基于MLR–SARIMA模型的土石坝位移预测
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摘要
为分析周期因子与时效因子分别对土石坝位移的影响,更好地掌握土石坝位移变化的成因和趋势,进行土石坝位移数据中周期成分和趋势成分的变化规律和预测方法研究。采用HP(Hodrick–Prescott)滤波将实测位移序列分解为趋势项和周期项两部分,对趋势项建立基于MLR(multiple linear regression)的预测模型,对周期项建立基于SARIMA(seasonal auto-regressive integrated moving average)的预测模型,结合以上两模型的结果对土石坝位移进行预测,即MLR–SARIMA预测模型。该模型突出了MLR模型在趋势性数据上的预测优势和SARIMA模型在周期性数据上的预测优势,且仅从实测位移数据分析预测,可适用于缺少环境量数据的情况。实测位移序列经HP滤波分解后,趋势项位移呈缓慢增长趋势,年变幅从1.42至0.51 mm逐渐降低,表明由时效因子引起的土石坝趋势性位移量逐年减小,且已趋于稳定;周期项位移具有明显年周期性,这是由于土石坝位移受到年周期性变化的水位和温度影响,年变幅约为7.00 mm,表明该土石坝位移量主要是由周期因子引起的周期性位移;该变化规律符合土石坝位移的一般变化规律,说明HP滤波可很好地提取土石坝位移数据中的周期成分和趋势成分。MLR–SARIMA模型预测结果准确,相对误差较小,均在5%以内,且均方根误差、平均绝对误差百分比和调整的平均绝对误差百分比这3个指标均优于单一SARIMA模型,表明MLR–SARIMA模型突出了其在预测周期性和趋势性数据方面的优势,可适用于土石坝位移预测。
In order to analyze the effects of periodic factors and trend factors on the displacement of earth-rockfill dam, and grasp the cause and trend of displacement change better, the change rule and prediction method of periodic component and trend component in displacement of earthrockfill dam were studied. HP filter was used to decompose measured displacement sequence into trend term and periodic term. MLR prediction model was established for the trend term and SARIMA prediction model was established for the periodic term, which is MLR–SARIMA model for displacement prediction of earth-rockfill dam. MLR–SARIMA model highlighted the prediction advantages of MLR model on trend data and SARIMA model on periodic data, and it only needed measured displacement data to carry out the prediction analysis. After the HP filter decompose, the trend displacement had a slow growth trend, and the annual amplitude decreased from 1.42 mm to 0.51 mm. It was shown that the trend displacement of earth-rock dam caused by aging factor decreased year by year and tended to be stable. The periodic displacement had a significant annual periodicity. This was due to the annual periodic changes of water level and temperature. The annual amplitude was about 7.00 mm. The displacement of the earth-rockill dam was mainly caused by periodic displacement.The change rule was consistent with the general earth-rockfill dam. The results showed that the HP filter can be used to extract the trend and periodic terms in displacement data of earth-rockfill dam. The prediction results of MLR–SARIMA model were accurate, the relative error was small, within 5%, the RMSE, MAPE and AMAPE evaluation index of the model were both better than single SARIMA model. It was shown that the MLR–SARIMA model highlighted its advantages in predicting trend and periodicity data, which can be applied to prediction of horizontal displacement of earth dam.
In order to analyze the effects of periodic factors and trend factors on the displacement of earth-rockfill dam, and grasp the cause and trend of displacement change better, the change rule and prediction method of periodic component and trend component in displacement of earthrockfill dam were studied. HP filter was used to decompose measured displacement sequence into trend term and periodic term. MLR prediction model was established for the trend term and SARIMA prediction model was established for the periodic term, which is MLR–SARIMA model for displacement prediction of earth-rockfill dam. MLR–SARIMA model highlighted the prediction advantages of MLR model on trend data and SARIMA model on periodic data, and it only needed measured displacement data to carry out the prediction analysis. After the HP filter decompose, the trend displacement had a slow growth trend, and the annual amplitude decreased from 1.42 mm to 0.51 mm. It was shown that the trend displacement of earth-rock dam caused by aging factor decreased year by year and tended to be stable. The periodic displacement had a significant annual periodicity. This was due to the annual periodic changes of water level and temperature. The annual amplitude was about 7.00 mm. The displacement of the earth-rockill dam was mainly caused by periodic displacement.The change rule was consistent with the general earth-rockfill dam. The results showed that the HP filter can be used to extract the trend and periodic terms in displacement data of earth-rockfill dam. The prediction results of MLR–SARIMA model were accurate, the relative error was small, within 5%, the RMSE, MAPE and AMAPE evaluation index of the model were both better than single SARIMA model. It was shown that the MLR–SARIMA model highlighted its advantages in predicting trend and periodicity data, which can be applied to prediction of horizontal displacement of earth dam.
引文
[1]Wu Zhongru,Chen Bo.A review on development of dam safety monitoring models[J].Modern Surveying and Mapping,2016,39(5):1-8.[吴中如,陈波.大坝变形监控模型发展回眸[J].现代测绘,2016,39(5):1-8.]
[2]Cheng Jiatang,Xiong Yan.Application of extreme learning machine combination model for dam displacement prediction[J].Procedia Computer Science,2017,107:373-378.
[3]Pei Liang,Wu Zhenyu,Cui Meng,et al.Research and application on the displacement hybrid-model of high earth dam[J].Journal of Sichuan University(Engineering Science Edition),2012,44(Supp 1):42-47.[裴亮,吴震宇,崔萌,等.高土石坝安全监测位移混合模型研究及应用[J].四川大学学报(工程科学版),2012,44(增刊1):42-47.]
[4]Zhao Tinghong,Zhang Sai.Research on deformation prediction of gravity dam based on MPGA-BP[J].Journal of Lanzhou University of Technology,2016,42(5):122-127.[赵廷红,张赛.基于MPGA-BP的重力坝变形预测研究[J].兰州理工大学学报,2016,42(5):122-127.]
[5]Yang Fan,Zhou Hongman,Xie Jiajun.Research on Verhulst-ARMA combination forecasting model of slope nonlinear displacement[J].Engineering of Surveying and Mapping,2015,24(12):17-20.[杨帆,周红满,谢佳君.边坡非线性位移的Verhulst-ARMA组合预测模型研究[J].测绘工程,2015,24(12):17-20.]
[6]Meng Meng,Chen Zhiqiang,Huang Da.Displacement prediction of landslide in Three Gorges Reservoir area based on H-P filter,ARIMA and VAR models[J].Rock and Soil Mechanics,2016,37(Supp 2):552-560.[孟蒙,陈智强,黄达.基于H-P滤波法、ARIMA和VAR模型的库区滑坡位移综合预测[J].岩土力学,2016,37(增刊2):552-560.]
[7]Li Jiong,Zhang Zhijun,Niu Ruiqing,et al.Prediction of landslide displacement based on ARIMA-MC model[J].Computer Engineering and Applications,2016,52(7):215-221.[李炯,张志军,牛瑞卿,等.基于ARIMA-MC模型的滑坡位移预测[J].计算机工程与应用,2016,52(7):215-221.]
[8]Fang Tingting,Lahdelma R.Evaluation of a multiple linear regression model and SARIMA model in forecasting heat demand for district heating system[J].Applied Energy,2016,179(1):544-552.
[9]Ma Cong.Application of integrated SARIMA and BP neural network for groundwater level forecasting[J].Pearl River,2015,33(4):112-115.[马聪.地下水位埋深的SARIMA与BP神经网络组合模型预测分析[J].人民珠江,2015,33(4):112-115.]
[10]Jiao Liang,Li Wenjie,Zhao Chaomin,et al.SARIMA prediction model for time series based on the Eviews[J].Henan Journal of Preventive Medicine,2015,26(5):349-352.[焦亮,李文杰,赵超敏,等.基于Eviews的季节时间序列(SAR-IMA)预测模型[J].河南预防医学杂志,2015,26(5):349-352.]
[11]Li Fuqiang.Study on analysis methods for dam safety monitoring data[D].Hangzhou:Zhejiang University,2012.[李富强.大坝安全监测数据分析方法研究[D].杭州:浙江大学,2012.]
[12]Xu Huaxuan.An empirical study of co-interation model of inter-temporal arbitrage based on HP filter[D].Nanjing:Nanjing University,2014.[徐华轩.基于HP滤波的股指期货跨期套利模型研究[D].南京:南京大学,2014.]
[13]高铁梅.计量经济分析方法与建模[M].北京:清华大学出版社,2013.
[14]Deng Guojun.Research on long-term and dynamic relationship between factors of power grid investment based on time series analysis[D].Hangzhou:Zhejiang University,2015.[邓国军.基于时间序列分析的电网投资影响因素长期及动态关系研究[D].杭州:浙江大学,2015.]
[15]Bunnoon P,Chalermyanont K,Limsakul C.Multi-substationcontrol central load area forecasting by using HP-filter and double neural networks(HP-DNNs)[J].Electrical Power and Energy Systems,2013,44(1):561-570.
[16]Cui Herui,Mu Yupei,Peng Xu.Medium-term power load forecasting based on SARIMA model with HP filter[J].Journal of North China Electric Power University,2016,43(4):79-86.[崔和瑞,穆玉佩,彭旭.基于HP滤波的SARIMA中期电力负荷预测[J].华北电力大学学报,2016,43(4):79-86.]
[17]Ruiz-Aguilar J J,Turias I J,Jiménez-Come M J.Hybrid approaches based on SARIMA and artificial neural networks for inspection time series forecasting[J].Transportation Research(Part E),2014,67(7):1-13.
[18]Zhang Jian.A case study of time series analysis applied for construction monitoring of long-span bridge[D].Guangzhou:South China University of Technology,2010.[张建.时间序列分析在大跨度桥梁施工监测中的应用[D].广州:华南理工大学,2010.]
[19]María del C B,Josefina O,Luisa B,et al.Evaluation of a multiple linear regression model and SARIMA model in forecasting 7Be air concentrations[J].Chemosphere,2017,177:326-333.
[20]顾冲时,吴中如.大坝与坝基安全监控理论和方法及其应用[M].南京:河海大学出版社,2006:36-40.
[21]李元章,何春雄.线性回归模型应用及判别[M].广州:华南理工大学出版社,2016:8-11.
[2]Cheng Jiatang,Xiong Yan.Application of extreme learning machine combination model for dam displacement prediction[J].Procedia Computer Science,2017,107:373-378.
[3]Pei Liang,Wu Zhenyu,Cui Meng,et al.Research and application on the displacement hybrid-model of high earth dam[J].Journal of Sichuan University(Engineering Science Edition),2012,44(Supp 1):42-47.[裴亮,吴震宇,崔萌,等.高土石坝安全监测位移混合模型研究及应用[J].四川大学学报(工程科学版),2012,44(增刊1):42-47.]
[4]Zhao Tinghong,Zhang Sai.Research on deformation prediction of gravity dam based on MPGA-BP[J].Journal of Lanzhou University of Technology,2016,42(5):122-127.[赵廷红,张赛.基于MPGA-BP的重力坝变形预测研究[J].兰州理工大学学报,2016,42(5):122-127.]
[5]Yang Fan,Zhou Hongman,Xie Jiajun.Research on Verhulst-ARMA combination forecasting model of slope nonlinear displacement[J].Engineering of Surveying and Mapping,2015,24(12):17-20.[杨帆,周红满,谢佳君.边坡非线性位移的Verhulst-ARMA组合预测模型研究[J].测绘工程,2015,24(12):17-20.]
[6]Meng Meng,Chen Zhiqiang,Huang Da.Displacement prediction of landslide in Three Gorges Reservoir area based on H-P filter,ARIMA and VAR models[J].Rock and Soil Mechanics,2016,37(Supp 2):552-560.[孟蒙,陈智强,黄达.基于H-P滤波法、ARIMA和VAR模型的库区滑坡位移综合预测[J].岩土力学,2016,37(增刊2):552-560.]
[7]Li Jiong,Zhang Zhijun,Niu Ruiqing,et al.Prediction of landslide displacement based on ARIMA-MC model[J].Computer Engineering and Applications,2016,52(7):215-221.[李炯,张志军,牛瑞卿,等.基于ARIMA-MC模型的滑坡位移预测[J].计算机工程与应用,2016,52(7):215-221.]
[8]Fang Tingting,Lahdelma R.Evaluation of a multiple linear regression model and SARIMA model in forecasting heat demand for district heating system[J].Applied Energy,2016,179(1):544-552.
[9]Ma Cong.Application of integrated SARIMA and BP neural network for groundwater level forecasting[J].Pearl River,2015,33(4):112-115.[马聪.地下水位埋深的SARIMA与BP神经网络组合模型预测分析[J].人民珠江,2015,33(4):112-115.]
[10]Jiao Liang,Li Wenjie,Zhao Chaomin,et al.SARIMA prediction model for time series based on the Eviews[J].Henan Journal of Preventive Medicine,2015,26(5):349-352.[焦亮,李文杰,赵超敏,等.基于Eviews的季节时间序列(SAR-IMA)预测模型[J].河南预防医学杂志,2015,26(5):349-352.]
[11]Li Fuqiang.Study on analysis methods for dam safety monitoring data[D].Hangzhou:Zhejiang University,2012.[李富强.大坝安全监测数据分析方法研究[D].杭州:浙江大学,2012.]
[12]Xu Huaxuan.An empirical study of co-interation model of inter-temporal arbitrage based on HP filter[D].Nanjing:Nanjing University,2014.[徐华轩.基于HP滤波的股指期货跨期套利模型研究[D].南京:南京大学,2014.]
[13]高铁梅.计量经济分析方法与建模[M].北京:清华大学出版社,2013.
[14]Deng Guojun.Research on long-term and dynamic relationship between factors of power grid investment based on time series analysis[D].Hangzhou:Zhejiang University,2015.[邓国军.基于时间序列分析的电网投资影响因素长期及动态关系研究[D].杭州:浙江大学,2015.]
[15]Bunnoon P,Chalermyanont K,Limsakul C.Multi-substationcontrol central load area forecasting by using HP-filter and double neural networks(HP-DNNs)[J].Electrical Power and Energy Systems,2013,44(1):561-570.
[16]Cui Herui,Mu Yupei,Peng Xu.Medium-term power load forecasting based on SARIMA model with HP filter[J].Journal of North China Electric Power University,2016,43(4):79-86.[崔和瑞,穆玉佩,彭旭.基于HP滤波的SARIMA中期电力负荷预测[J].华北电力大学学报,2016,43(4):79-86.]
[17]Ruiz-Aguilar J J,Turias I J,Jiménez-Come M J.Hybrid approaches based on SARIMA and artificial neural networks for inspection time series forecasting[J].Transportation Research(Part E),2014,67(7):1-13.
[18]Zhang Jian.A case study of time series analysis applied for construction monitoring of long-span bridge[D].Guangzhou:South China University of Technology,2010.[张建.时间序列分析在大跨度桥梁施工监测中的应用[D].广州:华南理工大学,2010.]
[19]María del C B,Josefina O,Luisa B,et al.Evaluation of a multiple linear regression model and SARIMA model in forecasting 7Be air concentrations[J].Chemosphere,2017,177:326-333.
[20]顾冲时,吴中如.大坝与坝基安全监控理论和方法及其应用[M].南京:河海大学出版社,2006:36-40.
[21]李元章,何春雄.线性回归模型应用及判别[M].广州:华南理工大学出版社,2016:8-11.