八層樓鋼構架振動台試驗模態參數與勁度矩陣識別

本研究的主要目的為識別八層樓鋼構架於振動台試驗下之模態參數，並在未使用剪力構架假設的前提下，決定構架的勁度矩陣。試驗所使用的鋼構架，在勁度的配置上共有七種，彼此各不相同，包含一樓切削、一樓加勁或一、三樓加勁等配置。本研究應用Meyer小波之連續小波轉換配合ARX(Autoregressive with exogenous input model)模型，於八層樓鋼構架之振動台試驗反應資料進行完全量測與不完全量測識別。因Meyer小波具有類似帶通濾波器之特性，即使量測自由度小於結構之總自由度非常多，仍能準確地識別出模態參數。最後，利用識別之模態參數配合Yuen於2010年所提出之貝氏機率模型更新法，更新三種構架(無加勁、無加勁且一樓切削以及一、三樓對稱加勁)之勁度矩陣。同時，利用有限元素軟體ETABS建置鋼構架之模型，所得三種構架之勁度矩陣即作為模型更新之初始值，探討於不同帶寬及不同初始值假設下所得勁度矩陣的結果差異。

關鍵字

小波轉換；模態參數；系統識別；模型更新

並列摘要

The main purpose of the work is to identify the modal parameters of seven eight-story steel frames under shaking table tests and determine the stiffness matrices of some of these frames without the assumption of shear building. These frames are different with each other by having cut-off in the columns of the first story or bracing at the first or third story. The weakened or strengthened stories are located from the identified stiffness matrices. An autoregressive with exogenous input (ARX) model with the continuous Meyer wavelet transform is applied to process the acceleration responses of these frames with considering incomplete measurements. Since Meyer wavelets are similar to band-pass filters, the modal parameters are accurately identified in a mode-by-mode base even when the measured degrees of freedom are much less than the total degrees of freedom of a structure. A Bayesian model updating method is applied to determine the stiffness matrices of three of these seven frames by using their identified modal parameters. The stiffness matrices of the three frames obtained from ETABS, which is a commercial finite element package and popularly used in designing a real building, based on their design data are used as the initial guessed stiffness matrices in the model updating method. No particular assumption is made on the stiffness matrix to be identified, except for the symmetry assumption. The effects of the bandwidth of stiffness matrix and initial guessed stiffness matrix on the identification of the stiffness matrix are investigated.

並列關鍵字

wavelet transform ； modal parameters ； identification ； modal updating

參考文獻

Adewuyi, A.P. & Wu, Z. (2011), Vibration-based Damage Localization in Flexural

Google Scholar

Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements, Computer-Aided Civil and Infrastructure Engineering, 26(3), 154-172.