應用貝氏機率法及模態域法於建築物健康診斷

Abstract

利用動態量測資料更新結構系統之勁度矩陣或阻尼矩陣，可作為修正原設計分析之有限元素模型或進行結構健康診斷。本研究旨在時間域與模態域提出新的目標函數及限制條件，提升用基因演算法配合梯度法的求解最佳解之效率。 本研究時間域之分析程序為修正Sun and Betti(2015)所提者；利用貝氏機率法建構新的目標函數，並以識別之模態參數作為限制條件，以減少用Runge-Kutta 解運動方程之次數，提升求解效率。在模態域的分析方法，本研究利用識別頻率及模態振形建立一不需配對模態參數之目標函數，過程中不需求解特徵值問題。 本研究所提分析流程，且先用一七層樓剪力構架受地震之數值模擬進行驗證 ，其中探討雜訊、勁度矩陣或阻尼矩陣帶寬、量測自由度數及阻尼機制(或模態數)對識別結果之影響。最後，應用至分析在國家地震工程研究中心所執行之八層樓鋼構架振動台試驗，共有三種構架，分別為原始構架、一樓柱削弱之弱化構架及在一、三樓加勁之強化構架。經分析可以很容易看出在弱化樓層及強化樓層之勁度變化。

The stiffness matrix and damping matrix of an existing structure estimated by using its dynamic responses are very useful to reevaluate its finite element mode established in the design stage and assess the possible damages in the structure. In this work, two new objective functions are proposed and constructed by measured dynamic responses and identified modal parameters of a structure, respectively. The optimal solutions of these objective functions are determined by genetic algorithm and gradient method. The optimal solution for the first objective function is solved in time domain, and constraints established by the identified modal parameters are introduced to enhance the efficiency for obtaining the optimal solution by reducing the number of using the Runge-Kutta approach to solve for equations of motion. The optimal solution for the second objective function is solved in mode domain, and no eigenvalue problems need to solve. Consequently, the latter is more efficient than the former in terms of computation time. Numerical simulation for a seven-story shear building is carried out to validate the proposed procedures. Parametric studies are performed for considering the effects of the bandwidth of stiffness and damping matrices, measured degrees of freedom, noise, damping mechanism or number of frequencies and mode shapes. Finally, the present approaches are employed to process the responses of three steel frames of eight stories under shaking table tests carried out in the National Center of Research for Earthquake Engineering. The three frames are named as original, stiffened, and weakened frames, respectively. The frames are typically the same, except that two pairs of braces are installed in the first and third stories of the stiffened frame, respectively, and two columns of the first story of the weakened frame are weakened by cutting. The stiffness matrices of the three frames found by the present approaches indeed reflect the expected facts.