RC構件之三維斷層掃描理論與數值驗證

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陳志賢(Chich-Shen Chen) 查詢紙本館藏

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土木工程學系

論文名稱

RC構件之三維斷層掃描理論與數值驗證
(Theory and Numerical Validation of the 3D Computational Tomography of Reinforced Concrete Components)

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摘要(中)

本論文回顧了基本的斷層掃瞄理論，選擇較適用於土木結構的級數法作為理論依據來進行模擬分析，來判斷出鋼筋混凝土內部的鋼筋以及孔隙之位置。
震波斷層掃瞄理論由兩個部分組成，分別為正算模式部分與反算模式部分。正算模式決定波的行經路徑，而反算模式部分則根據這些波徑算出物體內部的波速分佈情形。本論文使用正六面體格點方塊模型，並利用線性走時內差(Linear Traveltime Interpolation Method, LTI)法作為計算波行路徑的方法。在反算部份則選擇速度分布之聯立疊代重建(Simultaneous Iterative Reconstruction Technique, SIRT)法作為搭配，結合成完整的斷層掃描理論。
由於實體模型需要大量的網格來組成，以現階段個人電腦的計算速度而言需要太過龐大的計算時間，因此本文採用數值模擬的方式來進行研究。研究成果顯示，三維斷層掃描法可以成功計算出試體內部的波速分佈，以及利用鋼筋混凝土組成物(鋼筋、混凝土與孔隙)之波速皆有其固定範圍的概念，可以大幅縮短計算時間並提高顯像之解析度。

摘要(英)

In this paper, the series expansion method of computational tomography (CT) was selected to develop a nondestructive evaluation technique for reinforced concrete components. In general, the tomography analysis contains two different procedures. The first one is the forward modeling for a given wave propagation structure. The forward modeling uses the ray tracing technique in order to simulate the curved ray path through the medium. A 3D least traveltime construction method is developed for all the nodal points in the wave propagation structure to a given source. The second is the inversion for updating the wave propagation structure constructed previously. The ray tracing technique, linear traveltime interpolation (LTI) method, is selected to combine with simultaneous iterative reconstruction technique (SIRT) to develop a three dimensional computational tomography scheme for reinforced concrete (RC) components.
Numerical simulations verify that the accuracy and performance of this newly proposed 3D CT theory for RC components are acceptable. The convergent rate and image contrast of the CT calculation for RC component can be improved dramatically by taking the advantage that only three levels of wave speed, steel, concrete and void, are in a RC component. Once the calculated wave speed is close to a specific level, its value is enforced to set as the specific wave speed of the type of medium.

關鍵字(中)

★ 非破壞檢測
★ 斷層掃描
★ 線性走時內差法
★ 射線追蹤
★ 鋼筋混凝土

關鍵字(英)

★ ray tracing
★ travel time
★ reinforced concrete
★ tomography
★ NDT

論文目次

中文摘要 II
ABSTRACT IV
誌謝 V
表目錄 X
圖目錄 XI
第一章緒論 1
第二章文獻回顧與研究方法 4
2.1文獻回顧 4
2.2研究方法 9
2.3論文架構 10
第三章震波斷層掃描之原理方法 11
3.1震波斷層掃描基本原理 11
3.1.1 轉換法(Transform Method) 12
3.1.2 級數展開法(Series Expansion Method) 15
3.2震波斷層掃描於混凝土結構 16
3.3正算模式(FORWARD MODELING)的介紹 18
3.3.1 傳統的方法─Shooting method與Bending method 18
3.3.2 惠更斯原理法(Huygens’ principle method) 19
3.3.3費馬最短走時定理(Fermat’s principle) 20
3.3.4 正－反向法(Forward-backward method (Vidale’s approach)) 21
3.3.5 互易原理法(Reciprocity principle method) 22
3.3.6 最短路徑法(Shortest Path Method) 23
3.3.7 線性走時內差法(Linear Traveltime Interpolation method, LTI) 23
3.4 反算方法的介紹 24
3.4.1射線軌跡走時逆算法(Travel-time Inverse via Ray Tracing Method) 26
3.4.2 阻尼最小二乘法(Damped Least Squares Solution, DLS) 27
3.4.3 DLS Plus Averaging Smoother Solution 28
3.4.4 Convolutional Quelling Solution 28
3.4.5 正規化最小二乘法(Regularized Least Squares Solution, RLS) 29
3.4.6 Kaczmarz’s method 29
3.4.7 ART法與SIRT法 35
3.4.8 ART法與SIRT法求解非線性系統 38
第四章三維線性走時內差法之理論推導 40
4.1基本觀念 40
4.2 三維線性走時內差法之理論 41
4.2.1 XY平面之線性走時內差法之推導 41
4.2.2 YZ平面之線性走時內差法之推導 53
4.2.3 XZ平面之線性走時內差法之推導 60
4.3 牛頓-瑞福生法求解非線性聯立方程組 68
4.4 三維線性走時內差法之前算程序 73
4.5 三維線性走時內差法之回算程序 75
第五章程式驗證與數值模擬 77
5.1 正算模式驗證 77
5.1.1 前算程序驗證 77
5.1.2 回算程序驗證 78
5.2 正算模式算例 79
5.2.1模擬試體(一) 79
5.2.2模擬試體(二) 80
5.2.3模擬試體(三) 80
5.2.4模擬試體(四) 81
5.3 反算模式算例 81
5.3.1 反算算例(一) 82
5.3.2 反算算例(二) 82
5.4 斷層掃描法算例 83
5.4.1 算例(一)均質試體 83
5.4.2 算例(二)中央高波速區塊試體 84
5.4.3 算例(三)波速分佈複雜之算例 85
5.5 鋼筋混凝土的斷層掃描 86
第六章結論與建議 88
參考文獻 90

參考文獻

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2005-7-22

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