Multi-scale permutation entropy (MPE) is an effective nonlinear dynamic approach for complexity measurement of time series and it has been widely applied to fault feature representation of rolling bearing. However, the coarse-grained time series in MPE becomes shorter and shorter with the increase of the scale factor, which causes an imprecise estimation of permutation entropy. In addition, the different amplitudes of the same patterns are not considered by the permutation entropy used in MPE. To solve these issues, the time-shift multi-scale weighted permutation entropy (TSMWPE) approach is proposed in this paper. The inadequate process of coarse-grained time series in MPE was optimized by using a time shift time series and the process of probability calculation that cannot fully consider the symbol mode is solved by introducing a weighting operation. The parameter selections of TSMWPE were studied by analyzing two different noise signals. The stability and robustness were also studied by comparing TSMWPE with TSMPE and MPE. Based on the advantages of TSMWPE, an intelligent fault diagnosis method for rolling bearing is proposed by combining it with gray wolf optimized support vector machine for fault classification. The proposed fault diagnostic method was applied to two cases of experimental data analysis of rolling bearing and the results show that it can diagnose the fault category and severity of rolling bearing accurately and the corresponding recognition rate is higher than the rate provided by the existing comparison methods.

There are more and more bearing fault types under considering the fault location and degree, and the corresponding fault classification task is becoming increasingly heavy. Raw signals that have not been processed or simply processed are directly input into convolutional neural network (CNN) for classification, resulting in poor classification performance. Aiming at this issue, a time–frequency joint metric feature extraction technique named non-negative wavelet matrix factorization (NWMF) is developed to extract more effective features by comprehensively leveraging the advantages of continuous wavelet transform and non-negative matrix factorization. Based on the NWMF and CNN, an effective intelligent diagnosis framework is constructed to detect bearing fault. In the proposed framework, based on the NWMF, a non-negative basic matrix with smaller size is calculated from the original time–frequency spectrum and it includes bearing fault-related internal core information. In addition, a novel CNN is developed to identify locations and sizes of fault bearing based on the calculated internal core information. For verifying the effectiveness of the proposed framework in handling heavier tasks, the types of bearing faults in the experiments are set up to 15, the results and comparative analysis reveal that the feasibility and superiority of the proposed method are much better than the other traditional machine learning methods and original deep learning methods, such as the support vector machine, random forest and residual neural network.