中文摘要
題目：樑結構系統之健康監控
研 究 生：許培信
指導教授：鄭泗滄
本文主要針對一簡單樑結構模型系統，經由外力及量測結構模型時態的反應可以識別出損傷結構或未損傷結構的元素勁度矩陣及質量矩陣。首先利用有限元素法建立結構模型經過Guyan Reduction的過程將系統結構模型縮減，再利用正交函數展開法將系統的時態響應資料展開，配合最小平方誤差法識別出縮減模型系統的元素勁度矩陣及質量矩陣。由於識別出的資料不容易看出損傷狀況，所以再利用人工類神經網路(Artificial Neural Network)建立縮減前後系統模型的關連性以檢視元素的損傷狀況。人工類神經網路屬於非參數性識別，特點在於訓練完成後直接給予輸入便可利用訓練所得的權重及閥值求得輸出，但是在訓練過程中所得到的權重及閥值並沒有意義，且訓練需要大量的時間及訓練範例。基於這些原因，欲尋求其他的最佳化方法，在此採用另一種全域的搜索方法，基因演算法，經由自行定義參數，比起人工類神經網路更有物理意義。經由數值分析及模擬，可以驗證這樣的一套流程的確可以成功的找出結構損傷元素的位置及程度。

Abstract
Stiffness and Mass Matrices Identification of a Beam
Structure with Defect
Student : P. H. Hsu
Advisor : S. T. Jenq
This thesis is concerned with the damage identification of a simple beam structure in order to monitor the structural health condition. The damaged structural stiffness and mass matrices are to be identified based on the specified loading and measured response signals. The finite element beam model is simplified to a substructure model according to the Guyan reduction method and substructure method. The orthogonal polynomials approach is then used to extract the proposed distributed parameter model in question with structural response data. The identified structural stiffness and mass matrices for the reduced model with or without damage are furthermore transformed to the parameters which correspond to the global unreduced structural model by means of the back-propagation artificial neural network scheme or simple genetic algorithm. Based on the identified damaged structural stiffness and mass matrices, the damage locations and the degree of damage of the beam structure in question are then determined. Through the numerical validation, current identification process is capable of monitoring the structural health condition by using the time domain input and output signals.

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