Faculty of Geoengineering, University of Warmia and Mazury in Olsztyn, Olsztyn 10-957, Poland.
Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk 80-233, Poland.
Sensors (Basel). 2020 Jul 14;20(14):3913. doi: 10.3390/s20143913.
This paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface's vibrations is also assumed. Such noise disturbs the deformation's functional models. Surface monitoring with the use of the geodetic levelling network of a free control network class is carried out. Assuming that, in some cases, the control networks are insufficient in surface's deformation analysis, additional and non-measurable reference points have been provided. The prediction of these points' displacements and estimation of the free control network points' displacement are carried out using the collocation method applying the total least squares adjustment. The proposed theoretical solutions were verified by the simulation methods and on the example of a real control network.
本文提出了一种确定视为随机场的垂直变形的方法。假设监测表面不仅受到确定性变形的影响，还受到随机波动的影响。此外，还假设存在来自表面振动的随机噪声。这种噪声会干扰变形的功能模型。利用自由控制网级的大地水准测量网进行表面监测。假设在某些情况下，控制网在表面变形分析中不足，因此提供了额外的不可测量的参考点。使用配置法应用总体最小二乘调整来预测这些点的位移并估计自由控制网点的位移。所提出的理论解决方案通过模拟方法和实际控制网的例子进行了验证。
