摘要:
在損傷偵測的分析過程中，由於實際放置感測器的量測自由度數目與分析模型階數不合。通常的解決方法為藉由模式縮減法，將分析模型階數縮減至與量測自由度數目相同，再以二階段損傷偵測法識別損傷部位與損傷程度。但此作法於第一階段所識別的損傷部位中，包含的參數往往很多，導致容易發生可識別性問題，且亦增加了以最佳化方法估算參數值時的負擔。
本研究中，以振型擴充為出發點。利用線性擴充法擴充量測振型，再以損傷指標法識別損傷部位，更經由多階段的損傷部位識別來縮小識別損傷的範圍，藉以提高損傷部位識別的解析度；並減少以最佳化方法估算參數值的負擔，進而降低可識別性問題的發生。文中分別以鏈模型及懸臂梁為例，藉由數值模擬的方式驗證此概念的適用性。

Abstract:
In the process of the damage detection analysis, most skills are utilized model reduction technique to reduce the order of analytical model as same as the number of measured degree of freedom. Then, the approximate damaged area and degree of damage are located with two-step damage detection method. But the way to locate damaged region is always involved too many parameters. Therefore, it not only raised the probability of identifiability problem but also burdened with the calculation of parameter estimation.
In this thesis, base on shape-expansion methods to expand shape and locate damage region by damage-index method, and the concept of multiple-stage damage localization is proposed. It’s used to reduce the range of damage detection and increase the resolution of damage localization; also decrease the calculation of parameter estimation and further reduce the probability of identifiability problem. The idea is applied to chain model and cantilever beam in numerical simulation.

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