A data-driven fault diagnosis method is proposed in this study to address the challenge of handling a large volume of pressure data in the air brake pipe of high-speed trains. The suggested method utilizes a BP (back propagation) neural network to transform the time series pressure data into model elements in the model space, ensuring simplicity and stability. Various fitting functions, including Fourier basis, Gaussian basis, polynomial basis, sine basis, and others, are employed to accurately fit the pressure curve of the air brake pipe. The fault diagnosis process involves two steps: classifying the fault based on an optimal approximation equation and diagnosing it by analyzing the topological relationship of the model elements in the model space. The proposed method achieves an average fault diagnosis accuracy of 89.8%, with high accuracy rates for different fault states: 98% for normal state, 88% for blockage state, 84% for leakage state, and 96% for compressor fault state. Compared to the hidden Markov model method, the proposed method improves the average diagnostic accuracy by 2% for known working conditions and 4.87% for all working conditions, demonstrating its effectiveness and reliability. The fault diagnosis of the air brake tube in high-speed trains is of great significance, which aims to realize accurate fault diagnosis and prediction through sensor data monitoring and signal processing technology, 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.