基于神经网络与灰色理论的水质参数预测建模研究
摘要
经济的快速发展给水环境带来巨大压力,准确预测水质变化情况是保障水环境安全的关键和基础。本文以三峡库区常态水质参数时序数据为研究对象,进行水质参数预测建模研究。
由于三峡库区成库时间短、监测指标少、监测频率低、水质参数时序数据少且成库前后呈现跳变,传统的统计学预测方法不适用于本文的研究对象。本文结合灰色系统理论针对“贫信息”问题、BP神经网络较强的非线性拟合特性、最小二乘支持向量机(Least Squares Support Vector Machines, LS-SVM)专门解决小样本预测的特点,对三峡库区水质参数时序数据进行预测研究,形成如下研究成果:
①针对传统时间序列相空间重构嵌入维数计算复杂的问题,本文借鉴残差序列相关熵定阶法的基本思想,通过改进的相关熵算法确定时间序列相空间重构嵌入维数,并以2005年至2008年每月的水质参数平均浓度(非“贫信息”)为预测对象,分别采用BP神经网络和模拟退火算法(Simulated Annealing, SA)优选参数的LS-SVM模型进行预测。仿真结果表明,改进的相关熵算法确定时间序列的嵌入维数是有效的,BP神经网络的非线性拟合优势明显,对于波动范围较大的水质时序数据表现出更优的性能;LS-SVM模型在波动范围较小的水质时序数据短期预测中更有优势。
②针对1997年至2008年丰水期水质参数时序数据存在小样本和跳变现象,结合专门针对“贫信息”的灰色模型预测精度不高但计算速度快、BP神经网络强大的非线性拟合能力但需要大样本的特点,以及LS-SVM模型解决小样本预测问题的优势,本文提出灰色新陈代谢BP神经网络预测模型和ELS-SVM预测模型。灰色新代谢BP神经网络预测模型将灰色新陈代谢模型集群的输出作为BP神经网络的输入,从而解决了BP神经网络需要大量样本才能较好地逼近非线性函数的问题。ELS-SVM模型通过对原始数据预处理改善其平滑特性,将预处理后的数据作为LS-SVM的输入,并用SA算法优选LS-SVM参数。仿真结果表明,灰色新陈代谢BP神经网络的预测精度较BP神经网络和灰色新陈代谢模型明显提高;ELS-SVM模型的预测精度比LS-SVM模型高,与灰色新陈代谢BP神经网络相当,是对小样本跳变时序数据预测方法的补充。
根据三峡库区水质参数时序数据的特点建立预测模型,不仅客观地反应了水质发展趋势,为科学决策提供依据,更拓宽了时序预测技术的理论研究和应用领域。
Rapid economic development has brought enormous pressure on water environment, predicting changes of water quality exactly is critical and basal to protect the safety of water environment. This thesis studies on the prediction modeling method of water quality parameters based on normal time-series data in the background of the Three Gorges Reservoir.
As the Three Gorges Reservoir started water storage for a short time, monitoring parameters are simple, monitoring frequency is low, the time series data of water quality parameters are characterized by small samples and sudden change of some sections in Three Gorges, traditional statistical forecasting methods are not fit for the application. According to the gray system theory for the“poor information”problem, BP neural network with strong nonlinear fitting capability, and Least Squares Support Vector Machines (LS-SVM) specifically for small samples of forecasting, the following main research findings and conclusions, which studied on the time series data of water quality parameters of Three Gorges Reservoir, are brought forward:
①As the computational complexity of traditional time series embedding dimension of phase space reconstruction, using related entropy to determine model order of residual sequence for reference, the improved related entropy algorithm was brought forward to determine Phase Space Reconstruction embedding dimension, and the monthly average concentration of water quality parameters from 2005 to 2008 are used as time series data. Comparison between the predicting results of BP neural network and LS-SVM model using simulated annealing (SA) for optimization parameters indicates the feasibility of the improved related entropy algorithm, BP shows obvious advantages of nonlinear fitting for time series data of larger scope, and LS-SVM shows better performance in short time predicting for time series data of smaller fluctuation range.
②According to the characteristics of small samples and sudden change of water quality parameters in flood season from 1997 to 2008, combined with grey predicting model for“poor information”is characterized by low forecast accuracy but calculation speed, BP neural network with strong nonlinear fitting capability but requiring large number of samples, and the advantage of LS-SVM for small samples, the gray metabolism BP neural network prediction model and EL-SVM prediction model were proposed. The outputs of gray metabolism predicting model sets are used for the inputs of BP neural network, which solves the huge learning samples on nonlinear fitting. The pretreatment model is put forward to improve the smoothness of time series data for the inputs of LS-SVM, which uses SA for optimization parameters. Simulation results show that the grey metabolism BP prediction model improves the prediction accuracy significantly compared with BP and grey metabolism model; ELS-SVM is better than LS-SVM, shows the considerable prediction accuracy of grey metabolism BP model, and renews the prediction methods of time series data with small sudden change samples.
According to the characteristics of time series data of water quality parameters in Three Gorges Reservoir, the forecasting models are established, which not only objectively reflect the trends of water quality, and provide the basis for the scientific decision-making, but also widen the theoretical research and applications of time series prediction technology.
由于三峡库区成库时间短、监测指标少、监测频率低、水质参数时序数据少且成库前后呈现跳变,传统的统计学预测方法不适用于本文的研究对象。本文结合灰色系统理论针对“贫信息”问题、BP神经网络较强的非线性拟合特性、最小二乘支持向量机(Least Squares Support Vector Machines, LS-SVM)专门解决小样本预测的特点,对三峡库区水质参数时序数据进行预测研究,形成如下研究成果:
①针对传统时间序列相空间重构嵌入维数计算复杂的问题,本文借鉴残差序列相关熵定阶法的基本思想,通过改进的相关熵算法确定时间序列相空间重构嵌入维数,并以2005年至2008年每月的水质参数平均浓度(非“贫信息”)为预测对象,分别采用BP神经网络和模拟退火算法(Simulated Annealing, SA)优选参数的LS-SVM模型进行预测。仿真结果表明,改进的相关熵算法确定时间序列的嵌入维数是有效的,BP神经网络的非线性拟合优势明显,对于波动范围较大的水质时序数据表现出更优的性能;LS-SVM模型在波动范围较小的水质时序数据短期预测中更有优势。
②针对1997年至2008年丰水期水质参数时序数据存在小样本和跳变现象,结合专门针对“贫信息”的灰色模型预测精度不高但计算速度快、BP神经网络强大的非线性拟合能力但需要大样本的特点,以及LS-SVM模型解决小样本预测问题的优势,本文提出灰色新陈代谢BP神经网络预测模型和ELS-SVM预测模型。灰色新代谢BP神经网络预测模型将灰色新陈代谢模型集群的输出作为BP神经网络的输入,从而解决了BP神经网络需要大量样本才能较好地逼近非线性函数的问题。ELS-SVM模型通过对原始数据预处理改善其平滑特性,将预处理后的数据作为LS-SVM的输入,并用SA算法优选LS-SVM参数。仿真结果表明,灰色新陈代谢BP神经网络的预测精度较BP神经网络和灰色新陈代谢模型明显提高;ELS-SVM模型的预测精度比LS-SVM模型高,与灰色新陈代谢BP神经网络相当,是对小样本跳变时序数据预测方法的补充。
根据三峡库区水质参数时序数据的特点建立预测模型,不仅客观地反应了水质发展趋势,为科学决策提供依据,更拓宽了时序预测技术的理论研究和应用领域。
Rapid economic development has brought enormous pressure on water environment, predicting changes of water quality exactly is critical and basal to protect the safety of water environment. This thesis studies on the prediction modeling method of water quality parameters based on normal time-series data in the background of the Three Gorges Reservoir.
As the Three Gorges Reservoir started water storage for a short time, monitoring parameters are simple, monitoring frequency is low, the time series data of water quality parameters are characterized by small samples and sudden change of some sections in Three Gorges, traditional statistical forecasting methods are not fit for the application. According to the gray system theory for the“poor information”problem, BP neural network with strong nonlinear fitting capability, and Least Squares Support Vector Machines (LS-SVM) specifically for small samples of forecasting, the following main research findings and conclusions, which studied on the time series data of water quality parameters of Three Gorges Reservoir, are brought forward:
①As the computational complexity of traditional time series embedding dimension of phase space reconstruction, using related entropy to determine model order of residual sequence for reference, the improved related entropy algorithm was brought forward to determine Phase Space Reconstruction embedding dimension, and the monthly average concentration of water quality parameters from 2005 to 2008 are used as time series data. Comparison between the predicting results of BP neural network and LS-SVM model using simulated annealing (SA) for optimization parameters indicates the feasibility of the improved related entropy algorithm, BP shows obvious advantages of nonlinear fitting for time series data of larger scope, and LS-SVM shows better performance in short time predicting for time series data of smaller fluctuation range.
②According to the characteristics of small samples and sudden change of water quality parameters in flood season from 1997 to 2008, combined with grey predicting model for“poor information”is characterized by low forecast accuracy but calculation speed, BP neural network with strong nonlinear fitting capability but requiring large number of samples, and the advantage of LS-SVM for small samples, the gray metabolism BP neural network prediction model and EL-SVM prediction model were proposed. The outputs of gray metabolism predicting model sets are used for the inputs of BP neural network, which solves the huge learning samples on nonlinear fitting. The pretreatment model is put forward to improve the smoothness of time series data for the inputs of LS-SVM, which uses SA for optimization parameters. Simulation results show that the grey metabolism BP prediction model improves the prediction accuracy significantly compared with BP and grey metabolism model; ELS-SVM is better than LS-SVM, shows the considerable prediction accuracy of grey metabolism BP model, and renews the prediction methods of time series data with small sudden change samples.
According to the characteristics of time series data of water quality parameters in Three Gorges Reservoir, the forecasting models are established, which not only objectively reflect the trends of water quality, and provide the basis for the scientific decision-making, but also widen the theoretical research and applications of time series prediction technology.
引文
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