A posterior probability-guided kernel-space oversampling machine learning method for imbalanced rolling bearing health monitoring

Abstract Rolling bearings are core components of rotating machinery and electric drive systems, widely used in electric motors, generators, and wind power equipment; their health monitoring is crucial in intelligent manufacturing. Machine learning-based fault diagnosis often faces the problem of severe imbalance between healthy and faulty samples, leading to a shift in the SVM decision hyperplane and reduced generalization capability. To address this, this paper proposes a Kernel-Space Posterior Probability-Adaptive Oversampling (Kernel-PAO) method, shifting oversampling from the input space to the kernel space. It utilizes Gaussian kernel density estimation to calculate the posterior probability of the minority class, designs a bell-shaped weighting weighting function to concentrate sample generation near the decision boundary, and synthesizes new samples via kernel distance interpolation. An SVM is trained on the augmented Gram matrix to ensure spatial consistency between sample generation and classification. Experiments on the UORED bearing dataset (with imbalance ratios ranging from 1:2 to 1:16) show that Kernel-PAO achieves G-mean and F-value on par with the best oversampling baselines (e.g., SMOTE and uniform oversampling) across all imbalance ratios. Ablation studies confirm the contribution of kernel-space oversampling and identify the RBF kernel and N = 1 as the recommended configuration. Perturbation tests confirm the method's stability under feature uncertainty. Kernel-PAO provides a theoretically rigorous and experimentally validated machine learning solution for imbalanced bearing health monitoring, offering significant potential for engineering applications.