遞迴式隨機子空間系統識別分析於結構損傷探測之應用

Abstract

本研究結合遞迴式子空間系統識別法與狀態空間損傷定位向量法發展結構損傷探測技術，做為發展即時結構健康監測系統之基礎。遞迴式子空間系統識別法係根據投影近似子空間追蹤理論，結合工具變數與協方差型隨機子空間系統識別分析之概念所發展。經由數值模擬分析與國家地震工程研究中心之振動台地震模擬試驗結果顯示，吾人可在未知輸入擾動資訊下，透過結構全域之地震反應即時更新系統參數，作為損傷探測分析之依據，多數情況下均能定位出結構之局部受損樓層，有相當之可信度。本文並探討RSSI-COV法追蹤結構系統變化之能力、噪訊的影響以及初始矩陣之選擇等議題，證明RSSI-COV法可有效追蹤系統在頻率上的變化，確認其發展成即時線上分析模組的潛力，惟在模態向量的辨識精度上略顯不足。未來若能將輸入擾動納入進行系統參數識別，應能得到改善。當噪訊比不超過20%情形下，損傷探測分析結果未受影響，驗證其過濾噪訊之強健性。此外，以數值很小之隨機矩陣為初始值，無論時變性或非時變性系統皆能得到良好的識別結果。

This study integrates the Recursive Stochastic Subspace Identification (RSSI) with the method of state-space damage localization vector (DLV) for structural damage detection which in turn serves as the basis for the development of a real-time (on-line) structural health monitoring system. The Recursive Stochastic Subspace Identification is developed based on the theory of Projection Approximation Subspace Tracking (PAST), along with the concepts of Instrumental Variable and Covariance-driven Stochastic Subspace Identification (SSI-COV). Via numerical simulations as well as the shaking table tests conducted in NCREE using the global responses of the structure under seismic excitation, the proposed scheme has been proved sufficient, without knowledge of the input, for on-line identification of the system parameters, and by which the damaged stories of the structure could be reliably located in most conditions. This study also explores issues on the tracking capability of the RSSI-COV for variable systems, the effects of noises and the choice of initial matrix. The RSSI-COV is found capable of tracking the frequency change of a variable system, confirming its potential in on-line system identification, yet it seems not quite sufficient in identifying the mode shapes with desired accuracy. It is believed that the result could be improved if the input signal is considered in the analysis. Moreover, it has been shown that the results of damage detection will not be affected if the noise-to-signal ratio (NSR) is under 20 percent, revealing the robustness of the RSSI-COV in noise filtering. In addition, adopting a small value random matrix as the initial values leads to good identification results, regardless of time-varying or time-invariant systems. .