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

作　　者：张双圣[1,2] 强静 刘喜坤 刘汉湖 朱雪强[1] ZHANG Shuangsheng1,2, QIANG Jing3. , 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, Chin)

机构地区：[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

出　　处：《山东大学学报（工学版）》2018年第1期131-136,共6页Journal of Shandong University（Engineering Science）

基　　金：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)

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。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 BayesianDE featuring rapid convergence and high accuracy.

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

分 类 号：X52[环境科学与工程—环境工程]