# 臺灣博碩士論文加值系統

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 本文主要是探討一種利用數位影像特性來獲得全場非線性應變資料的方法。數位影像關係法即所謂的DIC(Digital Image Correlation)是利用數位影像以數值來表示和記錄影像的特性，並對這些儲存影像的數值加以分析以得到所需的資訊。而在本文的領域中，藉著比對相關成對影像來得到全場應變和位移的分佈，在過程中所使用數值方法處理是主要的關鍵，除了在原始影像數值之間的平滑化和連續化處理之外，影像與影像的相關程度數值最佳化過程更是最重要的步驟。而在這最重要的步驟的處理上，本研究應用”選擇性地毯式”搜尋的觀念以收斂最後的結果，除此之外亦針對變數與目標函數的關係，設計數種數值方法以求解，再依此數值方法求得之結果，換算得到全場變形的各項參數。而最後將對已知材料性質的材料做測試中，將所有的數值方法得到的結果，與實際拉伸試驗機的結果加以比對，裨以建立一套方便有效準確性高的測量方法。
 This text presents a new numerical conception of digital image correlation to measure full-field strain in planar specimen which is suffering external force. This new method can afford strain information on entire field of specimen surface by processing two digital images which were respectively caught from the unforced and forced specimen. The new numerical procedures here aim at making this method a widely applicatory strain measuring method. It means that ideally this method can be applied in various conditions. Two numerical iterative methods are used to conclude the whole optimized strain solution in this research. Both two numerical methods can appropriately be called “selectively exhaustive optimization”.This is because each iterative method is an exhaustive optimization method with techniques of reducing time consumption. While all numerical procedures finished, the optimized strain solutions are verified and compared with the experimental results from MTS.
 中文摘要 …………………………………………………………… I英文摘要 …………………………………………………………… II誌謝 ……………………………………………………………. III目錄 …………………………………………………………… IV圖目錄 …………………………………………………………… VI第一章簡介……………………………………………………………..-1-1.1 前言……………………………………………………………. -1-1.2 DIC的特性及發展…………………………………………….. -1-1.3 DIC的潛力和優點………………………………………......... -3-1.4 研究動機及方向………………………………………………. -4-第二章理論基礎........………………………………..…………………-6-2.1 數位影像……………..………………………………………… -6-2.1.1 人類視覺…………………………………..…………………… -6-2.1.2 數位影像……………………………………………………….. -6-2.2 變形理論……………………………………………………….. -9-2.2.1 應變-位移(Strain-Displacement) 關係…………..……………. -9-2.2.2 應變和位移造成點的座標移動……………………………..… -13-2-3 標準化與交相關函數……………………………………….… -14-2.3.1 交相關函數………………………………………….………… -14-2.4 DIC運用在變形的量測……………………………………….. -15-2.4.1 基本構想……………………………………………………….. -15-　2.4.2 基本假設……………………………………………………….. -16-2.5 離散影像的平滑化…………………………………………….. -18-2.5.1 不連續影像的平滑化…………………...................................... -18-2.5.2 灰度內插……………………………………………………….. -20-第三章研究步驟及方法………………………………………………..-22-3.1 使用儀器……………………………………....………………. -23-3.2 試片取樣…….………………………………………………… -23-3.2.1 拉伸實驗流程及步驟….………………………………………. -23-3.2.1 剛體旋轉實驗流程及步驟…………………………………..… -25-3.3 數位影像在DIC上的前處理………………………………… -26-3.3.1 RGB數位影像的轉灰階過程………………………………… -26-3.3.2 維度轉換….……………………………………………………. -27-3.3.3 位移基準線(shift)……………………………………………… -27-3.4 DIC觀念於程式演繹………………………………………...... -29-3.4.1 程式的基本要求與大綱…………………………………….… -29-3.4.2 欲比對之成對陣列選定…………………………………….… -30-3.4.3 依照應變參數指定與原圖上CZ比對的CZ`…………….…… -31-3.4.4 以交互關聯函式(cross-corelation Function)判斷影像的相依性……………………………………………………………….-33-3.5 選擇性地毯式逼近法最佳化………………………………….. -34-3.5.1 地毯式搜索…………………………………………………….. -34-3.5.2 數值最佳化的過程-Iterative的過程(一)……………………… -34-3.5.3 數值最佳化的過程-回溯疊代的過程(二)…………………….. -38-3.5.4 保障條款……………………………………………………….. -39-第四章驗證與結果討論………………………………………………..-42-4.1 基本性質分析………………………………………………….. -42-4.1.1 交相關函數與變數的關係…………………………………….. -42-4.2 耗費計算時間分析…………………………………………….. -45-4.3 方法(一)的結果………………………………………………... -46-4.3.1 əV/ əy的檢驗………………………………………………….. -46-4.3.2 其餘變數之結果……………………………………………….. -46-4.3.3 法(一)剛體旋轉運動試片結果………………………………... -49-4.3.4 cz_size對結果造成的影響……………………………………. -50-4.4 方法(二)的結果………………………………………………... -51-4.4.1 數值求解的依據驗證過程中解的變化……………………….. -51-4.4.2 第二種方法過程中最佳解的統計…………………………….. -54-4.4.3 二種方法的比較……………………………………………….. -56-第五章結論…………………………………………………………….-59- 參考文獻……………………………………………………….. -60-
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 1 基因演算法應用於數位影像關係法及薄膜變形量測 2 發展數位影像相關三維位移量測系統 3 數位影像關係法於應變量測之參數探討與薄膜變形量測 4 數位影像關係法於高應變區域之探討 5 應用數位影像相關技術於平面位移量測 6 金屬箔片方杯微深引伸成形極限與破裂之研究 7 飛安構面與構件裂縫成長之模擬研究 8 不同角度光源對數位影像相關法量測影響之研究 9 數位影像相關法則於二維靜態位移量測之研究 10 非接觸式數位影像測量應用—以鞋子尺寸為例 11 藉由數位影像分析量測軟性基板彎曲應變

 1 1. 蔡雅芝，「淺談光子晶體」，物理雙月刊，廿一卷四期，p445。

 1 數位影像關係法於高應變區域之探討 2 數位影像關係法於應變量測之參數探討與薄膜變形量測 3 應用數位影像關係法於微試件變形之量測 4 基因演算法應用於數位影像關係法及薄膜變形量測 5 應用數位影像關係法於高應變區域探討與微試件變形量測 6 藉由數位影像分析量測軟性基板彎曲應變 7 數位影像關係法結合有限元素法之應變量測 8 三維數位影像相關法之新校正程序 9 數位影像相關法於三維變形量測之新應用 10 應用奈米粒子於微試件進行數位影像相關變形量測 11 結構變位與局部應變場之數位影像量測與分析 12 數位影像量測於結構實驗之應用 13 二階段式數位影像關 14 應用影像相關性量測變位 15 應用數位影像相關技術於平面位移量測

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