基于逻辑博弈概率Petri网的地铁应急决策建模与分析

doi:10.16182/j.issn1004731x.joss.22-0355

摘要/Abstract

摘要：

为解决逻辑Petri网不能很好地描述动态博弈过程的问题，提出逻辑博弈概率Petri网。将博弈的四要素融合到逻辑Petri网中，博弈的局中人被定义为token的一个属性，为其定义了策略集以及效用函数，并引入了信息库所。引入概率变迁和向量来表示博弈过程中先后验概率的转换关系，在贝叶斯公式的基础上引入模糊理论，以解决决策前期的信息缺失问题，并引入决策变迁来帮助理性人作出决策。使用逻辑博弈概率Petri网对地铁应急决策过程进行建模，构建系统可达图对问题进行分析，并应用Tina仿真验证模型性质，同时验证了所提出方法的可行性。

关键词: 逻辑博弈概率Petri网, 地铁应急决策, 模糊贝叶斯公式, 可达图

Abstract:

In order to solve the problem that logical Petri net can not describe dynamic game process well, logical game probabilistic Petri net is proposed. The four elements of the game are integrated into the logical Petri net, and the players of the game are defined as an attribute of Token, for which the strategy set and utility function are defined, and the information database is introduced. Probability change and vector are introduced to represent the transformation relationship of empirical probability in the process of game, and fuzzy theory is introduced on the basis of Bayes formula to solve the problem of information loss in the early stage of decision making, and decision change is introduced to help rational people make decisions. Logical game probability Petri net was used to model the subway emergency decision-making process, and the system reachable graph was constructed to analyze the problem. Tina simulation was used to verify the model properties, the feasibility of the proposed method was also verified.

Key words: logical game probability Petri net, metro emergency decision-making, fuzzy Bayes formula, reachable graph

中图分类号:

TP391.9

闫哲, 刘伟, 杜玉越. 基于逻辑博弈概率Petri网的地铁应急决策建模与分析[J]. 系统仿真学报, 2023, 35(7): 1602-1618.

Zhe Yan, Wei Liu, Yuyue Du. Modeling and Analysis of Metro Emergency Decision Based on Logical Game Probability Petri Net[J]. Journal of System Simulation, 2023, 35(7): 1602-1618.

图/表 16

图1

图2

图3

表1

表2

表3

表4

决策组第一阶段判断为Ⅰ级突发事故

状态	数值
M₂	[0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₃	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅰ), (1, Ⅰ), (1, Ⅰ), (1, Ⅰ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅰ$ ), (1, $U 12 Ⅰ$ ), (1, $U 13 Ⅰ$ ), (1, $U 10 Ⅰ$ ), 0, 0, 0, 0, 0]
M₆	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₇	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₈	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₉	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

表4

表5

决策组第一阶段判断为Ⅱ级突发事故

状态	数值
M₁₀	[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₁	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅱ), (1, Ⅱ), (1, Ⅱ), (1, Ⅱ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₂	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₃	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅱ$ ), (1, $U 12 Ⅱ$ ), (1, $U 13 Ⅱ$ ), (1, $U 10 Ⅱ$ ), 0, 0, 0, 0, 0]
M₁₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₁₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₁₆	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₁₇	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

表5

表6

决策组第一阶段判断为Ⅲ级突发事故

状态	数值
M₁₈	[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₉	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅲ), (1, Ⅲ), (1, Ⅲ), (1, Ⅲ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₀	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), , (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₁	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅲ$ ), (1, $U 12 Ⅲ$ ), (1, $U 13 Ⅲ$ ), (1, $U 10 Ⅲ$ ), 0, 0, 0, 0, 0]
M₂₂	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₂₃	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₂₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₂₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

表6

表7

决策组判断为警报误报

状态	数值
M₂₆	[0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₇	[0, 0, 1, 0, 0, 0, 0, 0, (1, 0), (1, 0), (1, 0), (1, 0), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₈	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), , (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₉	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 110$ ), (1, $U 120$ ), (1, $U 130$ ), (1, $U 100$ ), 0, 0, 0, 0, 0]
M₃₀	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₃₁	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₃₂	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₃₃	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

表7

表8

表9

图4

图5

表10

表11

参考文献 23

1	田野, 刘宏, 张智峰, 等. 中国地下空间学术研究发展综述[J]. 地下空间与工程学报, 2020, 16(6): 1596-1610.
	Tian Ye, Liu Hong, Zhang Zhifeng, et al. A Summary of the Development of Underground Space Academic Research in China[J]. Chinese Journal of Underground Space and Engineering, 2020, 16(6): 1596-1610.
2	林晓飞, 喻箫, 侯正波, 等. 地铁应急疏散影响因素研究[J]. 中国安全生产科学技术, 2020, 16(增1): 41-45.
	Lin Xiaofei, Yu Xiao, Hou Zhengbo, et al. Research on Influencing Factors of Emergency Evacuation in Subway[J]. Journal of Safety Science and Technology, 2020, 16(S1): 41-45.
3	佚名. 郑州地铁5号线"7·20事件"中有14人不幸遇难[J]. 城市轨道交通研究, 2021, 24(8): 164.
	Anon. 14 People Were Killed in the "July 20 Incident" of Zhengzhou Metro Line 5[J]. Urban Mass Transit, 2021, 24(8): 164.
4	Zhang Ming, Li Ping, Wang Fuzhang. The Emergency Decision Support Platform of Urban Rail Transit Based on Information Sharing and Digitalized Plan[C]//Tenth International Conference of Chinese Transportation Professionals (ICCTP). Reston, VA, USA: ASCE, 2010: 287-294.
5	Kyriakidis M, Hirsch R, Majumdar A. Metro Railway Safety: An Analysis of Accident Precursors[J]. Safety Science, 2012, 50(7): 1535-1548.
6	Wang Haiyong, Zhang Yanpeng, Gao Jieqiong, et al. Research on the Mobile Assistant Decision-making System Based on Service-oriented Architecture for Transport Accident Rescue[J]. Advances in Mechanical Engineering, 2018, 10(4): 1687814018767256.
7	王付宇, 王骏. 基于精炼贝叶斯均衡的地铁站突发事件应急管理[J]. 齐齐哈尔大学学报(哲学社会科学版), 2018(1): 18-21.
	Wang Fuyu, Wang Jun. Emergency Management of Subway Station Emergency Based on Refined Bias Equilibrium[J]. Journal of Qiqihar University(Philosophy & Social Science Edition), 2018(1): 18-21.
8	郑云水, 穆然, 林俊亭, 等. 铁路应急资源动态多阶段调度决策模型及算法研究[J]. 计算机工程与应用, 2015, 51(20): 213-219, 233.
	Zheng Yunshui, Mu Ran, Lin Junting, et al. Research of Dynamic Multi-stage Scheduling Decision Model and Algorithm for Railway Emergency Resources[J]. Computer Engineering and Applications, 2015, 51(20): 213-219, 233.
9	洪玲, 高佳, 邱树涵, 等. 基于改进势能场模型的地铁车站应急疏散动态仿真[J]. 同济大学学报(自然科学版), 2020, 48(3): 398-406.
	Hong Ling, Gao Jia, Qiu Shuhan, et al. Dynamic Simulation on Emergency Evacuation in Metro Stations Based on Improved Potential Energy Field Model[J]. Journal of Tongji University(Natural Science), 2020, 48(3): 398-406.
10	朱小马. 地铁车站突发性大客流应急疏散研究[D]. 兰州: 兰州交通大学, 2017.
	Zhu Xiaoma. Study on Emergency Evacuation of Sudden Passenger Flow on Subway Station[D]. Lanzhou: Lanzhou Jiaotong University, 2017.
11	Li Shiqi, Uzam M, Yin Li, et al. Robust Diagnosability Analysis of Discrete Event Systems Using Labeled Petri Nets[J]. IEEE Access, 2021, 9: 163504-163515.
12	刘伟, 史晓浩, 孙红伟. 基于逻辑混合Petri网的混合系统建模与分析[J]. 山东科技大学学报(自然科学版), 2021, 40(4): 65-75.
	Liu Wei, Shi Xiaohao, Sun Hongwei. Modeling and Analysis of Hybrid Systems Based on Logic Hybrid Petri Nets[J]. Journal of Shandong University of Science and Technology(Natural Science), 2021, 40(4): 65-75.
13	He Zhou, Dong Yuying, Ren Gongchang, et al. Path Planning for Automated Guided Vehicle Systems With Time Constraints Using Timed Petri Nets[J]. Measurement and Control, 2020, 53(9/10): 2030-2040.
14	Zhao Jiantao, Chen Zengqiang, Liu Zhongxin. Modeling and Analysis of Colored Petri Net Based on the Semi-tensor Product of Matrices[J]. Science China Information Sciences, 2018, 61(1): 010205.
15	陈金栋, 刘伟, 冯新, 等. 基于逻辑工作流网的有限无死锁组合[J]. 山东科技大学学报(自然科学版), 2020, 39(5): 89-97.
	Chen Jindong, Liu Wei, Feng Xin, et al. Finite Deadlock-free Combination Based on Logical Workflow Network[J]. Journal of Shandong University of Science and Technology(Natural Science), 2020, 39(5): 89-97.
16	张艺凡, 陈文瑛. 地铁运营突发事件应急响应模式的马尔科夫链分析[J]. 中国安全科学学报, 2015, 25(2): 165-170.
	Zhang Yifan, Chen Wenying. Markov Chain Analysis of Metro Network in Responding to Emergency[J]. China Safety Science Journal, 2015, 25(2): 165-170.
17	袁俊辉. 基于SCPN的地铁车站火灾应急处置流程建模研究[D]. 北京: 北京交通大学, 2017.
	Yuan Junhui. Research on Modeling of Subway Station Fire Emergency Response Process Based on SCPN[D]. Beijing: Beijing Jiaotong University, 2017.
18	You Dan, Wang Shouguang, Zhou Mengchu, et al. Supervisory Control of Petri Nets in the Presence of Replacement Attacks[J]. IEEE Transactions on Automatic Control, 2022, 67(3): 1466-1473.
19	Feng Xin, Lin Mao, Liu Wei, et al. Modeling and Analysis for Uncertainty in Logistic Chains Based on Logical Time Petri Nets[J]. IEEE Access, 2020, 8: 61665-61671.
20	Mohammadian M, Aminifar F, Amjady N, et al. Data-driven Classifier for Extreme Outage Prediction Based on Bayes Decision Theory[J]. IEEE Transactions on Power Systems, 2021, 36(6): 4906-4914.
21	宋瑶. 基于动态博弈的智慧城市灾害应急决策研究[D]. 天津: 天津大学, 2017.
	Song Yao. Research on the Emergency Decision-making of Disasters in Smart City Based on Dynamic Game Theory[D]. Tianjin: Tianjin University, 2017.
22	Zazo S, Valcarcel M S, Sánchez-Fernández Matilde, et al. Dynamic Potential Games With Constraints: Fundamentals and Applications in Communications[J]. IEEE Transactions on Signal Processing, 2016, 64(14): 3806-3821.
23	王振, 杜玉越, 亓亮. 扩展颜色逻辑Petri网及其可达性分析[J]. 山东科技大学学报(自然科学版), 2020, 39(3): 84-98.
	Wang Zhen, Du Yuyue, Qi Liang. Extended Colored Logic Petri Net and Its Reachability Analysis[J]. Journal of Shandong University of Science and Technology(Natural Science), 2020, 39(3): 84-98.

库所	库所含义
P₁	地铁突发事件
P₂	地铁应急决策组
P₃	地铁突发事件历史数据
P₄	决策组判断事故等级为Ⅰ级
P₅	决策组判断事故等级为Ⅱ级
P₆	决策组判断事故等级为Ⅲ级
P₇	决策组判断应急结束
P₈	计数库所
P₉	准备计算Ⅰ级概率
P₁₀	准备计算Ⅱ级概率
P₁₁	准备计算Ⅲ级概率
P₁₂	准备计算0级概率
P₁₃	事故等级Ⅰ的前验概率和条件概率
P₁₄	事故等级Ⅱ的前验概率和条件概率
P₁₅	事故等级Ⅲ的前验概率和条件概率
P₁₆	事故等级0的前验概率和条件概率
P₁₇	事故等级Ⅰ的后验概率
P₁₈	事故等级Ⅱ的后验概率
P₁₉	事故等级Ⅲ的后验概率
P₂₀	事故等级0的后验概率
P₂₁	选择应急方案1的效用
P₂₂	选择应急方案2的效用
P₂₃	选择应急方案3的效用
P₂₄	不选择应急方案的效用
P₂₅	选择应急方案1
P₂₆	选择应急方案2
P₂₇	选择应急方案3
P₂₈	不选择应急方案
P₂₉	实施所选应急方案

变迁	含义
t₁	警报
t₂	等级分类
t₃	传送专家组判断
t₄	计算在决策组判断为Ⅰ级事故时实际等级的后验概率
t₅	计算在决策组判断为Ⅱ级事故时实际等级的后验概率
t₆	计算在决策组判断为Ⅲ级事故时实际等级的后验概率
t₇	计算在决策组判断为Ⅲ级事故时实际等级的后验概率
t₈	计算在决策组判断为Ⅰ级事故时各应急方案的期望效用
t₉	计算在决策组判断为Ⅱ级事故时各应急方案的期望效用
t₁₀	计算在决策组判断为Ⅲ级事故时各应急方案的期望效用
t₁₁	计算在决策组判断为0级事故时各应急方案的期望效用
t₁₂	选择应急方案
t₁₃	实施应急方案
t₁₄	将实时信息汇总

条件概率	y₀	y₃	y₂	y₁
p(x₀\| y_k )	0.80	0.10	0.05	0.05
p(x₃\| y_k )	0.10	0.70	0.15	0.05
p(x₂\| y_k )	0.05	0.15	0.50	0.30
p(x₁\| y_k )	0.05	0.05	0.30	0.60

[1]	赵坦, 吴琳, 陶九阳, 李帅. 元宇宙概念及其军事运用[J]. 系统仿真学报, 2023, 35(7): 1405-1420.
[2]	王晓锋, 谌泰乾, 刘渊. 面向卫星互联网的动态仿真技术研究[J]. 系统仿真学报, 2023, 35(7): 1472-1486.
[3]	马苗苗, 董利鹏, 刘向杰. 基于Q-learning算法的多智能体微电网能量管理策略[J]. 系统仿真学报, 2023, 35(7): 1487-1496.
[4]	徐健, 宋鑫, 刘秀平, 陈博, 闫焕营. 基于数字孪生的装配机器人建模及系统实现[J]. 系统仿真学报, 2023, 35(7): 1497-1507.
[5]	杜利珍, 叶涛, 王宇豪, 张亚军, 宣自风. 改进粒子群算法的不相关并行批处理调度优化[J]. 系统仿真学报, 2023, 35(7): 1549-1561.
[6]	徐银, 蒲云, 刘海旭, 谭一帆. 考虑后视效应和速度差的智能驾驶模型仿真[J]. 系统仿真学报, 2023, 35(7): 1562-1571.
[7]	于豪, 蒋锦霞, 赖晓翰, 梅峰, 王庆. 基于自适应感受野的电力设备表面缺陷检测方法[J]. 系统仿真学报, 2023, 35(7): 1572-1580.
[8]	李盈萱, 王中训, 董云龙. 两种新的机动目标仿真模型[J]. 系统仿真学报, 2023, 35(7): 1581-1589.
[9]	董武, 王聪, 张宏立, 马萍. 异构超混沌系统有限时间组合-组合同步及应用[J]. 系统仿真学报, 2023, 35(7): 1590-1601.
[10]	邱志明, 李恒, 周玉芳, 卿杜政. 模拟仿真技术及其在训练领域的应用综述[J]. 系统仿真学报, 2023, 35(6): 1131-1143.
[11]	董泽, 姜炜, 王晓燕, 刘磊. 数字孪生在火电机组数字化转型中的应用[J]. 系统仿真学报, 2023, 35(6): 1144-1156.
[12]	卢自宝, 丁浩, 孙方云, 丁梓琼, 龚莉, 郑睿. 直流微电网中能量协调控制策略的研究[J]. 系统仿真学报, 2023, 35(6): 1215-1225.
[13]	陈奕梅, 石小凡, 李宝全. 基于改进虚拟弹簧模型的多机器人编队控制[J]. 系统仿真学报, 2023, 35(6): 1235-1244.
[14]	杨静, 陆铭华, 胡星辰, 吴金平. 基于不确定时间序列的来袭目标解算方法[J]. 系统仿真学报, 2023, 35(6): 1245-1259.
[15]	张腾飞, 胡蓉, 钱斌, 吕阳. 学习型变邻域搜索算法求解运输-装配协同优化问题[J]. 系统仿真学报, 2023, 35(6): 1260-1277.