二維測邊網應變主參數靈敏度分析

Abstract

在地球物理與工程力學領域的變形分析工作中，是藉由測量工作所得到的點位坐標資料，透過應變分析(Strain Analysis)，以應變張量(Strain Tensor)來描述物體相對變形行為。而網形設計是所有測量工作的基礎，因此網形結構強度之良窳會直接影響後續測量工作與應變分析成果的品質。過去對於網形設計的相關研究，大多是針對網形偵測點位位移的能力，提出各種網形結構強度評估指標，較少探討網形結構對應變分析之影響。因此本研究主要目的是提出網形偵測應變能力之評估指標，作為網形設計與優化之參考。 研究中考量應變分析對網形設計的需求，以評估網形偵測點位位移能力的靈敏度分析方法為基礎，配合不變函數應變分析模型，以自由網平差決定觀測量權矩陣，經推導後提出網形偵測應變能力之評估指標¬-應變主參數靈敏度指標。同時透過數值模擬實驗測試不同應變分析模型、統計參數、未知參數初值、觀測量精度，以及網形結構對應變主參數靈敏度指標之影響。實驗成果顯示，本研究所建立的應變主參數靈敏度指標，可正確反映網形偵測應變之能力。 而在實例分析方面，本研究以台灣一等衛星控制網作為實例資料，進行二維應變主參數靈敏度分析。由分析結果發現，台灣沿海地區受地形因素限制，應變主參數靈敏度較低。若配合研究中所歸納的應變監測網優化設計原則，可對台灣西南部一等衛星控制網的網形結構進行調整，進而提升該控制網形偵測二維應變的能力。

A strain tensor analysis plays an essential role in geophysics and engineering applications since it provides a numerical measure on the relative deformation behavior of the object under investigation. The parameters in a strain tensor can be estimated by observing the positional coordinates of the deforming network at different epochs. Consequently, the quality of a strain analysis is highly dependent on the network configuration. Most of the previous studies regarding network design have focused themselves on point displacements rather than on network strains. In this study, a strain sensitivity index – the minimum detectable principal strain parameter has been developed based on the concept of the invariant function and statistical theory. From numerical tests, it has been proven that the proposed sensitivity index realistically reflects the capability of a network in monitoring potential strains, and thus can be used as a concrete measure for the optimization of a monitoring network. In real-case applications, the strain sensitivity analysis has been performed on the first-order satellite network in Taiwan. Results reveal that the coastal areas have a lower sensitivity in detecting surface strains due to a poor network configuration. On the other hand, it has also been illustrated that, by incorporating the network optimization guidelines developed in this study, the strain sensitivity index can be substantially improved in these areas.