A Bayesian wavelet packet denoising criterion for mechanical signal with non-Gaussian characteristic

Abstract Three aspects of the traditional Bayesian wavelet packet denoising method have been rarely discussed in the literature for mechanical signals: (1) how to reduce noise if a precise prior description is needed for non-Gaussian data; (2) how to programmatically select a reasonable decomposition level; and (3) how to evaluate the denoising effect from multiple factors. Such three aspects have restricted the enhancement ability of the Bayesian denoising method. To seek the potential of application, this paper tries to establish a set of criteria. It develops the general Bayesian wavelet packet method based on the minimum mean square error, designs two indexes to select the decomposition level, and initially presents how to judge the denoising effect by multi-factor analysis. This criterion has two advantages: (1) if needed, any prior distribution can be employed to match with the signals; and (2) the selected decomposition level can maximize the distinction between real data and noise data. A comparison test is expected to show this enhancement ability of the proposed criterion. Simulated and experimental data demonstrate its excellent performance. This novel method keeps interpretable time-domain features and shows better denoising performance for weak information recognition than the published methods.