在非破壞檢測技術中，導波具有長距離傳遞且不易衰減的特性，能快速且大範圍的針對管線進行整體性的檢查，然而多模態及頻散現象，往往造成檢測上缺陷訊號辨識的難度。而運用於輸送各種流體的管線在煉油、石化工廠、發電廠及燃氣工業中為一相當普及的設備，也因為廠區的管路規劃及空間限制，勢必會使用彎管來連結直管，此一複雜之管線特徵將會造成訊號辨識的困難，且波傳能量亦會因為彎管之特殊的幾何造型使得傳遞路徑改變，呈現波傳能量往外側聚集的現象，此時彎管其他部份則易因波傳能量太小而形成檢測盲區。為了降低在訊號判讀上失誤的可能性，本研究利用有限元素法探討 T(0,1)扭矩導波經過彎管上缺陷之波傳行為，並針對缺陷回波訊號進行分析與後處理，提出以時間反轉法（Time Reversal Method）作為訊號解析方法，比較使用時間反轉法前後缺陷訊號之差異，評估時間反轉法之聚焦特性於彎管管線之可行性，同時也觀察管線上同時存在多個缺陷時對於聚焦結果的影響。而時間反轉法是一項自聚焦技術，能有效地形成空間上和時間上的聚焦。
由本研究結果可見，將時間反轉法應用於導波缺陷檢測上，對於訊雜比的改善是有助益的，如缺陷位於彎管末端時，藉由未使用與使用時間反轉法之缺陷回波振幅的比較，結果顯示在利用時間反轉法後，其缺陷回波振幅比無使用時間反轉法時有明顯的提升。此現象除了改善訊雜比使缺陷更容易辨識之餘，更說明波傳能量不會受到特殊幾何造型的彎管影響，不再任意聚焦至其他位置而能確實聚焦於缺陷位置處。針對多個缺陷對於聚焦能力的影響結果，如模擬中同時存有三個缺陷時之彎管管線，利用有限元素法模擬證實其聚焦能力並不會因為波傳能量行經多個缺陷而使聚焦偏離，即波傳能量行經其他缺陷及彎管區域並不會影響其聚焦特性。本研究亦藉由分析彎管上不同位置之缺陷分佈繪製出聚焦方位圖，其直觀的顯示反轉後之能量能精確聚焦於彎管上各缺陷的位置。

Among the non-destructive testing techniques, guided waves has the characteristics of propagating long distance and being hard to attenuate, and it can also detect quickly and widely for the entire pipelines. However, identifying the signals of defects during the test is frequently difficult as a result of its multimodal and dispersive characteristics. Pipelines system is widespread use in petrochemical industry to transport gas or fluid. In virtue of restriction of space and pipelines planning, elbow parts will certainly provide to connect pipes, and this kind of complex pipe feature will bring about not only difficult to recognize signals but change direction of wave energy, that is, the energy will gather together outside of the elbow because of its geometry, then rest of the elbow will be blind area for the testing. In order to reduce error probability on recognizing signals, this study applied finite element method to simulate the propagation of T(0,1) torsional guided wave through the defect on the elbow, proposing time reversal method to analyze in accordance with defects signals, comparing difference of defect echo with and without this method so as to evaluate the feasibility of focusing ability of time reversal method on the elbow and also observing the influence of multiple defects exist in pipes on the focusing results. Time reversal method, a self-focusing technique, it can effectively focus on the spatial and temporal domain.
The study results showed that it is beneficial to apply time reversal method to the improvement of signal-to-noise ratio on defect inspection for guided wave system. For instance, if defect exists at the end of elbow, and by comparing with defect reflective amplitude without and with time reversal method, it is clearly to show that the defect reflective amplitude with time reversal method is enhanced compared with that of without time reversal method. In addition to improving the signal-to-noise ratio and making defect easier to identify, it also showed that the wave energy will not be affected by the elbow, and can focus to the defect instead. Besides, when multiple defects exist in pipes, it will not make focusing behavior off the work either. For example, when there are three defects on the elbow pipeline, by using finite element method, the results showed that the focusing ability of wave energy will not be influenced even if it transmit through multiple defects on the pipe of straight part in advance, and can focus to the defect on the elbow part. The thesis also bring up the focusing oriented illustration which can easily to display the wave energy with time reversal method focus on elbow defects direction.

誌謝 i
中文摘要 ii
英文摘要 iii
目錄 v
圖目錄 vii
表目錄 xi
第一章 緒論 1
1.1前言 1
1.2研究動機與目的 3
1.3文獻回顧 4
1.4研究方法 7
1.5論文結構 8
第二章 導波法基本理論 12
2.1導波基本理論與分析 12
2.1.1導波於圓管之波動方程式 12
2.1.2頻散曲線 14
2.1.3波形結構 16
2.2時間反轉法 17
2.3有限元素法 19
第三章 模擬設定與分析 28
3.1有限元素法導波波傳模擬 28
3.1.1模型設定與網格劃分 29
3.1.2圓管導波激發與施加負載情形 30
3.1.3訊號擷取 31
3.2應用時間反轉法於圓管導波之有限元素模型 32
3.2.1模型建立及缺陷設置 32
3.2.2應用時間反轉法於圓管導波 33
3.3應用時間反轉法聚焦扭矩導波於彎管上缺陷處 34
3.3.1聚焦扭矩導波於彎管上缺陷 34
3.3.1.1彎管0°~15°之缺陷聚焦模擬結果 35
3.3.1.2彎管15°~30°之缺陷聚焦模擬結果 36
3.3.1.3彎管30°~45°之缺陷聚焦模擬結果 37
3.3.1.4彎管45°~60°之缺陷聚焦模擬結果 38
3.3.1.5彎管60°~75°之缺陷聚焦模擬結果 39
3.3.1.6彎管75°~90°之缺陷聚焦模擬結果 40
3.3.2缺陷數量對於聚焦能力之影響 42
第四章 結論與未來展望 106
4.1結論 106
4.2未來展望 107
參考文獻 108
附錄A 114

圖目錄
圖1.1 傳統的接觸式超音波檢測示意圖與實際操作圖 10
圖1.2 利用傳統超音波進行多點檢測 10
圖1.3 圓管導波檢測示意圖 11
圖1.4 彎管管線外側聚焦分析圖 11
圖2.1 無限長圓管其圓柱座標軸 21
圖2.2 圓管上縱向模態波傳模式 21
圖2.3 圓管上扭矩模態波傳模式 21
圖2.4 圓管上撓曲模態波傳模式 22
圖2.5 圓周向皆數與模態表示法，當 n=0時，為軸向對稱形式；當n=1時，沿著周向其質點位移有一個週期之相位變化，為非軸向對稱形式 22
圖2.6 以頻率為橫軸表示之頻散曲線圖。(a)相位速度頻散曲線；(b)群波速度頻散曲線 23
圖2.7 於6吋管中L(0,1)模態傳遞50公分之訊號，(a) 100 kHz、5 Cycles之波傳訊號；(b) 200 kHz、5 Cycles之波傳訊號 24
圖2.8 以頻厚積為橫軸表示之頻散曲線圖。(a)相位速度頻散曲線；(b)群波速度頻散曲線 25
圖2.9 導波模態波形結構圖 26
圖2.10 含缺陷之圓管示意圖 27
圖2.11 時間反轉法示意圖 27
圖3.1 ANSYS 14.0針對線彈性六面體元素Solid 45之說明 52
圖3.2 六英吋管線之90°彎管尺寸設定圖 52
圖3.3 模擬彎管管線之模型 52
圖3.4 管線模型網格分割示意圖 53
圖3.5 圓管上激振訊號源施加之位移負載示意圖 54
圖3.6 30 kHz作為單頻調制之基底訊號時，在5個週期數下所加權後的訊號及其頻域圖 54
圖3.7 扭矩導波波傳動態圖。(a)到達彎管前(b)到達彎管及(c)到達彎管後 55
圖3.8 入射波與缺陷回波時域訊號圖 56
圖3.9 彎管軸向分段位置示意圖 56
圖3.10 彎管圓周分段示意圖 57
圖3.11 兩缺陷於管線位置示意圖 57
圖3.12 三缺陷於管線位置示意圖 58
圖3.13 擷取缺陷訊號示意圖 58
圖3.14 時間反轉法之節點缺陷訊號與再激振訊號。(a) A1訊號 (b) A2訊號 59
圖3.15 Array Parameter設定示意圖 59
圖3.16 Table Parameter設定示意圖 60
圖3.17 圓管上再激振訊號源施加位移負載於節點示意圖 60
圖3.18 運用時間反轉法於圓管導波流程圖 61
圖3.19 彎管0°~15°缺陷時域訊號圖 62
圖3.20 缺陷於彎管0°~15°波傳動態聚焦圖 62
圖3.21 彎管0°~15°不同通道位置之反轉前後缺陷反射係數值 63
圖3.22 彎管0°~15°不同通道位置之反轉前後缺陷聲壓降幅值 63
圖3.23 彎管0°~15°通道1至通道4入射波能量及聚焦圖 64
圖3.24 彎管0°~15°通道5至通道8入射波能量及聚焦圖 65
圖3.25 彎管0°~15°通道9至通道12入射波能量及聚焦圖 66
圖3.26 彎管0°~15°通道13至通道16入射波能量及聚焦圖 67
圖3.27 彎管15°~30°缺陷時域訊號圖 68
圖3.28 缺陷於彎管15°~30°波傳動態聚焦圖 68
圖3.29 彎管15°~30°不同通道位置之反轉前後缺陷反射係數值 69
圖3.30 彎管15°~30°不同通道位置之反轉前後缺陷聲壓降幅值 69
圖3.31 彎管15°~30°通道1至通道4入射波能量及聚焦圖 70
圖3.32 彎管15°~30°通道5至通道8入射波能量及聚焦圖 71
圖3.33 彎管15°~30°通道9至通道12入射波能量及聚焦圖 72
圖3.34 彎管15°~30°通道13至通道16入射波能量及聚焦圖 73
圖3.35 彎管30°~45°缺陷時域訊號圖 74
圖3.36 缺陷於彎管30°~45°波傳動態聚焦圖 74
圖3.37 彎管30°~45°不同通道位置之反轉前後缺陷反射係數值 75
圖3.38 彎管30°~45°不同通道位置之反轉前後缺陷聲壓降幅值 75
圖3.39 彎管30°~45°通道1至通道4入射波能量及聚焦圖 76
圖3.40 彎管30°~45°通道5至通道8入射波能量及聚焦圖 77
圖3.41 彎管30°~45°通道9至通道12入射波能量及聚焦圖 78
圖3.42 彎管30°~45°通道13至通道16入射波能量及聚焦圖 79
圖3.43 彎管45°~60°缺陷時域訊號圖 80
圖3.44 缺陷於彎管45°~60°波傳動態聚焦圖 80
圖3.45 彎管45°~60°不同通道位置之反轉前後缺陷反射係數值 81
圖3.46 彎管45°~60°不同通道位置之反轉前後缺陷聲壓降幅值 81
圖3.47 彎管45°~60°不同通道位置之修正反轉後缺陷反射係數值 82
圖3.48 彎管45°~60°不同通道位置之修正反轉後缺陷聲壓降幅值 82
圖3.49 彎管45°~60°通道1至通道4入射波能量及聚焦圖 83
圖3.50 彎管45°~60°通道5至通道8入射波能量及聚焦圖 84
圖3.51 彎管45°~60°通道9至通道12入射波能量及聚焦圖 85
圖3.52 彎管45°~60°通道13至通道16入射波能量及聚焦圖 86
圖3.53 彎管60°~75°缺陷時域訊號圖 87
圖3.54 缺陷於彎管60°~75°波傳動態聚焦圖 87
圖3.55 彎管60°~75°不同通道位置之反轉前後缺陷反射係數值 88
圖3.56 彎管60°~75°不同通道位置之修正反轉後缺陷反射係數值 88
圖3.57 彎管60°~75°不同通道位置之反轉前後缺陷聲壓降幅值 89
圖3.58 彎管60°~75°不同通道位置之修正反轉後缺陷聲壓降幅值 89
圖3.59 彎管60°~75°通道1至通道4入射波能量及聚焦圖 90
圖3.60 彎管60°~75°通道5至通道8入射波能量及聚焦圖 91
圖3.61 彎管60°~75°通道9至通道12入射波能量及聚焦圖 92
圖3.62 彎管60°~75°通道13至通道16入射波能量及聚焦圖 93
圖3.63 彎管75°~90°缺陷時域訊號圖 94
圖3.64 缺陷於彎管75°~90°波傳動態聚焦圖 94
圖3.65 彎管75°~90°不同通道位置之反轉前後缺陷反射係數值 95
圖3.66 彎管75°~90°不同通道位置之修正反轉後缺陷反射係數值 95
圖3.67 彎管75°~90°不同通道位置之反轉前後缺陷聲壓降幅值 96
圖3.68 彎管75°~90°不同通道位置之修正反轉後缺陷聲壓降幅值 96
圖3.69 彎管75°~90°通道1至通道4入射波能量及聚焦圖 97
圖3.70 彎管75°~90°通道5至通道8入射波能量及聚焦圖 98
圖3.71 彎管75°~90°通道9至通道12入射波能量及聚焦圖 99
圖3.72 彎管75°~90°通道13至通道16入射波能量及聚焦圖 100
圖3.73 不同缺陷尺寸於彎管15°~30°通道4入射波振幅 101
圖3.74 兩缺陷案例一之時域訊號圖 102
圖3.75 兩缺陷案例一之波傳動態圖 102
圖3.76 兩缺陷案例二之時域訊號圖 103
圖3.77 兩缺陷案例二之波傳動態圖 103
圖3.78 三缺陷案例一之時域訊號圖 104
圖3.79 三缺陷案例一之波傳動態圖 104
圖3.80 三缺陷案例二之時域訊號圖 105
圖3.81 三缺陷案例二之波傳動態圖 105



















表目錄
表3.1 有限元素法模型材料性質 45
表3.2 90°彎管尺寸規格表– ANSI B16.9 45
表3.3 缺陷形式 46
表3.4 彎管0°~15°缺陷反射係數 46
表3.5 彎管15°~30°缺陷反射係數 47
表3.6 彎管30°~45°缺陷反射係數 48
表3.7 彎管45°~60°缺陷反射係數 49
表3.8 彎管60°~75°缺陷反射係數 50
表3.9 彎管75°~90°缺陷反射係數 51

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