Nonlinear Chirp Component Decomposition: A Method Based on Elastic Network Regression

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> 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.