变形监测网稳定点选取的平方型Msplit相似变换法

doi:10.11947/j.AGCS.2020.20200023

摘要/Abstract

摘要： 针对现有参考网稳定点选取方法在不稳定点数较多时正确性和稳健性不足的问题，通过引入平方型M_split相似变换，提出了一种稳健的稳定点选取方法，在不稳定点较多、甚至不稳定点数超过稳定点数的情况下仍然有效。具体思路是：在计算两期坐标的相似变换参数时，利用平方型M_split估计将参考点组一分为二，取点数多的一组为稳定点组并继续分裂，直至两个点组对应的相似变换参数无明显差异时停止，利用最终的稳定点组计算相似变换参数来开展变形分析。试验结果表明，当参考网中存在变形量较大的点或不稳定点总数接近甚至超过稳定点数时，本文方法与传统S变换和抗差S变换相比，稳定点的判断正确率最高，求得的变形量与模拟变形量相差最小，稳定点组对应的两期坐标差均方根最小，能够正确反映控制点的实际变形。

关键词: 平方型M_split估计, 相似变换, 变形监测参考网, 稳定点选取, 变形分析

Abstract: In order to improve the correctness and robustness of existing stable points selection methods of reference network when there are many unstable points, a robust stable points selection method using squared M_split similarity transformation is proposed. This method still works when the number of unstable points is close to or even more than the number of stable points. Firstly, the reference points are divided into two groups with square M_split estimation in the process of calculating the similar transformation parameters of two measurement epochs. Then, by taking the group with more points as stable one, the stable points group is divided into two groups continually until the similarity transformation parameters of the two groups have little difference. Finally, deformation analysis is conducted with the similarity transformation parameters which are calculated with the final stable points group. Experiments are carried out to compare the effect of traditional S transformation, robust S transformation and the proposed method under the condition that there exists some points with large deformation in reference network or the number of unstable points is close to or even more than the number of stable points. And the experimental results show that the proposed method has the highest correctness rate of stable points determination, gets the smallest difference between the calculated deformation and the simulated deformation, and gains the smallest root mean square of coordinates difference of the stable points group between two measurement epochs, which means that the result of the proposed method can correctly reveal the deformation of control points.

Key words: squared M_split estimation, similarity transformation, deformation monitoring reference network, stable points selection, deformation analysis

中图分类号:

P258

郭迎钢, 李宗春, 何华, 张冠宇, 冯其强, 杨浩. 变形监测网稳定点选取的平方型M_split相似变换法[J]. 测绘学报, 2020, 49(11): 1419-1429.

GUO Yinggang, LI Zongchun, HE Hua, ZHANG Guanyu, FENG Qiqiang, YANG Hao. A squared M_split similarity transformation method for stable points selection of deformation monitoring network[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(11): 1419-1429.

参考文献

[1] 王新洲, 邓兴升. 大坝变形预报的模糊神经网络模型[J]. 武汉大学学报(信息科学版), 2005, 30(7):588-591. WANG Xinzhou, DENG Xingsheng. Fuzzy neural network modeling for dam deformation prediction[J]. Geomatics and Information Science of Wuhan University, 2005, 30(7):588-591.
[2] 许章平, 栾元重, 刘中华, 等. 混沌理论支持下的桥梁变形监测研究[J]. 测绘通报, 2019(6):41-46. DOI:10.13474/j.cnki.11-2246.2019.0181. XU Zhangping, LUAN Yuanzhong, LIU Zhonghua, et al. Research on bridge deformation monitoring based on chaos theory[J]. Bulletin of Surveying and Mapping, 2019(6):41-46. DOI:10.13474/j.cnki.11-2246.2019.0181.
[3] LI Zongchun, LU Zhiyong, ZHANG Guanyu, et al. A precise calibration method on phase center of uplink antenna array considering its actual pointing[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1):93-101. DOI:10.11947/j.JGGS.2020.0110.
[4] 郭迎钢, 李宗春, 刘忠贺, 等. 加速器隧道控制网变形可监测性及稳定性分析[J]. 原子能科学技术, 2019, 53(9):1634-1642. GUO Yinggang, LI Zongchun, LIU Zhonghe, et al. Deformation detectability and stability analysis for tunnel control network of particle accelerator[J]. Atomic Energy Science and Technology, 2019, 53(9):1634-1642.
[5] 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, 2003. HUANG Shengxiang, YIN Hui, JIANG Zheng. Deformation monitoring data processing[M]. Wuhan:Wuhan University Press, 2003.
[6] 叶斌. 变形模型的分析研究以及变形的预测[D]. 上海:同济大学, 2006. YE Bin. The analysis of deformation model and deformation forecasting[D]. Shanghai:Tongji University, 2006.
[7] VELSINK H. On the deformation analysis of point fields[J]. Journal of Geodesy, 2015, 89(11):1071-1087.
[8] 张贵钢. 三门峡大坝变形监测的有限元分析及预测[D]. 西安:长安大学, 2007. ZHANG Guigang. The deformation monitoring finite element analysis and prediction on the Sanmen Xia Dam[D]. Xi'an:Chang'an University, 2007.
[9] 李宗春, 邓勇, 张冠宇, 等. 变形测量异常数据处理中小波变换最佳级数的确定[J]. 武汉大学学报(信息科学版), 2011, 36(3):285-288. LI Zongchun, DENG Yong, ZHANG Guanyu, et al. Determination of best grading of wavelet transform in deformation measurement data filtering[J]. Geomatics and Information Science of Wuhan University, 2011, 36(3):285-288.
[10] 范千, 方绪华, 许承权, 等. 变形监测数据预报的动态贝叶斯ELM方法[J]. 测绘学报, 2019, 48(7):919-925. DOI:10.11947/j.AGCS.2019.20180504. FAN Qian, FANG Xuhua, XU Chengquan, et al. Dynamic Bayesian ELM method for deformation monitoring data prediction[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(7):919-925. DOI:10.11947/j.AGCS.2019.20180504.
[11] 王穗辉. 变形数据处理、分析及预测方法若干问题研究[D]. 上海:同济大学, 2007. WANG Suihui. Research on several problems in deformation data processing, analysis and prediction[D]. Shanghai:Tongji University, 2007.
[12] 杨曦. 模糊聚类及综合评判在变形分析中的应用[D]. 成都:西南交通大学, 2014. YANG Xi. The application of fuzzy clustering and comprehensive evaluation in deformation analysis[D]. Chengdu:Southwest Jiaotong University, 2014.
[13] 杨学超, 何彩平. 平均间隙法和单点检验法在变形监测网中的应用[J]. 兰州交通大学学报, 2011, 30(6):30-32. YANG Xuechao, HE Caiping. Application of the method of mean GAP and the single point inspection to deformation monitoring network[J]. Journal of Lanzhou Jiaotong University, 2011, 30(6):30-32.
[14] VELSINK H. Testing deformation hypotheses by constraints on a time series of geodetic observations[J]. Journal of Applied Geodesy, 2017, 12(1):77-93.
[15] HEKIMOGLU S, ERDOGAN B, BUTTERWORTH S. Increasing the efficacy of the conventional deformation analysis methods:alternative strategy[J]. Journal of Surveying Engineering, 2010, 136(3):53-62.
[16] 杨元喜. 抗差估计理论及其应用[M]. 北京:八一出版社, 1993. YANG Yuanxi. Theory of robust estimation and its application[M]. Beijing:"August 1st" Publishing House, 1993.
[17] 方兴, 黄李雄, 曾文宪, 等. 稳健估计的一种改进迭代算法[J]. 测绘学报, 2018, 47(10):1301-1306. DOI:10.11947/j.AGCS.2018.20170576. FANG Xing, HUANG Lixiong, ZENG Wenxian, et al. On an improved iterative reweighted least squares algorithm in robust estimation[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(10):1301-1306. DOI:10.11947/j.AGCS.2018.20170576.
[18] 仝海波, 张国柱. 改进M估计的抗多个粗差定位解算方法[J]. 测绘学报, 2014, 43(4):366-371. DOI:10.13485/j.cnki.11-2089.2014.0055. TONG Haibo, ZHANG Guozhu. Robust positioning algorithm with modified M-estimation for multiple outliers[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(4):366-371. DOI:10.13485/j.cnki.11-2089.2014.0055.
[19] NOWEL K. Investigating efficacy of robust M-estimation of deformation from observation differences[J]. Survey Review, 2016, 48(346):21-30.
[20] NOWEL K, KAMIN'SKI W. Robust estimation of deformation from observation differences for free control networks[J]. Journal of Geodesy, 2014, 88(8):749-764.
[21] KOCH K P. Parameter estimation and hypothesis testing in linear models[M]. 2nd ed. Berlin Heidelberg:Springer, 1999.
[22] 周江文, 欧吉坤. 名次法及拟稳点的选定[J]. 测绘学报, 1987, 16(2):88-94. ZHOU Jiangwen, OU Jikun. The method of order and selection of quasi-stable points[J]. Acta Geodaetica et Cartographica Sinica, 1987, 16(2):88-94.
[23] 周江文, 欧吉坤. 拟稳点的更换——兼论自由网平差若干问题[J]. 测绘学报, 1984, 13(3):161-170. ZHOU Jiangwen, OU Jikun. On alteration of quasi-stable points and some problems concerning free net adjustment[J]. Acta Geodaetica et Cartographica Sinica, 1984, 13(3):161-170.
[24] 周江文. 经典误差理论与抗差估计[J]. 测绘学报, 1989, 18(2):115-120. ZHOU Jiangwen. Classical theory of errors and robust estimation[J]. Acta Geodaetica et Cartographica Sinica, 1989, 18(2):115-120.
[25] YANG Y. Robust estimation of geodetic datum transformation[J]. Journal of Geodesy, 1999, 73(5):268-274.
[26] 杨元喜, 宋力杰, 徐天河. 大地测量相关观测抗差估计理论[J]. 测绘学报, 2002, 31(2):95-99. DOI:10.3321/j.issn:1001-1595.2002.02.001. YANG Yuanxi, SONG Lijie, XU Tianhe. Robust parameter estimation for geodetic correlated observations[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2):95-99. DOI:10.3321/j.issn:1001-1595.2002.02.001.
[27] YANG Y, SONG L, XU T. Robust estimator for correlated observations based on bifactor equivalent weights[J]. Journal of Geodesy, 2002, 76(6-7):353-358.
[28] WIS'NIEWSKI Z. Estimation of parameters in a split functional model of geodetic observations (M_split estimation)[J]. Journal of Geodesy, 2008, 82(10):655.
[29] WIS'NIEWSKI Z. M_split(q) estimation:estimation of parameters in a multi split functional model of geodetic observations[J]. Journal of Geodesy, 2010, 84(6):355-372.
[30] WIS'NIEWSKI Z, ZIENKIEWICZ M H. Shift-M^*_split estimation in deformation analyses[J]. Journal of Surveying Engineering, 2016, 142(4):04016015.
[31] ZIENKIEWICZ M H. Application of M_split estimation to determine control points displacements in networks with unstable reference system[J]. Survey Review, 2015, 47(342):174-180.
[32] NOWEL K. Squared M_split(q) S-transformation of control network deformations[J]. Journal of Geodesy, 2019, 93(7):1025-1044.
[33] HUBER P J, RONCHETTI E M. Robust statistics[M]. 2nd ed. Hoboken, New Jersey:John Wiley & Sons, 2009.
[34] WIS'NIEWSKI Z. M_split estimation:squared M_split estimation and numerical examples[J]. Geodezja i Kartografia, 2009, 58(1):23-48.
[35] ALSADIK B. Adjustment models in 3D geomatics and computational geophysics:with MATLAB examples[M]. Amsterdam:Elsevier, 2019.
[36] BOCEAN V, COPPOLA G, FORD R, et al. Status report on the survey and alignment activities at Fermilab[C]//Proceedings of the 9th International Workshop on Accelerator Alignment. Stanford:SLAC, 2006.