有別於傳統上使用快速傅立葉轉換（Fast Fourier Transform, FFT）進行頻率域分析，本文藉由希爾伯特-黃轉換（Hilbert-Huang Transform, HHT）之輔助，探討房屋結構模型受不同強度地震作用下，系統加速度頻率反應曲線之變化，並提出新的結構損傷指標，相當阻尼比之比值（RED），作為偵測結構安全與提供預警之參考。
本文區分二大主軸，第一部份應用SAP2000有限元素軟體建立房屋結構模型，進行數值模擬分析，藉以瞭解RED對於偵測結損傷之敏感度。第二部分再以國家地震中心提供之鋼結構標竿模型試驗數據（NCREE-99-002與NCREE-06-020）進行分析，探討RED對於真實結構損傷診斷之可行性。上述研究同時採用HHT與FFT作為分析工具，並比較結果之差異性。最後提出一快速損傷評估流程，作為鋼結構房屋建築健康診斷之參考。
研究成果顯示：
1、當桿件斷面勁度折減為原來之90%時，觀察HHT加速度頻譜反應曲線即能發現頻寬有增大現象，表示結構已經產生損傷，但相同結果卻無法由FFT頻譜得知。
2、由四跨門型構架之HHT頻譜分析結果得知，僅斷面勁度產生折減之桿件的阻尼比有所提高，其餘完整桿件之RED值則維持不變，顯示HHT頻譜對於偵測桿件損傷與否的敏感度甚高。
3、依具遲滯型勁度折減之構架分析結果顯示，當結構系統維持線彈性反應時，無論以FFT或HHT分析，顯著頻率位置皆無變化，阻尼比亦僅有極微小之改變，即RED近似於1。
4、而當結構系統進入反應非線性階段，觀察HHT頻譜可發現RED有隨PGA值提高呈現正向遞增之趨勢。但由FFT頻譜得知，須在地震規模相當大，即結構受損嚴重時，相當阻尼比才有明顯改變。
5、透過HHT頻譜得知，房屋結構模型最先發生桿件降伏處的樓層，其相當阻尼比增加幅度亦較其他樓層明顯，表示觀察RED之變化量能判斷結構產生降伏的樓層位置。
6、隨地震力持續提高，結構非線性反應愈趨顯著，由HHT頻譜可看出頂樓處之RED增大幅度遠大於其他樓層。因此，量取頂樓之加速度反應進行HHT分析便能瞭解結構物發生損害之時機。
7、由鋼結構數值模型及標竿模型之相當阻尼比與最大層間變位角關係曲線分析結果顯示，當系統之相當阻尼比<3%，即RED<1.5時，結構物屬於輕微損壞階段。而在1.5 RED 2.5之間，系統達到中度破壞。若結構之相當阻尼比超過5%，也就是RED>2.5，則建築物可能已經進入嚴重破壞階段。
8、本研究提出以HHT頻譜為計算基礎之鋼結構房屋建築損傷評估流程，具備簡單且有效的診斷模式，其頂樓加速度頻譜能即時反應結構體之損傷程度，若能進一步量取其他樓層與可能優先破壞位置之地震訊號，則更利於偵測出建築物構件局部損傷之位置與時機。

This study investigates the feasibility of detecting structural damage using the HHT method. A damage detection index, the ratio of equivalent damping ratio (RED) is proposed. The nonlinear SDOF and MDOF with various predominant frequency models are then constructed by using the SAP2000 program, while the adjusted PGA El Centro and Chi-Chi (TCU068) earthquakes are used as excitations. Next, the damage index using the Hilbert-Huang Transform (HHT) and the Fast Fourier Transform (FFT) methods are evaluated separately based on the acceleration responses to earthquakes. Based on an analysis of shaking table test data from benchmark models subjected to adjusted Kobe and El Centro earthquakes are also used to demonstrate the efficiency of damage index in the HHT spectra in detecting structural damage.
Results indicate that, when the response of the structure is in the elastic region, the RED value only slightly changes in both the HHT and the FFT spectra. Additionally, RED values estimated from the HHT spectra vs. the PGA values change incrementally when the structure response is nonlinear i.e., member yielding occurs, but not in the RED curve from the FFT spectra. Moreover, the RED value of the top floor changes more than those from the other floors. Furthermore, structural damage is detected only when using the acceleration response data from the top floor.
Therefore, the ratio of equivalent damping ratio, RED, estimated from the smoothed HHT spectra is an effective and sensitive damage index for detecting structural damage. Finally, an effective structural monitoring procedure is proposed to detect the structural damage when during earthquakes. Results of this study also demonstrate that the HHT is a powerful method in analyzing the nonlinear responses of steel structures to strong ground motions.

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