Rotating machinery is widely used in industrial production, and its reliable operation is crucial for ensuring production safety and efficiency. Mechanical equipment often faces the challenge of variable speeds. However, existing research pays little attention to domain-adaptive and cross-device diagnostic tasks under time-varying conditions. To fill this research gap and address the serious domain shift problem in cross-device fault diagnosis tasks under time-varying speeds, this article proposes a deep multilayer sparse regularization time-varying transfer learning network (DMsrTTLN) with dynamic Kullback–Leibler divergence weights (DKLDW). The main contributions and innovations of DMsrTTLN are as follows: First, a multilayer sparse regularization module to effectively reduce speed fluctuations; second, an amplitude activation function to enhance the differentiation of data with different labels; third, the kurtosis maximum mean discrepancy, where the Gaussian kernel function adaptively adjusts according to the kurtosis values of the data to enhance domain adaptation capability; and finally, the DKLDW mechanism dynamically balances distance and adversarial metrics to improve model convergence and stability. The DMsrTTLN model with DKLDW exhibits strong generalization performance in cross-device domain shift scenarios. Experimental validation in the same-device and cross-device scenarios is performed on three mechanical machines under time-varying speeds, and the results are compared with those of six state-of-the-art approaches. The results showed that the DMsrTTLN has a better convergence effect and greater diagnostic accuracy.

Bearing fault diagnosis plays a pivotal role in the safe and reliable operation of modern mechanical systems. However, the existing fault diagnosis methods rarely deal with the problem of category imbalance and various speeds concurrently, which cannot work effectively in practical scenarios. Considering the underlying similarities of data in frequency domain, data mining under various speeds can help to reduce the deviation of domain distribution. Therefore, a novel fault diagnosis method based on spectrum alignment (SA) and deep transfer convolution neural network (DTCNN) is proposed, where the SA and data augmentation module are designed to extract SA features from the unbalanced bearing data. The DTCNN model based on joint distribution adaptation is built to facilitate learning reliable domain-invariant features. Different from the existing studies, a more general transfer task with time-varying speed is considered, even with complex faults. For 14 transfer tasks in two unbalanced fault diagnosis cases under variable speed, the average accuracy, F1-score, and area under curve of the proposed method can reach more than 97.76%, 97.57%, and 98.75%, respectively. The results show that this method has superior diagnostic effect and better generalization ability than various state-of-the-art methods.