变形监测网稳定点选取的平方型Msplit相似变换法

A squared Msplit similarity transformation method for stable points selection of deformation monitoring network

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Msplit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Msplit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。

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 Msplit 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 Msplit 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.