水质变化趋势的有效预测对于水资源综合管理具有重要意义。针对现有数据驱动模型不能有效反映研究对象物理机理的问题,提出了一种耦合动态方程的神经网络模型,并给出了动态方程的耦合方法。分别从数值算例和实际案例2个方面对传统网络模型和机理先验前馈网络模型进行了对比计算分析,拟合程度指标和计算误差指标都表明机理性先验知识的加入可以提高网络模型的预测精度和非线性拟合能力。同时,该模型在水质预测中具有适用性和合理性。在样本数量一定的情况下,机理性先验知识的耦合是进一步提高网络计算精度的有效途径。
Abstract
Precise prediction of water quality trend is of vital importance for water resources management. Commonly used data-driving models cannot reflect the physical characteristics of research objective. In view of this, a neural network coupled with dynamic equation is proposed in this paper, and the method to couple dynamic equation into model iteration is also given. A numerical case and a practical case are used to demonstrate the difference between network model with mechanism priori-knowledge and traditional network model. The results of fitting degree and calculation error indicate that the coupled priori-knowledge is able to improve calculation accuracy and enhance non-linear fitting. The proposed model is applicable and rational in water quality prediction. Sample size is the basis of neural network model application, and coupling mechanism priori knowledge under the circumstance of fixed sample size is an efficient approach to improving prediction accuracy.
关键词
水质预测 /
神经网络模型 /
耦合动态方程 /
机理性先验知识 /
Mackey-Glass混沌系统
Key words
water quality prediction /
neural network model /
dynamic equation /
mechanism priori knowledge /
Mackey-Glass chaotic system
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参考文献
[1] 刘俊威, 吕惠进. 人工神经网络在水质预测中的应用研究[J] . 长江科学院院报, 2012,29(9):95-97.
[2] 唐婉莹, 杨宇川, 黄 刚. BP神经网络用于水体中N综合污染评价[J] . 计算机与应用化学, 2002,19(4):438-440.
[3] ALY A H, PERALTA R C. Optimal Design of Aquifer Cleanup Systems under Uncertainty Using a Neural Network and a Genetic Algorithm[J] . Water Resources Research, 1999,35(8):2523-2532.
[4] CAI X,MCKINNEY D C,LASDON L S.Integrated Hydrologic-Agronomic-Economic Model for River Basin Management[J] . Journal of Water Resources Planning & Management, 2003,129(1):4-17.
[5] ABU-MOSTAFA Y S. Learning from Hints in Neural Networks[J] . Journal of Complexity, 1990,6(2):192-198.
[6] 娄海川, 苏宏业, 谢 磊. 融合过程先验知识的递归神经网络模型及其应用[J] . 化工学报, 2013,64(5):1665-1673.
[7] 史步海, 朱学峰, 陈锦威. 基于先验知识的混凝沉淀过程神经网络建模[J] . 华南理工大学学报(自然科学版), 2008,36(5):113-118.
[8] HU T, WU F, ZHANG X. Rainfall-runoff Modeling Using Principal Component Analysis and Neural Network[J] . Water Policy, 2007,38(3):235-248.
[9] CHUA L H C, WONG T S W. Runoff Forecasting for an Asphalt Plane by Artificial Neural Networks and Comparisons with Kinematic Wave and Autoregressive Moving Average Models[J] .Journal of Hydrology,2011,397(3/4):191-201.
[10] 胡铁松. 神经网络预测与优化[M] . 大连:大连海事大学出版社, 1997.
[11] 马 骋, 李 迅, 姚家晖, 等. 一种新的求解带约束的有限极大极小问题的精确罚函数[J] . 应用数学和力学, 2012,33(2):250-264.
[12] 韩艳丽. 约束优化问题的罚函数的研究[D] . 焦作:河南理工大学, 2011.
[13] 董 梅. 具时滞的Mackey-Glass混沌系统的Hopf分支分析[D] . 哈尔滨:哈尔滨工业大学, 2008.
[14] 王福军. 计算流体动力学分析——CFD软件原理与应用[M] . 北京: 清华大学出版社, 2004.
基金
国家自然科学基金项目(71171151,51509008);湖北省自然科学基金项目(2015CFA157)
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