Implementation of energy-efficient train driving strategy is an effective method to save train traction energy consumption, which has attracted much attention from both researchers and practitioners in recent years. Reducing the unnecessary braking during the journey and increasing the coasting distance are efficient to save energy in urban rail transit systems. In the steep downhill segment, the train speed will continue to increase without applying traction due to the ramp force. A high initial speed before stepping into the steep downhill segment will bring partial braking to prevent trains from overspeeding. Optimization of the driving strategy of urban rail trains can avoid the partial braking such that the potential energy is efficiently used and the traction energy is reduced. This paper presents an energy-efficient driving strategy optimization model for the segment with the steep downhill slopes. A numerical method is proposed to calculate the corresponding energy-efficient driving strategy of trains. Specifically, the steep downhill segment in the line is identified firstly for a given line and the solution space with different scenarios is analyzed. With the given cruising speed, a primary driving strategy is obtained, based on which the local driving strategy in the steep slope segment is optimized by replacing the cruising regime with coasting regime. Then, the adaptive gradient descent method is adopted to solve the optimal cruising speed corresponding to the minimum traction energy consumption of the train. Some case studies were conducted and the effectiveness of the algorithm was verified by comparing the energy-saving performance with the classical energy-efficient driving strategy of “Maximum traction–Cruising–Coasting–Maximum braking”.

In this article, we consider the identification problem of a class of nonlinear multiple-input single-output output-error autoregressive systems. First, a recursive generalized least squares algorithm using the auxiliary model identification idea is developed. Then, using the filtering technique, the identification model is decomposed into a filtered sub-identification model and a noise sub-identification model. For solving the difficulties that the filter is unknown and the information vectors contain the unknown variables, the interactive estimation theory and the the idea of replacing the unknown variables with their corresponding estimates are employed: the recursive least squares method is again used for identifying the system and noise model parameters, and the parameter estimates of the noise model are used to construct the estimated filter. Finally, a nonlinear example is given to verify the effectiveness of the algorithms, and the simulation results show that the recursive least squares algorithm using the filtering technique can produce more accurate parameter estimates under larger noise variances.