支持向量机回归(SVR)模型在非线性预测方面具有优良性能,基于该模型对供水系统余氯变化过程进行预测,并采用二阶振荡粒子群优化算法(SOPSO)对SVR模型参数进行优化调整,以提高小样本状态下模型的模拟精度,增强模型的泛化性能。将优化后的SVR模型应用于某供水系统余氯预测,结果表明:在有限样本状态下,优化后的SVR模型的预测平均误差小,明显优于BP神经网络模型和ARX模型,并具有较强的稳健性。该预测模型能较好地解决传统模型在小样本状态下余氯预测精度不高、预测效果较差的问题,为研究供水系统余氯变化过程及动态预测提供了新的途径。
Abstract
In view of its excellent prediction performance of support vector machine regression (SVR) model for nonlinear system, a model of residual chlorine prediction was put forward to predict changes in water supply system based on SVR. Moreover, two-order oscillating particle swarm optimization algorithm (SOPSO) was employed to optimize the SVR model parameters in order to enhance the model precision in small sample situations and improve the generalization ability of the model. This optimized model was applied to predict the residual chlorine in a water supply system, and the results showed that: in the case of limited samples, the average prediction error of the optimized SVR model is 3.86%, which is better than that of BP and ARX prediction models, and also has strong stability. This model could solve the problems of low fitting accuracy and poor efficacy of prediction which often appear by traditional models. It provides a new approach for the model construction and algorithm selection in residual chlorine prediction for water supply system.
关键词
余氯 /
支持向量机回归 /
粒子群算法 /
参数优化 /
供水系统
Key words
residual chlorine /
SVR /
PSO /
parameter optimization /
water supply system
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参考文献
[1] RODRIGUEZ M J, SRODES J B. Assessing Empirical Linear and Non-linear Modelling of Residual Chlorine in Urban Drinking Water Systems[J]. Environmental Modelling & Software, 1998, 14(1): 93-102.
[2] KOHPAEI J A, SATHASIVAN A. Chlorine Decay Prediction in Bulk Water Using the Parallel Second Order Model: An Analytical Solution Development[J]. Chemical Engineering Journal, 2011, 171(1): 232-241.
[3] HALLAM N B, WEST J R, FORSTER C F, et al. The Decay of Chlorine Associated with the Pipe Wall in Water Distribution Systems[J]. Water Research, 2002, 36(14): 3479-3488.
[4] FISHER L, KASTL G, SATHASIVAN A, et al. Suitability of Chlorine Bulk Decay Models for Planning and Management of Water Distribution Systems[J]. Critical Reviews in Environmental Science and Technology, 2011, 41(20): 1843-1882.
[5] 蒋 晖,姜文超,龙腾锐,等.基于多因素交互作用的主体水余氯衰减模型[J]. 华中科技大学学报(自然科学版),2013,41(2):128-132.(JIANG Hui, JIANG Wen-chao, LONG Teng-yue, et al. Multifactor Interaction-based Free Chlorine Decay Model in Bulk Water[J]. Journal of Huangzhong University of Science & Technology (Natural Science), 2013, 41(2): 128-132.(in Chinese))
[6] 刘 星,单金林,郝金敏,等.饮用水输配管网中的余氯衰减模型[J].中国给排水, 2003, 19(6): 42-43. (LIU Xing, SHAN Wei-xing, HAO Jin-min, et al. The Research of Chlorine Decay Model in Drinking Water Distribution System[J]. China Water and Wastewater, 2003,19(6): 42-43.(in Chinese))
[7] 王海霞,张信阳.供水管网余氯预测的研究[J]. 天津工业大学学报, 2003, 22(6): 34-36.(WANG Hai-xia, ZHANG Xin-yang. Study on Forecasting Concentration of Residual Chlorine in Water Distribution System[J]. Journal of Tianjin Polytechnic University, 2003, 22(6): 34-36. (in Chinese))
[8] 田一梅,吴迷芳,王 阳.基于SVR的城市供水管网余氯预测分析[J]. 重庆建筑大学学报, 2006, 28(2): 74-78. (TIAN Yi-mei, WU Mi-fang, WANG Yang. Prediction and Analyses of Residual Chlorine Based on Support Vector Regression in Urban Water Distribution System[J]. Journal of Chongqing Jianzhu University, 2006, 28(2): 74-78. (in Chinese))
[9] VAPNIK V N.Statistical Learning Theory[M]. New York:Springer, 1998.
[10]CHAPELLE O, VAPNIK V, BOUSQUET O, et al. Choosing Multiple Parameters for Support Vector Machines[J]. Machine Learning, 2002, 46(1-3): 131-159.
[11]SOYUPAK S. KILIC H, KARADIREK I E, et al. On the Usage of Artificial Neural Networks in Chlorine Control Applications for Water Distribution Networks with High Quality Water[J]. Journal of Water Supply, 2011, 60(1): 51-60.
[12]谢 昕,郭鹏飞,詹小丽.基于RBF神经网络的余氯浓度预测模型研究[J].传感器与微系统,2012, 31(8): 64-65. (XIE Xin, GUO Peng-fei, ZHAN Xiao-li. Research on Prediction Model of Residual Chlorine Concentration Based on RBF Neural Network[J]. Transducer and Microsystem Technologies, 2012, 31(8): 64-65. (in Chinese))
基金
陕西省水利厅科技项目(SLKJ201105,SLKJ201314);中央高校基本科研业务费专项资金(22050205)