利用結構物的振動資料進行損壞偵測(Vibration-based Damage Detection, VBDD)為損壞偵測其中一項重要的課題，不僅能偵測出損壞的發生且能偵測出損壞的位置並量化損壞的程度。本研究應用唯輸出(Output-only)的量測資料進行分析，並提出一套系統性的損壞評估架構，包含識別損壞位置與損壞程度的量化。本研究提出四種程度的損壞識別方法，首先，為了識別是否有損傷發生，使用(1)主子空間(Subspace)與零子空間(Null-space)損壞因子，(2)奇異譜分析法(Singular Spectrum Analysis, SSA)之奇異值差異，(3)互相關函數之振幅向量確信準則(Cross Correlation Function Amplitude Vector Assurance Criterion, CVAC)、(4)功率譜密度函數之振幅向量確信準則(Power Spectral Density Function Amplitude Vector Assurance Criterion, PSDAC)與(5)兩階段式AR-ARX模型偵測損壞。接著使用隨機子空間識別法(Stochastic Subspace Identification, SSI)觀察具有物理意義的系統參數的變化。為了找出損壞位置，使用(1)奇異譜分析法之重建訊號與原訊號之差異與(2)由小波封包轉換(Wavelet Packet Transform, WPT)之Novelty Index。最後為了量化損壞程度，(1)依據識別的模態參數配合Model Updating的技術與(2)使用正規化之勁度矩陣計算樓層間的勁度折減率(Stiffness Reduction Ratio)。除了使用從水工試驗廠進行的水工沖刷試驗與於國家地震中心進行的六層樓鋼構架切割鋼柱的振動台試驗記錄到的實驗資料外，於宜蘭牛鬥橋進行現地量測以驗證所提出的方法之適用性。最後討論使用方法之計算效率並探討進行即時損壞偵測的可行性。

One of the important issues to conduct the damage detection of a structure using vibration-based damage detection (VBDD) is not only to detect the damage but also to locate and quantify the damage. In this paper a systematic way of damage assessment, including identification of damage location and damage quantification, is proposed by using output-only measurement. Four level of damage identification algorithms are proposed. First, to identify the damage occurrence, (1) Subspace and Null-space damage index. (2) from Singular Spectrum Analysis (SSA) compute the eigenvalue difference ratio. (3) Cross Correlation Function Amplitude Vector Assurance Criterion (CVAC). (4) Power Spectral Density Function Amplitude Vector Assurance Criterion (PSDAC). (5) Two Stage AR-ARX are discussed for detecting the damage. Second, use Stochastic Subspace Identification (SSI) to detect the change of dynamic characteristics. Thirdly, to locate the damage, (1) from SSA we can compute the difference between original signal and reconstruct signal. (2) Novelty Index, defined as the Euclidean norm of the time-frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structure, is applied to locate the damage. Finally, to quantify the damage (1) combine modal parameters with the model updating technique. (2) from normalized stiffness matrix identify the inter-story stiffness reduction ratio. Experimental data collected except from the bridge foundation scouring in hydraulic lab and a series of shaking table test of a 6-story steel structure with the cut in column member, in situ structure like Niu-Dou Bridge are used to demonstrate the applicability of the proposed methods. The compotation efficiency of each method is also discussed so as to accommodate the online damage detection.

口試委員審定書 #
誌謝 i
摘要 ii
ABSTRACT iii
目錄 v
圖目錄 viii
表目錄 xi
第一章 導論.. 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究架構與內容 3
第二章 結構損壞評估方法 5
2.1 主子空間(Subspace-based)與零子空間(Null-space)損壞偵測 6
2.1.1 主子空間與零子空間定義 6
2.1.2 使用主子空間與零子空間進行損壞偵測 6
2.2 隨機子空間識別法 7
2.2.1 狀態空間模型 7
2.2.2 隨機過程之定義 11
2.2.3 量測資料重組 12
2.2.4 協方差型隨機子空間識別法 13
2.2.5 系統模態參數萃取 15
2.3 使用Novelty Analysis識別損壞位置 16
2.3.1 小波封包轉換(WPT) 17
2.3.2 時間狀態下瞬間相位與瞬時頻率 18
2.3.3 Novelty Index 18
2.4 奇異譜分析法 19
2.4.1 特徵值變化率 20
2.4.2 由反應訊號使用SSA計算誤差 20
2.5 互相關函數之振幅向量確信準則 21
2.6 功率譜密度函數之振幅向量確信準則 22
2.7 兩階段式 AR-ARX 損壞偵測方法 23
2.8 使用勁度折減率進行損壞量測 24
2.8.1 定義正規化勁度折減率 25
2.9 使用有限元素模型進行Model Updating 26
第三章 隨機子空間識別法敏感度分析 27
3.1 系統階數選擇與穩態圖之繪製 27
3.2 Reference-based SSI-COV 29
3.3 敏感度分析 30
第四章 結構損壞頻估方法之應用 32
4.1 六層樓鋼構架 32
4.1.1 實驗配置 32
4.1.2 Level I: 偵測整體結構是否有異常 32
4.1.3 Level II: 識別模態參數變化 33
4.1.4 Level III: 識別發生損壞的位置 33
4.1.5 Level IV: 量化損壞程度 34
4.2 水工沖刷試驗(實驗日期2011/1/26) 34
4.2.1 實驗配置 34
4.2.2 Level I: 偵測整體結構是否有異常 35
4.2.3 Level II: 識別系統參數的變化 36
4.2.4 Level III: 識別發生損壞的位置 37
4.2.5 Level IV: 量化損壞程度 37
4.3 水工沖刷試驗(實驗日期2011/3/29) 38
4.3.1 Level I: 偵測整體結構是否有異常 38
4.3.2 Level II: 識別系統參數變化 39
4.3.3 Level III: 識別損壞發生的位置 40
4.3.4 Level IV: 量化損壞的程度 40
4.4 牛鬥橋試驗 40
4.4.1 Level I: 偵測整體結構是否有異常 41
4.4.2 Level II: 識別模態參數變化 42
4.4.3 Level III: 識別發生損壞的位置 42
第五章 結論與未來展望 43
5.1 結論 43
5.2 未來展望 44
參考文獻 45

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