Synthetic minority oversampling (SMOTE) has been widely used in dealing with the imbalance classification in the mechanical fault diagnosis field. However, the classical SMOTE model generates poor quality data, which leads to a low diagnostic accuracy of the classification model. This article proposes an oversampling generation model based on the Gaussian mixture model (GMM) and boundary joint optimization (BDOP-GMM-SMOTE). First, GMM is utilized to cluster minority class bearing fault data, and weights of different classes should be distributed according to the cluster density distribution function. Then, the minority classes should be resampled to balance intraclass. Third, the data boundary is established by calculating intraclass and interclass distances between the minority class and other failure-class samples. And penalty coefficient is introduced to optimize data generation boundary by minimizing intraclass and maximizing interclass principle. Afterward, a generated fault dataset satisfied intraclass and interclass balance is obtained. Finally, the generation effectiveness and robustness of the proposed method are verified by bearing experiment data, especially in diagnostic accuracy and processing speed.

Traditional bearing fault diagnosis mainly based on periodic feature extraction from bearing fault pulses. However, the diagnostic accuracy was limited due to the absence of rotation speed information. Firstly, through envelope analysis and order tracking to extract roller passing frequency (RPF) and fault order, this paper verifies the performance of vibration and acoustic emission signals (AE) on diagnosis of bearing fault in low-speed. Secondly, the advantages of fault source localization of AE are also verified and analyzed. In order to accurately extract the pulse generated by the fault source, a method for AE event extraction using short time autocorrelation function is proposed, which is verified to be efficient and reliable under different working conditions of low-speed bearings.

Recurrence-plot (RP) analysis is a graphical tool to visualize and analyze the recurrence of nonlinear dynamic systems. By combining the advantages of the RP and a convolutional neural network (CNN), a fault-classification scheme for planetary gear sets is proposed in this paper. In the proposed approach, a vibration is first picked up from the planetary-gear test rig and converted into an angular-domain quasistationary signal through computed order tracking to eliminate the frequency blur caused by speed fluctuations. Then, the signal in the angular domain is divided into several segments, and each segment is processed by the RP to constitute the training sample. Moreover, a two-dimensional CNN model was developed to adaptively extract faulty features. Experiments on a planetary-gear test rig with four conditions under three operating speeds were carried out. The results of measured vibration demonstrated the validity of CNN and recurrence plot analysis for the fault classification of planetary-gear sets.

Recently, the enhanced frequency band entropy (EFBE) was proposed based on the replacement of short-time Fourier transform (STFT) with wavelet packet transform (WPT). In view of the shortcomings of EFBE, a feasible solution is provided, namely modified frequency band envelope kurtosis (MFBEK), which can be described as follows: Firstly, the modified adaptive resonance bandwidth (MARB) based on the bearing inner-race fault frequency is proposed. The kurtosis of the envelope signal as an available indicator and the MARB are used to determine the optimal depth of MFBEK. Secondly, this special case, that is, the resonant frequency occurs at the junction of two adjacent sub-bands is considered, and a corresponding effective solution is provided to determine the optimal sub-band(s). Then, the reconstructed signal can be obtained. And then, if necessary, a band-pass filter is designed to process the reconstructed signal to enhance the noise reduction performance. Finally, envelope power spectrum analysis is performed on the reconstructed signal or the filtered signal to extract the fault characteristic frequency. In addition, a modified indicator is proposed to measure the analysis results. Analysis results on simulated and vibration signals measured from actual bearing have revealed that the MFBEK can obtain more robust performance.