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研究生: 顏奕豪
Yen, Yi-Hao
論文名稱: 應用二維離散小波轉換及類神經網路於多裂縫平板之損傷偵測
Damage Detection of a Plate with Multiple Cracks by two-Dimensional Discrete Wavelet Transforms and Artificial Neural Network
指導教授: 楊澤民
Yang, Joe-Ming
學位類別: 碩士
Master
系所名稱: 工學院 - 系統及船舶機電工程學系
Department of Systems and Naval Mechatronic Engineering
論文出版年: 2013
畢業學年度: 101
語文別: 中文
論文頁數: 143
中文關鍵詞: 二維離散小波轉換類神經網路損傷指標平板裂縫
外文關鍵詞: two-dimensional discrete wavelet transform, artificial neural network, damage index, plate, crack
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  • 結構物的損傷在工程上一直是個很重視的課題,若能及時的檢測出來,則可以預防許多災難的發生。近年來,小波轉換被廣泛應用於各個方面,如影像壓縮、雜訊去除、邊緣偵測、通訊等,本研究將利用二維離散小波轉換於偵測平板的裂縫位置。而類神經網路可以快速處理大量的資訊,建立輸入與輸出間的相對關係,並且不斷的學習、修正,因此本文將以類神經網路配合二維離散小波轉換來判別裂縫的損傷程度。
      在數值模擬上,先探討雙裂縫平板的損傷指標趨勢與裂縫位置及長度變化的關係,之後嘗試改變損傷指標的選取範圍,並改以單裂縫平板之損傷指標做為類神經網路的訓練樣本,來判別多裂縫平板上各單一裂縫的破損程度,建立一個可以適用於多裂縫平板的偵測方法。實驗部分,會將實驗量測無裂縫平板與模擬無裂縫平板間的模態差異,來修正含裂縫平板之模態振型,讓實驗更貼近模擬的情況,探討此方法對於損傷程度判別誤差的影響。

    Structural damage has been a very important issue in engineering. If damage can be detected in a timely manner, many disasters can be prevented. In recent years, wavelet transform methods have been widely used in various domains, such as image compression, noise removal, edge detection, communication, etc.This study will use the two-dimensional discrete wavelet transform method to detect the position of cracks in plate. Running data through the artificial neural network allows for large computations to be calculated at rapid speeds, and relationships between input and output are quickly achieved. The network will continuously learn and make corrections. The artificial neural network along with the two-dimensional discrete wavelet transform method is used to identify the degree of damage in this study.
    During the analytical simulation, several plates with cracks are analyzed and damage indexes are assigned to represent the length and the distance between the two cracks. After which, we narrowed our selection area to a single crack on the board to obtain new damage indexes. These new damage indexes, which is the training sample is then inputted into the artificial neural network. We are then able to take the damage indexes from other plate samples to be analyzed with-in the artificial neural network to obtain the length of the crack. As a result we were able to devise a method for analyzing cracks on a plate efficiently and systematically. Lastly, in order to narrow the gap between the simulations and the actual experiments, we eliminated the mode shapes’ difference between simulations and experiments, with the intention to obtain more precise results from the artificial neural network.

    摘要 I Abstract II 誌謝 III 目錄 IV 表目錄 IX 圖目錄 XII 符號說明 XVII 第一章 緒論 1 1.1 研究目的 1 1.2 文獻回顧 2 1.3 本文架構 8 第二章 振動與模態分析理論 9 2.1 前言 9 2.2 離散系統的自由振動 9 2.3 含損傷平板之振動模態推導 12 2.4 平板之振動分析 17 2.5 實驗模態分析 20 2.5.1頻率響應函數 20 2.5.2 振型分析 21 2.5.3 自然頻率分析 22 2.6 振動問題解析程序 23 第三章 訊號分析及小波簡介 24 3.1 前言 24 3.2 傅立葉轉換(Fourier Transform) 24 3.3 短時傅立葉轉換(STFT) 27 3.4 小波轉換 28 3.4.1 小波函數 29 3.4.2 Symlet (SymN)小波系 32 3.4.3 連續小波轉換 34 3.5 離散小波轉換 36 3.5.1 近似空間與細節空間 38 3.5.2 Mallat運算法 39 3.5.3 正交基底 42 3.6 小波包分析 43 3.6.1 小波包的構造 44 3.6.2 小波包節點範數 45 3.7 二維離散小波轉換 46 3.8 傅立葉轉換與小波轉換之比較 47 第四章 類神經網路 50 4.1 類神經網路簡介 50 4.1.1 生物神經元模型 51 4.1.2 類神經元模型 52 4.1.3 轉移函數 54 4.2 類神經網路架構 56 4.3 倒傳遞類神經網路 59 4.3.1 前饋傳遞過程 60 4.3.2 倒傳遞過程 62 4.3.3 倒傳遞網路演算法 66 4.3.4 LM (Levenberg-Marquardt)演算法 67 4.4 倒傳遞網路的參數 69 4.5 類神經網路運作流程 71 第五章 數值分析 73 5.1 前言 73 5.2 ANSYS模擬 73 5.3 模擬雙裂縫平板 75 5.3.1 雙裂縫平板caseA之損傷指標趨勢 76 5.3.2 雙裂縫平板caseB之損傷指標趨勢 80 5.3.3 雙裂縫平板caseC之損傷指標趨勢 83 5.3.4 雙裂縫平板caseD之損傷指標趨勢 86 5.4 改變損傷指標的選取範圍 89 5.4.1 雙裂縫平板caseI之類神經網路偵測 94 5.4.2雙裂縫平板caseII之類神經網路偵測 96 5.4.3雙裂縫平板caseIII之類神經網路偵測 98 5.5 模擬實驗case 101 5.5.1 Ecase1─雙裂縫平板 101 5.5.2 Ecase2─雙裂縫平板(裂縫寬度2mm) 106 5.5.3 Ecase3─三裂縫平板 110 5.5.4 Ecase4─單裂縫深度平板 114 第六章 實驗量測與結果 118 6.1 實驗流程 118 6.2 訊號取樣頻率 120 6.3 平板材料尺寸與實驗量測區 121 6.4 小波包轉換與實驗模態振型 122 6.5 實驗case 124 6.5.1 Ecase1─雙裂縫平板實驗結果 124 6.5.2 Ecase2─雙裂縫平板實驗結果 127 6.5.3 Ecase3─三裂縫平板實驗結果 130 6.5.4 Ecase4─單裂縫深度平板實驗結果 133 第七章 結論 136 7.1 結論 136 7.2 未來展望 137 參考文獻 138

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