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研究生: 楊正瑋
Yanf, Zheng-wei
論文名稱: 小波轉換應用於板架結構的損傷偵測
Damage Detection in Stiffened Plates by 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: 2008
畢業學年度: 96
語文別: 中文
論文頁數: 136
中文關鍵詞: 板架結構損傷偵測二維離散小波分析小波包
外文關鍵詞: wavelet packet, stiffened structure, damage detection, two-dimensional discrete wavelet analysis
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  • 近年來將小波分析方法應用於結構的損傷偵測是一個相當熱門的研究領域,但是其研究範圍多半侷限在樑、平板、軸承等簡單的結構上。然而應用在實際的工程問題上時,這些簡單的結構極少單獨存在。為了使破損偵測的研究能使用於實際的船舶結構上,本研究針對板架結構,探討使用小波分析方法偵測其損傷位置的可能性。
    本研究首先以有限元素模擬含有缺陷的板架結構,並以二維離散小波分析板架結構的模態振型以找出缺陷的位置,然後對四個不同的板架結構進行實驗。實驗時先以激振器給予板架結構ㄧ個衝擊,然後以加速規量測板架結構的振動訊號,接下來以小波包轉換從振動訊號中找出板架結構的模態振型,最後以二維離散小波分析找出裂縫的位置。有限元素模擬及實驗結果顯示本研究所提出之損傷偵測方法有良好的損傷識別能力,並且較以往的方法能大幅地減少所需的量測點。

    Wavelet analysis has been the useful tool to detect damage in structures during recent decades. However, almost all researches have focused on the damage identification in basic structures, such as beams, plates, and bearings. In practical application, the basic structures do not exist alone. Instead, they are usually accompanied with one another. Stiffened structures are commonly used in ship structures and are investigated in this study. The present investigation focuses on the estimation of damage location in damaged stiffened structures by wavelet analysis.
    In numerical analysis, the first mode shape of the damaged stiffened panels is simulated by finite element method, and the damage locations are detected by two-dimensional discrete wavelet analysis. In experimental analysis, four different damaged stiffened structures are considered. The experiment consists of four steps. Firstly, a shaker was used to make an impact on the damaged structure. Secondly, accelerometers were used to measure the vibration responses of the structure. In the third step, the first mode shape of the structure is obtained by using the wavelet packet. Finally, two-dimensional discrete wavelet analysis was applied to determine the location of cracks.
    The results of numerical analysis and experimental investigation reveal that the proposed method is applicable to detect single crack or multi-cracks of a stiffened structure. The experimental results also show that fewer measurement points are required by utilizing the proposed method in comparison to those presented in previous studies.

    摘要...................................................I Abstract ..............................................II 目錄...................................................III 表目錄.................................................VII 圖目錄.................................................VIII 符號說明...............................................XVI 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........................................ 5 第二章 振動與模態分析理論........................... 6 2.1前言............................................. 6 2.2離散系統的自由振動............................... 6 2.3含損傷板之振動模態推導........................... 9 2.4實驗模態分析..................................... 14 2.4.1頻率響應函數................................... 14 2.4.2振型分析....................................... 15 2.4.3自然頻率分析................................... 16 2.5實驗模態分析流程................................. 16 第三章 訊號分析及小波簡介........................... 18 3.1前言............................................. 18 3.2傅力葉轉換....................................... 18 3.3短時傅力葉轉換................................... 21 3.4小波轉換......................................... 22 3.4.1小波函數....................................... 23 3.4.2 Symlet(SymN)小波系.......................... 26 3.4.3連續小波轉換................................... 28 3.5離散小波轉換..................................... 31 3.5.1近似空間與細節空間............................. 32 3.5.2 Mallat運算法................................... 34 3.5.3正交基底....................................... 36 3.6小波包分析....................................... 37 3.6.1小波包的構造................................... 38 3.6.2小波包的元素................................... 39 3.6.3小波包節點範數................................. 40 3.7 二維離散小波轉換................................ 41 3.8傅力葉轉換與小波轉換之比較....................... 43 第四章 數值分析..................................... 45 4.1前言............................................. 45 4.2有限元素的劃分................................... 45 4.3單缺陷板架結構的有限元素分析..................... 48 4.3.1單缺陷板架結構整體模態振型分析................. 48 4.3.2單缺陷板架結構部分區域的模態振型分析........... 52 4.4模擬分析進行實驗時單缺陷板架結構所需要的量測點... 59 4.5模態振型取樣分析法............................... 65 4.6缺陷位置不同的單缺陷板架結構之有限元素分析....... 72 4.7不同情形之含缺陷板架結構的有限元素分析........... 78 4.7.1 case1異向雙裂縫之板架結構...................... 78 4.7.2 case2同向雙裂縫之板架結構...................... 84 4.7.3 case3單裂縫之複雜板架結構(1)................. 87 4.7.4 case4單裂縫之複雜板架結構(2)................. 90 4.8缺陷後之峰值產生的原因分析....................... 93 4.9 加強材對板架結構模態振型的影響.................. 98 第五章 實驗架構與訊號量測........................... 102 5.1實驗流程......................................... 102 5.2訊號之取樣頻率................................... 104 5.3實驗材料尺寸及振動訊號之量測..................... 105 第六章 實驗結果分析................................. 111 6.1前言............................................. 111 6.2自然頻率的量測................................... 111 6.3離散小波包轉換................................... 112 6.4 Case1異向雙裂縫板架結構......................... 114 6.5 Case2同向雙裂縫板架結構......................... 120 6.6 Case3單裂縫複雜板架結構(1).................... 123 6.7 Case4單裂縫複雜板架結構(2).................... 126 第七章 結論......................................... 129 7.1結論............................................. 129 7.2未來研究方向與建議............................... 131 參考文獻.............................................. 132

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