Accidental failures of rotating machinery components such as rolling bearings may trigger the sudden breakdown of the whole manufacturing system, thus, fault diagnosis is vital in industry to avoid these massive economical costs and casualties. Since convolutional neural networks (CNN) are poor in extracting reliable features from original signal data, the time-frequency analysis method is usually called for to transform 1D signal into a 2D time-frequency coefficient matrix in which richer information could be exposed more easily. However, realistic fault diagnosis applications face a dilemma in that signal time-frequency analysis and fault classification cannot be implemented together, which means manual signal conversion work is also needed, which reduces the integrity and robustness of the fault diagnosis method. In this paper, a novel network named WPT-CNN is proposed for end-to-end intelligent fault diagnosis of rolling bearings. WPT-CNN creatively uses the standard deep neural network structure to realize the wavelet packet transform (WPT) time-frequency analysis function, which seamlessly integrates fault diagnosis domain knowledge into deep learning algorithms. The overall network architecture can be trained with gradient descent backpropagation algorithms, indicating that the time-frequency analysis module of WPT-CNN is also able to learn the dataset characteristics, adaptively representing signal information in the most suitable way. Two experimental rolling bearing fault datasets were used to validate the proposed method. Testing results showed that WPT-CNN obtained the testing accuracies of 99.73% and 99.89%, respectively, in two datasets, which exhibited a better and more reliable diagnosis performance than any other existing deep learning and machine learning methods.

Bearing fault features are presented as repetitive transient impulses in vibration signals. Narrowband demodulation methods have been widely used to extract the repetitive transients in bearing fault diagnosis, for which the key factor is to accurately locate the optimal band. A multitude of criteria have been constructed to determine the optimal frequency band for demodulation. However, these criteria can only describe the strength of transient impulses, and cannot differentiate fault-related impulses and interference impulses that are cyclically generated in the signals. Additionally, these criteria are easily affected by the independent transitions and background noise in industrial locales. Therefore, the large values of the criteria may not appear in the optimal frequency band. To overcome these problems, a new method, referred to as multiband envelope spectra extraction (MESE), is proposed in this paper, which can extract all repetitive transient features in the signals. The novelty of MESE lies in the following aspects: (1) it can fuse envelope spectra at multiple narrow bands. The potential bands are selected based on Jarque-Bera statistics of narrowband envelope spectra; and (2) fast independent component analysis (fastICA) is introduced to extract the independent source spectra, which are fault- or interference-related. The multi-band strategy will preserve all impulse features and make the method more robust. Meanwhile, as a blind source separation technique, the fastICA can suppress some in-band noise and make the diagnosis more accurate. Several simulated and experimental signals are used to validate the efficiency of the proposed method. The results show that MESE is effective for enhanced fault diagnosis of rolling element bearings. Bearing faults can be detected even in a harsh environment.

A vibration signal observed from a gearbox is normally composed of the vibrations of bearing and gear components as well as the strong background noise. Sparse regularization performs as an effective method to deal with vibration signal denoising and compound fault diagnosis for the gearbox. In this article, a multivariate and non-convex logarithm penalty based on the generalized infimal convolution smoothing (GICS) is deduced. To guarantee the global minimum of the overall cost function, we also derive a convexity condition to prescribe the non-convex penalty. In this way, the optimal sparse solution to the cost function can be calculated by a convex algorithm. Multiplied by respective transform matrices, all fault components in a compound signal can be simultaneously reconstructed, and then each fault characteristic frequency can be extracted. Numerical and experimental analyses demonstrate the effectiveness of the proposed method. Compared with the classical convex $L1$ norm and newly developed non-convex generalized minimax-concave (GMC) penalties, the proposed method is superior in terms of inducing sparsity effectively and enhancing the estimation accuracy of signal components.