Research on Probabilistic Contrastive Learning and Quadratic Convolutional Neural Network for Intelligent Diagnosis of Long-Tailed Bearing Data

Deep learning methods have demonstrated impressive effectiveness in diagnosing bearing faults. Nevertheless, their performance tends to decline significantly in the presence of long-tailed distributions, where certain fault types are underrepresented, which is common in industrial environments where fault occurrences are rare. To address the challenges posed by long-tailed data in fault diagnosis, this paper proposes the Probabilistic Contrastive Quadratic Network (PCQNet), a novel framework designed to enhance the diagnostic capabilities of neural networks under class imbalance conditions. PCQNet consists of three core components: a quadratic convolutional residual network that strengthens feature representations through higher-order interactions; a Probabilistic Contrastive Loss (PCL) that models class features using the von Mises-Fisher (vMF) distribution, combining class expectations and prior probabilities to adaptively balance the contributions of each class, effectively mitigating long-tail bias; and a logit-adjusted cross-entropy loss that improves the discrimination ability for minority classes while enhancing classification fairness. The parabolic decay formula dynamically adjusts the dominance of these two loss functions during training, ensuring the model achieves both effective feature learning and accurate classification.The effectiveness of PCQNet is validated on one public dataset and two self-constructed datasets, demonstrating its superior performance in handling long-tailed data. Analysis of the attention mechanism derived from quadratic neurons further explains the excellent feature extraction capability of the quadratic network. Building on this analysis, ablation studies further verify the independent contributions and synergistic effects of each module, confirming their critical roles in improving diagnostic performance.