Rotating machinery often works under time-varying speeds, and nonstationary conditions as well as harsh environments make its key parts, such as rolling bearings and gears, prone to faults. Therefore, a number of fault diagnosis methods including nonstationary signal processing methods and data-driven methods have been developed. This paper presents a comprehensive review on the fault diagnosis of rotating machinery under time-varying speeds proposed mainly during the last five years. First, spectrum analysis-based methods, including order tracking, cyclic spectrum correlation and generalized demodulation, are reviewed. Second, the time-frequency analysis (TFA) methods in machinery fault diagnosis are divided into postprocessing methods and chirplet transform-based methods and are reviewed. Then, the artificial feature extraction- and deep learning-enabled intelligent diagnosis methods proposed specifically for time-varying speed conditions are reviewed. Finally, the research prospects are discussed. We not only review the relevant state-of-art methods and analyze how they overcome the problems caused by speed fluctuations but also discuss their advantages and disadvantages as well as the challenges that will be encountered when applying them to industrial applications. This paper is expected to provide new graduate students, institutions and companies with a preliminary understanding of the methods on this topic.

Planetary gearboxes have various merits in mechanical transmission, but their complex structure and intricate operation modes bring large challenges in terms of fault diagnosis. Deep learning has attracted increasing attention in intelligent fault diagnosis and has been successfully adopted for planetary gearbox fault diagnosis, avoiding the difficulty in manually analyzing complex fault features with signal processing methods. This paper presents a comprehensive review of deep learning-based planetary gearbox health state recognition. First, the challenges caused by the complex vibration characteristics of planetary gearboxes in fault diagnosis are analyzed. Second, according to the popularity of deep learning in planetary gearbox fault diagnosis, we briefly introduce six mainstream algorithms, i.e. autoencoder, deep Boltzmann machine, convolutional neural network, transformer, generative adversarial network, and graph neural network, and some variants of them. Then, the applications of these methods to planetary gearbox fault diagnosis are reviewed. Finally, the research prospects and challenges in this research are discussed. According to the challenges, a dataset is introduced in this paper to facilitate future investigations. We expect that this paper can provide new graduate students, institutions and companies with a preliminary understanding of methods used in this field. The dataset can be downloaded from https://github.com/Liudd-BJUT/WT-planetary-gearbox-dataset.

Rotating machinery fault diagnosis under nonstationary conditions still mainly relies on manual analysis of the frequency spectrums or the time-frequency representations of vibration signals. However, not only do the results of those methods depend on heavily the expert experience, but for some samples, the intricate interference frequency components caused by the complex modulation characteristics and the operation conditions also make it difficult to identify the frequency content. In this article, a novel intelligent fault diagnosis method for rolling bearings under nonstationary conditions is investigated. A new flexible generalized demodulation method is firstly proposed. Different from traditional demodulation methods, it can map the interest time-varying frequencies of extensive samples under different speed conditions to the defined base frequency as well as its multiples, and thus overcomes the effects of operation conditions on demodulation spectrums. Based on the demodulation method, a fault feature extraction method is further proposed to capture the useful fault information in the spectrums. Experiments validate that, for some samples, the health conditions cannot be manually identified by the demodulation spectrums due to the interference frequency components, but can be recognized by the proposed method automatically, and because of the definite physical meaning, the method is more adaptive to new operation conditions.

Deep-learning-based intelligent diagnosis is a popular method to ensure the safe operation of rolling bearings. However, practical diagnostic tasks are often subject to a lack of labeled data, resulting in poor performance in scenarios with insufficient training samples. Moreover, conventional intelligent diagnosis methods suffer from a deficiency in interpretability. In this article, an auto-embedding transformer (AET) method is proposed to implement the interpretable few-shot fault diagnosis of rolling bearings. First, an auto-embedding module is developed to improve the embedding quality of the signal, which is designed based on a novel asymmetric convolutional encoder–decoder architecture. This module can leverage the merits of unsupervised learning in data mining and allow the transformer to learn more diagnostic knowledge from limited data. Second, an attention scoring method is proposed that utilizes positionwise attention to quantify the importance of each signal embedding for diagnosis, thereby interpreting the AET method. Experimental results confirm that, even with limited training samples, the AET method outperforms various comparison methods in terms of recognition accuracy and convergence rate. Furthermore, the attention scores assigned to each embedding facilitate the interpretability of the AET method.

Domain adaptation-based transfer learning methods have been widely investigated in fault diagnosis of rotating machinery, but their basic convolution or recurrent structure is subject to poor global feature representation ability, which hinders the learning of domain-irrelevant modulation information. In addition, the “black box” nature of deep learning models limits their applications in high risk-sensitive scenarios. In this paper, an interpretable domain adaptation transformer (IDAT) is proposed for the transferable fault diagnosis of rotating machinery. First, a multi-layer domain adaptation transformer framework is proposed, which can capture the global information that is crucial for learning the modulation information of different domains, and meanwhile reduce the feature distribution discrepancy. Second, an ensemble attention weight is applied to enable the transfer learning framework to be interpretable, which is implemented by averaging the integral values of the multi-head attention maps along the key direction. In addition, the raw vibration signals are embedded as the input of the model, which provides an end-to-end fault diagnosis. The proposed IDAT is tested by various cross-condition and cross-machine bearing fault diagnosis tasks, and results confirm the advantages of the method.