Multiscale permutation entropy based on natural visibility graph and its application to rolling bearing fault diagnosis

Rolling bearings being important components of mechanical equipment, the accurate fault diagnosis method of rolling bearings is of great importance to ensure production safety. Permutation entropy is a nonlinear measure of the irregularity of time series, which involves calculating permutation patterns, that is, defining permutations by comparing adjacent values of the time series. When using graph signal processing technology to analyze the vibration signal of rolling bearing, the natural visibility graph (NVG) can better reflect the dynamic characteristics of the vibration signal than path graph (PG). In this paper, the multiscale permutation entropy (MPE) is defined on NVG, and it is used to characterize the different fault characteristics of rolling bearings. The sand cat swarm optimization (SCSO) algorithm is employed to optimize the parameters of support vector machine (SVM); The MPEs of different faults of rolling bearing which defined on NVG are regarded as the fault feature set input into optimized SVM, and it is applied to characterize the different fault characteristics of rolling bearings, realizing fault diagnosis of rolling bearing. The proposed method is used to analyze the experimental data which contain both normal and faulty rolling bearings. The experiment results show that the proposed method can diagnose the bearing faults effectively. The MPE based on NVG is superior to MPE based on PG and MPE based on the vibration signal in distinguishing the different damage states of rolling bearings. The classification accuracy of optimized SVM based on SCSO algorithm is higher than other classical models. The effectiveness and feasibility of defining entropy on the graph signal and as the fault feature vectors for rolling bearing to realize fault diagnosis is validated. The results indicate that the proposed method can effectively detect bearing faults, and demonstrate its effectiveness and robustness for rolling bearing fault diagnosis.