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

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.