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研究生: 楊政穎
Cheng-Yin Yang
論文名稱: 鋼筋混凝土構件斷層掃描之顯像處理
A Study on the Image Process of Computational Tomography for Concrete Structure
指導教授: 王仲宇
Chung Yue Wang
口試委員:
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
畢業學年度: 91
語文別: 中文
論文頁數: 143
中文關鍵詞: 非破壞檢測斷層掃描線性內差走時法土木工程
外文關鍵詞: ray, nondestructive, tomography, concrete, seismic, traveltime
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  • 摘要
    斷層掃描(Tomography)是一種經由物體外部量測的資料,以進行物體內部顯像的技術,利用震波作為外部量測工具,並且以震波傳遞理論作為顯像技術的理論基礎,特稱為震波斷層掃描(Seismic Tomography)。斷層掃描發展至今在醫學診斷與地質探勘皆具良好成效,然而於土木工程的非破壞檢測上,由於鋼筋混凝土的高度非均質性造成波在其中傳遞行為複雜,並且在檢測缺陷或孔洞尺寸較小的情況下,尚未能發展出較實用的模式。因此本論文回顧了基本的斷層掃描理論,選擇較適用於土木結構的級數法作為理論依據,並嘗試利用應力波對一些土木基本構件做斷層掃描的檢測。
    本文所用的應力波斷層掃描理論是由兩部分組成,分別為正算模式部份與反算部份,利用正算模式決定波的行進路徑,而反算部份再根據這些路徑算出內部的波速分布。有鑑於直線的路徑並不能良好的模擬實際應力波在混凝土中傳遞的情形,因此本研究使用格點方塊模型(gridded cell model),並利用線性走時內差(LTI)法作為計算波行路徑的方法,這個方法對選擇最短路徑有最精確的結果。在反算部份則選擇速度分布之聯立疊代重建(SIRT)法作為搭配,以進行斷層掃描的分析。
    為求在大型非均質混凝土構件中獲得較清晰之顯像結果,本研究利用彈簧槍作為應力波發射源,並採用壓電材料作為觸發裝置。根據前人研究之經驗,本論文將初步顯像結果作了些許的修正,並對波速分布做部分修正,加強影像的對比改善顯像結果,可有效地將土木構件中鋼筋、孔洞、裂縫的位置及尺寸顯像出來。


    Abstract
    Tomography is an inner image technique which generates a cross sectional picture of an object by utilizing the object’s response to the nondestructive, probing energy of an external source. Seismic tomography makes use of sources that generate seismic waves which base on the theory of wave transmission. Nowadays the theories and techniques of tomography have been well developed and applied to a number of fields such as Geophysics and Medicine. However, this technique is not well applied in civil engineering. In this thesis, reviews of some basic theories and methods of seismic tomography were conducted first. Then, the series expansion method of tomography was selected to develop the nondestructive evaluation technique for structure components.
    In general, the tomography analysis contains two different procedures. The first one is the forward modeling for a given subsurface model. The second is the inversion for updating the subsurface model. At the early development stage of the tomography technology, a straight ray path was adopted. In the seismic tomography, however, it became clear that curved ray paths should be considered. Therefore, the linear traveltime interpolation (LTI) method, which can be applied to curved ray paths is selected to combine with SIRT inversion technique to develop a computational tomography (CT) scheme for concrete structure.
    In order to gain more clear image of large inhomogeneous object, BB gun is used to generate seismic wave, and a piezo-electric material is used as the trigger device for signal acquisition. An image processing technique is proposed to improve the vague images and make those pictures more clear. Experimental results show that computed images can help engineers to identify sizes and position of voids, reinforcement size inside a structure component quite well.

    目錄 中文摘要 Ⅰ 英文摘要 Ⅱ 致謝 Ⅲ 目錄 Ⅳ 圖目錄 Ⅶ 照片目錄 Ⅹ 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.3 研究方法及目標 5 1.4 本文架構 6 第二章 斷層掃描之原理方法 8 2.1 斷層掃描基本原理 8 2.1.1 轉換法(Transform Method) 9 2.1.2 級數展開法(Series Expansion Method) 11 2.2 震波斷層掃描於混凝土結構 14 2.3 正算模式的介紹 15 2.3.1 惠更斯定理法(Huygens’ principle method(Graph theory method)) 16 2.3.2 正-反向法(Forward-backward method (Vidale’s approach)) 17 2.3.3 互易原理法(Reciprocity principle method) 18 2.3.4 線性走時內插法(Linear Traveltime Interpolation method, LTI) 18 2.4 反算方法的介紹 19 2.4.1 射線軌跡走時逆算法(Travel-time Inverse via Ray Tracing Method) 20 2.4.2 阻尼最小二乘法(Damped Least Squares Solution, DLSS) 21 2.4.3 正規化最小二乘法(Regularized Least Squares Solution, RLSS) 21 2.4.4速度分布代數重建法(Algebraic Reconstruction Technique Method) 22 2.4.5速度分佈之聯立疊代重建法(Simultaneous Iterative Reconstruction Method) 25 第三章 線性走時內插法之理論推導 27 3.1 基本觀念 27 3.2 二維理論 27 3.2.1 二維線性走時內插法理論 27 3.2.2 前算程序(forward process) 30 3.2.3 回算程序(backward process) 32 3.3 三維理論 33 3.3.1 三維線性走時內插法理論 33 3.3.2 三維前算程序(3-D forward process) 39 3.3.3 三維回算程序(3-D backward process) 41 3.4線性走時內差法程式的流程與驗證 42 第四章 檢測方法與試體設計 45 4.1 檢測方法概述 45 4.2 試體配置 45 4.3 儀器設備 47 4.4 實驗檢測步驟 49 4.5 走時數據的取得 52 第五章 顯像結果與討論 54 5.1 前言 54 5.2 影像重建方法 55 5.2.1波速數值分配平均法 55 5.2.2波速範圍篩選重製法 56 5.3 顯像結果 57 5.3.1 波速分布初始值 57 5.3.2 試體(一) 58 5.3.3 試體(二) 60 5.3.4 試體(三) 62 5.4 顯像修正與討論 63 5.4.1 試體(一) 64 5.4.2 試體(二) 66 5.4.3 試體(三) 68 5.5 討論 70 第六章 結論與建議 72 參考文獻 74

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