Fast multivariate all time-scale decomposition method and its application in gear fault diagnosis

Aiming at the limitations of existing multivariate signal decomposition methods such as fast multivariate empirical mode decomposition (FMEMD) and completely adaptive projection multivariate local characteristic-scale decomposition (CAPMLCD) for gear fault diagnosis, this paper proposes a fast multivariate all-time-scale decomposition (FMATD) method. FMATD incorporates the ATD as its one-dimensional kernel within an efficient “projection-decomposition-reconstruction” framework, preserving the mode separation capability and adaptivity of ATD. Meanwhile, the efficient decomposition framework enhances computational efficiency and avoids over-decomposition. Furthermore, a fast projection strategy is designed to select the projection vectors in real time based on the signal energy distribution, thereby enhancing computational efficiency and decomposition accuracy. Applying FMATD to gear simulation signals and real vibration signals from faulty face gears demonstrates that the proposed method can effectively extract fault modes from face gear signals. Compared with FMEMD, CAPMLCD, and multivariate variational mode decomposition, FMATD yields the component with the clearest fault features in the envelope spectrum. In terms of computational efficiency, FMATD outperforms both FMEMD and CAPMLCD.