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研究生： 曾韋鳴
Tseng, Wei-Ming
論文名稱： 利用類神經網路結合離散小波轉換進行樑與板之破損偵測
A Study of Crack Identification of A Beam and Plate by Artificial Neural Network Method and Discrete Wavelet Transform
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： 2010
畢業學年度： 98
語文別： 中文
論文頁數： 139
中文關鍵詞： 小波分析 、小波包 、倒傳遞 、有限元素
外文關鍵詞： Wavelet Analysis, Wavelet Packet, Back Propagation, Finite Element
相關次數： 點閱：144  下載：3 
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    • 類神經網路已被廣泛的運用於各種領域，如工程系統診斷與監控、數位影像處理分析、語音辨識、聲納與地震訊號分類以及商業金融管理等。這是因其能處理大量複雜的資訊，建立輸入與輸出間的對應關係，並進行學習與修正，從而得到一辨識系統。
    本研究藉由離散小波轉換與類神經網路理論，來找出帶有損傷之鋁合金懸臂樑與平板的破損位置與破損程度。在數值模擬上，本研究首先以有限元素模擬含有缺陷之懸臂樑與平板結構，藉由模態分析獲得結構物之模態振型，再以離散小波分解模態振型後，重構各層之高頻部份並取均方根值(RMS)計算獲得各層破損指標，以此作為類神經網路所需之訓練樣本，建立一套損傷識別系統。在實驗分析上，先以衝擊鎚給於懸臂樑結構一個外力衝擊，並以加速規量取結構物之振動訊號，隨後利用小波包轉換振動訊號得到實驗結構物的模態振型，最後將實驗所得之模態振型，經由離散小波分解與重構，並同樣地取RMS計算來求得實驗之破損指標。最後匯入已測試好的模擬類神經網路中，以期所建立的類神經網路的損傷識別系統，能找出懸臂樑之破損深度。

    Neural networks have been widely used in various fields, such as diagnosis and monitoring of industrial engineering system, digital image processing and analysis, speech recognition, sonar and seismic signal classification, and financial management. The method can process complex information and establish the mapping relationship between input and output by learning and revision. Finally, an identification system is acquired.
    The aim of this study is to find the depth of the damage of an aluminum bar and to detect the approximate length of the crack of a damaged plate by the discrete wavelet transform and the neural network method. In numerical analysis, the first mode shape of a damaged cantilever beam and plates are simulated by the finite element method. The obtained mode shapes of the damaged cantilever beam and plates are then transformed by the discrete wavelet transform. The damage index of the beam or plates can be obtained by reconstructed the high frequencies detail signals of each layer and used to be the neural networks training samples, and then the damage identification system for beams and plates can finally be established. In experiment analysis, several accelerometers are used to measure the vibration responses of the beam, and the first mode shapes of the beam is attained by using the wavelet packet node norm. Finally, the experimental damage index are obtained and used as inputs of the identification system to find the approximate depth of the damage of a cantilever beam. It is believed that the proposed crack identification system is feasible to identify the damage depths of cantilever beams.

    目錄 摘要.......................................................I Abstract ................................................II 誌謝.....................................................III 目錄.....................................................IV 表目錄..................................................VIII 圖目錄....................................................X 符號說明.................................................XIV 第一章 緒論................................................1 1.1 研究動機............................................1 1.2 文獻回顧............................................2 1.3 本文架構............................................6 第二章 振動與模態分析理論....................................7 2.1 前言................................................7 2.2 離散系統的自由振動....................................7 2.3 懸臂樑之振動分析....................................10 2.4 含損傷板之振動模態推導...............................13 2.5 實驗模態分析........................................17 2.5.1 頻率響應函數...........................18 2.5.2 振型分析...............................19 2.5.3 自然頻率分析...........................19 2.6 實驗模態分析流程..............................20 第三章 訊號分析及小波簡介.............................22 3.1 前言.........................................22 3.2 傅立葉轉換....................................22 3.3 短時傅立葉轉換................................25 3.4 小波轉換.....................................26 3.4.1 小波函數...............................27 3.4.2 Symlet（SymN）小波系...................30 3.4.3 連續小波轉換............................32 3.5 離散小波轉換..................................35 3.5.1 近似空間與細節空間.......................36 3.5.2 Mallat運算法...........................38 3.5.3 正交基底...............................40 3.6 小波包分析....................................41 3.6.1 小波包的構造............................42 3.6.2 小波包的元素............................43 3.6.3 小波包節點範數..........................44 3.7 二維離散小波轉換..............................45 3.8 傅立葉轉換與小波轉換之比較.................. ...47 第四章 類神經網路....................................49 4.1 類神經網簡介................................49 4.1.1 生物神經元模型.........................50 4.1.2 類神經元模型...........................52 4.2 類神經網路的架構..............................55 4.3 倒傳遞類神經網路..........................58 4.3.1 前饋傳遞過程...........................59 4.3.2 倒傳遞過程.............................61 4.3.3 倒傳遞網路演算法........................65 4.4 倒傳遞網路的參數..............................66 4.5 類神經網路的運行方式...........................68 第五章 數值模擬分析..................................70 5.1 前言........................................70 5.2 有限元素的劃分................................70 5.3 懸臂樑.......................................75 5.3.1 裂縫寬度10mm之懸臂樑....................75 5.3.2 裂縫寬度3mm之懸臂樑......................83 5.3.3 不同破損位置之懸臂樑.....................87 5.4 平板.........................................95 5.4.1 單破損深度之平板.........................95 5.4.2 單破損長度之平板.........................101 5.4.3 不同破損位置之平板.......................104 5.5 實驗誤差分析..................................112 第六章 實驗量測與結果.................................114 6.1 實驗流程.....................................114 6.2 訊號之取樣頻率................................115 6.3 實驗材料尺寸及振動訊號之量測....................117 6.4 實驗分析......................................120 6.4.1 離散小波包轉換...........................120 6.4.2 實驗模態振型分析.........................122 第七章 結論...........................................131 7.1 結論..........................................131 7.2 未來研究方向與建議..............................133 參考文獻..............................................134

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