For the two shortcomings of SVD: (1) the determination of the reconstruction order; (2) the poor noise reduction ability; an enhanced SVD is introduced in this paper. The core ideas include: first, an efficient method to determine the reconstructed order of SVD that the relative-change rate of the singular envelope kurtosis (SEK) is presented, composing improved SVD (ISVD). Then, the method to select the optimal node of wavelet packet transform (WPT) by the criterion of envelope kurtosis maximum (CEKM) is presented, composing improved WPT (IWPT). The flexible filter design and superior noise reduction abilities of the IWPT and the passband denoise ability of the ISVD are organic combined to form E-SVD method. In addition, an indicator is introduced to evaluate the performance of the results. Firstly, performing ISVD on the original signal to obtain the reconstructed signal. Secondly, IWPT is executed on the reconstructed signal to achieve the optimal node. Finally, the filtered signal combined with the envelope power spectrum to extract the bearing fault characteristic frequency. The method's validity and superiority are verified by the analysis of simulated data and actual cases of rolling bearing.

The advent of Industry 4.0 has heightened the demand for the interpretability of intelligent diagnostics, especially for high-risk industrial assets. However, the comprehensive interpretation of neural networks remains inadequately explored. To address this challenge and develop a fully interpretable network, we propose a transparent operator network incorporating a parameterized signal operator node. This node is realized by a learnable Morlet wavelet operator in frequency domain with signal-wise gated matrix and skip connection. By stacking multichannel and multilayered nodes as signal operator layers, along with incorporating statistical features and a linear classifier, all modules are physically understandable. A case study demonstrates that despite having fewer parameters, the proposed model achieves better diagnosis performance. Furthermore, the learnable filters, fault signature enhancement, and physically understandable features demonstrate the transparency of the proposed model, indicating that it offers a promising tool for constructing a knowledge-informed and fully interpretable industrial decisions.

The increasing integration and complexity of rotating machinery have led to the difficulty of its fault diagnosis. Condition-based maintenance (CBM) strategy is becoming more and more important in the initial fault diagnosis of rotating machinery. Resonance demodulation technology is the one fault diagnosis technology widely used in the machinery industry field. Spectral kurtosis (SK) and frequency band entropy (FBE) are two typical resonance demodulation methods, in which SK has been extensively and deeply studied both theoretically and practically, while the FBE has not attracted much attention from researchers. In this paper, two typical resonance demodulation techniques, SK and FBE, and their applications in fault detection of rotating machinery are reviewed and summarized, aiming to provide comprehensive reference resources for the research of the two resonant demodulation methods, FBE and SK. In addition, it is hoped that it will play a certain role in promoting the development of FBE theory. The problems and challenges faced by Resonance demodulation technologies, especially SK and FBE, and their applications in mechanical fault diagnosis are analyzed, in order to provide valuable guidance for researchers. Therefore, the prospects of the two methods are also given. Some examples are offered to illustrate their performance. It is reasonable to expect that the further development of SK, and further research and applications of FBE will flourish in the near future.

The singular value decomposition (SVD) based on the Hankel matrix is commonly used in signal processing and fault diagnosis. The noise reduction performance of SVD based on the Hankel matrix is affected by three factors: the reconstruction component(s), the structure of the Hankel matrix, and the point number of the analysis data. In this article, the three influencing factors are systematically studied, and a method based on correlated SVD (C-SVD) is proposed and successfully applied to bearing fault diagnosis. First, perform SVD analysis on the collected original signal. Then, the reconstructed component(s) determination method of SVD based on the combination of singular value ratio (SVR) and correlation coefficient is proposed. Then, based on the SVR, using the envelope kurtosis as the indicator, the optimal structure of the Hankel matrix (number of rows and columns) is studied. Then, the number of data points of the analysis signal is discussed, and the constraint range is given. Finally, the envelope power spectrum analysis is performed on the reconstructed signal to extract the fault features. The proposed C-SVD method is compared with the existing typical methods and applied to the simulated signal and the actual bearing fault signal, and its superiority is verified.