares method through iterations to update unknown structural damage indices in a finite element model of the structure. To demonstrate the capability of the proposed method, the problem of damage detection in a composite laminate plate and a spatial truss structure, as examples of structures with closely-spaced eigenvalues, is solved. Moreover, the results obtained from the proposed method are compared against two other methods from the literature. The results show that the proposed method is far more effective at updating damage indices when incomplete highly noisy data is available.