唯輸出理論之地震損傷探測分析與實驗驗證

Abstract

本研究針對唯輸出系統之SSI系統識別與損傷探測方法進行理論分析與試驗驗證，並與SRIM系統識別分析進行比較。針對唯輸出系統， SSI系統識別法係在隨機預測狀態空間系統之架構下，以觀測結構所有或部分樓層之加速度反應歷時訊號為輸出向量，由輸出向量序列間之協方差關係識別出狀態空間參數，作為後續結構損傷探測分析的依據。在結構損傷探測方法上，除採用Bernal所提出之狀態空間DLV法之外，本研究並提出直接位移法﹙Direct Displacement Method, DDM﹚，兩者皆可由識別所得之等效系統參數進行損傷探測分析。直接位移法的概念係考量剪力屋架之樓層剪力與層間變位之線性關係，將判斷結構受損與否之加權應力指標（Weighted Stress Index, WSI）轉換為加權相對位移指標（Weighted Drift Index, WDI）。振動台試驗以White Noise及El Centro地震為輸入擾動，並考慮完全觀測（Full Observation）與部分觀測（Partial Observation）條件下進行損傷探測分析。整體而言，SRIM之系統識別結果較精確，但SSI忍受噪音干擾之能力較佳，特別是在高頻振態的識別上。振動台試驗結果顯示，在完全觀測條件下，無論輸入擾動為White Noise或El Centro地震，以狀態空間DLV法進行損傷探測時，幾乎都能成功定位出結構之受損樓層，無論系統識別方法採用SRIM或SSI，其中又以結合SRIM系統識別結果之辨識度較佳。若以DDM法進行損傷探測，則在單一樓層破壞時，兩種識別方法皆能成功辨識受損樓層；惟複數樓層破壞時，則兩者無法成功辨識受損樓層。部分觀測僅採用DLV法進行損傷探測分析，在單一樓層受損之條件下，由兩種識別分析結果均能成功定位出破壞樓層，除了於1樓或5樓（頂樓）未作觀測時可能發生誤判的情形；在複數樓層破壞時，損傷探測之成功率皆不高。

In this study, theoretical and experimental verifications of stochastic subspace identification (SSI) and damage localization techniques for output-only systems have been explored and compared with the SRIM method. The SSI technique is developed for output-only systems under the framework of stochastic state-space system by observing full or partial floor acceleration responses of the structures. Parameters of the state-space system are identified from the covariance matrix consisting of the output state vector sequences, and in turn serve as the basis for damage detection of the structures. The DLV method developed by Bernal has been adopted for damage detection, along with the direct displacement method (DDM) proposed in this study. Both methods utilize the equivalent system parameters from system identification for damage localization analysis. The concept of DDM is based on the linear correlation of the story-shear with the story-drift for shear-type buildings so that the weighted drift index (WDI) is considered instead of the weighted stress index (WSI) for judgment of damage condition. In the shaking table tests, both a white noise scenario and the 1940 El Centro earthquake are considered as the seismic inputs with full or partial observation on structural responses for damage detection. Simulation results indicate that the SRIM is in general better than the SSI in terms of accuracy of the identified parameters, despite the SSI shows better noise-bearing capability in the identification of mode shapes, for high-frequency modes in particular. Experimental results indicate that, for either the white noise or El Centro earthquake as the input under the condition of full observation, almost all the damaged conditions can be successfully identified if the state-space DLV method is adopted for damage detection, regardless of SRIM or SSI is considered for system identification. Those with SRIM for system identification perform better in terms of correctness on damage localization. When the DDM is adopted for single-damage conditions with full observation, both the SRIM and SSI helps in successfully identifying the damaged story. Both methods fail, however, in multiple-damage conditions. In partial observation conditions, only the DLV method is adopted in the analysis. Under single-damage conditions, both the SRIM and SSI help in successfully identifying the damaged story, except that miss-judgment might occur if the first or top story is not observed. Both methods fail in multiple-damage conditions with partial observation of the state vector.