Iterative nonlinear chirp mode decomposition: A Hilbert-Huang transform-like method in capturing intra-wave modulations of nonlinear responses

Intra-wave modulations are a class of inherent nonlinear characteristics, exhibiting a fast oscillating instantaneous frequency and/or amplitude of responses. With the aid of the well-known Hilbert-Huang transform (HHT), such phenomena have been observed and utilized in many practical nonlinear systems including mechanical, power, ocean and even human biological systems. However, the empirical nature of the HHT makes the results physically uninterpretable and sensitive to perturbations of noise. Variational nonlinear chirp mode decomposition (VNCMD) is a recently proposed tool for analyzing wideband multicomponent signals, including intra-wave modulated responses. On the other hand, the VNCMD has strict requirements on the priori information of the signal. In this paper, we combine the framework of the VNCMD with that of the HHT, by replacing the joint-optimization scheme of the VNCMD with a recursive procedure adopted in the HHT. In this way, the new method becomes more adaptive without losing the rigorous mathematical foundation. This construction leads to a descendant of VNCMD, named the iterative nonlinear chirp mode decomposition (INCMD). Through dynamic simulations and applications to real data, it is demonstrated that the INCMD considerably outperforms state-of-the-art techniques of the same class. Using the INCMD, intra-wave modulations can be captured with high accuracy and strong noise-robustness. Extracted modulation features by the INCMD greatly help to detect and identify nonlinear systems. •A novel method termed the INCMD is proposed to deal with nonlinear data.•The INCMD combines the framework of the HHT with that of the VNCMD.•The INCMD captures intra-wave modulations with high accuracy and noise-robustness.•The INCMD decomposes M-DOF nonlinear responses into nonlinear modes.•The INCMD is utilized to identify the breathing crack in the beam.