基于热传导方程的城市犯罪时空数值源分析  

Spatiotemporal numerical source analysis of urban crime based on heat conduction equation

作　　者：丁伟杰[1,2,3] 周凯 沈守枫[4] DING Wei-jie;ZHOU Kai;SHEN Shou-feng(Big-data and Network Security Research Institute,Zhejiang Police College,Hangzhou 310053,China;Key Laboratory of Public Security Information Application Based on Big-data Architecture,Ministry of Public Security,Hangzhou 310053,China;College of Information Engineering,Zhejiang University of Technology,Hangzhou 310023,China;Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China)

机构地区：[1]浙江警察学院大数据与网络安全研究院,浙江杭州310053 [2]基于大数据架构的公安信息化应用公安部重点实验室,浙江杭州310053 [3]浙江工业大学信息工程学院,浙江杭州310023 [4]浙江工业大学应用数学系,浙江杭州310023

出　　处：《高校应用数学学报（A辑）》2022年第2期187-194,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省基础公益研究计划(LGF19G010001);公安部科技强警基础专项(2020GABJC35)。

摘　　要：运用热力学原理构建热传导方程,刻画城市犯罪指数在时空上的分布规律以及时空交互联系性.首先推导城市犯罪指数在时间维度,空间维度扩散的热传导方程模型.然后构建该方程的反问题,采用差分方式估计重要参数,并据此评估城市的治安管理能力,定位城市犯罪的源头.最后依托杭州市某区各街道2018-2020年内案件数量对方程进行计算,验证方法的有效性.Based on the principle of thermodynamics,this paper constructs a heat conduction equation to describe the spatial-temporal distribution law and spatial-temporal interaction.Firstly,a partial differential equation model of the diffusion of urban crime index in time and space dimensions is presented.Then,the inverse problem of this equation and corresponding optimization model is established.Some important parameters are estimated by the difference method,so as to evaluate the public security management ability of each urban district and locate the source of urban crime in each district.Finally,based on the number of cases in each street of the block B of Hangzhou from 2018 to 2020,the model proposed in this paper is calculated and compared with the real situation to illustrate the effectiveness of the method.

关 键 词：热力学原理 热传导方程 有限差分 参数估计 犯罪源定位 

分 类 号：O175.14[理学—数学]