Research into rolling bearing fault diagnosis methods is of great significance because rolling bearings are a key part of mechanical equipment. The effect of iterative generalized demodulation (IGD) on the demodulation of the fundamental frequency component is obvious in the fault diagnosis of rolling bearings at variable speeds. However, there is a problem; the frequency curve of the demodulation octave frequency component overlaps, and multiple determinations of the bandpass filter parameters produce an artificial error that leads to the misdiagnosis of faults. Therefore, a method for rolling bearing fault diagnosis based on adaptive generalized demodulation (AGD) is proposed. First, the resonance band is intercepted by the fast kurtogram and its envelope results. Second, the adaptive chirp mode decomposition (ACMD) algorithm is used to decompose the envelope signal, the relationship between the time and frequency of the signal is clearly characterized by the form of multimedia pictures, and the instantaneous frequency of each signal component is calculated. Third, the instantaneous frequency is used as the phase function to perform generalized demodulation for each signal component. Last, all the demodulated signals are accumulated, and a fast Fourier transform (FFT) is used to extract the fault's characteristic frequency. The proposed method is compared with IGD by using simulation signals and actual bearing signals collected by sensors under the Internet of Things (IoT). An adaptive diagnosis function is realized through this proposed method at variable speeds. Moreover, the average frequency spectrum identification rate of rolling bearing faults is improved by more than 2.6 times compared with that of the IGD in the simulation signal verification and by more than 1.7 times compared with that of the IGD in the real signal verification. This method is strongly immune to noise. INDEX TERMS Fault diagnosis, rolling bearing, adaptive generalized demodulation, Internet of Things, multimedia.

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Intelligent fault diagnosis of rolling bearings under non-stationary and time-varying speed conditions is still a challenging task. At the same time, a reasonable explanation for an intelligent diagnosis model based on features is currently lacking. Therefore, we exploit an explainable one-dimensional convolutional neural network (1DCNN) model by combining with the demodulated frequency features of vibration signals and apply it to the fault classification of rolling bearings under time-varying speed conditions. First, the speed signals obtained by the speed encoder were transformed into generalized demodulation operator (GDO). Second, combined with the sensitive frequency band and GDO, the generalized demodulation algorithm was used to extract the frequency features from the amplitude envelope of the vibration signal. Subsequently, the proposed lightweight 1DCNN was trained to classify the frequency features and identify the health states of the rolling bearing. Finally, the local interpretable model-agnostic explanations model was utilized to explain the proposed model based on the features which own weight. It is found that the internal classification mechanism of the lightweight 1DCNN is realized according to the distribution of fault features, which is consistent with the process of human brain analysis. Two kinds of time-varying speed datasets which come from the University of Ottawa and XJTU are tested and verified. The results show that compared with other intelligent fault diagnosis methods, the identification error of the proposed method is lower and the diagnosis stability is better. The average diagnostic accuracy was 96.26% and 99.82%, respectively.

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The data-driven intelligent fault diagnosis method of rolling bearings has strict requirements regarding the number and balance of fault samples. However, in practical engineering application scenarios, mechanical equipment is usually in a normal state, and small and imbalanced (S & I) fault samples are common, which seriously reduces the accuracy and stability of the fault diagnosis model. To solve this problem, an auxiliary classifier generative adversarial network with spectral normalization (ACGAN-SN) is proposed in this paper. First, a generation module based on a deconvolution layer is built to generate false data from Gaussian noise. Second, to enhance the training stability of the model, the data label information is used to make label constraints on the generated fake data under the basic GAN framework. Spectral normalization constraints are imposed on the output of each layer of the neural network of the discriminator to realize the Lipschitz continuity condition so as to avoid vanishing or exploding gradients. Finally, based on the generated data and the original S & I dataset, seven kinds of bearing fault datasets are made, and the prediction results of the Bi-directional Long Short-Term Memory (BiLSTM) model is verified. The results show that the data generated by ACGAN-SN can significantly promote the performance of the fault diagnosis model under the S & I fault samples.