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.

Rolling bearings are key components of rotating machinery. Thus the prediction of remaining useful life (RUL) is vital in condition based maintenance. This paper proposes a new method for RUL prediction of bearings based on time-varying Kalman filter, which can automatically match different degradation stages of bearings and effectively realize the prediction of RUL. The evolution of monitoring data in normal and slow degradation stages is linear trend, and the evolution in accelerated degradation stage is non-linear. So Kalman filter models based on linear and quadratic functions are established respectively. Meanwhile, a sliding window relative error is constructed to adaptively judge the bearing degradation stages. It can automatically switch filter models to process monitoring data at different stages. Then the RUL can be predicted effectively. Two groups of bearing run-to-failure datasets are utilized to demonstrate the feasibility and validity of the proposed method.

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.

A novel method is proposed for quantitative and localization diagnosis of a bearing outer ring defect in this paper. This method aims to distinguish these defects with different angular positions and different sizes based on the natural multiples of the ball angular spacing. Defects that differ in size by natural multiples of the ball angular spacing will have the same time interval, which may lead to misdiagnosis. Distinguishing such defects accurately is the goal for some industries. Therefore, the synchronized signal in the vertical and horizontal directions of the bearing systems with different angular positions and different size defects are quantitatively analyzed based on the presented five indices to explore the mechanism and method of distinguishing these defects. The simulation and experimental results show that the vertical-horizontal synchronized root mean square (VHSRMS) index can distinguish such defects effectively, and the defect angle position can be diagnosed using the VHSRMS ^-1 . More importantly, the VHS analysis method expands the location of the outer ring defect to 265-275° in quantitative diagnosis and realizes the localization diagnosis of the defect angle position. The research results provide a new approach and method for quantitative and localization diagnosis of a defective bearing.

An enhanced intelligent diagnosis method for rotary equipment is proposed based on multi-sensor data-fusion and an improved deep convolutional neural network (CNN) models. An improved CNN based on LeNet-5 is constructed that can enhance the features of the samples by stacking bottleneck layers without changing the size of the samples. A new conversion approaches are also proposed for converting multi-sensor vibration signals into color images, and it can refine features and enlarge the differences between different types of fault signals by the fused images transformed in red-green-blue (RGB) color space. In the last stage of network learning, visual clustering is realized with t-distributed stochastic neighbor embedding (t-SNE) to evaluate the performance of the network. To verify the effectiveness of the proposed method, examples in practice such as the diagnosis for the wind power test rigs and industrial fan system are provided with the prediction accuracies of 99.89% and 99.77%, respectively. In addition, the efficiency of other comparative baseline approaches such as the deep belief network (DBN) and support vector machine (SVM) is evaluated. In conclusion, the proposed intelligent diagnosis method based on multi-sensor data-fusion and CNN shows higher prediction accuracy and more obvious visualization clustering effects.