本研究針對在振動反應量測模態數不完整與雜訊影響的情況下，利用系統識別理論配合二階段損傷偵測法進行結構損傷偵測分析。在第一階段進行損傷位置的標定時，吾人對模態殘餘力法與柔度法進行修改，以便能更有效地標定出可能的損傷位置，進而減少待識別參數數目。於第二階段再利用模態殘餘力法與全域最佳化的方法針對可能之損傷元素進行損傷程度的評估。經由數值模擬，探討不同方法應用於鏈模型之損傷偵測分析，結果顯示本文所提出的方法於不完整模態與含雜訊的情況下仍具有良好的精確性與強健性。最後則將整套方法應用於較複雜的桁架結構損傷偵測分析，以驗證其適用性。結果顯示本文所提出的方法對於較複雜結構仍可有效求出損傷位置及程度。

In this thesis, structural damage detection analysis is studied with consideration of incomplete modal data under noisy conditions. In the process of damage detection, a two-step method in combination with system identification technique is employed. In the first step, we proposed a modification to the residual force method and the flexibility method, respectively, so that possibly damaged elements can be located more reliably. In the second step, the damage extent of possibly damaged elements is then evaluated using the residual force method and a global optimization method, respectively. Using numerical simulation, results of structural damage detection of a chain model obtained from different detection techniques are compared and discussed. Results show that the proposed method is accurate and robust using incomplete modal data under noisy conditions. Finally, applicability and effectiveness of the proposed method is demonstrated by damage detection of a truss structure.

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