JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2018, Vol. 48 ›› Issue (1): 131-136.doi: 10.6040/j.issn.1672-3961.0.2017.146

Previous Articles    

Inverse problems of pollution source identification based on Bayesian-DE

ZHANG Shuangsheng1,2, QIANG Jing3*, LIU Xikun2, LIU Hanhu1, ZHU Xueqiang1   

  1. 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

PDF (PC)

559

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

CLC Number: 

  • X52
[1] WEI H, CHEN W, SUN H, et al. A coupled method for inverse source problem of spatial fractional anomalous diffusion equations[J]. Inverse Problems in Science and Engineering, 2010, 18(7): 945-956.
[2] JHA M, DATTA B. Three-dimensional groundwater contamination source identification using adaptive simulated annealing[J]. Journal of Hydrologic Engineering, 2012, 18(3): 307-317.
[3] HOLLAND J. Adaptation in natural and artificial systems [M]. Ann Arbor: University of Michigan Press, 1975.
[4] RUZEK B, KVASNICKA M. Differential evolution algorithm in the earthquake hypocenter location[J]. Pure and Applied Geophysics, 2001, 158(4): 667-693.
[5] 赵光权. 基于贪婪策略的微分进化算法及其应用研究 [D].哈尔滨:哈尔滨工业大学, 2007. ZHAO Guangquan. Differential evolution algorithm with greedy strategy and its applications[D]. Harbin: Harbin Institute of Technology, 2007.
[6] 苏海军, 杨煜普, 王宇嘉. 微分进化算法的研究综述[J].系统工程与电子技术, 2008, 30(9):1793-1797. SU Haijun, YANG Yupu, WANG Yujia. Research on differential evolution algorithm: a survey[J]. Systems Engineering and Electronics, 2008, 30(9):1793-1797.
[7] STRON R, PRICE K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4):341-359.
[8] ABBASS H A. The self-adaptive Pareto differential evolution algorithm[C] //Proceedings of 2002 IEEE Congress on Evolutionary Computation. Honolulu, USA: IEEE, 2002:831-836.
[9] STRON R, PRICE K. Minimizing the real functions of the ICEC'96 contest by differential evolution[C] //IEEE International Conference on Evolutionary Computation. Nagoya, Japan:IEEE, 1996:842-844.
[10] BECERRA R, COELLO C. Cultured differential evolution for constrained optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(33-36):4303-4322.
[11] BREST J, GREINER S, BOSKOVIC B, et al. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems[J]. IEEE Transaction on Evolutionary Computation, 2006, 10(6):646-657.
[12] FAN H, LAMPINEN J. A trigonometric mutation operation to differential evolution[J]. Journal of Global Optimization, 2003, 27(1):105-129.
[13] CHAKRABORY U, DAS S, KONAR A. Differential evolution with local neighborhood[C] //IEEE Congress on Evolutionary Computation. Vancouver, Canada:IEEE, 2006:2042-2049.
[14] 郝竹林, 冯民权, 闵涛, 等. 地下水渗流参数反演的微分进化算法[J].自然灾害学报, 2015, 24(1):55-60. HAO Zhulin, FENG Minquan, MIN Tao, et al. Differential evolution algorithm for parameter inversion of groundwater seepage flow[J]. Journal of Natural Disasters, 2015, 24(1):55-60.
[15] 刘英霞, 王希常, 唐晓丽, 等. 基于小波域特征和贝叶斯估计的目标检测算法[J]. 山东大学学报(工学版), 2017, 47(2):63-70. LIU Yingxia, WANG Xichang, TANG Xiaoli, et al. Object detection algorithm based on Bayesian probability estimation in wavelet domain[J]. Journal of Shandong University(Engineering Sciences), 2017, 47(2):63-70.
[16] HAARIO H, SAKSMAN E, TAMMINEN J. An adaptive metropolis algorithm[J]. Bernoulli, 2001, 7(2): 223-242.
[17] ZENG L, SHI L, ZHANG D, et al. A sparse grid based Bayesian method for contaminant source identification[J]. Advances in Water Resources, 2012, 37(1):1-9.
[18] 王海军, 葛红娟, 张圣燕. 基于L1范数和最小软阈值均方的目标跟踪算法[J].山东大学学报(工学版), 2016, 46(3):14-22. WANG Haijun, GE Hongjuan, ZHANG Shengyan. Object tracking via L1 norm and least soft-threshold square[J]. Journal of Shandong University(Engineering Sciences), 2016, 46(3):14-22.
[19] 曹瑛, 王明文, 陶亮. 基于Markov 网络的检索模型[J]. 山东大学学报(理学版), 2006, 41(3):126-130. CAO Ying, WANG Mingwen, TAO Liang. Information retrieval model based on Markov network[J]. Journal of Shandong University(Natural Science), 2006, 41(3):126-130.
[20] 曾平, 王婷. 贝叶斯错误发现率[J]. 山东大学学报(医学版), 2012, 50(3):120-124. ZENG Ping, WANG Ting. Bayesian false discovery rate[J]. Journal of Shandong University(Health Sciences), 2012, 50(3):120-124.
[21] 陈海洋, 腾彦果, 王金生, 等. 基于Bayesian-MCMC方法的水体污染识别反问题[J]. 湖南大学学报(自然科学版), 2012, 39(6):74-78. CHEN Haiyang, TENG Yanguo, WANG Jinsheng, et al. Event source identification of water pollution based on Bayesian-MCMC[J]. Journal of Hunan University(Natural Sciences), 2012, 39(6):74-78.
[22] 杨海东, 肖宜, 王卓民, 等.突发性水污染事件溯源方法[J].水科学进展, 2014, 25(1):122-128. YANG Haidong, XIAO Yi, WANG Zhuomin, et al. On source identification method for sudden water pollution accidents[J]. Advances in Water Science, 2014, 25(1):122-128.
[23] 闵涛, 周孝德, 张世梅, 等. 对流-扩散方程源项识别反问题的遗传算法[J]. 水动力学研究与进展, A辑, 2004, 19(4):520-524. MIN Tao, ZHOU Xiaode, ZHANG Shimei, et al. Genetic algorithm to an inverse problem of source term identification for convection-diffusion equation[J]. Journal of Hydrodynamics(Ser.A), 2004, 19(4):520-524.
[24] 牟行洋.基于微分进化算法的污染物源项识别反问题研究[J]. 水动力学研究与进展(A辑), 2011, 26(1):24-30. MOU Xingyang. Research on inverse problem of pollution source term identification based on differential evolution algorithm[J]. Journal of Hydrodynamics(Ser.A), 2011, 26(1):24-30.
[25] 郑春苗, BENNETT G D. 地下水污染物迁移模拟(第二版)[M]. 北京:高等教育出版社, 2009:70-79.
[1] YANG Longhao, FU Yanggeng, GONG Xiaoting. Parallel differential evolution algorithm for parameter learning of belief rule base [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2015, 45(1): 30-36.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of Journal of Shandong University (Engineering Science)
Supported by Beijing Magtech Co.Ltd