基于贝叶斯-微分进化算法的污染源识别反问题

doi:10.6040/j.issn.1672-3961.0.2017.146

山东大学学报(工学版) ›› 2018, Vol. 48 ›› Issue (1): 131-136.doi: 10.6040/j.issn.1672-3961.0.2017.146

• • 上一篇

基于贝叶斯-微分进化算法的污染源识别反问题

张双圣^1,2,强静^3*,刘喜坤²,刘汉湖¹,朱雪强¹

1. 中国矿业大学环境与测绘学院, 江苏徐州 221116;2. 徐州市城区水资源管理处, 江苏徐州 221018;3. 中国矿业大学数学学院, 江苏徐州 221116

收稿日期:2017-04-01 出版日期:2018-02-20 发布日期:2017-04-01
通讯作者: 强静(1983— ),女, 山东汶上人, 讲师, 博士,主要研究方向为计算数学. E-mail:jingqiangsd@hotmail.com E-mail:zhang_-shuangsheng@163.com
作者简介:张双圣(1983— ), 男, 山东昌邑人,博士研究生, 主要研究方向为水污染控制. E-mail:zhang_-shuangsheng@163.com
基金资助:
江苏省水利科技基金资助项目(2016056);水体污染控制与治理科技重大专项基金资助项目(2015ZX07406005)

Inverse problems of pollution source identification based on Bayesian-DE

ZHANG Shuangsheng^1,2, QIANG Jing^3*, LIU Xikun², LIU Hanhu¹, ZHU Xueqiang¹

1. School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China;
2. Xuzhou City Water Resource Administrative Office, Xuzhou 221018, Jiangsu, China;
3. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received:2017-04-01 Online:2018-02-20 Published:2017-04-01

摘要/Abstract

摘要： 针对污染源瞬时排放的河流水污染事件反问题,通过贝叶斯统计方法和二维水质对流-扩散方程,建立水体污染识别模型,得到关于污染源强度、污染源位置和污染源排放时刻3个未知参数的后验概率密度函数。运用最大似然估计的思想,采用微分进化算法,求解使后验概率密度函数达到最大值的参数,作为模型未知参数的估计值。算例表明:运用贝叶斯微分进化算法,3个未知参数估计值迭代50次时可以达到稳定,当迭代次数达到280次时,可与真值完全重合;与贝叶斯-蒙特卡洛法相比,贝叶斯-微分进化算法可使3个未知参数估计值达到稳定时的迭代次数降低97.5%,均值误差分别减少1.69%、2.12%和4.03%,具有收敛快、精度高的特点。

关键词: 突发性水污染, 二维水质模型, 贝叶斯统计, 微分进化算法, 贝叶斯-马尔科夫链蒙特卡洛法

Abstract: Aiming at the inverse problem of water pollution of river with pollutant source discharged instantaneously, a methodical model was constructed based on Bayesian statistical method and two-dimensional water quality model. The posterior probability distribution of unknown parameters including source's position, intensity and discharging time was deduced. The parameters made the posterior probability density function reach the maximum value by the idea of maximum likelihood estimate and differential evolution algorithm(DE), which were viewed as the estimates of model parameters. The example showed that three estimate parameters could reach the stable state based on Bayesian-DE after 50 iterations, and correspond with truth values after 280 iterations. Compared with Bayesian-Markov chain Monte Carlo simulation(Bayesian-MCMC), 97.5% iterations of three estimate parameters reaching the stable state could be reduced, and the mean errors were decreased by 1.69%, 2.12% and 4.03% through the use of Bayesian-DE featuring rapid convergence and high accuracy.

Key words: two-dimensional water quality model, Bayesian statistical method, sudden water pollution, Bayesian-Markov chain Monte Carlo simulation, differential evolution algorithm

中图分类号:

张双圣,强静,刘喜坤,刘汉湖,朱雪强. 基于贝叶斯-微分进化算法的污染源识别反问题[J]. 山东大学学报(工学版), 2018, 48(1): 131-136.

ZHANG Shuangsheng, QIANG Jing, LIU Xikun, LIU Hanhu, ZHU Xueqiang. Inverse problems of pollution source identification based on Bayesian-DE[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(1): 131-136.

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基于贝叶斯-微分进化算法的污染源识别反问题

Inverse problems of pollution source identification based on Bayesian-DE

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