Rolling bearings are critical in industrial mining machinery. Due to strong Gaussian noise, frequent random shocks, and disordered loads in industrial settings, it is usually difficult to detect weak fault symptoms in vibration signals from a bearing. To detect incipient bearing faults, this paper proposes a new multi-domain kernel extreme learning machine (MKELM) based on variational modal decomposition (VMD) and a cyclic correntropy function. A normalized approximation algorithm for a cyclic correntropy function (NACCF) was first built to suppress the impulsive background noise. This approach is suitable for machine learning. To eliminate the Gaussian noise effectively, genetic mutation particle swarm optimization (GMPSO) with cyclic information entropy (CIE) was used to optimize the VMD parameters. The CIE was created as a fitness function in GMPSO to search for the best hyperparameters. It can be used to select effective intrinsic mode functions (IMFs) to reconstruct denoised signals. Then, statistical functions based on NACCF were used to extract the cyclic frequency-domain characteristics of the denoised signal, and the singular values of the IMFs were obtained as timedomain features of the signal. Finally, the multi-dimensional features from the two domains were input into MKELM to classify the health of the bearing. Experimental studies were carried out to investigate the proposed method in bearing fault detection and identification. The results demonstrated the effectiveness of the proposed method in motor-bearing failure detection and its robustness to noise when analyzing bearing vibration signals under different working loads.

Bearing damage is one of the main causes of mechanical malfunction , and its vibration signal has the characteristics of nonlinear, non-stationary and difficult to be extracted. In order to solve the problem of eigenvalues and eigenvectors, the concept of multi-scale sub-band sample entropy is proposed, which cannot accurately extract weak signals from complexity. First, the wavelet packet decomposition of multi-scale signals is obtained, and then, the scale of each signal is sub-band-decomposing. Finally, the sample entropy of each subband can be solved. This method can deeply mine the basic characteristic signals. In this paper, a set of normal fault, inner ring fault, spherical fault and outer ring fault signal are used as the original data to verify the effectiveness of the method. The experimental results show that the method can effectively extract bearing fault features.

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