The determination of limit wheel profile for hunting instability of railway vehicles using stacking feature deep forest

Wheel and rail profiles have significant impacts on the vehicle system dynamics. Improper wheel and rail profiles lead to the decay of vehicle dynamics performance, hunting instability and derailment. In this study, we propose a model, stacking feature deep forest, to determine the limit wheel profile for hunting instability using wheel/rail geometric contact parameters. We calculate the critical speed of the vehicles under various wheel and rail profiles and record their wheel/rail geometric contact parameters as samples. Two experiments are conducted. One is the binary classification aiming to identify whether the wheel/rail geometric contact parameters guarantee the vehicle's critical speed is higher than the threshold of its operational speed. The other is the multi-classification to determine the interval of the critical speed. The results show the stacking feature deep forest achieves an accuracy of 85.10% on the test set which is higher than other popular ensemble models. However, all models' accuracy is lower than 70% in multi-classification. The Shapley additive explanations are utilized to enhance the explainability of the stacking feature deep forest. The Shapley additive explanation importance reveals that the equivalent conicity of 1 mm has the most impact on hunting. Its importance is 1.32 times more than the equivalent conicity of 3 mm. Nevertheless, the equivalent conicity of 3 mm is nearly positively correlated to the hunting probability and this characteristic is suitable as a qualitative criterion.