A Novel Nonlinear Analysis Tool: Multi-scale Symbolic Sample Entropy and Its Application in Condition Monitoring of Rotary Machinery

Sample entropy (SE) has been employed for fault diagnosis of rotary machinery (FDRM). However, SE has low computation efficiency for long time series. To solve this problem, symbolic sample entropy (SSE), a novel measure of time series regularity, is proposed to estimate the complexity. However, SSE fails to account for the multiple scale information inherent in measured vibration signals. Therefore, we combine the concept of multi-scale analysis with SSE, called multi-scale SSE (MSSE). To evaluate the effectiveness of the proposed MSSE method, we apply several simulated signals to verify the merits of SSE in impulsion detection and calculation efficiency. Furthermore, we utilize one experimental data to validate its effectiveness in recognizing several fault types of rotary machinery. Experimental results indicate that MSSE has an advantage in extracting fault features compared with multi-scale entropy (MSE), multi-scale fuzzy entropy (MFE), and multi-scale permutation entropy (MPE) methods.