３D網形穩健度分析研究──以台中市圖根點監測網為例

A Study of 3D Robustness Analysis-Application to the Taichung Control Point Network

穩健度分析是結合可靠度分析及彈性力學中應變分析理論的技術，利用尺度、形狀及局部微旋轉等獨立的變形指標來檢驗點位及網形的穩健度。本文將穩健度理論由2D推展至3D，以適用於包括GPS及各種測量網形，並進一步推導穩健度理論方程式，來證實多餘觀測數與穩健度的關係。文中亦提出單一向量的最大移位向量法，以簡化及精進計算程序，而且更適合於3D的情況，並可做更進一步的研究。本文以台中市圖根點監測網來測試前述理論推導，目前得到初步結果為：除了局部微旋轉外，其餘的穩健度指標與點位總變形有很大的相關性；最弱的穩健度發生在台中市南區。 Robustness analysis is a natural merger of reliability analysis, and geometrical strength analysis using strain techniques. This analyzing technique provides a more complete and detailed description of the 3D network deformation in terms of the three independent measures represented by; robustness in scale, shape and local rotation. In this paper, the Maximum-Displacement-Vector Approach (MDVA) is presented to simplify the computing progress for evaluating these deformation measures. Each point in the network has a unique deformation vector for the three deformation measures. All of the three measures can be computed from the same vector, making MDVA easy and suitable for applying to the 3D case. To verify the relationship between the redundancies of the observations and the deformations, the deformation vector equation has been expanded. This study uses the Taichung Control Point Network as a test for applying the robustness analysis. The results obtained from the Taichung Control Point reveal that, except for local rotation, there are high correlations for strain and shear with total deformation. In addition, the experiment shows that the robustness in the south region in Taichung is the weakest.

Robustness analysis is a natural merger of reliability analysis, and geometrical strength analysis using strain techniques. This analyzing technique provides a more complete and detailed description of the 3D network deformation in terms of the three independent measures represented by; robustness in scale, shape and local rotation. In this paper, the Maximum-Displacement-Vector Approach (MDVA) is presented to simplify the computing progress for evaluating these deformation measures. Each point in the network has a unique deformation vector for the three deformation measures. All of the three measures can be computed from the same vector, making MDVA easy and suitable for applying to the 3D case. To verify the relationship between the redundancies of the observations and the deformations, the deformation vector equation has been expanded. This study uses the Taichung Control Point Network as a test for applying the robustness analysis. The results obtained from the Taichung Control Point reveal that, except for local rotation, there are high correlations for strain and shear with total deformation. In addition, the experiment shows that the robustness in the south region in Taichung is the weakest.