A Fast Signal Estimation Method Based on Probability Density Functions for Fault Feature Extraction of Rolling Bearings

Fault diagnosis of rolling bearings is essential to ensure the efficient and safe operation of mechanical equipment. The extraction of fault features of the repetitive transient component from noisy vibration signals is key to bearing fault diagnosis. However, the bearing fault-induced transients are often submerged by strong background noise and interference. To effectively detect such fault-related transient components, this paper proposes a probability- and statistics-based method. The maximum-a-posteriori (MAP) estimator combined with probability density functions (pdfs) of the repetitive transient component, which is modeled by a mixture of two Laplace pdfs and noise, were used to derive the fast estimation model of the transient component. Subsequently, the LapGauss pdf was adopted to model the noisy coefficients. The parameters of the model derived could then be estimated quickly using the iterative expectation-maximization (EM) algorithm. The main contributions of the proposed statistic-based method are that: (1) transients and their wavelet coefficients are modeled as mixed Laplace pdfs; (2) LapGauss pdf is used to model noisy signals and their wavelet coefficients, facilitating the computation of the proposed method; and (3) computational complexity changes linearly with the size of the dataset and thus contributing to the fast estimation, indicated by analysis of the computational performance of the proposed method. The simulation and experimental vibration signals of faulty bearings were applied to test the effectiveness of the proposed method for fast fault feature extraction. Comparisons of computational complexity between the proposed method and other transient extraction methods were also conducted, showing that the computational complexity of the proposed method is proportional to the size of the dataset, leading to a high computational efficiency.