應用不變函數與虛擬觀測平差法於均質應變分析

Using Invariant Functions and Unified least-Squares Approach in a Homogeneous Strain Analysis

林湘玲(Shiang-Ling Lin)

指導教授 ： 韓仁毓

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02891

摘要

變形分析的主要工作在於透過點位坐標觀測量的變化，歸納出物體各點位的相對運動行為。然而各點位間坐標值變動的原因，除了受到真實變形的影響，亦有可能是受到因物體本身的剛體運動、或來自坐標參考框架變異所產生的被動運動等因素所造成，因此如何消除這些與之無關的位移訊號以獲取正確變形成果，是為變形監測工作的關鍵步驟之一。本文首先將透過數值模擬方式，探討在剛體及被動運動的影響下，利用不變函數法進行變形參數估計的適用性，接著將不變函數應用於實際的物體變形分析，考量物體外部特性資訊對應變成果之影響，建立適當的約制方程式，最後設計一套嚴謹的估計分析方法，以有效的解決由上述因素所造成的變形參數估計偏差問題，進而提高變形分析工作成果的可靠度。

關鍵字

變形分析 ； 剛體運動 ； 被動運動 ； 坐標框架變異 ； 不變函數

並列摘要

The main objective of deformation analysis is to determine relative motions between points through observing the variation of coordinates of these points. However, a rigid-body motion and a passive motion caused by reference frame variations may also result in coordinate changes. Therefore, a key issue of defoemation analysis is to find the correct deformation results by eliminating those unrelated displacement signals. Firstly, the invariant function approach was tested on its feasibilities for deformation analysis under the effects of rigid-body motion and passive motion by using numerical examples. After that, in order to apply invariant function on the deformation analysis of real objects, we constructed the suitable constraint equations by considering the effect of deformation parameter estimations of external information. Finally, we designed a rigorous method to reduce estimation biases for improving the quality and reliability of deformation analysis task.

並列關鍵字

Deformation Analysis ； Rigid-body Motion ； Passive Motion ； Reference Frame Variation ； Invariant Function

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