Kurtogram can adaptively select the resonant frequency band, and then the characteristic fault frequency can be obtained by analyzing the selected band. However, the kurtogram is easily affected by random impulses and noise. In recent years, improvements to kurtogram have been concentrated on two aspects: (a) the decomposition method of the frequency band; and (b) the selection index of the optimal frequency band. In this article, a new method called Teager Energy Entropy Ratio Gram (TEERgram) is proposed. The TEER algorithm takes the wavelet packet transform (WPT) as the signal frequency band decomposition method, which can adaptively segment the frequency band and control the noise. At the same time, Teager Energy Entropy Ratio (TEER) is proposed as a computing index for wavelet packet subbands. WPT has better decomposition properties than traditional finite impulse response (FIR) filtering and Fourier decomposition in the kurtogram algorithm. At the same time, TEER has better performance than the envelope spectrum or even the square envelope spectrum. Therefore, the TEERgram method can accurately identify the resonant frequency band under strong background noise. The effectiveness of the proposed method is verified by simulation and experimental analysis.

Feature extraction and fault recognition of vibration signals are two important parts of bearing fault diagnosis. In this article, a fault diagnosis method based on teager energy entropy of each wavelet subband and improved fuzzy C-means is proposed. First, bearing vibration signal is decomposed into wavelet packet and normalized teager energy entropy feature matrix is constructed as clustering index. Principal component analysis is applied to the high-dimensional teager energy entropy feature matrix, and the principal components are determined by cumulative contribution rate to construct feature vectors. Then, the mean-shift method is used to search for the high probability density region of principal components so as to determine the cluster number and cluster center. Finally, fuzzy C-means is used to update the clustering center and membership value, and confirm the optimal clustering center and the type of clustering. Through simulated and experimental analysis, the proposed method has two advantages. The feature vector constructed by this method has better specificity than wavelet energy entropy. The initial clustering center of fuzzy C-means is confirmed by the mean-shift method, which can improve the clustering performance of fuzzy C-means and solve the misclassification without preknowing the number of categories.

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature via the envelope demodulation method. However, the FSK method has some limitations due to its susceptibility to noise and random knocks. To overcome this shortage, a new method is proposed in this paper. Firstly, we use the binary wavelet packet transform (BWPT) instead of the finite impulse response (FIR) filter bank as the frequency band segmentation method. Following this, the Shannon entropy of each frequency band is calculated. The appropriate center frequency and bandwidth are chosen for filtering by using the inverse of the Shannon entropy as the index. Finally, the envelope spectrum of the filtered signal is analyzed and the faulty feature information is obtained from the envelope spectrum. Through simulation and experimental verification, we found that Shannon entropy is—to some extent—better than kurtosis as a frequency-selective index, and that the Shannon entropy of the binary wavelet packet transform method is more accurate for fault feature extraction.

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature by the envelope demodulation method. However, in practical applications, the fault source may be located in different resonant frequency bands; plus in noise interference, the weak side of the compound fault is not easy to be identified by the FSK. In order to improve the accuracy of fast spectral kurtosis analysis method, a modified method based on maximum correlation kurtosis deconvolution (MCKD) is proposed. According to the possible fault characteristic frequencies, the period of MCKD is calculated, and the appropriate filter length is selected to filter the original compound fault signal. In this way, the compound fault located in different resonance bands is separated. Then, the signal after MCKD filtering is analyzed by FSK. Through the simulation and experimental analysis, the MCKD can separate the compound fault information in different frequency band and eliminate the noise interference; the FSK can accurately identify the resonance frequency and identify the weak fault characteristics of compound fault.

At present, the fault diagnosis methods for rolling bearings are all based on research with fewer fault categories, without considering the problem of multiple faults. In practical applications, the coexistence of multiple operating conditions and faults can lead to an increase in classification difficulty and a decrease in diagnostic accuracy. To solve this problem, a fault diagnosis method based on an improved convolution neural network is proposed. The convolution neural network adopts a simple structure of three-layer convolution. The average pooling layer is used to replace the common maximum pooling layer, and the global average pooling layer is used to replace the full connection layer. The BN layer is used to optimize the model. The collected multi-class signals are used as the input of the model, and the improved convolution neural network is used for fault identification and classification of the input signals. The experimental data of XJTU-SY and Paderborn University show that the method proposed in this paper has a good effect on the multi-classification of bearing faults.