## 5 Application for Reciprocating Compressor
### Application for Reciprocating Compressor Fault Diagnosis
#### 5.3.3 Calculate the Different Entropies in the Three States  
The signal samples of different states are preprocessed using the VMD method, and the components containing the main feature information are preferred for signal reconstruction. The MHDME algorithm was used to analyse and process each group of reconstructed signals, and the entropy under 20 scales for each state was calculated as state features. At the same time, the same process was used to calculate the MSE and MPE of the pre-processed signals by VMD, and the pre-selected scales were set at \(K=5\) in VMD. To assess the stability of various algorithms, the values were calculated for three distinct working conditions. Parameter selection for entropy calculation was as follows: \(m=2\), \(\tau=20\), \(r=0.15\times SD\) (\(SD\) is the standard deviation), time delay \(t=1\) in MHDME, \(m=6\), \(\tau=20\), \(t=1\) in MPE, \(m=2\), \(\tau=20\), \(r=0.15\times SD\), \(t=1\) in MSE. The alterations in entropy for distinct bearing conditions are depicted in Figure 15a-c.  
It can be seen from Figure 15a that, within 20 scales of the MHDME, there is no crossover of entropy between different states, and the separability and stationarity between fault types are preferable. The entropy information of different compressor fault states on a large scale not only shows the necessity of multi-scale analysis but also shows the complexity of vibration signals. In the normal state, the unit operation has randomness and irregularity, so the signal chaos degree is larger, and the entropy amplitude is larger. When the bearing of a reciprocating compressor has a failure with different degrees of wear, the distinction between the states is obvious. The entropy of the bearing under a normal state is greater than that under other fault states, indicating that the signal under a normal state is relatively random and complex, and when the fault occurs, the signal has a certain regularity and the signal complexity is reduced.  
According to the analysis in Figure 15b,c, it can be seen that the entropy curves of MPE and MSE after pretreatment have different degrees of crossover under different scale ranges. When the scale factor \(\tau=1\), only comparing the MPE in different states is insufficient  
Figure 14: The reconstructed signal of the first five orders of BLIMF.  
to achieve accurate prediction and diagnostic outcomes. MPE exhibits some degree of crossover at a scale factor \(2\leq\tau\leq 5\), and the separability of different states is poor at larger scales. In addition, MSE fluctuates more on 20 scales, and the crossover of different states is serious at scales \(2\leq\tau\leq 7\). At the same time, the normal state and moderate wear faults appear to be intermixed at larger scales. The experimental data of MPE and MSE show that the two methods can achieve pattern differentiation, but the stability and separability are unfavorable, resulting in lower recognition accuracy. MHDME exhibits a narrower error margin compared to MPE and MSE, which demonstrate broader error margins. This indicates that the MHDME algorithm yields more stable results, with enhanced consistency between measurements, thereby providing more accurate information. In conclusion, the MHDME, MPE and MSE of the three working conditions are compared and analyzed. The stability of both MPE and MSE is unsatisfactory at most scales, while the MHDME algorithm exhibits stability and discernibility. The MHDME algorithm can accurately depict the defect features exhibited by the vibration signal of the reciprocating compressor bearing.