As one of the core components of the traction system of rail vehicles, the failure of the supporting capacitor will seriously affect the safe and stable operation of the train. Therefore, it is of great significance to study the fault prognostics and health management (PHM) technology of the support capacitor and realize the online health state prediction of the support capacitor. In this paper, firstly, the structure design, working characteristics and aging mechanism of the supporting capacitor are deeply studied, and the degradation rate of capacitance value and ESR value is taken as the failure criterion of the support capacitor. Then, a soft sensing model of capacitance value and ESR value is constructed based on mathematical statistics and polynomial regression algorithm. A large number of test data are used to train and optimize the model, Finally, the accuracy of the soft sensing results is evaluated from two aspects of the soft sensing error and the consistency of mathematical statistics distribution. The experimental results show that the mathematical statistics + polynomial regression soft sensing model can effectively soft sensing the support capacitance and ESR values in different sample sets and different working conditions, which verifies the feasibility and accuracy of the model.