带扰动算子的量子粒子群在水污染源识别中的应用

系统仿真学报 ›› 2015, Vol. 27 ›› Issue (7): 1628-1637.

带扰动算子的量子粒子群在水污染源识别中的应用

田娜^1,2, 纪志成²

1.江南大学田家炳教育科学学院,无锡 214122;
2.江南大学电气自动化研究所,无锡 214122

收稿日期:2014-07-17 修回日期:2014-11-21 出版日期:2015-07-08 发布日期:2020-07-31
作者简介:田娜(1983-)女, 河北, 博士, 副教授, 研究方向为智能控制, 系统辨识; 纪志成(1959-)男, 浙江, 教授, 博士, 研究方向为智能控制, 系统辨识。
基金资助:
江苏省博士后基金(1401004B); 国家粮食局公益性行业科研专项(201313012)

Estimation of Contamination Source by Using QPSO with Perturbation Operator

Tian Na^1,2, Ji Zhicheng²

1. School of Tianjiabing Educational Sciences, Jiangnan University, Wuxi 214122, China;
2. Institute of Electrical Automation, Jiangnan University, Wuxi 214122, China

Received:2014-07-17 Revised:2014-11-21 Online:2015-07-08 Published:2020-07-31

摘要/Abstract

摘要： 提出一种带扰动算子的量子行为粒子群优化算法,将其用于求解对流-扩散反问题中的估计随时间变化的污染源问题。污染源是时变函数,问题归结为函数估计问题(function estimation problem)。为了将反问题转化为优化问题,我们采用了非线性最小二乘模型。考虑到采样数据可能存在噪声,Tikhonov正则化方法用来取得稳定解,L-curve方法用来求得正则参数。仿真结果表明：带扰动算子的量子粒子群算法明显优于传统量子粒子群算法,能够帮助粒子从局部最优中跳出来。从不同的角度对算法进行了测试(正则项,噪声级别,传感器的位置等)。

关键词: 扰动算子, 量子粒子群, 水污染源识别, 偏微分方程

Abstract: An improved quantum-behaved particle swarm optimization (QPSO) with perturbation operator was proposed and applied to solve the convection-diffusion inverse problem of estimating time-varying contamination source. Because the contamination source is time-dependent, the inverse problems are classified into function estimation problem. To transform the inverse problem to optimization problem, the nonlinear least square method was used. Meanwhile, Tikhonov regularization was used to stablize the solution with noisy measured data. And the regularization parameter was chosen by L-curve method. The simulation results tell that QPSO with perturbation operator outperforms QPSO and PSO. Moreover, tests over different views (regularization terms, noise level, sensor positions) were performed.

Key words: perturbation operator, quantum-behaved particle swarm optimization, contamination source estimation, partial differential equation

中图分类号:

TP399

田娜, 纪志成. 带扰动算子的量子粒子群在水污染源识别中的应用[J]. 系统仿真学报, 2015, 27(7): 1628-1637.

Tian Na, Ji Zhicheng. Estimation of Contamination Source by Using QPSO with Perturbation Operator[J]. Journal of System Simulation, 2015, 27(7): 1628-1637.

参考文献

[1] P Sidauruk.Parameter determination for multi-layered aquifer and groundwater contaminant transport [D]. USA: University of Delaware, 1996.
[2] S M Gorelick, B Evans, I Remson.Identifying sources of groundwater pollution: An optimization approach[J]. Water Resources Research (S1944-7973), 1983, 19(3): 779-790.
[3] B J Wagner.Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modeling[J]. Journal of Hydrology (S0022-1694), 1992, 135(1/4): 275-303.
[4] S Zou, A Parr.Estimation of dispersion parameters for two dimensional plumes[J]. Ground Water (S1745-6584), 1993, 31(3): 389-392.
[5] H T Skaggs, Z J Kabala.Recovering the release history of a groundwater contaminant[J]. Water Resources Research (S1944-7973), 1994, 30(2): 71-79.
[6] H T Skaggs, Z J Kabala.Limitations in recovering the history of a groundwater contaminant plume[J]. Journal of Contaminant Hydrology (S0619-7722), 1998, 33(3/4): 347-359.
[7] H T Skaggs, Z J Kabala.Recovering the history of a groundwater contaminant plume: method of quasi-reversibility[J]. Water Resources Research (S1944-7973), 1995, 31(11): 2669-2673.
[8] A D Woodbury, T J Ulrych.Minimum relative entropy inversion: Theory and application to recovering the release history of a groundwater contaminant[J]. Water Resources Research (S1944-7973), 1996, 32(9): 2671-2681.
[9] A D Woodbury, E Sudicky, T J Ulrych, R Ludwig.Three-dimensional plume source reconstruction using minimum relative entropy inversion[J]. Journal of Contaminant Hydrology (S0619-7722), 1998, 32(1/2): 131-158.
[10] M F Snodgrass, P K Kitanidis.A geostatistical approach to contaminant source identification[J]. Water Resources Research (S1944-7973), 1997, 33(4): 537-546.
[11] N Z Sun.Inverse Problems in Groundwater Modeling[M]. Dordrecht, The Netherlands: Kluwer, 1994.
[12] C Liu, W P Ball.Application of inverse methods to contaminant source identification from aquitard diffusion profiles at Dover AFB, Delaware[J]. Water Resources Research (S1944-7973), 1999, 35(7): 1975-1985.
[13] T V Bharat, P V Sivapullaiah, M M Allam.Accurate parameter estimation of contaminant transport inverse problem using particle swarm optimization[C]// IEEE Swarm Intelligence Symposium, St Louis, USA, 2008. USA: IEEE, 2008.
[14] H X Long, J Sun, X G Wang, C-H Lai, W B Xu.Using selection to improve quantum-behaved particle swarm optimization[J]. International Journal of Innovative Computing and Applications (S1751-6498), 2009, 2(2): 100-114.
[15] J Kennedy, R C Eberhart.Particle swarm optimization[C]// IEEE Int. Conf. on Neural Networks, Perth, Australia, 1995. USA: IEEE, 1995.
[16] F Van den Bergh. An analysis of particle swarm optimizers [D]. South Africa: University of Pretoria, 2001.
[17] J Sun, W B Xu, W Fang.A diversity-guided quantum-behaved particle swarm optimization algorithm[C]// Simulated Evolution and Learning, Hefei, China, 2006. Berlin, Germany:(Springer Berlin Heidelberg), 2006: 497-504.
[18] J Sun, W B Xu, W Fang.Quantum-behaved particle swarm optimization algorithm with controlled diversity[C]// ICCS, Reading, UK, 2006. Berlin, Germany:(Springer Berlin Heidelberg), 2006: 847-854.
[19] M Clerc.The swarm and the queen: towards a deterministic and adaptive particle swarm optimization [C]// Proc Cong. on Evolutionary Computation. Washington D C, USA: IEEE Press, 1999: 1951-1957.
[20] R C Eberhart, Y Shi.Comparing inertia weights and constriction factors in particle swarm optimization [C]// Proc. the IEEE Cong. on Evolutionary Computation. San Diego, USA: IEEE Press, 2000: 84-88.
[21] Y Shi, R C Eberhart.Parameter selection in particle swarm optimization[C]// Proc. the Seventh Annual Conf. on Evolutionary Programming, New York, USA. Berlin, Germany: Springer Berlin Heidelberg, 1998: 591-600.