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The study of dispersive signals has received widespread attention in numerous fields, such as structural health monitoring, nondestructive testing, and geological exploration. The decomposition of multicomponent dispersive signals generated by real systems is challenging since the group delay (GD) of each component varies nonlinearly with frequency and may overlap with each other. Meanwhile, the amplitude mutation components also bring difficulties to the decomposition. Aiming at these problems and inspired by the dispersion compensation method (DCM) and generalized dispersive mode decomposition (GDMD), we propose the nonlinear dispersive component decomposition method (NDCD) in this article. We establish an optimization model with a hybrid regularization term for frequency domain signal decomposition. By solving the optimization problem using composite split denoising (CSD) and the split augmented Lagrange shrinkage algorithm (SALSA), we can get the signal components along with high-resolution time-frequency representation. Simulation signals, bearing fault diagnosis, and Lamb wave experiments show that NDCD has better decomposition ability for signals containing mutation amplitude and overlapped GD. Moreover, it also has better noise robustness and lowers computational complexity, better than methods such as GDMD, DCM, synchrosqueezing transform (SST), time-reassigned SST (TSST), and TSET. [ABSTRACT FROM AUTHOR]

Variational nonlinear chirp mode decomposition (VNCMD) is a recently proposed time-frequency analysis method that combines variational mode decomposition with the sparse representation framework. It can effectively decompose crossed and adjacent nonlinear chirp components. However, due to its optimization target’s ridge regression characteristic, VNCMD cannot accurately reconstruct amplitude mutation components in fast-time-varying signals. Based on the framework of VNCMD and the sparsity and smoothness of Elastic Network Regression, we propose the nonlinear chirp component decomposition (NCCD) algorithm to decompose nonlinear chirps with strong piecewise linear characteristics accurately. We establish our new joint optimization model by adding weighted $l_{1}$ norm regulation term to the optimized objective function of VNCMD and solves the model by alternating direction method of multipliers. Meanwhile, we use the dynamic path optimization (DPO) algorithm to extract the time-frequency distribution ridge and initialize the instantaneous frequency. Simulation signals suggest that our method has higher decomposition accuracy for fast-time-varying nonstationary signals, smaller end effect, better convergence and noise robustness, and lower computational complexity. Furthermore, experimental signals of rotor rubbing suggest that our method can be more effectively applied to process strong modulation vibration signals than other methods such as synchrosqueezing transform (SST), synchro-extracting transform (SET), time reassigned-SST (TSST), and VNCMD. [ABSTRACT FROM AUTHOR]