Modal identification of structural systems using an effective method based on combining the transmissibility and wavelet transform

Recently, a new approach called Transmissibility based Operational Modal Analysis (TOMA) has been presented in order to identify the dynamic characteristics of structural systems that determines the modal parameters of structures using the concept of transmissibility. In the TOMA approach, unlike OMA methods that use the assumption of white noise input, no limiting assumption is considered for the input excitations, and the modal parameters of structural systems are extracted based on the features of transmissibility matrix. The transmissibility methods, like other frequency domain methods, do not present very satisfactory results in identifying the damping values. Therefore, in the present paper, a new combined method called Fourier Spectral Transmissibility-Wavelet Transform (FST-WT) is proposed which, in addition to determining the natural frequencies and mode shapes of the system, also addresses the exact detection of damping values based on the features of wavelet transform. In this research, the capability of the FST-WT method in identifying and extracting the modal parameters of a 5-DOF system under free vibration is investigated using the responses obtained from the MATLAB Simulink model. For this purpose, the frequencies and mode shapes are respectively extracted from the inverse of the second singular value and the first left singular vector of transmissibility matrix, and the damping values are also determined using the single frequency signals (wavelet coefficients) obtained from wavelet transform based on the minimal Shannon entropy criterion. The comparison of the identification results shows a good agreement with the exact values.