應用狀態空間DLV法在扭轉耦合結構之地震損傷探測

Abstract

狀態空間DLV法是以狀態空間參數建立結構之柔度矩陣為基礎，由結構受損前、後之差異柔度矩陣經奇異值分解萃取出破壞定位向量，凡於破壞定位向量作用下應力為零之桿件，即視為潛在之受損元素。本研究先以二維平面結構為分析對象，探討以SRIM系統識別分析結合狀態空間DLV法於結構損傷探測之可行性，並探討在不足觀測條件下之分析方法。考量建築結構因不對稱而有扭轉耦合之行為，基於實用性目的，本文發展適用於扭轉耦合結構之損傷探測技術，並將結構損傷探測技術由過去僅能定位出受損樓層的層次，推升至定位個別受損桿件之層次。分析結果顯示，本文提出以 SRIM系統識別分析結合狀態空間DLV法，可由結構全域之地震反應資料（樓層加速度反應歷時）偵測出局部受損之樓層或個別桿件，甚至多重受損之情況，確認其可行性與未來實際應用之潛力。

The state-space damage localization method is based on the flexibility matrix of structures constructed using the system parameters in state-space. The damage locating vectors (DLVs) are obtained by performing the singular value decomposition (SVD) on the flexibility differential matrix of the structure before and after the damage state. Members with zero stress (or force) under the DLVs as external loads to the structure are considered potentially damaged. In this study, feasibility of the state-space damage localization method integrated with the system realization of information matrix (SRIM) for damage detection of structures is explored first using a planar structure. Methodologies for damage detection of structures under the condition of insufficient observation are also developed. In view of the torsion-coupling behavior for non-symmetric structures, techniques for damage localization of torsionally coupled structures are then developed for practical purposes. The damage localization technique has been advanced, in this study, to a higher level of being able to detect individual members that are damaged rather than simply the damaged stories by the existing methods. Results indicate that localized damage of stories or members can be identified from the global seismic response data (specifically the floor accelerations recorded), regardless of single or multiple damages, by using the state-space DLV method with the SRIM for system identification. Feasibility of the proposed scheme and its potential, in practical applications are therefore confirmed.