A survey on optimal trajectory planning for train operations

Wang, Yihui; Ning, Bing; Cao, Feilong; Schutter, Bart De; Boom, T.J.J. van den

doi:10.1109/soli.2011.5986629

Cited by 57 publications

(30 citation statements)

References 27 publications

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“…Wang et al (2011) considered the EETC problem with varying gradients, curves and speed restrictions. They used kinetic energy and time as state variables in the independent variable distance and assumed a linear resistance force as in Franke et al (2000).…”

Section: Direct Exact Methodsmentioning

confidence: 99%

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Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

303

136

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The energy consumption of trains is highly efficient due to the low friction between steel wheels and rails, although the efficiency is also influenced largely by the driving strategy applied and the scheduled running times in the timetable. Optimal energy-efficient driving strategies can reduce operating costs significantly and contribute to a further increase of the sustainability of railway transportation. The railway sector hence shows an increasing interest in efficient algorithms for energy-efficient train control, which could be used in real-time Driver Advisory Systems (DAS) or Automatic Train Operation (ATO) systems. This paper gives an extensive literature review on energy-efficient train control (EETC) and the related topic of energy-efficient train timetabling (EETT), from the first simple models from the 1960s of a train running on a level track to the advanced models and algorithms of the last decade dealing with varying gradients and speed limits, and including regenerative braking. Pontryagin's Maximum Principle (PMP) has been applied intensively to derive optimal driving regimes that make up the optimal energy-efficient driving strategy of a train under different conditions. Still, the optimal sequence and switching points of the optimal driving regimes are not trivial in general, which led to a wide range of optimization models and algorithms to compute the optimal train trajectories and more recently to use them to optimize timetables with a trade-off between energy efficiency and travel times.

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Section: Direct Exact Methodsmentioning

confidence: 99%

“…Wang et al (2013) reconsidered the EETC problem of Y. Wang et al (2011) but now considered maximum traction force as a usual nonlinear function of speed, which they approximated by PWA functions. The resistance equation was still assumed linear in the kinetic energy.…”

Section: Direct Exact Methodsmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

303

136

View full text Add to dashboard Cite

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“…It controls the train speed to achieve safe and efficient driving. ATO system consists of two levels of control actions [4]: High-level control for calculating and updating the optimal trajectory and Low-level control for tracking the target speed and feedback. Based on ATO, a cooperative level could be set up for coordinated train control (Fig.…”

Section: Introductionmentioning

confidence: 99%

An Optimization Approach for Real-Time Headway Control of Railway Traffic

Xun

Chen

2015

IEICE Trans. Inf. ^|^ Syst.

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SUMMARYHeadway irregularity not only increases average passenger waiting time but also causes additional energy consumption and more delay time. A real-time headway control model is proposed to maintain headway regularity in railway networks by adjusting the travel time on each segment for each train. The adjustment of travel time is based on a consensus algorithm. In the proposed consensus algorithm, the control law is obtained by solving the Riccati equation. The minimum running time on a segment is also considered. The computation time of the proposed method is analyzed and the analysis results show that it can satisfy the requirement on real-time operation. The proposed model is tested and the consensus trend of headways can be observed through simulation. The simulation results also demonstrate that the average passenger waiting time decreases from 52 to 50 seconds/passenger. Additionally, the delay time is reduced by 6.5% at least and energy consumption can be reduced by 0.1% at most after using the proposed method.

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“…After the proposal applicable to actual train operation, some research groups have proposed various types of methods to solve the speed profile optimization problem [2][3], however the DP based method still has substantial advantages of coping with complicated conditions easily, e.g. speed limitation, non-linear tractive effort and running resistance, effects of regenerative electric energy and so on.…”

Section: Introductionmentioning

confidence: 99%

Optimal train speed profiles by dynamic programming with parallel computing and the fine-tuning of mesh

Matsuura¹,

Miyatake²

2014

WIT Transactions on the Built Environment

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In this paper the authors investigated an algorithm optimizing a train speed profile by the Bellman's Dynamic Programming (DP). The DP-based method has substantial advantages of coping with complicated conditions easily, e.g. speed limitation, non-linear tractive effort and running resistance, effects of regenerative electric energy and so on. One of the major drawbacks of DP is that it requires a lot of computation time. If high accuracy of solutions is required, computation time for the optimization will increase. In this paper, the authors introduce the parallel computing technique for DP. The parallel computing technique will shorten computation time sharply and succeed in both raising accuracy of simulation and shortening of computation time. While distance between stations for the profile optimization is 1000m at the longest in our previous work, it will be prolonged significantly, keeping a comparable computation time. In this paper the computation times with and without parallel computing will be compared. DP has a further advantage in its use as a real time control algorithm to which the optimal profile can be easily reconfigured against some disturbances such as signalling.

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A survey on optimal trajectory planning for train operations

Cited by 57 publications

References 27 publications

Review of energy-efficient train control and timetabling

Review of energy-efficient train control and timetabling

An Optimization Approach for Real-Time Headway Control of Railway Traffic

Optimal train speed profiles by dynamic programming with parallel computing and the fine-tuning of mesh

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