## 5 Conclusions  
In this paper, a new fault identification method of the diesel engine valve clearance was proposed, which was based on the improved VMD and RF. It not only could alarm the valve abnormality, but also could identify the specific fault type accurately. In the key process of the nonstationary signal  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Classification Result**} & \\ \cline{3-6}
**Fault Type** & **Number of Test’s Group** & **Increased Intake** & **Increased Exhaust** & **Increased Enhust** & **Recognition** & **Average Recognition** \\  & & **Valve** & **Valve** & **Both Valve** & **Rate/\%** & **Rate/\%** \\  & & **Clearance** & **Clearance** & **Clearance** & & \\ \hline Increased intake valve clearance & 120 & 111 & 5 & 4 & 92.5 & \\ Increased exhaust valve clearance & 120 & 5 & 112 & 3 & 93.33 & \\ Increased in both valve clearance & 120 & 4 & 4 & 112 & 93.33 & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Confusion matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{**Recognition Rate/\%**} \\ \hline \multirow{2}{*}{**Fault Mode**} & \multicolumn{4}{c}{**Statistical Characteristics in Time**} \\  & **and Frequency Domain + KNN** & **EMD + Decision Tree** & **VMD + RF** \\  & \multicolumn{4}{c}{**(K-Nearest Neighbor)**} \\ \hline Increased intake valve clearance & 85.71 & 88.57 & 92.5 \\ Increased exhaust valve clearance & 71.43 & 80 & 93.33 \\ Increased in both valve clearance & 91.43 & 85.71 & 93.33 \\ Average recognition rate/\% & 82.86 & 84.76 & 93.06 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of different fault diagnosis methods.  
decomposition of this method, a novel parameters optimization strategy for VMD was carried out, which was based on reducing the energy leakage of the IMF component frequency spectrum and the minimum IMF component of power spectral entropy. Moreover, the RF algorithm was employed to rank the importance of all the extracted features for the purpose of reducing the dimension and improving the computational efficiency. According to the threshold value, the features with greater importance were selected to form the feature vector. The verification results under the variable operating condition of the diesel engine proved that the fault diagnosis method could effectively recognize the specific fault type of valve clearance, of which the average recognition accuracy reached more than 90%. In addition, this paper also made a comparative analysis with frequently-used feature extraction and fault detection methods. The combined VMD and RF method proposed in this paper had a better identification rate for the three valve clearance faults. In the future, the valve clearance detection approach will be further studied on different engines and finally built into a real-time monitoring system.  
Conceptualization, N.Z. and Z.M.; methodology, D.W.; software, H.Z.; validation, Z.M., J.Z. and Z.J.; investigation, H.Z.; resources, Z.J.; data curation, N.Z.; writing--original draft preparation, N.Z.; writing--review and editing, Z.M.; visualization, N.Z.; supervision, J.Z.; project administration, Z.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Plan, grant number 2016 YFF0203305 and by the Fundamental Research Funds for the Central Universities, grant number JD1815.  
The authors declare no conflicts of interest.