Composite Multiscale Transition Permutation Entropy-Based Fault Diagnosis of Bearings

When considering the transition probability matrix of ordinal patterns, transition permutation entropy (TPE) can effectively extract fault features by quantifying the irregularity and complexity of signals. However, TPE can only characterize the complexity of the vibration signals at a single scale. Therefore, a multiscale transition permutation entropy (MTPE) technique has been proposed. However, the original multiscale method still has some inherent defects in the coarse-grained process, such as considerably shortening the length of time series at large scale, which leads to a low entropy evaluation accuracy. In order to solve these problems, a composite multiscale transition permutation entropy (CMTPE) method was proposed in order to improve the incomplete coarse-grained analysis of MTPE by avoiding the loss of some key information in the original fault signals, and to improve the performance of feature extraction, robustness to noise, and accuracy of entropy estimation. A fault diagnosis strategy based on CMTPE and an extreme learning machine (ELM) was proposed. Both simulation and experimental signals verified the advantages of the proposed CMTPE method. The results show that, compared with other comparison strategies, this strategy has better robustness, and can carry out feature recognition and bearing fault diagnosis more accurately and with improved stability.