Nonlinear Dispersive Component Decomposition: Algorithm and Applications

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.