Modal Parameter Identification of Nonlinear Systems Based on Hilbert Vibration Decomposition

This paper proposes a modal parameter identification method based on the Hilbert vibration decomposition (HVD). The HVD is used to decompose structural vibrational signals into modal responses which can be considered as mono-component signals. The empirical envelope method is subsequently employed to compute the modal frequencies and modal damping ratio from the modal responses. Case studies are provided to validate the accuracy of the HVD-based method and demonstrate its superiority relative to the empirical mode decomposition (EMD)-based methods. The results show that the HVD-based method is capable of identifying the modal parameters of nonlinear systems with amplitude-dependent frequencies and amplitude-dependent damping ratios. The amplitude-dependency of the modal parameters is a typical feature for large-scale civil structures, e.g., long-span bridges, and hence the HVD-based method can serve as a competitive candidate for modal parameter identifications of similar structures. The HVD-based method has a higher frequency resolution relative to the EMD-based method. In addition, the HVD-based method is applicable for signals with relatively large noises and high damping ratios.