Automatic train operation (ATO) systems are fast becoming one of the key components of the intelligent high-speed railway (HSR). Designing an effective optimal speed trajectory for ATO is critical to guide the high-speed train (HST) to operate with high service quality in a more energy-efficient way. In many advanced HSR systems, the traction/braking systems would provide multiple notches to satisfy the traction/braking demands. This paper modelled the applied force as a controlled variable based on the selection of notch to realise a notch-based train speed trajectory optimisation model to be solved by mixed integer linear programming (MILP). A notch selection model with flexible vertical relaxation was proposed to allow the traction/braking efforts to change dynamically along with the selected notch by introducing a series of binary variables. Two case studies were proposed in this paper where Case study 1 was conducted to investigate the impact of the dynamic notch selection on train operations, and the optimal result indicates that the applied force can be flexibly adjusted corresponding to different notches following a similar operation sequence determined by optimal train control theory. Moreover, in addition to the maximum traction/braking notches and coasting, medium notches with appropriate vertical relaxation would be applied in accordance with the specific traction/braking demands to make the model feasible. In Case study 2, a comprehensive numerical example with the parameters of CRH380AL HST demonstrates the robustness of the model to deal with the varying speed limit and gradient in a real-world scenario. The notch-based model is able to obtain a more realistic optimal strategy containing dynamic notch selection and speed trajectory with an increase (1.622%) in energy consumption by comparing the results of the proposed model and the non-notch model.
Analysis of the Influence of Karst on Pile Foundation of High-Speed Railway Bridge
