Hierarchical Multiscale Fluctuation-Based Symbolic Fuzzy Entropy: A Novel Tensor Health Indicator for Mechanical Fault Diagnosis

Fuzzy entropy (FE), a powerful tool for measuring the complexity of nonlinear time series, has been widely used in bearing fault diagnosis and health monitoring. However, FE measures complexity only at a single scale, failing to consider valuable information in large-scale features of time series and failing to consider both high-frequency information and low-frequency information. To address these limitations, a new tensor-based entropy method called hierarchical multiscale fluctuation-based symbolic FE (HMFSFE) is proposed in this article. The proposed HMFSFE uses wave symbols to quantify the complexity of time series and extract tensor features, enhancing anti-noise performance and computational efficiency. In addition, the HMFSFE assesses the dynamic properties of vibration data across various hierarchical layers and scales to further enhance fault extraction from signals. Based on the superiorities of the HMFSFE in nonlinear feature extraction and unique feature representation, a bearing fault diagnosis method approach based on the HMFSFE and the convolutional neural network (CNN) was proposed. Through analysis of experimental bearing data and comparison with existing fault diagnosis methods, the experimental results demonstrate that the proposed diagnosis scheme excels in health status recognition and offers significant advantages in terms of diagnostic accuracy and stability.