[1F4] Variational Bayesian logistic regression-based optimised weights for machine condition monitoring
J Jian¹,², J Antoni² and K Gryllias¹
¹KU Leuven, Belgium
²INSA Lyon, France
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 generalisability in real applications. Recently, an interpretable method based on a classic machine learning approach, namely logistic regression, has been proposed to optimise 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 maximises the distance between normalised 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 that two hyperparameters are predefined: the regularisation factor and the gradient descent rate. The tuning of hyperparameters is relatively easy in cases where the spectra are normalised, while it becomes tricky when dealing with raw or unnormalised spectra. In such cases, inappropriate hyperparameters may induce non-convergence. To address this limitation, this paper proposes variational inference-based Bayesian logistic regression for optimising spectral weights. In the proposed approach, the Gaussian precision of the weights serves as the regularisation 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.
