以時間序列模型識別結構之模態參數

Abstract

線性或非線性結構之量測反應與外力，可透過時間序列模型架構結構之輸入與輸出關係，此模型被廣泛應用於各個領域。此論文主要提出各種建構時間序列模型之方法，並且透過架構之模型進一步估算結構之模態參數。 連續小波轉換第一次被應用於架構ARX ( autoregressive with exogenous input model ) 模式。應用連續小波轉換於量測之地震反應或自由衰減反應，可利用連續小波轉換之平移不變性與發揮其濾波功能提升識別結構模態特性之效率及準確性。透過六層樓剪力構架模擬之數值反應進一步驗證各種小波函數、尺度因子與雜訊之干擾等參數對識別結果之影響。並將此方法應用於三層樓鋼構之振動台試驗與橋樑現地衝擊試驗等實測資料。 本研究亦提出移動最小平方差法結合多項式函數或小波包函數建構TVARX ( time-varying autoregressive with exogenous input model )模型。此方法僅須使用少量之基底函數。研究中亦證明結構之瞬時模態參數可透過由位移反應建構之TVARX時變係數直接求得；但若使用速度或加速度反應，則會造成系統誤差。透過單自由度模擬之數值反應驗證各種參數對識別結果之影響，並與傳統基底函數展開法所得之分析結果比較，證明所得之識別方法較優越。最後將此方法應用於處理RC構架振動台非線性反應資料，識別其瞬時模態特性，識別結果與觀察到之物理現象一致。

Time series models are often employed to establish input-output relationships of linear and nonlinear structure systems from their dynamic responses and input forces, and find many applications in various fields. The main purposes of the dissertation are to propose various novel techniques to establish different time series models and to determine structural modal parameters from the established time series models. The continuous wavelet transform is first applied to establish the ARX model (autoregressive with exogenous input model). The shift property and filtering ability of the continuous wavelet transform enhance the efficiency of the proposed approach in accurately identifying the modal parameters of a structure from its earthquake responses or free vibration responses. The effects of noise and various wavelet functions on determining the modal parameters of structures are also explored in processing the numerically simulated acceleration responses of a six-story shear building subjected to base excitation. The proposed approach is also employed to obtain the modal parameters of a three-story non-symmetric steel frame from its measured acceleration responses in a shaking table test. The moving least-squares technique with polynomial basis functions or wavelet functions is adopted to establish the TVARX model (time-varying autoregressive with exogenous input model). It is proved that the instantaneous modal parameters of a linear time variant structure can be directly estimated from the coefficient functions of the TVARX model if the TVARX model is established using the displacement responses of the structure. Numerical studies are carried out to investigate the effects of parameters in the proposed approach on accurately determining instantaneous modal parameters. Numerical analyses also demonstrate that the proposed approach is superior to conventional basis expansion techniques in accurately estimating instantaneous modal parameters of a structure. The proposed approach is further applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified instantaneous modal parameters are consistent with observed physical phenomena.