以基於小波之方法識別結構之瞬時模態參數及其應用

Abstract

結構物由於材料老化或受極大外力，很可能造成損壞；若能得知損壞程度，可避免進一步之災害。利用結構物之模態參數評估結構物損壞程度是一常用之手段；因此，從結構物之動態反應準確估算該結構之模態參數是必需的。本論文主要為發展可準確估算時變系統之瞬時模態參數之識別方法。所提之方法分為三部分：1. 以連續Meyer小波轉換結合移動最小平方差法應用於時變系統之識別 2.應用Cauchy小波轉換配合分段多項式以識別系統之瞬時模態 3.發展基於子結構TVARX模型及Baeysian Probabilistic Method之結構損傷診斷方法。 首先提出以連續Meyer小波轉換結合移動最小平方差法建構TVARX模型， TVARX之時變係數將以移動最小平方差法建立之基底函數展開，並於小波域中估算各個基底函數對應之權重係數。透過五層樓剪力構架之數值模擬反應驗證識別方法之優越性，進一步將此法應用於分析八層樓鋼構架振動台實驗資料。本研究亦提出結合Cauchy小波轉換及TVARX模型，將TVARX模型之時變係數矩陣用分段式低階多項式基底展開，利用Cauchy小波轉換將多項式基底與狀態空間參數反應之乘積轉至小波域，進行多項式係數矩陣之識別，再由TVARX模型之AR係數矩陣直接估算瞬時模態參數。透過數值模擬之單自由度及多自由度系統反應進行驗證；其中將探討多個參數對識別結果之影響，例如雜訊、多項式之階數、分段視窗之長度、Cauchy小波。最後將本識別方法應用至分析五層樓鋼構架之振動台試驗，處理此鋼構達降伏之非線性反應。最後利用識別所得之模態參數，結合子結構TVARX模型及Baeysian Probabilistic Method，對結構系統進行損傷評估，判斷其損傷與否及其損傷之位置。分別以一組五層樓剪力構架及兩組六層樓剪力構架之數值模擬反應驗證子結構TVARX模型及Baeysian Probabilistic Method之可行性。於Baeysian Probabilistic Method之驗證中，探討勁度矩陣初始值、帶寬大小及不完全量測反應對勁度矩陣識別結果之影響。最後亦將此二法分別應用至八層樓及五層樓鋼構架振動台實驗資料，所得結果和觀察到的物理現象一致。

A structure may sustain damage either when subjected to severe loading, such as a strong earthquake, or when its material is degraded. The serviceability and safety of structures depend on the detection and location of structural damage. Early detection of structural degradation can prevent catastrophic failure. Modal parameters of a structure are often applied to determine the severity of the damages. Therefore, it is essential to accurately determine instantaneous modal parameters of a structure from its dynamic responses. The main purposes of the dissertation are to develop novel techniques to accurately identify structural time-varying modal parameters. The MLS (moving least-squares) technique with continuous Meyer wavelet is adopted to establish the TVARX model (time-varying autoregressive with exogenous input model). The coefficient functions of a TVARX model are expanded through the MLS approach with a set of polynomial basis functions. These coefficient functions are determined in a wavelet domain. The effectiveness of the proposed approach is validated using numerically simulated earthquake responses of a five-story shear building with time-varying stiffness and damping coefficients. The proposed method is also applied to process the dynamic responses of an eight-story steel frame in shaking table tests and identify its instantaneous modal parameters. The TVARX model with the CCWT (continuous Cauchy wavelet transform) is also employed to accurately identify the instantaneous modal parameters of a time-varying linear system. The time-varying coefficients of the TVARX are expanded as piecewise polynomial functions. Then, the CCWT is applied to establish the TVARX model. Numerical simulations of systems with single and multiple degrees of freedom are carried out to validate the effectiveness of the proposed procedure in accurately estimating their instantaneous modal parameters. The effects of noise and various parameters are also explored. The proposed approach is further applied to handle the dynamic acceleration responses of a five-story steel frame in a shaking table test, in which the columns of the frame yield. Finally, a sub-structural TVARX model technique and a Baeysian approach using those identified time-varying modal parameters are further proposed to assess damage of a building. The damage of a building can be located and the severity of damage can be determined. These two approaches are validated through processing numerically simulated acceleration responses of a five-story shear building and two six-story shear buildings with time varying stiffness and damping under base excitation, respectively. The effects of nominal values of stiffness, assumed bandwidth of stiffness matrix and incomplete measurements are also investigated in the Baeysian approach. The two procedures are further applied to process the dynamic responses of an eight-story steel frame and a five-story steel frame in shaking table tests, respectively. The identified results are consistent with observed physical phenomena.