## 3 Results
### Application for Reciprocating Compressor Fault Diagnosis  
One of the pieces of power equipment that is frequently utilized to compress natural gas for long-distance transportation is the reciprocating compressor. This type of compressor features high efficiency and strong reliability, allowing it to adapt to various operating conditions and environmental situations [34; 35]. In this work, the vibration signal of a reciprocating compressor of type 2D12-70 operating with excessive bearing clearance is investigated. The compressed medium is natural gas. Table 3 provides the main parameters of the 2D12-70 reciprocating compressor. The connecting rod in the transmission mechanism connects the crankshaft and crosshead pin with rotate joints, and these joints usually use sliding bearings in the actual structure due to the heavy load. After a long period of friction and wear, the clearance in bearings will increase gradually [36]. Oversized bearing clearances can result in a vibratory operating situation that seriously impairs the performance of the device. Therefore, monitoring and diagnosing excessive bearing clearance effectively and accurately can assist in lowering maintenance costs. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**PF2**} & \multicolumn{2}{c}{**PF3**} & \multirow{2}{*}{**Time (s)**} \\ \cline{2-2} \cline{4-5}  & **MSE** & **Iterations** & **MSE** & & **Iterations** \\ \hline LMD & 65.482 & 12 & 98.994 & 14 & 0.871 \\ CSI & 25.281 & 9 & 14.584 & 8 & 0.701 \\ MPCHI & \multirow{2}{*}{16.203} & \multirow{2}{*}{8} & \multirow{2}{*}{20.420} & \multirow{2}{*}{7} & \multirow{2}{*}{0.677} \\ LMD & & & & & \\ DIMIR & \multirow{2}{*}{7.130} & \multirow{2}{*}{5} & \multirow{2}{*}{6.051} & \multirow{2}{*}{5} & \multirow{2}{*}{0.733} \\ LMD & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of simulation signal decomposition results with different LMD methods. This failure was purposely induced in the bearing between the first-stage crankshaft pin and connecting rod as part of a fault simulation experiment on large bearing clearance states that was carried out in a genuine operating environment. On the cylinder surface during the test, one measuring point was set up to record the vibration signal. Figure 13a,b illustrate the reciprocating compressor and sensor positioning. The test time was 4 s, and the sampling frequency was 50 kHz. Piezoelectric acceleration sensors, specifically model CA-YD-186, were employed. Acceleration sensors are displayed in Figure 13c. Table 4 shows the main parameters of the CA-YD-186 acceleration sensor. Two clearance states, namely a normal clearance state and a medium-worn state, were tested, using a normal bushing in 0.1 mm clearance and a worn bushing in 0.2 mm clearance [37]. The normal and worn bushings and the connecting rod are shown in Figure 14. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Type** & **Parameter Value** \\ \hline Shaft power (\(kW\)) & 500 \\ Air displacement (m\({}^{3}\)/min) & 70 \\ Primary exhaust pressure (MPa) & 0.2746–0.2942 \\ Secondary exhaust pressure (MPa) & 1.2749 \\ Piston stroke (mm) & 240 \\ Crank speed (rpm) & 496 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main parameters of 2D12-70 reciprocating compressor. Figure 13: Reciprocating compressor fault test platform. (**a**) Reciprocating compressor and sensor location. (**b**) Sensor location of 3D model. (**c**) CA-YD-186 acceleration sensor. The normal bearing clearance vibration signal is shown in Figure 15. The vibration signal in the oversized bearing clearance state is shown in Figure 16. When an oversized clearance arises in the bearing, strong contact forces are excited due to the direct impact between the journal and bushing.