## 3 Results
### Application for Reciprocating Compressor Fault Diagnosis
The journal and bushing usually impact twice for their relative movement direction change two times in one rotation period, and these strong contact forces lead to a peak on double rotation frequency in the envelope frequency spectrum as shown in Figure 17. The vibration signals of the reciprocating compressor, however, may exhibit many interference frequencies due to the nonlinear factors such as clearance and stiffness present in the complex vibration transmission path. This submerges the double rotation frequency caused by bearing clearance and prevents the accurate identification of fault information. As a result, reliable identification of the large bearing clearance status from the noisy vibration signal requires the use of a suitable feature extraction approach, such as LMD. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Type** & **Parameter Value** \\ \hline Sensitivity (mV/ms\({}^{-2}\)) & 10.04 \\ Maximum lateral sensitivity ratio (\%) & \textless{}5 \\ Maximum allowable acceleration (ms\({}^{-2}\)) & 5\(\times 10^{2}\) \\ Electrical property & + \\ Operating temperature (\({}^{\circ}\)C) & \textless{}40\textless{}120 \\ Working current (mA) & 2\textless{}10 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main parameters of CA-YD-186 acceleration sensor. Figure 14: Connecting rod and bearing bushing for oversized clearance fault test. (**a**) Normal clearance bushing. (**b**) Medium-worm bushing. (**c**) Connecting rod. Figure 15: Vibration signal of reciprocating compressor in normal bearing clearance. Usually, the main fault information is contained in the first several PF components, so the first three PF components are given in Figures 18-21 for four LMD methods. We can see that the periodical shocks caused by bearing clearance dominate the first PF component and that the frequency and amplitude steadily decrease in the succeeding PF components. The mutation of the envelope estimation function causes a significant distortion in the second and third PF components of CSILMD. The decomposition results of LMD and MPCHILMD have some local distortion in their second and third PF components, and those of the DIMIRLMD are relatively stable. Figure 16: Vibration signal of reciprocating compressor in oversized bearing clearance. Figure 17: Envelope frequency spectrum of fault signal. Figure 18: LMD decomposition result of fault signal. In Figures 22-25 four LMD approaches' envelope frequency spectra for the first PF component are provided. The interference frequencies are further suppressed compared to the original envelope frequency spectrum in Figure 17 because some interference frequencies are eliminated during the LMD decomposition process. They all exhibit a distinct peak in the double rotation frequency and several gradually attenuated multi-rotation frequencies. The peak value refers to the difference between the highest or lowest value of the signal and the average value in a period. According to Formula (21), the peak index which is defined as the ratio between the peak value in double rotation frequency and root mean square (RMS) is employed to compare performance differences of the envelope frequency spectrum. \[Peak\quad Index=\frac{P}{RMS} \tag{21}\]  
Figure 21: DIMIRLMD decomposition result of fault signal. Figure 20: MPCHILMD decomposition result of fault signal. Figure 22: Envelope frequency spectrum of first PF1 in LMD. The five envelope frequency spectra are derived from the original signal and the first PF component of four LMDs, and the peak index, peak value in double rotation frequency, and RMS value of each are displayed in Table 5 in that order. The peak and the RMS value of the original envelope frequency spectrum are the highest in the five spectra, while the peak index is the lowest, which indicates the fault information is submerged in the background noise seriously.