## 基于AlphaZero的地铁列车大量速度曲线自动生成算法

1 福建工程学院计算机科学与数学学院，福建 福州 350118

2 福建工程学院交通运输学院，福建 福州 350118

3 福州大学数学与计算机科学学院，福建 福州 350108

## Algorithm for automatically generating a large number of speed curves of subway trains based on AlphaZero

LU Yuqi1, CHEN Dewang2,3, ZHAO Zhaolin2

1 School of Computer Science and Mathematics, Fujian University of Technology, Fuzhou 350118, China

2 School of Transportation, Fujian University of Technology, Fuzhou 350118, China

3 College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China

 基金资助: 国家自然科学基金资助项目.  61976055福建省财政厅教育科研专项资金资助项目.  GY-Z21001

Revised: 2021-05-13   Online: 2021-06-15

 Fund supported: The National Natural Science Foundation of China.  61976055Special Fund of Education and Scientific Research of Fujian Provincial Finance Department.  GY-Z21001

Abstract

In the previous research on subway trains automatic driving, subway driving data is usually obtained through simulation to generate a single operating curve and manual driving data sampling.Not only is the implementation method more complicated, but also the efficiency is low and the versatility is not strong.Inspired by AlphaZero system, the idea of artificial generation of virtual metro operation data was put forward.Firstly, according to a running method of five section subway trains speed curve, the calculation of virtual data was realized.Then, combined with the experience of human experts, the actual parameters such as the classification of traction braking section, the classification of actual running speed, the classification of station spacing and variable speed distance were set to narrow the range of curve data and rationalize it.Finally, a large amount of data was obtained by Python programming, saved as a data set, and the frequency distribution map of subway trains operation time was drawn.It can be observed that the virtual data covers all kinds of operation time, which is more conducive to the research of subway trains intelligent driving algorithm than traditional data.

Keywords： human-machine hybrid enhanced intelligence ; subway trains speed curve ; AlphaZero idea ; virtual data gen-eration

LU Yuqi. Algorithm for automatically generating a large number of speed curves of subway trains based on AlphaZero. Chinese Journal of Intelligent Science and Technology[J], 2021, 3(2): 179-184 doi:10.11959/j.issn.2096-6652.202118

## 3 相关参数计算

### 3.1 第一次变速阶段

${\text{th}}_{1}=\frac{{\text{lef}}_{\text{1}}}{{v}_{\mathrm{max}1}} \left(2\right)$

${\text{lef}}_{1}=\text{dis}-{s}_{1} \left(3\right)$

${s}_{1}=\frac{1}{2}{v}_{\mathrm{max}1}{t}_{1} \left(4\right)$

${T}_{1}={t}_{1}+{\text{th}}_{\text{1}} \left(5\right)$

### 3.2 第二次变速阶段

${\text{th}}_{2}=\frac{{\text{lef}}_{\text{2}}}{{v}_{\mathrm{max}2}} \left(7\right)$

${\text{lef}}_{\text{2}}=\text{dis}-{s}_{2} \left(8\right)$

${s}_{2}=\frac{1}{2}\left({v}_{\mathrm{max}2}-{v}_{\mathrm{max}1}\right){t}_{2} \left(9\right)$

${T}_{2}={t}_{2}+{\text{th}}_{\text{2}} \left(10\right)$

### 3.3 匀速行驶阶段

$\text{runtime}=\frac{\text{runtance}}{{v}_{\mathrm{max}2}} \left(11\right)$

### 3.4 第三次变速阶段

${\text{th}}_{3}=\frac{{\text{lef}}_{\text{3}}}{{v}_{\mathrm{max}2}} \left(13\right)$

${\text{lef}}_{\text{3}}=\text{dis}-{s}_{3} \left(14\right)$

${s}_{3}=\frac{1}{2}\left({v}_{\mathrm{max}2}-{v}_{\mathrm{max}3}\right){t}_{3} \left(15\right)$

${T}_{3}={t}_{3}+{\text{th}}_{\text{3}} \left(16\right)$

### 3.5 第四次变速阶段

${\text{th}}_{4}=\frac{{\text{lef}}_{\text{4}}}{{v}_{\mathrm{max}3}} \left(18\right)$

${\text{lef}}_{\text{4}}=\text{dis}-{s}_{4} \left(19\right)$

${s}_{4}=\frac{1}{2}{v}_{\mathrm{max}3}{t}_{4} \left(20\right)$

${T}_{4}={t}_{4}+{\text{th}}_{\text{4}} \left(21\right)$

### 3.6 最快运行状态运行时间计算

$\text{alltime}={T}_{1}+{T}_{2}+{T}_{3}+{T}_{4}+\text{runtime} \left(22\right)$

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

[D]. 南京:南京理工大学, 2013.

WANG Y B .

Simulation research on traction energy saving by using genetic algorithm to optimize multi interval speed curve and stop time of Metro

[D]. Nanjing:Nanjing University of Science and Technology, 2013.

WANG G Y , XIAO S , CHEN X ,et al.

Application of genetic algorithm in automatic train operation

[J]. Wireless Personal Communications, 2018,102(2): 1695-1704.

[J]. 铁道学报, 2020,42(12): 90-96.

HE Z Y , XU N .

Automatic train operation control algorithm based on nonparametric iterative learning control

[J]. Journal of the China Railway Society, 2020,42(12): 90-96.

GONG D D , LI G L .

Research on multi-objective optimized target speed curve of subway operation based on ATO system

[J]. International Core Journal of Engineering, 2020,6(2): 133-137.

[J]. 铁道学报, 2019,41(8): 1-8.

YANG J , WU J Y , WANG B ,et al.

Optimization algorithm of target speed curve of train energy saving operation based on heuristic genetic algorithm

[J]. Journal of the China Railway Society, 2019,41(8): 1-8.

[J]. 控制理论与应用, 2017,34(12): 1529-1546.

TANG Z T , SHAO K , ZHAO D B ,et al.

Progress of deep reinforcement learning:from AlphagGo to AlphaGo Zero

[J]. Control Theory and Application, 2017,34(12): 1529-1546.

[C]// 2020 中国自动化大会(CAC2020)论文集. 北京:中国自动化学会, 2020.

CHENG R J , CHEN D W , TIAN L J .

Research on the framework of metro train enhanced intelligent driving based on man machine hybrid intelligence

[C]// Proceedings of the China Society of Automation. Beijing:China Society of Automation, 2020.

AlphaZero原理与启示

[J]. 航空兵器, 2020,27(3): 27-36.

TANG C , TAO Y R , MA Y L .

Principle and enlightenment of AlphaZero

[J]. Aero Weaponry, 2020,27(3): 27-36.

[J]. 智能科学与技术学报, 2019,1(1): 1-3.

ZHENG N N .

The new era of artificial intelligence

[J]. Chinese Journal of Intelligent Science and Technology, 2019,1(1): 1-3.

[J]. 铁道学报, 2014(2): 62-68.

LENG Y L , CHEN D W , YIN J T .

An intelligent train operation (ITO) algorithm based on expert system and online adjustment

[J]. Journal of the China Railway Society, 2014(2): 62-68.

YIN J T , CHEN D W , LI L X .

Intelligent train operation algorithms for subway by expert system and rein for cement learning

[J]. IEEE Transaction son Intelligent Transportation Systems, 2014,15(6): 2561-2571.

ZHANG H R , JIA L M , WANG L .

Energy consumption optimization of train operation for railway systems:algorithm development and real-world case Study

[J]. Journal of Cleaner Production, 2019,214: 1024-1037.

[Z]. 2019.

Publicity of investigation report on environmental protection acceptance of Fuzhou rail transit line 1 project (phase I)

[Z]. 2019.

[Z]. 2021.

Publicity of environmental protection acceptance report of Fuzhou rail transit line 2 project

[Z]. 2021.

[D]. 北京:北京交通大学, 2016.

LI Z Y .

Research on energy-saving optimization of train speed trajectories based on swarm intelligence algorithms

[D]. Beijing:Beijing Jiaotong University, 2016.

ZHAO X H , KE B R , LIAN K L .

Optimization of train speed curve for energy saving using efficient and accurate electric traction models on the mass rapid transit system

[J]. IEEE Transactions on Transportation Electrification, 2018,4(4): 922-935.

KIM K M , SUK-MUM O ,, HAN M .

A mathematical approach for reducing the maximum traction energy; the case of Korean MRT trains

[C]// Proceedings of the International Multi Conference of Engineers and Computer Scientists.[S.l.:s.n.], 2010: 2169-2173.

/

 〈 〉