Composite multi-scale phase reverse permutation entropy and its application to fault diagnosis of rolling bearing

Permutation entropy has been used as a powerful nonlinear dynamic tool for randomness measurement of time series and has been used in the area of condition monitoring and early failure fault detection of rolling bearing. However, the detail size relationship between adjacent amplitudes of signal is ignored in the calculation process of the original permutation entropy algorithms. The reverse permutation entropy was developed as a new nonlinear dynamic parameter through introducing distance information to time series with different lengths to improve the performance and stability of permutation entropy. Since the single-scale permutation entropy or reverse permutation entropy cannot completely reflect the complexity features of time series, in this paper, the phase reverse permutation entropy is proposed by introducing phase information into reverse permutation entropy to improve the detection ability of signal dynamic changes as much as possible. Based on phase reverse permutation entropy, the composite multi-scale phase reverse permutation entropy is proposed to extract the complexity information hidden in different time scales and overcome the defects of traditional coarse-grained multi-scale. Also, phase reverse permutation entropy is compared with reverse permutation entropy through simulation data and the result shows that the introduced phase information can increase the sensitivity of phase reverse permutation entropy in mutation characteristics detection of signal. After that, a new fault diagnosis method of rolling bearing was proposed based on composite multi-scale phase reverse permutation entropy for fault feature extraction and the whale optimization algorithm support vector machine for failure mode identification. Finally, the proposed fault diagnosis method was applied to the experimental data analysis of rolling bearing by comparing it with the composite multi-scale permutation entropy, the multi-scale permutation entropy, as well as multi-scale phase reverse permutation entropy based fault diagnosis approaches. The comparison results shows that the proposed method can effectively the fault location and severity of rolling bearings and reaches the highest fault recognition rate among the mentioned methods above.