Sample entropy is a nonlinear dynamic analysis method of measuring time sequence complexity

and is also a powerful tool for fault characterization of rolling bearing. However

one-dimensional sample entropy only analyzes the signal information in time domain

while two-dimensional sample entropy can measure the complexity information of the signal in time-frequency distribution. But two-dimensional sample entropy is low efficient and easy to be disturbed by noise. To this end

using symbolic dynamic filtering to eliminate background noise and improve computational efficiency

the paper proposes a new measure of two-dimensional symbolic sample entropy for the complexity of signal time-frequency distributions. At the same time

in order to extract the multi-scale feature of the signal

the two-dimensional symbol sample entropy is extended to multi-scale analysis

and two-dimensional multi-scale symbol sample entropy is proposed. Then a new fault diagnosis method of rolling bearing is proposed based on two-dimensional multi-scale symbol sample entropy and firefly algorithm to optimize support vector machine. Finally

it is compared with the two-dimensional multi-scale sample entropy and two-dimensional multi-scale arrangement by analog signals and measured data analysis

and the results show that the fault diagnosis method is more accurate.