基于区间分析理论的变形监测数据处理方法
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摘要
基于点变量方式的变形监测数据分析与处理,由于变形观测数据的近似或扰动,与真实形变存在一定误差,在一定的观测手段和方法下,这类误差导致目标函数的变化并不大,但其所求的理论分析模型参数却会存在巨大差异。针对点变量表达方式不能充分反映结构变形信息的复杂性,提出了以区间分析理论来进行变形监测数据分析与处理。基于区间分析理论,建立起基于区间变量和区间分析理论的变形监测数据处理方法。提出了区间参数变量的4种取值方法:概率统计取值法、仪器精度法、最大最小值法及综合误差法;基于区间超宽度扩展理论,提出了减小区间超宽度的3种措施:改写监测数据处理的表达式、缩小监测参数的区间宽度及选择合理的数据处理模型。基于时间序列模型及灰色系统模型,以区间参数代替点参数,采用区间分析定义的运算法则,对工程变形监测数据序列进行了分析。工程算例表明:一般点参数预测模型的预测值,由于变形体变形规律的复杂性,即使采用与变形规律拟合程度很好的数学模型,也很难与实测变形值符合,但对于预测的区间值,实测变形值落在预测值的区间内,概率是比较大的。区间预测值能较点预测值进一步提高理论预测模型的预测准确性,也能更好地反映工程实体变形的复杂特点。
Due to the approximation or disturbance,the deformation monitoring data analysis and processing based on the point variable method has certain errors with the real deformation. Under certain observation methods,such errors lead to little change in the objective function,but there are huge differences in the theoretical analysis model parameters that are sought. In view of the expression of point variables cannot fully reflect the complexity of structural deformation information,the analysis and processing of deformation monitoring data by interval analysis theory is proposed. Based on the interval analysis theory,a deformation monitoring data processing method based on interval variable and interval analysis theory is established. Four methods for determining the interval parameter variables are proposed: probability and statistical value method,instrument precision method,maximum and minimum method,and comprehensive error method.Based on the interval hyper-width expansion theory,3 measures to reduce the interval hyper-width are proposed: rewriting the expression of monitoring data processing,narrowing the interval width of monitoringparameters,and selecting a reasonable data processing model. Based on the time series model and the gray system model, the interval parameters are used to replace the point parameters, and the engineering deformation monitoring data sequence is analyzed by the algorithm defined by the interval analysis. The engineering example shows that for the prediction value obtained by the general point parameter prediction model,due to the complexity of the deformation rule of the deformation body,even if using a mathematical model with a good degree of fitting with the deformation rule,it is difficult to match the measured deformation value,but for the predicted interval value,the measured deformation value falls within the interval of the predicted value,and the probability is relatively large. The interval prediction value can further improve the prediction accuracy of the theoretical prediction model compared with the point prediction value,and can better reflect the complex characteristics of the engineering entity deformation.
Due to the approximation or disturbance,the deformation monitoring data analysis and processing based on the point variable method has certain errors with the real deformation. Under certain observation methods,such errors lead to little change in the objective function,but there are huge differences in the theoretical analysis model parameters that are sought. In view of the expression of point variables cannot fully reflect the complexity of structural deformation information,the analysis and processing of deformation monitoring data by interval analysis theory is proposed. Based on the interval analysis theory,a deformation monitoring data processing method based on interval variable and interval analysis theory is established. Four methods for determining the interval parameter variables are proposed: probability and statistical value method,instrument precision method,maximum and minimum method,and comprehensive error method.Based on the interval hyper-width expansion theory,3 measures to reduce the interval hyper-width are proposed: rewriting the expression of monitoring data processing,narrowing the interval width of monitoringparameters,and selecting a reasonable data processing model. Based on the time series model and the gray system model, the interval parameters are used to replace the point parameters, and the engineering deformation monitoring data sequence is analyzed by the algorithm defined by the interval analysis. The engineering example shows that for the prediction value obtained by the general point parameter prediction model,due to the complexity of the deformation rule of the deformation body,even if using a mathematical model with a good degree of fitting with the deformation rule,it is difficult to match the measured deformation value,but for the predicted interval value,the measured deformation value falls within the interval of the predicted value,and the probability is relatively large. The interval prediction value can further improve the prediction accuracy of the theoretical prediction model compared with the point prediction value,and can better reflect the complex characteristics of the engineering entity deformation.
引文
[1] MOORE R E. Interval Arithmetic and Automatic Error Analysis in Digital Computing[D]. Stanford:Stanford University,1962.
[2] MOORE R E. Interval Analysis[M]. Englewood Cliffs:Prentice-Hall,1966.
[3]苏永华,何满潮,赵明华,等.基于区间变量的响应面可靠性分析方法[J].岩土工程学报,2005,27(12):1408-1413.SU Yong-hua,HE Man-chao,ZHAO Ming-hua, et al.Reliability Analysis of Response Surface Method Based on Interval Variables[J]. Chinese Journal of Geotechnical Engineering,2005,27(12):1408-1413.
[4]王朝晖,王选仓,马士宾.基于区间数逼近法的路面使用性能综合评价[J].公路交通科技,2009,26(1):21-25.WANG Chao-hui,WANG Xuan-cang,MA Shi-bin. An Approximation Method of Interval Numbers for Comprehensive Evaluation of Pavement Performance[J].Journal of Highway and Transportation Research and Development,2009,26(1):21-25.
[5]朱向平,颜可珍,刘杰.沥青路面预养护方案的区间关联模糊优化决策[J].中南林业科技大学学报,2011,31(11):166-170.ZHU Xiang-ping, YAN Ke-zhen, LIU Jie. Premaintenance Measure of Asphalt Pavement Interval Related Fuzzy Optimization Decision-making[J]. Journal of Central South University of Forestry&Technology,2011,31(11):166-170.
[6]于生飞,陈征宙,张明瑞,等.基于区间不确定分析方法的边坡稳定性分析[J].工程地质学报,2012,20(2):228-233.YU Sheng-fei,CHEN Zheng-zhou,ZHANG Ming-rui,et al. Interval Analysis Model of Geomaterial Parameters for Uncertainties in Slope Stability Assessment[J]. Journal of Engineering Geology,2012,20(2):228-233.
[7]唐利民,郑健龙.基于区间适定和区间不适定性理论的参数反演方法[J].土木工程学报,2016,49(11):91-96.TANG Li-min,ZHENG Jian-long. Parametric Inversion Method Based on Interval Well-posedness and Interval Illposedness Theory[J]. China Civil Engineering Journal,2016,49(11):91-96.
[8]唐利民,郑健龙.区间分析岩土工程理论与方法[M].北京:科学出版社,2017.TANG Li-min, ZHENG Jian-long. Interval Analysis Theory and Method of Geotechnical Engineering[M].Beijing:Science Press,2017.
[9]黄声享,尹晖,蒋征.变形监测数据处理[M].武汉:武汉大学出版社,2010.HUANG Sheng-xiang, YIN Hui, JIANG Zheng.Deformation Monitoring Data Processing[M]. Wuhan:Wuhan University Press,2010.
[10]唐利民.贵州省毕节至威宁高速公路赫章特大桥11#高墩施工过程中的形变规律研究[R].长沙:长沙理工大学,2013.TANG Li-min. Study on Deformation Law of Construction of 11th High Pier of Hezhang Bridge of Bijie-Weining Expressway in Guizhou Province[R]. Changsha:Changsha University of Science and Technology,2013.
[11]唐利民.贵州省赤水至望谟高速公路仁赤段二郎河特大桥主桥施工测量控制研究[R].长沙:长沙理工大学,2014.TANG Li-min. Research on Construction Survey Control of Main Bridge of Erlanghe Bridge in Renchi Section of Chishui-Wangmo Expressway in Guizhou Province[R].Changsha:Changsha University of Science and Technology,2014.
[12] REVOL N,THVENY P. Parallel Implementation of Interval Matrix Multiplication[J]. Reliable Computing,2013(19):91-106.
[13] HASHEMI B, TAVAKOLIPOUR H. A Non-induced Interval Matrix Norm[J]. Reliable Computing,2013(18):144-146.
[14] RUMP S M. INTLAB:INTerval LABoratory[M]//CSENDES T. Developments in Reliable Computing.Dordrecht:Kluwer Academic Publishers,1999:77-104.
[15] RUMP S M. The Matlab/Octave Toolbox for Reliable Computing[EB/OL].(2013-01-14)[2017-06-09]. http://www. ti3. tu-harburg. de/rump/intlab/.
[16]邓聚龙.灰色控制系统[M]. 1版.武汉:华中工学院出版社,1985:293-360.DENG Ju-long. Grey Control System[M]. 1st ed. Wuhan:Huazhong Institute of Technology Press,1985:293-360.
[17]唐利民. GM(1,1)病态问题求解的调整计量单位法[J].武汉大学学报:信息科学版,2014,39(9):1038-1042.TANG Li-min. Adjust Measurement Unit Algorithm for Illposed Problem of GM(1,1)Model[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9):1038-1042.
[18]肖大海,谢全敏,杨文东.基于多变量的集成预测模型在隧道拱顶沉降变形预测中的应用[J].公路交通科技,2017,34(12):119-121.XIAO Da-hai, XIE Quan-min, YANG Wen-dong.Application of Integrated Forecasting Model Based on Multivariable in Tunnel Vault Settlement Forecasting[J].Journal of Highway and Transportation Research and Development,2017,34(12):119-121.
[2] MOORE R E. Interval Analysis[M]. Englewood Cliffs:Prentice-Hall,1966.
[3]苏永华,何满潮,赵明华,等.基于区间变量的响应面可靠性分析方法[J].岩土工程学报,2005,27(12):1408-1413.SU Yong-hua,HE Man-chao,ZHAO Ming-hua, et al.Reliability Analysis of Response Surface Method Based on Interval Variables[J]. Chinese Journal of Geotechnical Engineering,2005,27(12):1408-1413.
[4]王朝晖,王选仓,马士宾.基于区间数逼近法的路面使用性能综合评价[J].公路交通科技,2009,26(1):21-25.WANG Chao-hui,WANG Xuan-cang,MA Shi-bin. An Approximation Method of Interval Numbers for Comprehensive Evaluation of Pavement Performance[J].Journal of Highway and Transportation Research and Development,2009,26(1):21-25.
[5]朱向平,颜可珍,刘杰.沥青路面预养护方案的区间关联模糊优化决策[J].中南林业科技大学学报,2011,31(11):166-170.ZHU Xiang-ping, YAN Ke-zhen, LIU Jie. Premaintenance Measure of Asphalt Pavement Interval Related Fuzzy Optimization Decision-making[J]. Journal of Central South University of Forestry&Technology,2011,31(11):166-170.
[6]于生飞,陈征宙,张明瑞,等.基于区间不确定分析方法的边坡稳定性分析[J].工程地质学报,2012,20(2):228-233.YU Sheng-fei,CHEN Zheng-zhou,ZHANG Ming-rui,et al. Interval Analysis Model of Geomaterial Parameters for Uncertainties in Slope Stability Assessment[J]. Journal of Engineering Geology,2012,20(2):228-233.
[7]唐利民,郑健龙.基于区间适定和区间不适定性理论的参数反演方法[J].土木工程学报,2016,49(11):91-96.TANG Li-min,ZHENG Jian-long. Parametric Inversion Method Based on Interval Well-posedness and Interval Illposedness Theory[J]. China Civil Engineering Journal,2016,49(11):91-96.
[8]唐利民,郑健龙.区间分析岩土工程理论与方法[M].北京:科学出版社,2017.TANG Li-min, ZHENG Jian-long. Interval Analysis Theory and Method of Geotechnical Engineering[M].Beijing:Science Press,2017.
[9]黄声享,尹晖,蒋征.变形监测数据处理[M].武汉:武汉大学出版社,2010.HUANG Sheng-xiang, YIN Hui, JIANG Zheng.Deformation Monitoring Data Processing[M]. Wuhan:Wuhan University Press,2010.
[10]唐利民.贵州省毕节至威宁高速公路赫章特大桥11#高墩施工过程中的形变规律研究[R].长沙:长沙理工大学,2013.TANG Li-min. Study on Deformation Law of Construction of 11th High Pier of Hezhang Bridge of Bijie-Weining Expressway in Guizhou Province[R]. Changsha:Changsha University of Science and Technology,2013.
[11]唐利民.贵州省赤水至望谟高速公路仁赤段二郎河特大桥主桥施工测量控制研究[R].长沙:长沙理工大学,2014.TANG Li-min. Research on Construction Survey Control of Main Bridge of Erlanghe Bridge in Renchi Section of Chishui-Wangmo Expressway in Guizhou Province[R].Changsha:Changsha University of Science and Technology,2014.
[12] REVOL N,THVENY P. Parallel Implementation of Interval Matrix Multiplication[J]. Reliable Computing,2013(19):91-106.
[13] HASHEMI B, TAVAKOLIPOUR H. A Non-induced Interval Matrix Norm[J]. Reliable Computing,2013(18):144-146.
[14] RUMP S M. INTLAB:INTerval LABoratory[M]//CSENDES T. Developments in Reliable Computing.Dordrecht:Kluwer Academic Publishers,1999:77-104.
[15] RUMP S M. The Matlab/Octave Toolbox for Reliable Computing[EB/OL].(2013-01-14)[2017-06-09]. http://www. ti3. tu-harburg. de/rump/intlab/.
[16]邓聚龙.灰色控制系统[M]. 1版.武汉:华中工学院出版社,1985:293-360.DENG Ju-long. Grey Control System[M]. 1st ed. Wuhan:Huazhong Institute of Technology Press,1985:293-360.
[17]唐利民. GM(1,1)病态问题求解的调整计量单位法[J].武汉大学学报:信息科学版,2014,39(9):1038-1042.TANG Li-min. Adjust Measurement Unit Algorithm for Illposed Problem of GM(1,1)Model[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9):1038-1042.
[18]肖大海,谢全敏,杨文东.基于多变量的集成预测模型在隧道拱顶沉降变形预测中的应用[J].公路交通科技,2017,34(12):119-121.XIAO Da-hai, XIE Quan-min, YANG Wen-dong.Application of Integrated Forecasting Model Based on Multivariable in Tunnel Vault Settlement Forecasting[J].Journal of Highway and Transportation Research and Development,2017,34(12):119-121.
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