Difference mode decomposition for adaptive signal decomposition

Abstract

Adaptive extraction of concerned components (CC) from mixed frequency components remains to be a challenging topic in various research domains. Most existing adaptive mode decomposition algorithms for extracting CC, such as wavelet transform, wavelet packet transform, singular value decomposition, empirical mode decomposition, empirical wavelet transform, and variational mode decomposition, are intrinsically adaptive band-pass filter banks and they face the following two tough problems. The first problem is that they cannot separate CC from interferential components in same frequency bands. The second problem is that it is not fully effective in automatically selecting CC distributed in different frequency bands by using some designed criteria. In this paper, a new decomposition approach called difference mode decomposition (DMD) is proposed to adaptively decompose a mixed signal into CC, reference components, and noise, and enrich the domain of adaptive mode decomposition. The proposed DMD relies on convex optimization and Fourier transform, and its decomposition is mathematically justified and composes physical interpretations. Analyses of simulated and real-world bearing and gear vibration signals are used to verify the effectiveness and superiority of the proposed DMD over existing adaptive mode decomposition algorithms. It is demonstrated that the proposed DMD can effectively extract CC such as repetitive transients caused by bearing and gear faults. Moreover, since the proposed DMD is based on Fourier transform expanded by trigonometric basis functions, the proposed DMD can be easily extended to other domains by expanding basis functions besides the frequency domain.