# Failure Type Prediction Using Physical Indices and Data Features for Solenoid Valve +
## 5 Conclusions  
The high-speed solenoid valve is a key component of the braking system. Its reliability is closely related to the safe operation of the braking system. Previous work paid more attention to predicting the remaining useful life of the solenoid valve, based on which the solenoid valve could be replaced timely before it fails. However, in actual operations, there are two main causes of the failure of the high-speed solenoid valve: the aging of the coil and the failure of the lubricant. It is more reasonable to repair the solenoid valve with lubricant failure rather than to replace it directly by adding lubricant oil. To improve the maintenance quality and to ensure the reliability of the solenoid valve, this paper proposes a failure type prediction method using physical indices and data features for high-speed solenoid valve in braking systems. Five physical indices are extracted from the driven current curve, and eight frequency band energy features are extracted from the current change rate curve by wavelet packet decomposition. Then, the physical indices and energy features are combined into a comprehensive feature vector. Finally, the random forest is applied to predict the failure type based on the comprehensive feature vector.  
The proposed method is validated on a data set consisting of 60 high-speed solenoid valves periodically switched under accelerated aging test conditions. The prediction performance of the proposed method is compared with the performance based on physical index vector and data feature vector, and the result shows that the proposed method has the precision of 95.95% and 94.68% for the two failures at the 3000 th life cycle of the solenoid valve, respectively. It is higher than both physical-based and data-based methods, which means that the combination of physical indices and data features is effective in improving the prediction performance of the random forest. In addition, the prediction performance of the applied random forest is compared with several commonly used machine learning algorithms such as KNN, SVM, and DT. As an ensemble classifier with multiple decision trees, the random forest makes decisions based on the predictions of all decision trees and thus could get better performance than just a single classifier. The experiment results also prove that the prediction performance of the random forest is the best in almost all life stages of the high-speed solenoid valve.  
Conceptualization, J.P. and X.T.; methodology, X.T. and R.Z.; software, X.T.; validation, X.T.; formal analysis, F.J.; investigation, R.Z., and X.Z.; resources, D.G.; data curation, B.C.; writing--original draft preparation, X.T.; writing--review and editing, R.Z.; visualization, Y.Y.; supervision, Z.H.; project administration, J.P.; funding acquisition, J.P. and X.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant Nos.61672537, 61873353, and 61672539).  
This research was funded by the National Natural Science Foundation of China (grant Nos. 61672537, 61873353, and 61672539).  
The authors declare no conflict of interest.