Multi-scale Manifold for Machinery Fault Diagnosis

The wavelet transform has been widely used in the field of machinery fault diagnosis for its merit in flexible time-frequency resolution. This chapter focuses on wavelet enveloping, and proposes an enhanced envelope demodulation method, called multi-scale manifold (MSM), for machinery fault diagnosis. The MSM addresses manifold learning on the high-dimensional wavelet envelopes at multiple scales. Specifically, the proposed method is conducted by three following steps. First, the continuous wavelet transform (CWT) with complex Morlet wavelet base is introduced to obtain the non-stationary information of the measured signal in time-scale domain. Second, a scale band of interest is selected to include the fault impulse envelope information of measured signal. Third, the manifold learning algorithm is conducted on the wavelet envelopes at selected scales to extract the intrinsic manifold of fault-related impulses. The MSM combines the envelope information of measured signal at multiple scales in a nonlinear approach, and may thus preserve the factual impulses of machinery fault. The new method is especially suited for detecting the fault characteristic frequency of rotating machinery, which is verified by means of a simulation study and a case of practical gearbox fault diagnosis in this chapter.