Robust condition monitoring of rotating machinery is crucial in modern industry. With the continuous development of artificial intelligence, machine learning-based methodologies have been extensively investigated and have shown promising results for condition monitoring. However, these methods often lack physical interpretability, resulting in poor reliability and generalizability in real applications. Recently, an interpretable method based on a classic machine learning approach, namely, logistic regression, has been proposed to optimize spectral weights in an online manner for condition monitoring. This method leverages the classification ability of logistic regression and aims to train an online-updated hyperplane that maximizes the distance between normalized healthy and faulty spectra. Studies have shown that the weights defining the hyperplane can prominently indicate faulty frequencies, and the weighted sum of spectra is an effective health indicator. This approach is explainable and mathematically straightforward. Thus, it and its derivatives have been widely studied. However, logistic regression requires to predefine two hyperparameters: the regularization factor and the gradient descent rate. The tuning of hyperparameters is relatively easy in cases where the spectra are normalized, while it becomes tricky when dealing with raw or unnormalized spectra. In such cases, inappropriate hyperparameters may induce non-convergence. To address this limitation, this paper proposes variational inference-based Bayesian logistic regression for optimizing spectral weights. In the proposed approach, the Gaussian precision of the weights serves as the regularization factor and is estimated as a variable. Consequently, the method is fully adaptive and non-parametric. Experimental examples demonstrate the effectiveness and advantages of the proposed method for condition monitoring, particularly in comparison with the conventional logistic regression-based approach.
Jian et al. (Wed,) studied this question.