線性時變結構系統瞬時勁度矩陣更新

Updating Instantaneous stiffness matrices of time-variant structures

莊武諺(Wu-Yan Zhuang)

指導教授 ： 黃炯憲 ； 劉俊秀

國立交通大學/工學院/土木工程系所/碩士(2018年)

摘要

摘要

本研究主要目的為識別兩棟五層樓鋼構架於振動台實驗下之模態參數，並使用其模態參數進行瞬時勁度矩陣更新，並從勁度矩陣去判斷損傷的位置與損傷程度，而試驗之鋼構架，一棟為因構架之第一樓層柱降伏而損傷，另一棟則是模擬在第一及第三樓層有急遽的勁度變化。
本研究利用連續Cauchy小波轉換(Continuous Cauchy Wavelet Transforms, CCWT)結合多項式基底函數架構state variable的TVARX模型，於五層樓鋼構架之振動台試驗反應進行完全量測及不完全量測之識別，在取不同時間點所識別到之模態參數配合G.A結合Gradient法，更新勁度矩陣。利用有限元素軟體ETABS建置兩構架之模型，所得之勁度矩陣即為模型更新之初始值，探討在不同帶寬配合不同模態數及模態頻率所得之勁度矩陣之差異，並進行損傷評估。

關鍵字

線性時變結構系統 ； 瞬時勁度矩陣更新 ； 柯西小波 ； 基因演算法

並列摘要

Abstract

The main purpose of this study is to determine the instantaneous stiffness matrices of two five-story steel frames, which showed nonlinear dynamic behaviors in shaking table tests, by using their identified instantaneous frequencies and mode shapes. The stories with stiffness changes are further located, and the amounts of changes in stiffness are also determined. One of the frames was designed to experience yielding of the columns in the first story during the tests, while the other was designed to have sharp changes of stiffness in the first and third stories.
A time-varying autoregressive with exogenous input (TVARX) model with the continuous Cauchy wavelet transform is applied to process the acceleration responses of these frames with considering complete or incomplete measurements and identify their instantaneous modal parameters. A genetic approach along with a gradient method is adopted to update stiffness matrices of the frames by using their identified modal parameters at different time. The stiffness matrices of the two frames obtained from the commercial finite element package ETABS by using the design data are used as the initial guessed values in the model updating process. The effects of assumed different bandwidths of matrices and using different numbers of modal frequencies and shapes on the accuracy of the estimated stiffness matrixes are investigated.

並列關鍵字

time-variant structures ； Updating Instantaneous stiffness matrices ； Cauchy Wavelet ； Genetic Algorithm

參考文獻

參考文獻

Acharya, U. R., Vinitha Sree, S., Alvin, A. P. C. & Suri, J. S. (2012), Application of Non-Linear and Wavelet based Features for the Automated Identification of Epileptic EEG Signals, International Journal of Neural Systems, 22(2), 1250002-14.

Adewuyi, A.P. & Wu, Z. (2011), Vibration-based Damage Localization in Flexural Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements, Computer-Aided Civil and Infrastructure Engineering, 26(3), 154-172.

Ahmadian, H., Gladwell, G. M. L. & Ismail, F. (1997), Parameter Selection Strategies in Finite Element Model Updating, Journal of Vibration and Acoustics, ASME, 119, 37-45.

Allemang, R. J. & Brown, D. L. (1983), A Correltaion Coefficient for Modal Vector Analysis, Proceedings of The First International Modal Analysis Conference.