﻿ 台风疏散时间选择决策建模与仿真
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (4): 793-798  DOI: 10.11990/jheu.201706043 0

### 引用本文

SONG Yan, SUN Dian, SU Zifeng. Modeling and simulating evacuation timing decisions during typhoon disasters[J]. Journal of Harbin Engineering University, 2018, 39(4), 793-798. DOI: 10.11990/jheu.201706043.

### 文章历史

Modeling and simulating evacuation timing decisions during typhoon disasters
SONG Yan, SUN Dian, SU Zifeng
School of Economics and Management, Harbin Engineering University, Harbin 150001, China
Abstract: To enable an improved estimate of the dynamic distribution of evacuation demands, traffic network clearance time, and improve typhoon evacuation efficiency, and by considering how strategic evacuation timing choices made by individuals aggregate to form an equilibrium distribution on the evacuation of people, a typhoon evacuation timing choice model based on quantal response equilibrium is established by integrating interaction factors for evacuees into the discrete choice model. To verify the feasibility and validity of the model, Matlab is used to analyze the effects of parameter changes on the evacuation timing decision under equilibrium strategies. Results show that the expected utility of evacuees, the interaction between individuals, and the individual inference ability have a significant influence on the evacuation time choices.
Key words: typhoon evacuation    timing decision-making    quanta response equilibrium    bounded rationality    discrete choice model    game    evacuees    expected utility    interaction effect

1 问题描述及博弈分析

 $\sum\limits_{{{s}_{ij}}\in {{S}_{i}}}{{{p}_{i}}({{s}_{ij}})}=1$ (1)

 ${{U}_{i}}({{p}_{i}})=\sum\limits_{j=1}^{J}{{{p}_{ij}}\cdot {{U}_{i}}({{s}_{ij}}, {{p}_{-i}})}$ (2)
2 台风疏散时间决策模型 2.1 模型假设

2.2 模型构建

 ${{U}_{ij}}={{U}_{j}}^{g}+{{U}_{j}}^{d}+{{\varepsilon }_{ij}}$ (3)

 ${{U}_{j}}^{g}=\beta {{x}_{j}}={{\beta }_{1}}{{x}_{j}}^{\text{risk}}+{{\beta }_{2}}{{x}_{j}}^{\text{cost}}$ (4)

 ${{U}_{j}}^{d}=h({{f}_{j}}\left( n \right), n)$ (5)

 $F({{\varepsilon }_{ij}})=\text{exp}[-\text{exp}(-{{\varepsilon }_{ij}}/\mu )]$ (6)

3 有限理性的均衡策略求解及分析

 $\begin{array}{l} \;\;\;\;\;\;\;{U_{ij}}({s_{ij}},{p_{ - ij}}) \ge {U_{ij\prime }}({s_{ij\prime }},{p_{ - ij\prime }}) = \\ {\rm{E}}[{{\bar U}_j}({p_{ - ij}}) + {\varepsilon _{ij}}] \ge {\rm{E}}[{{\bar U}_{j\prime }}({p_{ - ij\prime }}) + {\varepsilon _{ij\prime }}]\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\forall i,\forall j \ne j\prime \end{array}$ (7)

 ${{p}_{j}}^{*}=\frac{\text{exp}(\text{E}[{{{\bar{U}}}_{j}}]/\mu )}{\sum\limits_{j\prime =1}^{J}{\text{exp}(\text{E}[{{{\bar{U}}}_{j\prime }}]/\mu )}}$ (8)

4 模型仿真与分析 4.1 示例说明

 $\text{E}[{{{\bar{U}}}_{j}}]={{\beta }_{^{1}}}{{X}_{j}}^{1}+{{\beta }_{2}}{{X}_{j}}^{2}+h(\left( N-1 \right){{p}_{j}}^{*}+1)$ (9)

4.2 仿真过程

1) 生成1 000个随机变量的集合, 共有10个维度的偏好矢量, 密度分布服从均值为0方差为1的正态分布, 每个集合定义一个主体的类型, 即代表一个被疏散车辆;

2) 定义每个个体的效用值时在其随机量基础上加平均效用偏好值;

3) 利用以上步骤得到的数值和式(5)计算每个主体选择特定起始时间的概率;

4) 将1 000个仿真主体的每个起始时间的概率求和, 总结出10段撤离时间选择的分布。

4.3 结果和分析

4.3.1 备选策略效用的敏感性分析

 Download: 图 1 备选策略效用变化对疏散人口时间分布的影响 Fig. 1 Choice alternative impact on the time distribution of evacuation number

1) 将被疏散群体的对疏散时间策略的平均风险感知值进行调整, 从对不同时间有相同感知的模式Xrisk={10, 10, 10, 10, 10, 10, 10, 10, 10, 10}, 调整为不同时间策略有不同的风险感知值的模式Xrisk′={3, 3, 3, 10, 10, 10, 10, 10, 2, 2}, 反映了对于台风来临的风险感知, 起初处于信息接收阶段, 对于风险的感知能力较低; 而中间时段台风来临的环境线索愈加明显, 对于撤离的意愿愈加强烈; 在最后两阶段由于时间的压力, 以及撤离行动过程不可预知的风险, 会导致撤离意愿下降。对比图 1中的风险线和初始线发现, 其他条件不变, 被疏散个体在集计层面的撤离行动的分布依据不同时段的平均风险感知水平变化模式成比例的变化, 在4~8几个时段的风险感知的程度最高, 虽然与初始设置值相同, 但在这几个时段疏散的人数会明显高于初始设置和其他时段, 而其他时段的风险感知程度偏低, 疏散人数则低于初始设置水平。说明当不考虑成本消耗的时间差别和被疏散个体之间的相互作用时, 被疏散群体的撤离时间决策的总体分布取决于对各个时段风险水平的感知程度, 且成比例变化。

2) 将与时间相关的成本消耗从相同值Xcost={10, 10, 10, 10, 10, 10, 10, 10, 10, 10}变为Xcost′={5, 5, 5, 10, 10, 10, 10, 10, 2, 2}时, 表现出在不同时段被疏散人群愿意为选择某时段撤离而付出的成本花费, 起初由于风险的不确定性并不愿意花费过多成本出行; 而中间阶段当确定台风来临的可能性增加, 且完成撤离准备工作后, 此时愿意付出更多的成本选择撤离; 在最后阶段随着已经撤离的人数增多, 剩余被疏散者的疏散意愿较低, 且出行风险较高, 导致愿意付出成本减少。结果如图 1所示, 疏散成本线为成本消耗变化后得到的疏散人口数量, 当其他条件不变, 可以适当的调节疏散过程的成本消耗, 以此影响疏散总人数的时间分布。这说明, 当被疏散人群的风险感知依据时间有差别, 且忽略其相互作用时, 疏散成本的变化会对选择不同时间疏散的人数有一定的影响力, 可以起到调节作用。

3) 将成本消耗的权重改变时, 固定其他参数值, 将原权重的系数-0.6分别取值-0.3(βcost=-0.3)和-0.9(βcost=-0.3), 得到结果如图 1所示。观察发现, 随着成本消耗的权重系数的改变, 疏散的总人口数量的时间分布也会改变。说明当被疏散群体对于成本消耗的敏感性越高, 调节疏散成本对疏散人口时间分布的影响越大, 符合实际生活中的认知。

 Download: 图 2 不同效用作用下的累积疏散比率 Fig. 2 Accumulated evacuation rate under different utilities
4.3.2 被疏散者交互作用的敏感性分析

 Download: 图 3 交互作用对疏散人口时间分布的影响 Fig. 3 Interaction impact on the time distribution of evacuation number
4.3.3 估计的不确定性的敏感性分析

 Download: 图 4 估计的不确定性对疏散人口时间分布的影响 Fig. 4 Uncertainty of conjecture on the time distribution of evacuation number
5 结论

1) 被疏散者在有限理性下基于期望效用来决定何时采取撤离的行动, 构成了基于疏散需求的分布曲线, 因此本模型可为预测疏散需求提供支持;

2) 由被疏散者内生决定的交互作用也与外生变量同样影响疏散时间策略的选择, 即其他个体的疏散时间决策会影响被疏散个体的疏散时间选择;

3) 被疏散者个体对于其他个体选择的推断能力对疏散个体时间选择的分布也有显著的影响, 因此当为被疏散个体提供足够的信息时, 可以提高其推断能力, 进而达到信息提供者的目标。

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