應用連續柯西小波轉換於結構物之勁度與阻尼矩陣識別

Abstract

系統識別為一項重要之研究課題，可應用於結構系統的損傷診斷。一般藉由結構系統之振動反應，可推估其動態特性，識別得結構之自然振動頻率、阻尼比及振動模態。識別自然振動頻率有助於判斷結構之損傷程度，但難以準確判斷結構損傷的位置。為準確判斷結構的損傷位置，直接觀察其勁度的變化是最佳的方法。 本研究以連續柯西小波轉換配合最小平方差法，識別結構系統之勁度與阻尼矩陣，並且計算得結構之模態參數。先利用數值模擬資料進行識別分析，驗證此方法之正確性與可行性；並考慮在雜訊影響下，調整識別之參數設定以求最佳的識別結果。同時考慮勁度折減系統，探討此方法應用於結構損傷判斷的可行性。最後，分析具完整柱及切削柱八層樓鋼構之振動台試驗反應資料，驗證此方法在真實量測案例之可行性。

System identification, which can be applied to assess damages of structures, has been an important research theme for civil engineering in the last two decades. Dynamic characteristics of a structure, namely natural frequencies, damping ratios and mode shapes, are determined from its vibration responses. The decrease of stiffness in a structure can be possibly judged by comparing the natural frequencies of the structure at the current state with those at the state with no damage. However, it is difficult to locate the damages from the modal parameters. Comparisons of stiffness matrices of a structure at different states can be a good way to accurately locate the damages in the structure. This study identifies stiffness and damping matrices of a structure via continuous Cauchy wavelet transform (CCWT) with a least-squares technique. The validity of the proposed approach is first confirmed by processing the numerically simulated responses of seven-story shear buildings with different story stiffness under base excitation. This study also investigates the effects of noise and different Cauchy wavelets on the accuracy of the identified stiffness and damping matrices. The proposed method is also applied to process the dynamic responses of two eight-story steel frames, which are not shear buildings, in shaking table tests. The differences in the story stiffness among these frames are accurately reflected in the stiffness matrices that are obtained by the proposed approach.