Auto-OBSD: Automatic parameter selection for reliable Oscillatory Behavior-based Signal Decomposition with an application to bearing fault signature extraction

Bearing signals are often contaminated by in-band interferences and random noise. Oscillatory Behavior-based Signal Decomposition (OBSD) is a new technique which decomposes a signal according to its oscillatory behavior, rather than frequency or scale. Due to the low oscillatory transients of bearing fault-induced signals, the OBSD can be used to effectively extract bearing fault signatures from a blurred signal. However, the quality of the result highly relies on the selection of method-related parameters. Such parameters are often subjectively selected and a systematic approach has not been reported in the literature. As such, this paper proposes a systematic approach to automatic selection of OBSD parameters for reliable extraction of bearing fault signatures. The OBSD utilizes the idea of Morphological Component Analysis (MCA) that optimally projects the original signal to low oscillatory wavelets and high oscillatory wavelets established via the Tunable Q-factor Wavelet Transform (TQWT). In this paper, the effects of the selection of each parameter on the performance of the OBSD for bearing fault signature extraction are investigated. It is found that some method-related parameters can be fixed at certain values due to the nature of bearing fault-induced impulses. To adaptively tune the remaining parameters, index-guided parameter selection algorithms are proposed. A Convergence Index (CI) is proposed and a CI-guided self-tuning algorithm is developed to tune the convergence-related parameters, namely, penalty factor and number of iterations. Furthermore, a Smoothness Index (SI) is employed to measure the effectiveness of the extracted low oscillatory component (i.e. bearing fault signature). It is shown that a minimum SI implies an optimal result with respect to the adjustment of relevant parameters. Thus, two SI-guided automatic parameter selection algorithms are also developed to specify two other parameters, i.e., Q-factor of high-oscillatory wavelets and regularization parameter. Based on the index-guided parameter selection algorithms, an automatic parameter selection method is then proposed for the application of OBSD to bearing fault signature extraction. The proposed method is then validated with simulated signals and experimental data.