利用自我迴歸模型與模態曲率理論以研究懸臂樑結構之損傷偵測

Using AR Model and Theory of Curvature Modal Shape to Study Damage Detection of Cantilever Beam

鄧皓元(Hao-Yuan Teng)

指導教授 ： 柯文俊

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.02815

摘要

損傷偵測於結構工程問題中為一門重要研究，而樑式結構於工程中又有著廣泛之應用，如：橋梁、建築等。對於樑式結構使用上之安全檢測已存在許多方法；有鑑於近年來結構系統識別發展的完善，並參考了以結構模態參數作為偵測結構損傷狀況之相關文獻後，其內容多以有限元素法作數值上之模擬，但未有許多考慮實際應用狀況之研究。因此本文將結構系統識別所得之模態參數結合結構系統之模態曲率理論考慮實際狀況下偵測懸臂樑結構損傷之情形。
　　本文使用自我迴歸模型及狀態空間系統理論實際識別出懸臂樑結構之模態參數，利用上述識別成果估算結構之雷利阻尼矩陣係數，透過此方式建立近似於實際狀況懸臂樑之有限元模型並由電腦程式分別模擬多種受損狀況下受損與未受損懸臂樑結構含雜訊之輸出響應，由此一流程即可模擬在僅含輸出響應之情況下，首先以自我迴歸模型反向識別出懸臂樑之模態參數，並基於結構模態曲率之理論對懸臂樑作損傷狀況之偵測。而在考慮實際情況所假設之各種不同受損狀況中，本文以上述方式模擬之成果顯示此損傷偵測方法於實際情況下對受損懸臂樑結構能給予一定程度之鑑別功效。

關鍵字

系統識別 ； 自我迴歸模型 ； 狀態空間系統 ； 損傷偵測 ； 模態曲率

並列摘要

Problems of damage detection in structural engineering are a major research topic. Beams have extensive applications in structures. For example, bridges and buildings are about that. The use of beam structure already exists in many safety testing methods. The development of structural system identification plays a good role in these fields in recent years. With the references of damage detection by structures modal parameters, its content are more about using finite element method to simulate damage detection. This thesis consider a way to detect the injury situation of cantilever structure through modal parameters obtained from system identification and the curvature modal shape theory.
This thesis uses the Autoregressive model and the state-space system to identify modal parameters of cantilever beam structure and estimate its coefficient of Rayleigh damping. With the above steps, this thesis create finite element model to be similar to the actual cantilever beam. By generating responses of damaged and undamaged cantilever beams from a computer program, we can simulate the damage detection based on curvature modal shapes. The results showed that the proposed method for the variety injury situations has a good effect.

並列關鍵字

System Identification ； AutoregRessive Model(AR) ； State-Space System ； Damage Detection ； Curvature Modal Shape

參考文獻

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