Optimization under uncertainties of high-speed train speed to limit energy consumption
Résumé
The speed profile of a train plays an important role in energy consumption and resulting costs. The industrial objective of this work is to develop a method, which optimizes the train speed under constraints, in order to reduce the energy consumed over a journey. Some articles have presented similar problems solved with other methods [1, 2]. In this work, we choose to describe the dynamic problem thanks to a rigid body approach (Lagrangian formalism), which is projected onto the longitudinal axis. The aerodynamic, traction, and braking forces applied to the train are taken into account. The pneumatic braking is dissociated from dynamic braking that can recover energy.
The aim is to reduce the energy consumed (cost function) playing on the driver commands (traction and braking forces) respecting comfort, security, and punctuality constraints. As the track topology is an important parameter, we describe track slopes and curves to fit with industrial needs. The railway system depends on uncertainties derived from weather and from the power available at the catenary. As speed is a functional feature of the curvilinear abscissa of the track, a discretization strategy is used. The optimization problem under uncertainties is solved using a CMA-ES method where the constraints are implemented using an augmented Lagrangian. The method is applied to a real high-speed line and the model has been validated with experimental measurements. The optimal trajectory is compared to the in-line trains.
REFERENCES
[1] P. Wang, R. Goverde, Multiple-phase train trajectory optimization with signaling and operational constraints. Transportation Research Part C: Emerging Technologies, 192, 913 – 922, 2016.
[2] G. Scheepmaker, R. Goverde, L. Kroon, Review of energy-efficient train control and timetabling. European Journal of Operational Research, 257, 355 – 376, 2017.