基于经验模态分解的空气质量指数组合预测方法及应用
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摘要
空气质量发展趋势的预测对于空气污染问题的防治具有非常重要的意义。因此,本文提出了基于经验模态分解(EMD)的空气质量指数(AQI)的一种组合预测方法。我们首先运用经验模态分解(EMD)的方法对非平稳、非线性且呈剧烈波动的时间序列即AQI原始数据进行多尺度分解。其次,我们分别使用4种常用的单项预测方法:灰色预测(GM)、ARIMA、BP神经网络和支持向量回归(SVR),分别对于分解后的本征模态函数(IMF)序列和趋势序列进行预测,得到单项预测结果。为了提高预测的精度,我们选用平均相对误差(MRE)较小的前三种单项预测方法,并对它们的预测结果进行组合预测。最后,运用熵权法分别计算出IMF序列和趋势序列的组合预测值,并将所有预测值求和得到AQI的最终预测结果。为了评价模型的预测效果,我们选用四种常用误差评价指标,对各个模型的预测结果进行评价比较,而仿真实验的结果表明了本文提出的基于经验模态分解的空气质量指数组合预测方法具有较高的预测精度和良好的适用性。
The prediction of air quality development trend is very important for the prevention and control of air pollution problems.Therefore, this paper proposes an air quality index(AQI) combination forecasting method based on empirical mode decomposition(EMD).First, the empirical modal decomposition method(EMD) is used to perform multi-scale decomposition of non-stationary, nonlinear and violently fluctuating time series AQI raw data. Secondly, four different single prediction methods, gray prediction(GM), ARIMA, BP neural network and support vector regression(SVR), are used to predict the decomposed intrinsic mode function(IMF) sequence and trend sequence respectively, and obtain the single prediction methods forecast results. Then, in order to improve the prediction accuracy, we use the first three single prediction methods with small mean relative error(MRE) for combined prediction. Finally, the combined prediction values of the IMF sequence and the trend sequence are calculated by the entropy weight method, and all the predicted values are summed to obtain the final prediction result of the AQI. At the same time, in order to evaluate the prediction effect of the model, four error evaluation indicators are used to evaluate the prediction results of each model. The simulation results show that the proposed method based on empirical mode decomposition has high prediction accuracy and good applicability.
The prediction of air quality development trend is very important for the prevention and control of air pollution problems.Therefore, this paper proposes an air quality index(AQI) combination forecasting method based on empirical mode decomposition(EMD).First, the empirical modal decomposition method(EMD) is used to perform multi-scale decomposition of non-stationary, nonlinear and violently fluctuating time series AQI raw data. Secondly, four different single prediction methods, gray prediction(GM), ARIMA, BP neural network and support vector regression(SVR), are used to predict the decomposed intrinsic mode function(IMF) sequence and trend sequence respectively, and obtain the single prediction methods forecast results. Then, in order to improve the prediction accuracy, we use the first three single prediction methods with small mean relative error(MRE) for combined prediction. Finally, the combined prediction values of the IMF sequence and the trend sequence are calculated by the entropy weight method, and all the predicted values are summed to obtain the final prediction result of the AQI. At the same time, in order to evaluate the prediction effect of the model, four error evaluation indicators are used to evaluate the prediction results of each model. The simulation results show that the proposed method based on empirical mode decomposition has high prediction accuracy and good applicability.
引文
[1]齐甜方,蒋洪迅,石晓文.面向多源数据沈阳市PM2.5浓度预测研究及实证分析[J].系统工程,2018,36(05):108-119.
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[12]张晨,杨仙子.基于多频组合模型的中国区域碳市场价格预测[J].系统工程理论与实践,2016,36(12):3017-3025.
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[14]Dragomiretskiy K,Zosso D.Variational Mode Decomposition[J].IEEE Transactions on Signal Processing,2014,62(3):531-544.
[15]王书平,朱艳云.基于多尺度分析的小麦价格预测研究[J].中国管理科学,2016,24(5):85-91.
[16]Xu Y,Yang W,Wang J.Air quality early-warning system for cities in China[J].Atmospheric Environment,2016,148:239-257.
[17]刘金培,郭艺,陈华友,任贺松,陶志富.基于非结构数据流行学习的碳价格多尺度组合预测[J].控制与决策,2019,34(02):279-286.
[18]Huang N E,Shen Z,Long S R.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proceedings A,1998,454(1971):903-995.
[19]马雪莹,蔡如华,宁巧娇,等.基于辅助粒子滤波与灰色预测的时间序列NAR模型状态估计[J].统计与决策,2019,4:25-29.
[20]曹学晨,张顺堂.基于ARIMA模型和BP人工神经网络的产品质量预测[J].价值工程,2018,37(35):198-201.
[21]李越洋.基于熵权-TOPSIS的PPP项目融资风险评价[J].价值工程,2019,5:69-72.
[2]Kumar A,Goyal P.Forecasting of daily ai r quality index in Delhi[J].Science of the Total Environment,2011,409(24):5517-5523.
[3]Vlachogianni A,Kassomenos P,Karppinen A.Evaluation of a multiple regression model for the forecasting of the concentrations of NOx and PM10 in Athens and Helsinki[J].Science of the Total Environment,2011,409(8):1559-1571.
[4]Jian L,Zhao Y,Zhu Y P.An application of ARIMA model to predict submicron particle concentrations from meteorological factors at a busy roadside in Hangzhou,China[J].Science of the Total Environment,2012,426(1):336-345.
[5]Slini T,Karatzas K,Moussiopoulos N.Statistical analysis of environmental data as the basis of forecasting:an air quality application[J].Science of the Total Environment,2002,288(3):227-237.
[6]李翔.基于GAB和模糊BP神经网络的空气质量预测[J].华中科技大学学报,2013,41(z1):63-65.
[7]尹琪,胡红萍,白艳萍.基于GA-SVM的太原市空气质量指数预测[J].数学的实践与认识,2017,47(12):113-120.
[8]Kumar A,Goyal P.Forecasting of air quality in Delhi using principal component regression technique[J].Atmospheric Pollution Research,2011,2(4):436-444.
[9]Yun zhenXu,PeiDu,JianzhouWang.Research and application of an air quality early warning system based on a modified least squares support vector machine and a cloud model[J].Environmental Pollution,2017,223:435-448.
[10]Voukantsis D,Karatzas K,Kukkonen J.Intercomparison of air quality data using principal component analysis,and forecasting of PM10 and PM2.5 concentrations using artificial neural networks,in Thessaloniki and Helsinki[J].Science of the Total Environment,2011,409(7):1266-1276.
[11]刘金培,林盛,郭涛.一种非线性时间序列预测模型及对原油价格的预测[J].管理科学,2011,24(6):104-112.
[12]张晨,杨仙子.基于多频组合模型的中国区域碳市场价格预测[J].系统工程理论与实践,2016,36(12):3017-3025.
[13]Ma X,Jin Y,Dong Q.A generalized dynamic fuzzy neural network based on singular spectrum analysis optimized by brain storm optimization for short-term wind speed forecasting[M].Elsevier Science Publishers B.V.2017.
[14]Dragomiretskiy K,Zosso D.Variational Mode Decomposition[J].IEEE Transactions on Signal Processing,2014,62(3):531-544.
[15]王书平,朱艳云.基于多尺度分析的小麦价格预测研究[J].中国管理科学,2016,24(5):85-91.
[16]Xu Y,Yang W,Wang J.Air quality early-warning system for cities in China[J].Atmospheric Environment,2016,148:239-257.
[17]刘金培,郭艺,陈华友,任贺松,陶志富.基于非结构数据流行学习的碳价格多尺度组合预测[J].控制与决策,2019,34(02):279-286.
[18]Huang N E,Shen Z,Long S R.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proceedings A,1998,454(1971):903-995.
[19]马雪莹,蔡如华,宁巧娇,等.基于辅助粒子滤波与灰色预测的时间序列NAR模型状态估计[J].统计与决策,2019,4:25-29.
[20]曹学晨,张顺堂.基于ARIMA模型和BP人工神经网络的产品质量预测[J].价值工程,2018,37(35):198-201.
[21]李越洋.基于熵权-TOPSIS的PPP项目融资风险评价[J].价值工程,2019,5:69-72.