变异函数模型参数估计的信息熵加权回归法
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摘要
将熵权理论引入到变异函数理论模型的参数估计中,对加权多项式回归的加权方法进行改进,以信息熵定权,并用实际变形监测数据进行实验。实验结果表明,该方法综合了距离和样本点对数对权重的影响,加权回归确定的变异函数模型更准确,插值预报效果更优。
The information entropy theory was introduced into parameter estimation of variogram model,to improve weighting method of weighted polynomial regression using the entropy weight method.An experiment was taken with real deformation monitoring data,considering the influence of both distance and the number of point pairs at the same distance.The experimental results show that the variogram model determined by information entropy weighted regression is more reasonable,and interpolating prediction is more accurate.
The information entropy theory was introduced into parameter estimation of variogram model,to improve weighting method of weighted polynomial regression using the entropy weight method.An experiment was taken with real deformation monitoring data,considering the influence of both distance and the number of point pairs at the same distance.The experimental results show that the variogram model determined by information entropy weighted regression is more reasonable,and interpolating prediction is more accurate.
引文
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2 王仁铎,胡光道.线性地质统计学[M].北京:地质出版社,1988.(Wang Renduo,Hu Guangdao.Linear geostatistics[M].Beijing:Geological Press,1988)
3 矫希国,刘超.变差函数的参数模拟[J].物探化计算机技术,1996,18(2):157-161.(Jiao Xiguo,Liu Chao.Estimation of variation parameter[J].Computing Techniques for Geophysical and Geochemical Exploration,1996,16(2):157-161)
4 李冠林,等.改进的克里金法在海面风场计算中的应用[J].气象水文海洋仪器,2013(1):73-76.(Li Guanlin,et al.Application of improved Kriging to calculating sea wind field[J].Meteorological,Hydrological and Marine Instruments,2013(1):73-76)
5 李玲,等.变异函数线性化的统一参数估计方法研究[J].长江大学学报:理工卷,2010(2):127-129.(Li Ling,et al.Study on the unity parameter estimation method of linear variogram[J].Journal of Yangtze University:Nat Sci Edit,2010(2):127-129)
6 周访滨,朱建军,陈永奇.基于熵的数据污染率估算[J].大地测量与地球动力学,2013(4):92-95.(Zhou Fangbin,Zhu Jianjun,Chen Yongqi.Contamination rate estimation based on entropy[J].Journal of Geodesy and Geodynamics,2013(4):92-95)
7 谢赤,钟赞.熵权法在银行经营绩效综合评价中的应用[J].中国软科学,2002,9(4):60-63.(Xie Chi,Zhong Zan.Entropy method and its application in comprehensive evaluation of bank’s performance[J].China Soft Science,2002,9(4):60-63)
8 王永弟,许承权.熵权理论在测量平差中的应用[J].测绘通报,2012(11):52-54.(Wang Yongdi,Xu Chengquan.Application of entropy theory to measurement adjustment[J].Bulletin of Surveying and Mapping,2012(11):52-54)
9 刘玉成.熵法确定权重的地基沉降组合预测模型[J].中国科技论文在线,2010,5(11):875-878.(Liu Yucheng.A combined prediction model for foundation subsidence using the entropy weight method[J].Sciencepaper Online,2010,5(11):875-878)
10 程勖,等.变异函数在异常空间插值中的应用[J].世界地质,2007,26(3):298-303.(Cheng Xu,et al.Application of variogram in interplation of abnormal space[J].Global Geology,2007,26(3):298-303)
11 顾春雷,杨漾,朱志春.几种建立DEM模型插值方法精度的交叉验证[J].测绘与空间地理信息,2011,34(5):100 -102.(Gu Chunlei,Yang Yang,Zhu Zhichun.Accuracy cross-validation of several interpolation methods of DEM[J].Geomatics&Spatial Information Technology,2011,34(5):100-102)
12 张晓明,赵剡.基于克里金插值的局部地磁图的构建[J].电子测量技术,2009,32(4):122-125.(Zhang Xiaoming,Zhao Yan.Local geomagnetic field mapping based on Kriging interpolation method[J].Electronic Measurement Technology,2009,32(4):122-125)
13 易长荣,王淼,徐冬.GPS连续站监测天津市地面沉降的初步结果[J].现代测绘,2009(1):12.(Yi Changrong,Wang Miao,Xu Dong.Preliminary results of land subsidence monitored by continuous GPS stations in Tianjin[J].Modern Surveying and Mapping,2009(1):12)