Vibration Signal Analysis of Rolling Bearing Based on Permutation Entropy

Permutation entropy (PE) is usually used as a statistical feature combined with classification algorithms to identify the state of rolling bearings and has achieved high recognition accuracy. The purpose of this paper is to study the potential behavior of PE at varying parameters in rolling bearing vibration signals for the normal state and three fault states (including inner race, outer race, and ball fault). The influence of the vibration signal length (N) and the parameter embedding dimension (m) on the PE were studied, and the signal length when they reached stability was analyzed. Then PE with varying signal lengths of each state at m=3 and m=5 was compared. Finally, the ordinal patterns found and their relative frequency in each state's vibration signal with varying m were analyzed, and the differences were discussed. The results indicated that the different states of rolling bearing could be effectively distinguished with a shorter time series than the $N \gg m !$ recommendation. PE could sensitively distinguish between the normal state and fault states, which may be due to the difference in the number of ordinal patterns found at the same length signal and the difference in relatively high-frequency ordinal pattern types and their relative frequency. The identification of outer race and ball fault is more difficult than that of inner race fault by PE, which may be due to the fact that the ordinal patterns and their relative frequency in the vibration signals between the outer race and ball fault are similar to a certain extent, while inner race fault is different from them.