最优组合预测模型在高填方体沉降中的应用研究
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摘要
针对Logistic和Gompertz路堤沉降预测模型对于高填方土体后期沉降量预测精度较差的问题,该文基于Logistic和Gompertz预测模型的共性和个性,在充分考虑二者各自优势和特定局限性的基础上,对二者进行了最优化组合。以组合模型的最小对数误差平方和为目标函数求解最优加权系数,进而推导出最优加权几何平均组合预测模型,以提高高填方土体沉降预测精度的置信度。通过各预测模型对实际高填方土体工程的实测沉降数据进行拟合分析,验证最优组合预测模型在高填方土体沉降预测中的可行性。结果表明:最优组合预测模型的精度及可靠性均优于任一单一模型,适应性更强,尤其当监测时间超过曲线拐点后,几乎接近实测值。组合预测模型能够适用于多个模型优化组合,可涵盖各单一模型的优劣势,只要在权重比不出现负值的情况下,可大幅度的提高沉降预测精度。因而此组合预测模型可作为高填方土体后期沉降预测的一种有效方法。
Aiming at the problem of poor precision of two common settlement prediction of Logistic model and Gompertz model for predicting the final settlement of high fill body. Based on the commonness and individuality of Logistic model and Gompertz model, in order to give full play to their respective prediction advantages and complement their specific limitations, this paper optimizes the combination of the two models. Solving the optimal weighting coefficient with the objective function of minimizing the sum of squares of logarithmic errors of the combined model, and the optimal weighted geometric mean combination forecasting model is derived, so as to improve the confidence degree of the prediction accuracy of the settlement of the high fill.. The feasibility of the optimal combination forecasting model in engineering prediction is verified by fitting the monitoring data of specific high fill projects with each settlement prediction model. The results show that the precision and reliability of the optimal combination prediction model are better than any single model, and the adaptability is stronger. Especially, when the monitoring time exceeds the curve inflection point, it is almost close to the measured value. The combined prediction model can be applied to the optimization combination of multiple models, and can cover the advantages and disadvantages of each single model. As long as the weight ratio does not have negative value, the accuracy of settlement prediction can be greatly improved. so the combined forecasting model can be used as an effective method for predicting the settlement of high fill embankment in the later stage of engineering.
Aiming at the problem of poor precision of two common settlement prediction of Logistic model and Gompertz model for predicting the final settlement of high fill body. Based on the commonness and individuality of Logistic model and Gompertz model, in order to give full play to their respective prediction advantages and complement their specific limitations, this paper optimizes the combination of the two models. Solving the optimal weighting coefficient with the objective function of minimizing the sum of squares of logarithmic errors of the combined model, and the optimal weighted geometric mean combination forecasting model is derived, so as to improve the confidence degree of the prediction accuracy of the settlement of the high fill.. The feasibility of the optimal combination forecasting model in engineering prediction is verified by fitting the monitoring data of specific high fill projects with each settlement prediction model. The results show that the precision and reliability of the optimal combination prediction model are better than any single model, and the adaptability is stronger. Especially, when the monitoring time exceeds the curve inflection point, it is almost close to the measured value. The combined prediction model can be applied to the optimization combination of multiple models, and can cover the advantages and disadvantages of each single model. As long as the weight ratio does not have negative value, the accuracy of settlement prediction can be greatly improved. so the combined forecasting model can be used as an effective method for predicting the settlement of high fill embankment in the later stage of engineering.
引文
[1]刘博榕.延安新区高填方沉降监测与预测研究[D].西北大学,2016(Liu Borong.Study on monitoring and prediction of settlement of high fill in Yan'an new area[D].Northwestern University,2016(in Chinese))
[2]张雷.高填方路堤沉降预估模型对比分析[D].武汉:湖北工业大学,2017(Zhang Lei.Comparative analysis of settlement prediction model of high fill embankment[D].Wuhan:Hubei University of Technology,2017(in Chinese))
[3]刘寒冰,向一鸣,阮有兴.背景值优化的多变量灰色模型在路基沉降预测中的应用[J].岩土力学,2013,34(1):173-181(Liu Hanbing,Xiang Yiming,Ruan Youxing.Application of multivariable grey model with optimized background value in subgrade settlement prediction[J].Rock and Soil Mechanics,2013,34(1):173-181(in Chinese))
[4]陈晖东,余湘娟,高磊.越南河内-海防高速公路路基沉降预测模型研究[J].公路工程,2014,39(2):16-20(Chen Huidong,Yu Xiangjuan,Gao Lei.Study on prediction model of subgrade settlement of Henei-Haifang expressway in vietnam[J].Road Engineering,2014,39(2):16-20(in Chinese))
[5]唐葭,刘霁,蒋建清.基于非等距预测模型的填土路基沉降量分析[J].中南大学学报:自然科学版,2014,45(6):2054-2061(Tang Jia,Liu Ji,Jiang Jian-qing.Settlement analysis of filling subgrade based on non-equidistant prediction model[J].Journal of Central South University:Natural Science,2014,45(6):2054-2061(in Chinese))
[6]冯忠居,曹文海.软弱地基上高填方路堤沉降观测及数值分析[J].兰州理工大学学报,2013,39(2):126-129(Feng Zhongju,Cao Wenhai.Observation and numerical analysis of settlement of high fill embankment on soft foundation[J].Journal of Lanzhou University of Technology,2013,39(2):126-129(in Chinese))
[7]刘赪炜,韩煊,陈昌彦,等.高填方路基沉降预测的半数值半解析方法[J].地下空间与工程学报,2011,7(3):491-496(Liu Zhenwei,Han Xuan,Chen Changyan,et al.Semi-numerical and semi-analytical method for predicting settlement of high embankment[J].Journal of Underground Space and Engineering,2011,7(3):491-496(in Chinese))
[8]冯怀平,耿会岭,韩博文,等.非饱和土地区高速铁路路基沉降预测模型[J].岩土工程学报,2017,39(6):1089-1095(Feng Huaiping,Geng Huiling,Han Bowen,et al.Prediction model for subgrade settlement of high speed railway in unsaturated soil region[J].Journal of Geotechnical Engineering,2017,39(6):1089-1095(in Chinese))
[9]Siew A.Hyperbolic method for settlement in clays with verticaldrains[J].Canadian Geotechnical Journal,1994,31(1):125-131
[10]Akira A.Observational procedure of settlement predictions[J].Soils and Foundations,1978,18(4):87-101
[11]Siew A T,Soon H C.Comparison of the hyperbolic and Asaoka observational method of monitoring consolidation with vertical drains[J].Soils and foundation,1996,36(3):31-42
[12]雷学文,白世伟,孟庆山.灰色预测在软土地基沉降分析中的应用[J].岩土力学,2000,21(2):145-147(Lei Xuewen,Bai Shiwei,Meng Qingshan.Application of grey prediction in settlement analysis of soft soil foundation[J].Rock and Soil Mechanics,2000,21(2):145-147(in Chinese))
[13]宋彦灰,聂德新.基础沉降预测的Verhuslst模型[J].岩土力学,2003,24(1):123-126(Song Yanhui,Nie Dexin.Verhuslst model for prediction of foundation settlement[J].Rock and Soil Mechanics,2003,24(1):123-126(in Chinese))
[14]赵明华,曾广冼,向臻峰.高填石路堤沉降的灰色优化-马尔柯夫预测模型[J].公路交通科技,2006,23(11):19-22(Zhao Minghua,Zeng Guangxian,Xiang Zhenfeng.Grey optimum-markov prediction model for settlement of high fill embankment[J].Road Traffic Technology,2006,23(11):19-22(in Chinese))
[15]牛志强,闫长斌.高填方路堤工后沉降理论预测模型研究[J].公路工程,2018,43(1):110-113(Niu Zhiqiang,Yan Changbin.Study on theoretical prediction model of settlement after construction of high fill embankment[J].Road Engineering,2018,43(1):110-113(in Chinese))
[16]朱才辉,李宁,刘明振,等.吕梁机场黄土高填方地基工后沉降时空规律分析[J].岩土工程学报,2013,35(2):293-301(Zhu Caihui,Li Ning,Liu Mingzhen,et al.Temporal and spatial analysis of post-construction settlement of loess high fill foundation at Lv-Liang AIRPORT[J].Journal of Geotechnical Engineering,2013,35(2):293-301(in Chinese))
[17]余闯,刘松玉.路堤沉降预测的Gompertz模型应用研究[J].岩土力学,2005,26(1):82-86(Yu Chuang,Liu Songyu.Application of gompertz model to prediction of embankment settlement[J].Geomechanics,2005,26(1):82-86(in Chinese))
[18]张宇亭,孙浩,王金祥.Gompertz曲线模型在海堤软土地基沉降预测中的应用研究[J].水道港口,2009,30(4):257-260,276(Zhang Yuting,Sun Hao,Wang Jinxiang.Application of gompertz curve model to settlement prediction of soft soil foundation of sea embankment[J].Port of Waterways,2009,30(4):257-260,276(in Chinese))
[19]吴起星,胡辉.基于Gompertz成长曲线的真空预压软土沉降规律分析[J].岩石力学与工程学报,2006,25(S2):3600-3606(Wu Qixing,Hu Hui.Analysis of settlement of soft soil under vacuum preloading based on gompertz growth curve[J].Journal of Rock Mechanics and Engineering,2006,25(S2):3600-3606(in Chinese))
[20]徐洪钟,施斌,李雪红.全过程沉降量预测的Logistic生长模型及其适用性研究[J].2005,26(3):387-391(Xu Hongzhong,Shi Bin,Li Xuehong.Study on logistic growth model and its applicability for prediction of total process settlement[J].2005,26(3):387-391(in Chinese))
[21]梅国雄,宰金珉,殷金泽,等.沉降-时间曲线呈“S”型的证明及其应用-从土的本构关系[J].岩土力学,2005,26(S1):21-24(Mei Guoxiong,Zai Jinmin,Yin Jinze,et al.The proof of the"S"shape of the settlement-time curve and its application from the constitutive relation of the soil[J].Geomechanics,2005,26(S1):21-24(in Chinese))
[22]唐小我.最优组合预测方法及其应用[J].数理统计与管理,1992,11(1):31-35
[23]王鹏,巨玉文.Logistic-双曲线组合模型用于黄土高填方路堤沉降预测的研究[J].公路,2018,63(4):12-17(Wang Peng,Ju Yuwen.Study on Logistic-hyperbolic composite model for prediction of loess embankment settlement[J].Road,2018,63(4):12-17(in Chinese))
[2]张雷.高填方路堤沉降预估模型对比分析[D].武汉:湖北工业大学,2017(Zhang Lei.Comparative analysis of settlement prediction model of high fill embankment[D].Wuhan:Hubei University of Technology,2017(in Chinese))
[3]刘寒冰,向一鸣,阮有兴.背景值优化的多变量灰色模型在路基沉降预测中的应用[J].岩土力学,2013,34(1):173-181(Liu Hanbing,Xiang Yiming,Ruan Youxing.Application of multivariable grey model with optimized background value in subgrade settlement prediction[J].Rock and Soil Mechanics,2013,34(1):173-181(in Chinese))
[4]陈晖东,余湘娟,高磊.越南河内-海防高速公路路基沉降预测模型研究[J].公路工程,2014,39(2):16-20(Chen Huidong,Yu Xiangjuan,Gao Lei.Study on prediction model of subgrade settlement of Henei-Haifang expressway in vietnam[J].Road Engineering,2014,39(2):16-20(in Chinese))
[5]唐葭,刘霁,蒋建清.基于非等距预测模型的填土路基沉降量分析[J].中南大学学报:自然科学版,2014,45(6):2054-2061(Tang Jia,Liu Ji,Jiang Jian-qing.Settlement analysis of filling subgrade based on non-equidistant prediction model[J].Journal of Central South University:Natural Science,2014,45(6):2054-2061(in Chinese))
[6]冯忠居,曹文海.软弱地基上高填方路堤沉降观测及数值分析[J].兰州理工大学学报,2013,39(2):126-129(Feng Zhongju,Cao Wenhai.Observation and numerical analysis of settlement of high fill embankment on soft foundation[J].Journal of Lanzhou University of Technology,2013,39(2):126-129(in Chinese))
[7]刘赪炜,韩煊,陈昌彦,等.高填方路基沉降预测的半数值半解析方法[J].地下空间与工程学报,2011,7(3):491-496(Liu Zhenwei,Han Xuan,Chen Changyan,et al.Semi-numerical and semi-analytical method for predicting settlement of high embankment[J].Journal of Underground Space and Engineering,2011,7(3):491-496(in Chinese))
[8]冯怀平,耿会岭,韩博文,等.非饱和土地区高速铁路路基沉降预测模型[J].岩土工程学报,2017,39(6):1089-1095(Feng Huaiping,Geng Huiling,Han Bowen,et al.Prediction model for subgrade settlement of high speed railway in unsaturated soil region[J].Journal of Geotechnical Engineering,2017,39(6):1089-1095(in Chinese))
[9]Siew A.Hyperbolic method for settlement in clays with verticaldrains[J].Canadian Geotechnical Journal,1994,31(1):125-131
[10]Akira A.Observational procedure of settlement predictions[J].Soils and Foundations,1978,18(4):87-101
[11]Siew A T,Soon H C.Comparison of the hyperbolic and Asaoka observational method of monitoring consolidation with vertical drains[J].Soils and foundation,1996,36(3):31-42
[12]雷学文,白世伟,孟庆山.灰色预测在软土地基沉降分析中的应用[J].岩土力学,2000,21(2):145-147(Lei Xuewen,Bai Shiwei,Meng Qingshan.Application of grey prediction in settlement analysis of soft soil foundation[J].Rock and Soil Mechanics,2000,21(2):145-147(in Chinese))
[13]宋彦灰,聂德新.基础沉降预测的Verhuslst模型[J].岩土力学,2003,24(1):123-126(Song Yanhui,Nie Dexin.Verhuslst model for prediction of foundation settlement[J].Rock and Soil Mechanics,2003,24(1):123-126(in Chinese))
[14]赵明华,曾广冼,向臻峰.高填石路堤沉降的灰色优化-马尔柯夫预测模型[J].公路交通科技,2006,23(11):19-22(Zhao Minghua,Zeng Guangxian,Xiang Zhenfeng.Grey optimum-markov prediction model for settlement of high fill embankment[J].Road Traffic Technology,2006,23(11):19-22(in Chinese))
[15]牛志强,闫长斌.高填方路堤工后沉降理论预测模型研究[J].公路工程,2018,43(1):110-113(Niu Zhiqiang,Yan Changbin.Study on theoretical prediction model of settlement after construction of high fill embankment[J].Road Engineering,2018,43(1):110-113(in Chinese))
[16]朱才辉,李宁,刘明振,等.吕梁机场黄土高填方地基工后沉降时空规律分析[J].岩土工程学报,2013,35(2):293-301(Zhu Caihui,Li Ning,Liu Mingzhen,et al.Temporal and spatial analysis of post-construction settlement of loess high fill foundation at Lv-Liang AIRPORT[J].Journal of Geotechnical Engineering,2013,35(2):293-301(in Chinese))
[17]余闯,刘松玉.路堤沉降预测的Gompertz模型应用研究[J].岩土力学,2005,26(1):82-86(Yu Chuang,Liu Songyu.Application of gompertz model to prediction of embankment settlement[J].Geomechanics,2005,26(1):82-86(in Chinese))
[18]张宇亭,孙浩,王金祥.Gompertz曲线模型在海堤软土地基沉降预测中的应用研究[J].水道港口,2009,30(4):257-260,276(Zhang Yuting,Sun Hao,Wang Jinxiang.Application of gompertz curve model to settlement prediction of soft soil foundation of sea embankment[J].Port of Waterways,2009,30(4):257-260,276(in Chinese))
[19]吴起星,胡辉.基于Gompertz成长曲线的真空预压软土沉降规律分析[J].岩石力学与工程学报,2006,25(S2):3600-3606(Wu Qixing,Hu Hui.Analysis of settlement of soft soil under vacuum preloading based on gompertz growth curve[J].Journal of Rock Mechanics and Engineering,2006,25(S2):3600-3606(in Chinese))
[20]徐洪钟,施斌,李雪红.全过程沉降量预测的Logistic生长模型及其适用性研究[J].2005,26(3):387-391(Xu Hongzhong,Shi Bin,Li Xuehong.Study on logistic growth model and its applicability for prediction of total process settlement[J].2005,26(3):387-391(in Chinese))
[21]梅国雄,宰金珉,殷金泽,等.沉降-时间曲线呈“S”型的证明及其应用-从土的本构关系[J].岩土力学,2005,26(S1):21-24(Mei Guoxiong,Zai Jinmin,Yin Jinze,et al.The proof of the"S"shape of the settlement-time curve and its application from the constitutive relation of the soil[J].Geomechanics,2005,26(S1):21-24(in Chinese))
[22]唐小我.最优组合预测方法及其应用[J].数理统计与管理,1992,11(1):31-35
[23]王鹏,巨玉文.Logistic-双曲线组合模型用于黄土高填方路堤沉降预测的研究[J].公路,2018,63(4):12-17(Wang Peng,Ju Yuwen.Study on Logistic-hyperbolic composite model for prediction of loess embankment settlement[J].Road,2018,63(4):12-17(in Chinese))
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