Time-scale manifold and its ridge analysis for machine fault diagnosis

Wavelet transform is a useful tool for the analysis of non-stationary signals. The time-scale distribution (TSD) of wavelet coefficients can represent the non-stationary structure of machine faults. This paper proposes a novel time-scale signature, called time-scale manifold (TSM), with the combination of the TSD and manifold learning. The new signature is produced by executing phase space reconstruction (PSR), continuous wavelet transform (CWT) and manifold learning successively. The TSM carries the non-stationary information and reveals the non-linear structure of the fault, and is thus exactly appropriate to represent the machine fault pattern. A new demodulation method of a rotating machine fault signal is further proposed by extracting the wavelet ridge lying on the TSM and computing the instantaneous amplitude, which can be used to identify the fault characteristic frequency. The effectiveness of the TSM for machine fault signature representation and its ridge analysis for characteristic frequency identification is verified by two experimental studies of a gearbox vibration signal and a bearing acoustic signal.