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

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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

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