基于冗余工序编码的高速列车节能驾驶智能算法

doi:10.13229/j.cnki.jdxbgxb.20220094

Abstract

Abstract:

Two redundant operation code-based methods were proposed to solve the energy-efficient driving problem of a high-speed train with steep gradients and speed limits. Based on the necessary conditions for the optimal solution derived from the Pontryagin's maximum principle， the concept of redundant operation code， including redundant operation sequence and switching area， and the generation rules were proposed. Applying the new concept， PMP-LMGA and PMP-PSO algorithms were developed to merge redundant operations and find optimal switching points. The experimental results indicate that the redundant operation code can significantly speed up the calculation in complex scenarios. Total energy consumption can be effectively and stably reduced while meeting various operation rules. Multi-agent parallel computing can further improve solution efficiency.

Key words: railway transportation, redundant operation code, limited mutation genetic algorithm, particle swarm optimization

CLC Number:

U238

Pei-ran YING,Xiao-qing ZENG,Tuo SHEN,Teng-fei YUAN,Hai-feng SONG,Yi-zeng WANG. Redundant operation code-based intelligent algorithm for energy⁃efficient driving of high-speed train[J].Journal of Jilin University(Engineering and Technology Edition), 2023, 53(12): 3404-3414.

Figures/Tables 14

Fig.1

Fig.2

Table 1

Optimal control mode"

控制工况	速度	辅助协态变量	控制输出
全力牵引	$v ≤ V ˉ$	$ω > 1$	$u (x) = U ˉ (v)$
牵引巡航	$v = m i n v b q, V ˉ$	$ω = 1$	$u (x) = w 0 (v) + w j (x) ≥ 0$
惰行	$v ≤ V ˉ$	$ρ < ω < 1$	$u (x) = 0$
制动巡航	$v = m i n v b z, V ˉ$	$ω = ρ$	$u (x) = w 0 (v) + w j (x) ≤ 0$
全力制动	$v ≤ V ˉ$	$ω < ρ$	$u (x) = U ? (v)$

Table 1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 2

Parameters of the case studies"

参数		案例一	案例二	参数		案例一	案例二
适应度函数	$?$	15	3	冗余工序编码	$α$	1.50	2.00
	$ξ$	95	6		$β$	1.00	0.70
	$ψ$	260	35		$η$	1.00	0.70
	$θ$	425	80		$?$	0.70	0.20

Table 2

Table 3

Parameters of the algorithms"

算法	案例	参数
E-GA¹	一&二	$r c = S t r 2,0.40,0.20, r o u n d 0.50 ? N r m = S t r 3,0.20,0.04, r o u n d 0.10 ? N$
PMP-GA¹	一	$r c = S t r 2,0.60,0.30, r o u n d 0.50 ? N r m = S t r 2,0.80,0.10, r o u n d 0.20 ? N$
PMP-GA¹	二	$r c = S t r 4,0.30,0.10, r o u n d 0.70 ? N r m = S t r 2,0.80,0.05, r o u n d 0.10 ? N$
PMP-LMGA¹	一&二	$r c = S t r 4,0.40,0.10, r o u n d 0.50 ? N r m = S t r 2,0.80,0.40, r o u n d 0.20 ? N φ = S t r 3,1.00,0.001, r o u n d 0.15 ? N$
PMP-PSO	一	$ω = S t r 1,0.60,0.60, r o u n d 0.50 ? N c 1 = S t r 2,0.60,0.30, r o u n d 0.50 ? N c 2 = S t r 4,0.10,0.80, ? r o u n d 0.40 ? N$
PMP-PSO	二	$ω = S t r 3,0.90,0.40, r o u n d 0.14 ? N c 1 = S t r 1,0.40,0.40, r o u n d 0.40 ? N c 2 = S t r 4,0.05,0.65, r o u n d 0.40 ? N$

Table 3

Fig.9

Fig.10

Fig.11

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Redundant operation code-based intelligent algorithm for energy⁃efficient driving of high-speed train

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