- 學位論文
以頻率切片演算法分析並分離橋梁模態訊號與識別其阻尼
Application of Frequency Slice Algorithm to The Mode Analysis of Bridges
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摘要
頻率切片演算法(Frequency slice algorithm, FSA)為一個新的時間─頻率的分析方法，結合了頻率切片小波轉換(frequency slice wavelet transform, FSWT)與新的隨機遞減技術(random decrement technique, RDT)概念。 首先利用FSWT將訊號在時間及頻率域上，同時呈現模態頻率的反應，並透過頻率投影(Frequency projector)及時間投影(Time projector)的概念及態動尺度法(dynamic scale method)，使相近的模態頻率(包含具有高度阻尼的模態頻率)分離並有效地將之還原，最後利用新的RDT概念進行阻尼比的估計。 本研究為利用FSA進行愛蘭橋鋼纜模態頻率之阻尼識別分析，透過FSWT與一固定尺度(scale)在時頻譜之3D與2D影像，同時將橋體與鋼纜模態頻率呈現，吾人可輕易地判定鋼纜模態頻率並可清楚地知道車輛行經該檢測段的時間與激發之橋體頻率，並藉由動態尺度法及頻率與時間投影圖，吾人便可對於感興趣的頻率(即鋼纜頻率)輕易地將之分離並有效的還原，最後利用新的RDT概念與自由衰減反應(free-decay responses)公式，識別與確認其阻尼(比)之精確性。
並列摘要
Frequency slice algorithm (FSA) is a new time-frequency analysis method, combining the frequency slice wavelet transform (FSWT) with an new idea of random decrement technique (RDT). First, use FSWT to demonstrate the signal in time and frequency domain and to find the modal frequency response. Through frequency projector, the time projector, and dynamic scale method, the signal with similar modal frequencies (including the modal frequencies with a high damping) can be separated and effectively reconstructed, and the damping ratio can be estimated by the new RDT method. In this field study, the FSA is applied for damping identification of Ai-lan Bridge cable. The 2D and 3D spectrogram with a fixed scale (scale) was obtained through FSWT. Not only the cable modal frequency can be easily determined but also can the modal response of the bridge deck when the vehicles passed through. By dynamic scale method and frequency and time projection images, I can effectively separate and reconstruct the response at the frequency of interest (ex: cable frequency). Finally, the new RDT method is used to obtain the damping and the accuracy of the damping ratio is confirmed by free decay response formula.
參考文獻
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