Damage detection of composite laminate structures using VMD of FRF contaminated by high percentage of noise

A novel highly robust-to-noise and closely-situated eigenvalues damage detection method is proposed. The proposed method employs the Variational Mode Decomposition (VMD) algorithm to construct a new set of input signals obtained from the rows of the condensed Frequency Response Function (CFRF) to be used in a sensitivity-based model updating problem. Each row of the FRF matrix is replaced by its Unwrapped Instantaneous Hilbert Phase (UIHP). However, since the signal corresponding to the rows of the CFRF might not exhibit the mono-component property, and thus the UIHP will not be well-defined, VMD is used to obtain a set of constructive mono-component modes for each row, whereby the sum of UIHPs (SUIHP) for that row is obtained. The obtained SUIHPs for all rows of the CFRF are stacked up to obtain a new matrix to be fed into the optimisation problem. The proposed method is tested on a composite laminate plate with different configurations, as an example of structures with closely-situated eigenvalues. The results of the application of highly noisy measurement data for damage detection as well as comparison with two other methods demonstrate the superiority of the proposed method in damage detection of structures with closely-situated eigenvalues using highly noisy input data.