應用小波包轉換於結構物動態量測資料分析

Abstract

系統識別為結構動力分析之逆運算，可由量測之訊號反求得此結構系統之動態特性，這些特性包含有自然振動頻率，模態阻尼比等參數。倘若結構特性在受外力過程中發生改變，伴隨發生的是結構反應特徵之改變，此時必須揚棄傳統之非時變性參數識別法而尋求能夠彰顯出時變特徵之識別方法。 本研究主要針對結構系統之量測訊號，利用小波包分析配合結構系統之運動方程離散表示式識別出結構之動態特性。研究中除了利用小波包之特性對於地震訊號進行濾波，並進一步對於非線性反應之訊號進行識別分析以探討結構進入非線性之種種行為。並且藉由數值模擬與實例分析驗證此識別模式之可行性。

Wavelet transform has the capability of performing multiresolution analysis and representing the variation of frequency with time for a signal, while Fourier transform can only represent the signal in frequency domain. Wavelet transform has been applied to a variety of fields, especially for the fields related to signal processing or nonlinear problems. This work proposed a procedure of identifying the dynamic characteristics of a structure from its dynamic responses caused by earthquake, impulsive loading, or natural ambient excitations. The procedure uses the discrete transform of orthogonal wavelets to decompose the discretized equations of motion for a structure. First, we used the dynamic responses from a numerical simulation to verify the validity of the proposed procedure. Some parametric studies were also carried out to show the feasibility of the procedure. Finally we applied the method to real responses, such as seismic responses, free vibration responses or ambient vibration responses. The identified results were compared with the published results obtained by other methods.