Three-Dimensional Sparse Random Mode Decomposition for Mode Disentangling with Crossover Instantaneous Frequencies

TL;DR

This paper introduces 3D-SRMD, an advanced mode decomposition method that enhances mode separation, especially for overlapping frequencies with crossover instantaneous frequencies, by adding a third dimension and a new feature generation strategy.

Contribution

The paper proposes a 3D extension of SRMD with a novel feature generation strategy, improving separation of overlapped frequency components in mode decomposition.

Findings

Effective separation of overlapped frequency components.

Improved accuracy in mode disentangling.

Validated on simulated and real-world signals.

Abstract

Sparse random mode decomposition (SRMD) is a novel algorithm that constructs a random time-frequency feature space to sparsely approximate spectrograms, effectively separating modes. However, it fails to distinguish adjacent or overlapped frequency components, especially, those with crossover instantaneous frequencies. To address this limitation, an enhanced version, termed three-dimensional SRMD (3D-SRMD), is proposed in this letter. In 3D-SRMD, the random features are lifted from a two-dimensional space to a three-dimensional (3D) space by introducing one extra chirp rate axis. This enhancement effectively disentangles the frequency components overlapped in the low dimension. Additionally, a novel random feature generation strategy is designed to improve the separation accuracy of 3D-SRMD by combining the 3D ridge detection method. Finally, numerical experiments on both simulated and real-world signals demonstrate the effectiveness of our method.