基于IOWHA算子的路基沉降加权组合预测方法研究
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摘要
针对传统的加权组合预测模型赋权过程中的缺陷,分析诱导有序加权调和平均算子(IOWHA)的优势,建立一种基于诱导有序加权调和平均算子的泊松-指数曲线组合预测模型。其基本思想是,以单一模型在每个时刻的预测精度作为诱导值,根据其大小排序、赋权值,以组合预测误差倒数平方和最小为准则,得到最优模型的最优权系数解,进行组合模型预测。结合工程实测数据,利用组合模型进行预测。研究结果表明:基于IOWHA算子的组合预测模型预测平均绝对误差及平均绝对百分比误差均小于单一模型以及传统的最优加权几何平均组合模型,预测结果能很好的反映沉降趋势。
Aiming at the defects of the traditional weighted combination forecasting method,the characteristics of the induced ordered weighted harmonic averaging operator(IOWHA) was analyzed, and a Poisson exponential curve combination prediction model based on the induced ordered weighted harmonic averaging operator was established. The basic idea is that the prediction accuracy of a single model at each moment was used as the induction value, according to its size sorting; the data of model was assigned by weighted. In the context the quadratic sum of the reciprocal of combinatorial prediction error was minimum, the optimal weight coefficient was obtained by the optimal model so that combined model was applied to predict. The verification was carried out through the section settlement data. The results show that the mean absolute error and the mean absolute percentile error of the combined prediction model based on IOWHA operator are smaller than the single model and the traditional optimal weighted geometric mean combination model. The prediction results can settlement trend of the settlement very well.
Aiming at the defects of the traditional weighted combination forecasting method,the characteristics of the induced ordered weighted harmonic averaging operator(IOWHA) was analyzed, and a Poisson exponential curve combination prediction model based on the induced ordered weighted harmonic averaging operator was established. The basic idea is that the prediction accuracy of a single model at each moment was used as the induction value, according to its size sorting; the data of model was assigned by weighted. In the context the quadratic sum of the reciprocal of combinatorial prediction error was minimum, the optimal weight coefficient was obtained by the optimal model so that combined model was applied to predict. The verification was carried out through the section settlement data. The results show that the mean absolute error and the mean absolute percentile error of the combined prediction model based on IOWHA operator are smaller than the single model and the traditional optimal weighted geometric mean combination model. The prediction results can settlement trend of the settlement very well.
引文
[1] XU Ning, DANG Yaoguo. An optimized grey GM(2,1)model and forecasting of highway subgrade settlement[J].Mathematical Problems in Engineering, 2015(1):1-6.
[2] GAO Lei, ZHOU Qiuyue, YU Xiangjuan, et al. Analysis and model prediction of subgrade settlement for Linhai highway in China[J]. Electronic Journal of Geotechnical Engineering, 2014, 19:11-21.
[3] Kapetanios G, Labhard V, Price S. Forecast combination and the bank of England’s suite of statistical forecasting models[J]. Economic Modelling, 2008(2):772-792.
[4] YI Wen, WANG Yonghe, XIE Zixing, et al. Modeling subgrade settlement in the Wuhan-Guangzhou passenger rail line[J]. Electronic Journal of Geotechnical Engineering, 2015(20):4479-4495.
[5]丁建荣.基于最优组合模型的路基沉降预测方法[J].土工基础, 2014, 28(3):100-102.DING Jianrong. Embankment settlement prediction through an optimization model[J]. Soil Engineering and Foundation, 2014, 28(3):100-102.
[6]胡晓阳,王连俊,张光宗. Logistic及Verhulst预测模型在路基沉降预测中的拟合研究[J].铁道标准设计,2013(9):1-4.HU Xiaoyang, WANG Lianjun, ZHANG Guangzong.Research on the fitting of Logistic model and Verhulst model for subgrade settlement prediction[J]. Railway Standard Design, 2013(9):1-4.
[7]欧阳炼. GM(1,1)-Logistic路基沉降组合预测模型研究与应用[J].铁道科学与工程学报, 2010, 7(4):56-60.OUYANG Lian. Research and application of GM(1,1)and logistic combination forecasting model for subgrade settlement[J]. Journal of Railway Science and Engineering, 2010, 7(4):56-60.
[8]许明明,徐彬,曾浩中.路基沉降的加权组合预测方法研究[J].铁道科学与工程学报, 2016, 13(3):463-468.XU Mingming, XU Bin, ZENG Haozhong. Research on weighted combination prediction method for subgrade settlement[J]. Journal of Railway Science and Engineering, 2016, 13(3):463-468.
[9]徐彬,许明明,曾浩中.路基沉降趋势的组合预测方法研究[J].路基工程, 2016(2):1-4.XU Bin, XU Mingming, ZENG Haozhong. Research on combined forecast method of subgrade settlement trend[J]. Subgrade Engineering, 2016(2):1-4.
[10]刘光秀,曹海莹,李玉根.灰色-Gompertz组合模型在软土路基沉降预测中的应用[J].中国科技论文,2016(13):1488-1491.LIU Guangxiu, CAO Haiying, LI Yugen. Application of grey and Gompertz combination model in settlement prediction of soft soil subgrade[J]. China Sciencepaper,2016(13):1488-1491.
[11]陈威,唐德燕,张届.利用三点法-灰色组合模型预测铁路路基沉降[J].测绘科学, 2015, 40(7):37-40.CHEN Wei, TANG Deyan, ZHANG Jie. Application of three-point-method-gray GM(1,1)combination model in settlement prediction for a railway line[J]. Science of Surveying and Mapping, 2015, 40(7):37-40.
[12]刘军,孙江浩,甄龙,等.组合模型在高铁软土路基沉降预测中的应用[J].地理空间信息, 2016, 14(8):93-95.LIU Jun, SUN Jianghao, ZHEN Long, et al. Application of combined model in settlement prediction of soft soil subgrade of high speed railway[J]. Geospatial Information, 2016, 14(8):93-95.
[13]陈华友.组合预测方法有效性理论及其应用[M].北京:科学出版社, 2007.CHEN Huayou. Applications and effectiveness theory of combination forecasting method[M]. Beijing:Science Press, 2007.
[14]李程,徐琪.一种基于改进的IOWHA算子的组合预测方法[J].系统管理学报, 2013(5):737-741.LI Cheng, XU Qi. A new combined forecasting model based on induced ordered weighted harmonic averaging(IOWHA)operator[J]. Journal of Systems and Management, 2013(5):737-741.
[15]熊春宝,李法超,韩宝荔.泊松曲线模型预测基坑周边地面沉降[J].低温建筑技术, 2010, 32(11):73-75.XIONG Chunbao, LI Fachao, HAN Baoli. The possion convolution life model for foundation settlement in the base pit vicinity[J]. Low Temperature Architecture Technology, 2010, 32(11):73-75.
[16]熊春宝,李法超.指数曲线模型预测基坑周边地面沉降[J].测绘与空间地理信息, 2011, 34(4):4-6.XIONG Chunbao, LI Fachao. The exponential curve method model for predicting foundation settlement in the base pit vicinity[J]. Geomatics and Spatial Information Technology, 2011, 34(4):4-6.
[17]曾炜,孔祥兴.高填方路基沉降的泊松模型预测方法应用[J].公路与汽运, 2005(5):58-60.ZENG Wei, KONG Xiangxing. Application of Poisson model prediction method to settlement of high fill subgrade[J]. Highways and Automotive Applications,2005(5):58-60.(编辑涂鹏)
[2] GAO Lei, ZHOU Qiuyue, YU Xiangjuan, et al. Analysis and model prediction of subgrade settlement for Linhai highway in China[J]. Electronic Journal of Geotechnical Engineering, 2014, 19:11-21.
[3] Kapetanios G, Labhard V, Price S. Forecast combination and the bank of England’s suite of statistical forecasting models[J]. Economic Modelling, 2008(2):772-792.
[4] YI Wen, WANG Yonghe, XIE Zixing, et al. Modeling subgrade settlement in the Wuhan-Guangzhou passenger rail line[J]. Electronic Journal of Geotechnical Engineering, 2015(20):4479-4495.
[5]丁建荣.基于最优组合模型的路基沉降预测方法[J].土工基础, 2014, 28(3):100-102.DING Jianrong. Embankment settlement prediction through an optimization model[J]. Soil Engineering and Foundation, 2014, 28(3):100-102.
[6]胡晓阳,王连俊,张光宗. Logistic及Verhulst预测模型在路基沉降预测中的拟合研究[J].铁道标准设计,2013(9):1-4.HU Xiaoyang, WANG Lianjun, ZHANG Guangzong.Research on the fitting of Logistic model and Verhulst model for subgrade settlement prediction[J]. Railway Standard Design, 2013(9):1-4.
[7]欧阳炼. GM(1,1)-Logistic路基沉降组合预测模型研究与应用[J].铁道科学与工程学报, 2010, 7(4):56-60.OUYANG Lian. Research and application of GM(1,1)and logistic combination forecasting model for subgrade settlement[J]. Journal of Railway Science and Engineering, 2010, 7(4):56-60.
[8]许明明,徐彬,曾浩中.路基沉降的加权组合预测方法研究[J].铁道科学与工程学报, 2016, 13(3):463-468.XU Mingming, XU Bin, ZENG Haozhong. Research on weighted combination prediction method for subgrade settlement[J]. Journal of Railway Science and Engineering, 2016, 13(3):463-468.
[9]徐彬,许明明,曾浩中.路基沉降趋势的组合预测方法研究[J].路基工程, 2016(2):1-4.XU Bin, XU Mingming, ZENG Haozhong. Research on combined forecast method of subgrade settlement trend[J]. Subgrade Engineering, 2016(2):1-4.
[10]刘光秀,曹海莹,李玉根.灰色-Gompertz组合模型在软土路基沉降预测中的应用[J].中国科技论文,2016(13):1488-1491.LIU Guangxiu, CAO Haiying, LI Yugen. Application of grey and Gompertz combination model in settlement prediction of soft soil subgrade[J]. China Sciencepaper,2016(13):1488-1491.
[11]陈威,唐德燕,张届.利用三点法-灰色组合模型预测铁路路基沉降[J].测绘科学, 2015, 40(7):37-40.CHEN Wei, TANG Deyan, ZHANG Jie. Application of three-point-method-gray GM(1,1)combination model in settlement prediction for a railway line[J]. Science of Surveying and Mapping, 2015, 40(7):37-40.
[12]刘军,孙江浩,甄龙,等.组合模型在高铁软土路基沉降预测中的应用[J].地理空间信息, 2016, 14(8):93-95.LIU Jun, SUN Jianghao, ZHEN Long, et al. Application of combined model in settlement prediction of soft soil subgrade of high speed railway[J]. Geospatial Information, 2016, 14(8):93-95.
[13]陈华友.组合预测方法有效性理论及其应用[M].北京:科学出版社, 2007.CHEN Huayou. Applications and effectiveness theory of combination forecasting method[M]. Beijing:Science Press, 2007.
[14]李程,徐琪.一种基于改进的IOWHA算子的组合预测方法[J].系统管理学报, 2013(5):737-741.LI Cheng, XU Qi. A new combined forecasting model based on induced ordered weighted harmonic averaging(IOWHA)operator[J]. Journal of Systems and Management, 2013(5):737-741.
[15]熊春宝,李法超,韩宝荔.泊松曲线模型预测基坑周边地面沉降[J].低温建筑技术, 2010, 32(11):73-75.XIONG Chunbao, LI Fachao, HAN Baoli. The possion convolution life model for foundation settlement in the base pit vicinity[J]. Low Temperature Architecture Technology, 2010, 32(11):73-75.
[16]熊春宝,李法超.指数曲线模型预测基坑周边地面沉降[J].测绘与空间地理信息, 2011, 34(4):4-6.XIONG Chunbao, LI Fachao. The exponential curve method model for predicting foundation settlement in the base pit vicinity[J]. Geomatics and Spatial Information Technology, 2011, 34(4):4-6.
[17]曾炜,孔祥兴.高填方路基沉降的泊松模型预测方法应用[J].公路与汽运, 2005(5):58-60.ZENG Wei, KONG Xiangxing. Application of Poisson model prediction method to settlement of high fill subgrade[J]. Highways and Automotive Applications,2005(5):58-60.(编辑涂鹏)