Extracting weak fault characteristics with adaptive singular value decomposition and stochastic resonance

Abstract: Bearings are the important component of agricultural machinery and equipment, whose failure may seriously endanger the healthy operation of equipment and even lead to bodily injury. So the fault diagnosis of agricultural machinery and equipment gains more and more attention. Using the vibration signal to extract the fault characteristics is the most common method, but it is difficult to extract the weak fault characteristics in strong background noise. Therefore, the extraction of weak fault characteristics with very low SNR (signal-to-noise ratio) under strong background noise becomes the key to the fault diagnosis of agricultural machinery bearings. There are 2 general methods for weak feature extraction under weak background noise. One method is to extract weak faults from the perspective of suppressing or eliminating noise. The other one is not to eliminate noise but using noise to improve the SNR to extract the weak fault characteristics, such as stochastic resonance (SR) theory. Compared to the traditional noise reduction method, SR makes use of noise energy transfer to weak signal, so the weak fault characteristics are enhanced while some of the noises are weakened. Because of the excellent features of extracting weak fault characteristics in strong background noise, SR has become a hot topic for many scholars in recent years. In this paper, the weak fault characteristics extraction method of SR based on adaptive SVD (singular value decomposition) was proposed. In the method, firstly, the original signal was decomposed by singular value and reconstructed to obtain the component signal; the difference spectrum of mutual information was constructed, the mutual information of each component signal and the original signal was weighed, and the number of valid singular values was selected adaptively, in order to overcome the problem of existing methods including human subjective choice or only considering the size of singular values and other deficiencies. Using the mutual information difference spectrum, 3 and 10 effective singular values were obtained in the simulation signal and bearing outer ring signal, respectively. Secondly, the adaptive SR was performed for the component signal corresponding to the selected effective singular value which enhances weak fault characteristics. Finally, the enhanced component signals were statistically averaged to extract the weak fault characteristics. In this paper, constructing the mutual information differential spectrum, and considering the mutual information of the component signal and the original signal, on the one hand, it avoids the elimination of the useful signals; on the other hand, the adaptive selection is realized which avoids the subjectivity of the artificial selection. In addition, due to the presence of strong background noise, the larger singular value may have smaller mutual information, but it is not valid singular value. It indicates that large singular value does not necessarily contain useful information, and there may be noise interference. Hence, the selection of effective singular values should not be based on the size of the singular value. The above analysis shows that it is difficult to extract the weak fault characteristics by SVD in strong background noise. We combine the 2 methods to process the effective component signal selected by mutual information difference spectrum in SR, and the maximum spectral frequency of each component is obtained. The statistical average is used to achieve noise filtering in order to highlight the characteristics of weak fault frequency. The results of simulation and bearing outer ring test show that, the proposed method is superior to the SVD and SR method. The method can effectively extract 100 and 155.5 Hz weak fault characteristics respectively for simulation signal and bearing outer ring signal. The proposed method can be applied not only to the fault diagnosis of bearing in strong noise background, but also to provide reference for bearing fault diagnosis of agricultural machinery and equipment.