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研究生: 張力仁
Chang, Li-Jen
論文名稱: 基於有限元素模擬數據驅動之金屬板蘭姆波缺陷定位深度學習模型
Finite Element Simulation Data-Driven Deep Learning Model for Lamb Wave Defect Localization in Metallic Plates
指導教授: 梁育瑞
Liang, Yu-Jui
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 124
中文關鍵詞: 結構健康監測蘭姆波有限元素模擬物理知情神經網路缺陷定位
外文關鍵詞: Structural Health Monitoring, Lamb Wave, Finite Element Simulation, Physics-Informed Neural Network, Defect Localization
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  • 工程結構於服役期間易因環境與操作因素產生疲勞或損傷,結構健康監測(SHM)技術對確保結構安全至關重要。蘭姆波為板狀結構常用之主動式導波監測手段,然其固有之頻散與多模態特性,使傳統物理模型與淺層機器學習方法在特徵提取上面臨挑戰,且既有研究對頻散效應如何影響物理先驗特徵之設計仍缺乏探討。
    本研究以COMSOL Multiphysics建立鋁-6061薄板之壓電耦合有限元素模型,模擬蘭姆波殘差訊號並施以資料增強,建立無須真實損傷數據之訓練資料庫。據此提出三種結合物理先驗與1D-CNN之缺陷定位架構:模型A採用未修正頻散之TDoA先驗;模型B引入動態頻散補償機制修正到達時間;模型C則融合兩者。三模型皆以交叉注意力融合物理先驗與資料驅動特徵,並經多次五折交叉驗證與統計檢定比較。
    結果顯示,模型A訓練不穩定、誤差最高;模型B收斂穩定且精度顯著提升;模型C經集成預測後與模型B精度相當。本研究證實,物理先驗之「品質」較「數量」對模型性能更為關鍵,可為物理知情深度學習於結構健康監測之應用提供設計參考。

    Structural health monitoring (SHM) is essential for detecting fatigue damage in engineering structures. Lamb waves are widely used for active guided-wave monitoring of plates, but their dispersion and multimodal behavior challenge feature extraction, and how dispersion affects physics-informed prior design remains underexplored. This study builds a piezoelectrically coupled finite element model of an aluminum-6061 plate in COMSOL Multiphysics to simulate and augment Lamb wave residual signals without real damage data. Three 1D-CNN architectures fusing physics-based priors via cross-attention are proposed: Model A uses an uncorrected TDoA prior; Model B applies dynamic dispersion compensation; Model C fuses both. Compared via five-fold cross-validation, Model A is unstable with the largest error, Model B converges stably with significantly improved accuracy, and Model C matches Model B after ensemble prediction. This confirms prior quality outweighs quantity, guiding physics-informed deep learning design for SHM.

    摘要 i Abstract ii 致謝詞 vii 目錄 viii 圖目錄 xii 表目錄 xiv 第一章 緒論 1 1.1 研究背景與文獻回顧 1 1.1.1 結構健康監測與超音波導波技術 1 1.1.2 傳統物理模型與機器學習在SHM之挑戰 2 1.1.3 深度學習架構之演進與局限 4 1.1.4 1DCNN 之崛起與純模擬資料工作流程 5 1.2 研究動機與流程 7 第二章 方法論 10 2.1 蘭姆波傳播理論 10 2.1.1 彈性波動方程式 10 2.1.2 頻散與多模態特性 12 2.1.3 邊界散射與波形干涉 16 2.2 壓電效應與訊號收發 19 2.2.1 正逆壓電效應 19 2.2.2 主動式感測架構 20 2.3 訊號分析方法 22 2.3.1 短時傅立葉轉換 22 2.3.2 訊號包絡線提取 24 2.3.3 時間差定位法 26 2.4 深度學習理論基礎 28 2.4.1 前饋神經網路 28 2.4.2 損失函數與最佳化 29 2.4.3 反向傳播 31 2.4.4 物理感知神經網路 32 第三章 數值模型 34 3.1 模型幾何與材料參數 34 3.1.1 鋁板與壓電陣列幾何配置 34 3.1.2 缺陷幾何與空間採樣設計 37 3.1.3 材料參數定義 38 3.2 多物理場耦合與邊界條件 39 3.3 網格與時間步長分析 40 3.3.1 網格劃分 40 3.3.2 時間步長與CFL條件 45 3.4 數值模型物理保真度驗證 46 3.4.1 激發訊號設定 46 3.4.2 激發頻率保真度驗證 47 3.4.3 波模態到達時間驗證 49 3.5 訊號擷取與特徵分析 50 3.5.1 殘差訊號提取 50 3.5.2 數據結構化輸出 51 第四章 深度學習模型 54 4.1 資料庫建構與模型訓練設定 54 4.2 模型A:TDoA幾何先驗與空間注意力機制 57 4.3 模型B:波峰錨定與動態頻散補償 61 4.4 模型C:雙分支時空融合架構 67 第五章 結果與討論 70 5.1 評估指標與檢驗流程 70 5.1.1 定位誤差評估指標 70 5.1.2 訓練收斂特性與五折交叉驗證分析 71 5.1.3 資料增強抗噪飽和度探討 72 5.1.4 空間定位誤差分布圖分析 73 5.1.5 集成預測策略 73 5.1.6 統計顯著性檢定方法 74 5.2 模型A之效能評估 75 5.2.1 模型收斂性分析 75 5.2.2 資料增強飽和度分析 77 5.2.3 空間定位誤差分析 78 5.2.4 集成預測 80 5.3 模型B之效能評估 83 5.3.1 模型收斂性分析 83 5.3.2 資料增強飽和度分析 85 5.3.3 空間定位誤差分析 86 5.3.4 集成預測 87 5.4 模型C之效能評估 90 5.4.1 模型收斂性分析 90 5.4.2 資料增強飽和度分析 92 5.4.3 空間定位誤差分析 93 5.4.4 集成預測 94 5.5 誤差分佈與模型綜合表現探討 97 第六章 結論與未來展望 101 6.1 結論 101 6.2 未來展望 103 第七章 參考文獻 105

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