Multiscale Weighted Motif Entropy based on Radius Constrained Arc-Limited Penetrable Visibility Graph: Concepts and applications

The complexity, nonlinearity, and noise interference inherent in vibration signals pose a continuous challenge to the accurate diagnosis of rolling bearing faults. Under these conditions, traditional signal processing techniques often fail to robustly extract informative features. In recent years, visibility graphs have garnered significant attention due to their ability to effectively integrate graph theory and nonlinear dynamics in the analysis of complex signals. However, traditional visibility graphs exhibit poor noise resistance and lack quantitative evaluation of graph structures. Therefore, this study proposes a Radius Constrained Arc-Limited Penetrable Visibility Graph (RCALPVG) methodology and employs the Weighted Motif Entropy (WME) technique to quantitatively evaluate the RCALPVG network, thereby quantifying the complexity of its graph structure. First, the RCALPVG is compared with commonly used visibility graph models in terms of their features. The results indicate that RCALPVG offers significant advantages in classifying various signal types and exhibits greater robustness against noise interference. Next, the method was applied to diagnose rolling bearing faults. By integrating multiscale analysis, a graph multiscale WME model was developed to characterize various fault features of rolling bearings. Then, these features were input into a classification algorithm for diagnosing rolling bearing fault tasks. Multiple experiments were conducted using a real-world dataset to validate the proposed method’s efficacy. The experimental results demonstrate that the proposed method achieved the highest fault recognition accuracy under two specific operating conditions. Even with only 10% of the training dataset, the method exhibited excellent classification ability, with an average recognition accuracy of 98.64%. Therefore, these results validate the efficacy and feasibility of using WME in the graph domain for extracting fault features and performing rolling bearing fault diagnosis.