Denoising and extraction of the weak signals are crucial to mechanical equipment fault diagnostics, especially for early fault detection, in which cases fault features are very weak and masked by the noise. The wavelet transform has been widely used in mechanical faulty signal denoising due to its extraordinary timefrequency representation capability. However, the mechanical faulty signals are often non-stationary, with the structure varying significantly within each scale. Because a single wavelet filter cannot mimic the signal structure of an entire scale, the traditional wavelet-based signal denoising method cannot achieve an ideal effect, and even worse some faulty information of the raw signal may be lost in the denoising process. To overcome this deficiency, a novel mechanical faulty signal denoising method using a redundant non-linear second generation wavelet transform is proposed. In this method, an optimal prediction operator is selected for each transforming sample according to the selection criterion of minimizing each individual prediction error. Consequently, the selected predictor can always fit the local characteristics of the signals. The signal denoising results from both simulated signals and experimental data are presented and both support the proposed method.
The non-linear geometry of Banach spaces after Nigel Kalton
