局部柔度法 (Local flexibility method)係藉由量測模態參數便可判斷梁結構之局部剛度變化。其基本條件為使用一虛力組使應力集中於局部結構區域，而其餘區域為零；為換取較佳之診斷結果，近年有學者開發擬局部柔度法(Pseudo local flexibility method)，使應力集中於局部結構區域，其餘區域不為零，利用較少之模態，診斷超靜定梁結構之損傷程度，但其僅能診斷損傷位於某個區域內，未能精確定位至桿件，且僅用於簡易梁結構，尚未運用於複雜結構及實際橋梁，因此本研究擬以虛應變能相關之加權分配方式改良擬局部柔度法，使其能精確定位複雜結構及實際橋梁之損傷位置及嚴重度。
本研究透過結構受力後各元素之虛應變能比加權分配擬局部柔度法計算出之區域估計剛度比，使其分配至桿件之剛度比。在應用於二維簡支鋼桁架橋之數值模型分析中，發現若桿件的虛應變能相對過低時，其損傷程度不易被準確診斷，若適當增加量測自由度，使得各個桿件均有一定之虛應變能，則可以更為準確的推估損傷程度。此外，另以彎矩平方積分分配區域剛度比，觀察另一種改良方式之適用性及限制，但此方法亦受到數值問題而不穩定。
此外，本研究將以虛應變能比加權分配區域估計剛度比之方式應用於實際橋梁上，實際橋梁具有3種不同損壞情況，藉由三維橋樑模型的數值分析，已初步驗證了使用擬局部柔度法診斷桁架橋樑損壞的可行性。數值模擬的結果顯示，只需橋樑的前三個模態即可進行損傷定位。因此，應用於實際橋樑時，亦嘗試取前三模態進行，其結果顯示，本研究所提出之方法有其可行性。

Local flexible method (LFM) estimates local flexibility change of beam structures using modal parameters. Later, the pseudo local flexibility method (PLFM) which successfully detects damage to hyper-static beam structures using fewer modes was proposed. The PLFM eliminates the limitation of virtual forces inducing stress only to the local part of a structure, as is the case with the LFM. However, both LFM and PLFM only estimates local flexibility change of a region, but not that of an element. In other words, the estimated damaged locations are not specified. This study intends to modify the methods by distribute the estimated local flexibility change of a region to elements based on the weighting of virtual strain energy of elements, so that the estimated damaged locations can be more specific.
The regional estimated flexibility ratio is distributed to each elements based on the weighting of virtual strain energy ratio of each element. The regional estimated flexibility ratio is calculated by PLFM. In the application to a numerical model of a 2D simply-supported steel truss bridge, it is found that if the virtual strain energy of an element is relatively too small, the estimated damage extent of that element is not reliable. If appropriate degrees of freedom are measured, appropriate virtual forces can be applied to these elements. As a result, more accurate damage extent can be estimated when all the elements possess adequate virtual strain energy. In addition, another algorithm which distributes the regional estimated flexibility ratio to each element based on their virtual strain energy is proposed. However, unstable damage extents were obtained due to numerical problems, hence this algorithm is not used in the further study.
The proposed approach is applied to an experiment of a simply-supported steel truss bridge with three damage cases. The feasibility of the proposed approach is studied via the numerical study of the 3D simply-supported steel truss bridge. It is found that the first three modes are enough to estimate the damage locations. Based on this finding, three modes identified using the measured accelerations of limited degrees of freedom are used in the experimental tests, and the feasibility of proposed approach is verified.

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