結構系統識別與損傷探測之研究

Abstract

本研究主要是針對土木結構之系統識別與損傷探測方法進行理論分析與試驗驗證。在結構系統識別方面，本文分別針對非參數與物理參數兩種不同之系統識別方法進行探討。其中，非參數系統識別係採用推測-適應過濾法，於時間域中建立動態系統輸入與輸出間的遞迴時序關係，再由預測誤差之遞迴最小平方準則求出最佳系統模型參數，從而求出對應之結構振頻、模態阻尼比及傳遞函數等結構動力特性係數。此外，本研究亦根據遞迴預測誤差法的概念，針對TLCD(Tuned-Liquid Column Damper)在水平與旋轉運動模式下之落水頭損失係數進行識別，並驗證Wu’s formula(水頭損失係數與閥門阻塞率之關係式)之正確性，並提出Modified Wu’s formula以預測變斷面TLCD之落水頭損失係數。此外，由於非參數系統識別法無法用於隔震結構系統特性參數之識別，本研究遂採用物理參數識別法識別建築隔震系統的特性參數，包括LRB(降伏位移、雙線性勁度及阻尼係數…等)與FPS(摩擦係數、曲率半徑…等)。其中，有關FPS隔震結構的系統識別方法並完成振動台試驗之驗證。此外，本研究更將此識別方法擴展至剪力屋架及非剪力屋架結構之物理參數識別。在結構損傷探測方面，本研究採用Bernal所提之柔度矩陣本位DLV損傷探測方法。由於柔度矩陣主要係由低頻振態所貢獻，對於結構高階模態較不敏感，因而增加識別方法的敏銳度。此外，基於實用性之考量，結構健康診斷系統必須在有限觀測的條件下定位出結構損傷位置。因此，本研究亦發展了不足觀測條件下的系統識別方法，在觀測之自由度不小於最低容許值的前提下，結合推測-適應過濾法與模態向量間之正交特性，重建出結構系統各主要模態之特徵向量，做為建立柔度矩陣以及結構損傷探測分析的基礎，並以數值範例及振動台試驗驗證其可行性。

In this study, methods of system identification and damaged detection of civil structures have been analytically studied and experimentally verified. On the subject of system identification, both the non-parametric and physical-parameter identification methods have been explored. The stochastic adaptive filtering method is adopted for non-parametric system identification. This method establishes, in time domain, a recursive relation for the input-output time sequences of the dynamic system whose optimal coefficients then are determined via a recursive least-squares algorithm. The dynamic characteristics of the structure such as the natural frequencies, modal damping ratios, and transfer functions, are in turn abstracted from the identified system coefficients. Furthermore, the head-loss coefficients of the TLCD system in both translational and pitching motions are identified by using the concept of the recursive least-squares method, and accuracy of the Wu’s formula (an empirical formula relating the head-loss coefficient and blocking ratio of the valve) has been verified. The Wu’s formula has been further revised to predict the head-loss coefficients of TLCDs with variable cross-sections. Furthermore, since the non-parametric identification schemes are not adequate for identification of the structural isolation systems, a physical-parameter identification method is developed to identify the characteristics of the isolation systems, including LRB (yielding displacement, bilinear stiffness and damping coefficient… etc. ) and FPS (Friction coefficient and radius of curvature, … etc.). The identification method for structures isolated with FPS has been verified via shaking table tests. In addition, the physical-parameter identification method has been extended to identify both the shear-type and non-shear-type structures. On the subject of damage detection of structures, the flexibility-based Damage Locating Vector (DLV) technique proposed by Bernal is adopted. As the flexibility matrix is contributed primarily by the lower modes, it is less sensitive to the higher modes. This increases the sensitivity of the identification method as a result. Moreover, in view of practical application that a structural health monitoring system should be able to locate the damages with limited sensors, a system identification method under conditions of insufficient observation is also developed in this study. If the number of missed observing states is no more than the allowable degree of insufficient observation, the mode shapes of the primary modes can be reconstructed to serve as the basis for the flexibility matrix and DLV analysis, by integrating the stochastic-adaptive filtering method with the orthogonality criteria between the mode shapes. Feasibility of the proposed method has been verified via both numerical simulations and shaking table tests.