# Data-Driven Model Space Method for Fault Diagnosis of High-Speed Train Air Brake Pipes
### Fault Diagnosis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test Data**} & \multicolumn{2}{c}{**Distance between Test Data and Different Fault State**} & \multirow{2}{*}{**Diagnostic Type**} & \multirow{2}{*}{**Diagnostic Type**} & \multirow{2}{*}{**Diagnostic Result**} \\ \cline{2-3} \cline{5-6}  & **Normal** & **Leakage Fault** & **Blocking Fault** & **Compressor Fault** & & **Result** \\ \multicolumn{1}{c}{} & **State** & **State** & **State** & & & **Result** \\ \hline Test1 & 37.2358 & 1919.9133 & 2177.4830 & 721.9825 & Normal State & True \\ Test2 & 42.9296 & 1947.0545 & 2207.1937 & 685.5478 & Normal State & True \\ Test3 & 56.7879 & 1891.1919 & 2152.4350 & 709.6984 & Normal State & True \\ Test4 & 32.5843 & 1919.9875 & 2181.7044 & 700.9639 & Normal State & True \\ Test5 & 46.3860 & 1906.5605 & 2171.6021 & 706.2858 & Normal State & True \\ Test6 & 1957.1840 & 42.2385 & 421.4379 & 2554.5663 & Leakage Fault State & True \\ Test7 & 1907.3857 & 67.8710 & 401.3378 & 2509.9051 & Leakage Fault State & True \\ Test8 & 1949.0620 & 42.7162 & 421.0550 & 2535.3172 & Leakage Fault State & True \\ Test9 & 1929.0792 & 66.0089 & 466.9328 & 2523.4337 & Leakage Fault State & True \\ Test10 & 1956.9832 & 53.3107 & 381.9810 & 2558.9373 & Leakage Fault State & True \\ Test11 & 684.1946 & 2521.5848 & 2794.3020 & 34.7988 & Compressor Fault State & True \\ Test12 & 711.0597 & 2491.3055 & 2770.4532 & 57.9325 & Compressor Fault State & True \\ Test13 & 701.0328 & 2541.9890 & 2815.0319 & 16.6492 & Compressor Fault State & True \\ Test14 & 750.1892 & 2476.9892 & 2781.6865 & 82.7843 & Compressor Fault State & True \\ Test15 & 743.5008 & 2515.6166 & 2798.7663 & 53.8872 & Compressor Fault State & True \\ Test16 & 2174.0752 & 372.6418 & 44.4142 & 2785.1763 & Blocking Fault State & True \\ Test17 & 2187.7097 & 366.8166 & 50.4448 & 2793.8970 & Blocking Fault State & True \\ Test18 & 2204.5154 & 412.9392 & 25.7749 & 2813.7515 & Blocking Fault State & True \\ Test19 & 2222.2124 & 392.3571 & 93.9392 & 2827.8202 & Blocking Fault State & True \\ Test20 & 2213.5172 & 364.3250 & 49.3329 & 2827.1702 & Blocking Fault State & True \\ Test21 & 2300.7249 & 640.2812 & 304.0638 & 2982.2402 & Unknown Fault State & True \\ Test22 & 2891.1955 & 1142.1557 & 375.9846 & 3507.3801 & Unknown Fault State & True \\ Test23 & 2896.6145 & 1134.3446 & 728.9325 & 3511.5424 & Unknown Fault State & True \\ Test24 & 2913.3218 & 1110.7721 & 728.9557 & 3532.4020 & Unknown Fault State & True \\ Test25 & 2906.7712 & 1105.9850 & 717.0546 & 3517.6925 & Unknown Fault State & True \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of the air brake pipe fault diagnosis. The distance between the unknown fault model element and the known fault model element is far from the same, and the empirical distance difference is also maintained at one to two orders of magnitude. In addition, the norm between the normal model element of the duct and the compressor failure model element is smaller than the norm between the normal model element of the duct and the air duct blocking fault model element and the air duct leakage fault model element. The compressor fault model element also has this feature. According to the above known fault data (normal air duct, air duct obstruction, air duct leakage, compressor fault) and unknown fault data, the fault diagnosis experiment statistics are performed, and each of the four known faults completes 50 experiments, and the unknown fault is completed in six experiments. The diagnostic results are shown in Table 8.  
It can be seen from Table 8 that the diagnosis method based on the model space proposed in this paper has a considerable diagnostic effect. The average diagnostic hit rate is 89.8%. In addition, the statistical results again prove the experimental results in Table 7. The diagnosis of the normal model type of the air duct and the fault type of the compressor are mutually causal, and the diagnosis of the fault type of the air duct blockage and the fault type of the air duct leakage are mutually causal.