# Impact Features Extracting Method for a Reciprocating Compressor Based on the ABC-SGMD Model
## 4 Fault Simulation Experiment
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **RCMDE** & **ydz** & **Vpp** \\ \hline \multirow{3}{*}{Normal} & 1.551 & 0.574 & 4.998 \\  & 1.433 & 0.570 & 4.311 \\  & 1.480 & 0.554 & 4.654 \\ \hline \multirow{3}{*}{Spring failure} & 1.352 & 0.866 & 3.719 \\  & 1.333 & 1.075 & 4.072 \\  & 1.352 & 1.007 & 3.948 \\ \hline \multirow{3}{*}{Valve plate wear} & 1.677 & 0.410 & 2.723 \\  & 1.698 & 0.349 & 2.876 \\ \cline{1-1}  & 1.708 & 0.439 & 2.951 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Eigenvalues of the three working conditions. Figure 8: Time-frequency domain of the experimental signal. It can be observed that there are significant differences in the eigenvalues among different working conditions. Passively, the fault category can be accurately determined by inputting these eigenvalues into the Learning Machine. The output results of the Extreme Learning Machine (ELM) for the signal through SGMD and EMD are observed in Figure 10.  
From Figure 10, it is observed that, compared to the traditional EMD method, the SGMD method shows an improvement in accuracy of approximately 3%. Furthermore, when compared to the enhanced ABC-SGMD method, it is found that the accuracy rate is increased by an additional 13% through the improvement of the method using the Artificial Bee Colony algorithm. To eliminate the influence of random factors, the signal was repeatedly trained and recognized multiple times in this study, selecting 80% of the data as training samples and 20% as test samples. For both scenarios, multiple trainings were conducted by the study, and the average of the final recognition results is presented in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Decomposition Method** & **Average Accuracy Rate** & **Variance** \\ \hline EMD & 0.796 & 0.00214 \\ SGMD & 0.890 & 0.00026 \\ ABC-SGMD & 0.989 & 0.00012 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the recognition rates of the methods. Figure 9: IMF components after ABC-SGMD. It can be clearly seen that the test set accuracy rate of ABC-SGMD increased by an average of about 15% compared to the traditional EMD and SGMD methods. To verify the effectiveness of the multi-feature fusion model, it is assumed that each model contains only one feature vector. Each reconstructed matrix is input into the Self-Adaptive Differential Evolution Extreme Learning Machine (SaDE-ELM) method for recognition to determine its accuracy rate. The decomposition results are shown in Figure 11 below. To mitigate the influence of random factors, the signal was repeatedly trained and recognized in this study, as 80% of the data were selected as training samples and 20% as test samples. The training process was repeated several times, and the final recognition results are illustrated in Table 5.  
The comparison reveals that the average accuracy rate of the Fine Composite Multiscale Scattering Entropy method achieves the highest average accuracy rate at 83.4%. However, the accuracy of this method is not stable. In contrast, the accuracy of the peak-to-peak value is relatively stable, but its average accuracy rate is lower, at only 67.3%. Figure 10: Comparison of the test set accuracy. \begin{table}
\begin{tabular}{c c c} \hline
**Eigenvalue** & **Average Accuracy Rate** & **Variance** \\ \hline RCMDE & 0.834 & 0.01284 \\ ydz & 0.797 & 0.00881 \\ Vpp & 0.673 & 0.00592 \\ \hline \end{tabular}
\end{table} 
Table 5: Single feature value recognition accuracy. Compared to extracting individual eigenvalues and combining them into a multi-feature fusion model, these methods have certain gaps in accuracy and stability. To achieve better diagnostic results, the eigenvalues of the decomposed IMF components can be extracted, formed into a feature vector matrix, and analyzed through SaDE-ELM. This approach is expected to yield better diagnostic outcomes. In summary, Table 6 demonstrates that the ABC-SGMD-based method outperforms other methods in diagnostic performance under various noise conditions.