# Data-Driven Model Space Method for Fault Diagnosis of High-Speed Train Air Brake Pipes
## 5 Conclusions  
This paper proposes a fault diagnosis method for high-speed train ducts based on the model space, establishes a BP neural network learning model for train ducts, and proposes a method for transforming measured air pressure data in the model space and model elements in the model space. High-speed train air duct fault diagnosis and new fault capture is based on the model element topological relationship. Through the proposed data-driven model space method, accurate fault diagnosis and prediction are further realized, so as to ensure the safe operation of high-speed trains. These studies provide an important theoretical and practical basis for the improvement and application of fault diagnosis methods.  
In this study, according to the characteristics of the duct pressure data, the Fourier basis, Gaussian basis, polynomial basis, and sine basis are used to design the experiment in the continuous function space. Based on each basis, the multi-order function approximation equation is calculated, and the optimality is selected by fitting the K basis co-efficient and the equation coefficient, so that the learning result in the BP neural network is expressed as a function expression. The diagnosis process is divided into data learning and function approximation in the time series space. The BP neural network is used to learn the duct pressure data, and function approximation is used to transform the learning results into model elements in the model space through a set of optimal bases and coefficients to obtain the optimal equation. Finally, the topological relationship in the model space is used for fault diagnosis. The fault diagnosis results of the measured duct pressure data in high-speed trains show that the diagnostic accuracy in the model space method is higher than 84% in the diagnosis of normal duct, duct blockage fault, duct leakage fault, and compressor fault. The hit rate in fault diagnosis is 83%, and the average hit rate in overall fault diagnosis is 89.8%. Compared with the hidden fault diagnosis method based on the hidden Markov model, the average diagnostic hit rate in four known faults is increased by 2%, and the overall fault diagnosis rate is increased by 4.87%, which shows the effectiveness and reliability of the diagnosis method.  
Aiming at the problem of diagnostic accuracy, generalization, and robustness of high-speed train duct fault diagnosis methods, this paper uses the model space idea based on the model element field to study the fault diagnosis method. Although more effective results have been achieved, there are still some shortcomings to be further improved. However, only the problem of disjoint neighborhoods of the model elements is considered in the fault diagnosis, and the intersection problem is not considered. Therefore, the next step will be to study this aspect. In addition, when establishing the fault model, the method does not take into account the mode conversion between fault types and needs to be further improved.  
Conceptualization, W.M.; Methodology, W.M.; Validation, [PERSON]; Data curation, [PERSON]; Writing--original draft, J.W.; Writing--review & editing, [PERSON]; Visualization, J.Q. All authors have read and agreed to the published version of the manuscript.  
National Natural Science Foundation of China: U1734210.  
Not applicable.  
Data Availability Statement: Data available on request due to privacy.  
The authors declare no conflict of interest.