Balanced Adaptive Logit-Compensated Cross-Entropy and Quadratic Convolutional Network for Intelligent Fault Diagnosis Under Long-Tailed Data Distribution.

Long-tailed data are very common in industrial scenarios because equipment failures occur with a low probability, resulting in far fewer faulty samples than normal ones. However, when facing long-tailed data distributions, existing deep learning methods suffer from a significant degradation in performance and exhibit high bias. To overcome this limitation, this paper proposes a network that combines balanced adaptive logit-compensated cross-entropy loss with quadratic convolution (BALQNet) to improve diagnostic performance under long-tailed data conditions. The proposed method mainly consists of a balanced adaptive logit-compensated cross-entropy loss (BAL) and a quadratic convolution backbone. By jointly incorporating logit compensation, label smoothing, and class reweighting, BAL enhances the optimization of minority-class samples, thereby improving the classifier's ability to distinguish different categories without introducing additional architectural complexity. Meanwhile, quadratic convolution further improves the effectiveness of feature representation learning. Finally, experiments are conducted on self-built bearing, gear, and motor datasets. The results show that BALQNet maintains strong diagnostic performance when handling long-tailed data. In addition, the ablation results provide further evidence for the effectiveness of the proposed approach.