Bearing fault diagnosis based on incomplete Cholesky decomposition correntropy and bi-spectrum

Aiming at the problem of traditional bi-spectrum being difficult to effectively deal with strong noise interference and large calculation amount of correntropy, a bearing fault diagnosis method based on incomplete Cholesky decomposition correntropy and bi-spectrum analysis was proposed. Under the case of not solving kernel matrix, firstly, incomplete Cholesky decomposition algorithm and kernel function were used to calculate the lower triangular matrix of low rank decomposition of kernel matrix. Secondly, principal components of the lower triangular matrix were selected using Gini index, and principal components of the lower triangular matrix were used to calculate the low rank approximate matrix of kernel matrix and then the correntropy of bearing vibration signal was calculated. Finally, the bi-spectrum of correntropy of the signal was calculated, and bearing faults were identified using bi-spectrum characteristics of correntropy. It was shown that using incomplete Cholesky decomposition algorithm and Gini index to calculate correntropy of signal can not only compress the amount of data, highlight transient impact characteristics of bearing faults, and effectively suppress effects of noise, but also improve calculation efficiency and reduce occupation of computer memory. Simulated and actually measured bearing fault vibration signals' analysis showed that strong background noise can cause failure of traditional bi-spectrum fault diagnosis method, while the proposed method based on correntropy and bi-spectrum analysis can extract transient impact characteristics of bearing faults under strong background noise interference and accurately identify bearing faults. The proposed method's performance is better than those of traditional bi-spectrum and wavelet transform domain bi-spectrum, it is an effective method for bearing fault diagnosis. © 2022, Editorial Office of Journal of Vibration and Shock. All right reserved.