以基底展開法識別多自由度時變系統之瞬時模態參數

Abstract

摘要 本研究為利用移動最小平方差法(Moving Least Square method,MLS)從時變系統之動態位移反應架構TVARX(time-varying autoregressive with exogenous input model)模型，利用識別之時變係數直接估算瞬時模態參數。 透過三層樓剪力構架模擬之數值反應驗證可行性，接著考慮各種參數如節點數、指數權重函數之影響半徑、TVARX之模型階數(I,J)與雜訊之干擾等對識別結果之影響。進一步應用於分析五層樓鋼構與六層樓鋼構之振動台試驗等實測資料，識別其瞬時模態特性。識別結果與試驗觀察到之物理現象一致。 本研究亦提出以不同自由度所構成之子結構系統，建立TVARX模型，透過子結構系統之瞬時擬自然振動頻率可得知哪一自由度(或哪一層樓)可能損傷。

Abstract This study applies moving least square method (MLS) to construct the time varying autoregressive with exgenous input model (TVARX) for a structure from its dynamic displacement responses and further estimates the instantaneous model parameters of the structure from the time varying coefficients of TVARX model. Through the three-story shear structure of the numerical simulations verify the feasibility of reaction.The parameters under investigation include the order of TVARX model,nodal point,support length of exponential weighting function,and noise.The proposed approach is also employed to obtain the modal parameters of five-story steel frames and six-story frames from their measured displacement responses in shaking table tests. This study also proposes to freedom posed by the different sub-structure system, the creation TVARX model, through the sub-structure system, the natural vibration frequency of the transient to be able to know which degrees of freedom (or what floor) may be damage.