Adaptive multiwavelet hybrid construction method and applications in fault diagnosis

Vanishing moments and approximation orders of basis functions are both the important properties in the wavelet theory. The traditional adaptive multiwavelet construction methods can only reform either vanishing moments or approaching orders. Meanwhile, their time-frequency characteristics and waveform differences among the new multiple basis functions are quite small to lead to difficulties of efficiently adaptive extraction and identification of complex dynamic faults. Thus, the adaptive multiwavelet hybrid construction method combined with the two-scale similarity transformation and the lifting transformation was proposed. Using linear and nonlinear combinations of multi-scaling wavelet functions to extend the construction space, the multi-scaling functions with higher approximation orders and the multi-wavelet functions covered with multiple vanishing moments were obtained to enhance the regularity, smoothness, capability of signal approaching and local positioning, and to improve the signal analysis accuracy. It provided adaptive basis functions with super properties and a diagnosis method for weak and compound fault features extraction and identification. For the optimal selection of adaptive basis functions, the improved local fault field spectral entropy minimization rules were proposed to classify typical shaft systems, gear and rolling bearing faults and to simplify fault-classifying modes. The engineering applications showed that the method can effectively identify bearing weak inner-race damages under complex background noise, and successfully diagnose impact and rubbing compound faults with multiple features from thrust splints of gearbox in air-compressors.