基于最小二乘支持向量回归的水质预测
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摘要
水质系统是一个开放的、复杂的、非线性动力学系统,具有时变复杂性,针对水质预测方法的研究虽然已经取得了一些成果,但也存在预测精度与计算复杂度等难题。为此,本文提出一种基于最小二乘支持向量回归的水质预测算法。支持向量机是机器学习中一种常用的分类模型,通过核函数将非线性数据从低维映射到高维空间,在高维空间实现线性分类和回归,最小二乘支持向量回归(LS-SVR)利用所有的样本参与回归拟合,使得回归的损失函数不再只与小部分支持向量样本有关,而是由所有样本参与学习修正误差,提高预测精度;同时该算法将标准SVR求解问题由不等式的约束条件及凸二次规划问题转化成线性方程组来求解,提高了运算速度,解决了非线性复杂特性的水质预测问题。
The water quality system is an open, complex, and nonlinear dynamic system with time-varying complexity. Although some achievements have been made in the research of water quality prediction methods, there are still some difficulties such as prediction accuracy and computational complexity. Therefore, this paper proposes a water quality prediction algorithm based on least squares support vector regression. Support vector machine(SVM) is a kind of commonly used machine learning classification model, nonlinear data are mapped from low-dimensional space to high-dimensional space through the kernel function, linear classification and regression are realized in the high dimensional space, the least squares support vector regression(LS-SVR) uses all samples to participate in regression fitting, which makes the regression loss function be no longer only related to a small number of support vector samples, but all samples participate in learning to correct error and improve the prediction precision. At the same time, by this algorithm, the standard SVR solving problem is transformed from inequality constraint conditions and convex quadratic programming problem into solving linear equations, which increases operation speed and solves the water quality prediction problem with nonlinear complex characteristics.
The water quality system is an open, complex, and nonlinear dynamic system with time-varying complexity. Although some achievements have been made in the research of water quality prediction methods, there are still some difficulties such as prediction accuracy and computational complexity. Therefore, this paper proposes a water quality prediction algorithm based on least squares support vector regression. Support vector machine(SVM) is a kind of commonly used machine learning classification model, nonlinear data are mapped from low-dimensional space to high-dimensional space through the kernel function, linear classification and regression are realized in the high dimensional space, the least squares support vector regression(LS-SVR) uses all samples to participate in regression fitting, which makes the regression loss function be no longer only related to a small number of support vector samples, but all samples participate in learning to correct error and improve the prediction precision. At the same time, by this algorithm, the standard SVR solving problem is transformed from inequality constraint conditions and convex quadratic programming problem into solving linear equations, which increases operation speed and solves the water quality prediction problem with nonlinear complex characteristics.
引文
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[18] 阎辉,张学工,李衍达.支持向量机与最小二乘关系研究[J].清华大学学报(自然科学版),2001,41(9):77-80.
[19] KIM S E,SEO I W.Artificial neural network ensemble modeling with conjunctive data clustering for water quality prediction in rivers[J].Journal of Hydro-environment Research,2015,9(3):325-339.
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[21] CHATTERJEE S,SARKAR S,DEY N,et al.Application of cuckoo search in water quality prediction using artificial neural network[J].International Journal of Computational Intelligence Studies,2017,6(2/3):229-244.
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[23] 范玉刚,李平,宋执环.动态加权最小二乘支持向量机[J].控制与决策,2006,21(10):1129-1134.
[2] SAKIZADEH M.Artificial intelligence for the prediction of water quality index in groundwater systems[J].Modeling Earth Systems & Environment,2016,2(1):8.
[3] RIZO-DECELIS L D,PARDO-IG■ZQUIZA E,ANDREO B.Spatial prediction of water quality variables along a main river channel in presence of pollution hotspots[J].Science of the Total Environment,2017,605-606:276-290.
[4] 袁从贵.最小二乘支持向量回归及其在水质预测中的应用研究[D].广州:广东工业大学,2012.
[5] QIAO J F,HOU Y,HAN H G.Optimal control for wastewater treatment process based on an adaptive multi-objective differential evolution algorithm[J].Neural Computing & Applications,2017(1):1-14.
[6] HAN H G,ZHANG L,HOU Y,et al.Nonlinear model predictive control based on a self-organizing recurrent neural network[J].IEEE Transactions on Neural Networks & Learning Systems,2016,27(2):402.
[7] RINALDI S,SONCINISESSA R,ROMANO P.Parameter estimation of Streeter-Phelps models[J].Journal of the Environmental Engineering Division,1979,105(1):75-88.
[8] SINGH K P,BASANT A,MALIK A,et al.Artificial neural network modeling of the river water quality:A case study[J].Ecological Modelling,2009,220(6):888-895.
[9] HALASSI A,OUAZAR D,TAIK A.RBF methods for solving laterally averaged Saint Venant equations:Application to eutrophication prevention through aeration[J].International Journal of Computational Fluid Dynamics,2016,29(9-10):464-477.
[10] 刘坤,刘贤赵,王巍,等.模糊概率神经网络水质评价模型及其应用[J].数学的实践与认识,2006,36(12):138-144.
[11] 袁从贵,张新政,陈旭.基于偏互信息与定尺度最小二乘支持向量机的咸潮预测模型[C]//第三十届中国控制会议.2011:1482-1486.
[12] 吴青,刘三阳,杜晶.回归型模糊最小二乘支持向量机[J].西安电子科技大学学报(自然科学版),2007,34(5):773-778.
[13] LIU J L,LI J P,XU W X,et al.A weighted Lq adaptive least squares support vector machine classifiers:Robust and sparse approximation[J].Expert Systems with Applications,2011,38(3):2253-2259.
[14] 温雯,郝志峰,邵壮丰.迭代重加权最小二乘支持向量机快速算法研究[J].计算机科学,2010,37(8):224-228.
[15] 王定成,姜斌.在线稀疏最小二乘支持向量机回归的研究[J].控制与决策,2007,22(2):132-136.
[16] 李洪超,王伟刚,董雪梅.基于M-LS-SVR的变压器油中溶解气体浓度预测[J].电气技术,2016(1):76-80.
[17] 郭振凯,宋召青,毛剑琴.一种改进的在线最小二乘支持向量机回归算法[J].控制与决策,2009,24(1):145-149.
[18] 阎辉,张学工,李衍达.支持向量机与最小二乘关系研究[J].清华大学学报(自然科学版),2001,41(9):77-80.
[19] KIM S E,SEO I W.Artificial neural network ensemble modeling with conjunctive data clustering for water quality prediction in rivers[J].Journal of Hydro-environment Research,2015,9(3):325-339.
[20] BARZEGAR R,ADAMOWSKI J,MOGHADDAM A A.Application of wavelet-artificial intelligence hybrid models for water quality prediction:A case study in Aji-Chay River,Iran[J].Stochastic Environmental Research & Risk Assessment,2016,30(7):1797-1819.
[21] CHATTERJEE S,SARKAR S,DEY N,et al.Application of cuckoo search in water quality prediction using artificial neural network[J].International Journal of Computational Intelligence Studies,2017,6(2/3):229-244.
[22] DBRUYNE M,SERNEELS S,VERDONCK T.Robustified least squares support vector classification[J].Journal of Chemometrics,2009,23(9):479-486.
[23] 范玉刚,李平,宋执环.动态加权最小二乘支持向量机[J].控制与决策,2006,21(10):1129-1134.