本文旨在發展出一套適用的結構健康監控的法則，此健康監控法則將以系統的輸入與輸出的時域訊號來判別結構是否已有損傷，以及損傷的位置與大小。首先使用了應用蓋揚縮減的次結構法將一根11個點的樑縮減成兩個次結構，接下來將這兩個次結構邊界上的點所量到的外力、位移、以及角位移訊號都利用正交函數展開法展開求得相對應的係數；並且也利用正交函數展開法將系統的動態方程式由微分方程式積分變為線性代數方程式，此時使用最小平方誤差法就可以識別出縮減次結構的質量與勁度矩陣，最後再利用人工類神經網路與基因演算法將次結構的資訊求得整體結構的質量與勁度矩陣，就可以識別出結構的健康情形。
　　另外，適應性外力對於縮減大型結構物的系統參數也是有幫助的，此種方法也是屬於二階段損傷判別。在本文中，利用計算不同損傷位置對於各種不同頻率的外力的靈敏度，找出能夠判別各個損傷位置所相對的最適應外力；每次監控系統時，依次給予系統針對不同部位損傷所搭配的最適應外力，即可由量到的輸出判斷出損傷可能位置，則待求的系統未知參數，將能夠減少到僅剩損傷比例而已。
　　最後，本研究也對於如何求得樑結構的角位移訊號做了探討，這是因為在做實驗時角位移訊號是很難求得的。首先利用樑的解析解來算出樑的自然頻率與特徵值間的關係後以及求出不同的邊界條件時，樑的自然振動模態函數；由於角位移訊號是位移訊號對長度方向的偏微分，因此利用正交函數展開法求得各個不同頻率的係數，再將這些係數搭配著樑的自然振動模態函數在空間方向的微分結果，就可以計算出角位移訊號。
　　經由數值模擬的驗證，本研究中關於使用次結構法或適應性外力來識別樑結構的結構情形的結果是不錯的；而經由數值模擬與實驗的驗證，應用量取的位移訊號來求得角位移訊號也是可行的，這對於往後的結構健康監控將有不少的幫助。

　　This thesis is concerned with the development of damage identification technique for a simple beam structure in order to monitor the structural health condition. The damaged structural stiffness and mass matrices were identified based on the specified loading and response signals. The finite element beam model was simplified to become a substructure model according to the Guyan dynamic reduction method and the dynamic reduction process. The orthogonal polynomial approach was subsequently used to extract the proposed distributed parameter model in question. The identified structural stiffness and mass matrices for the reduced model with or without damage were furthermore transformed to the corresponding global unreduced structural matrices by means of the back-propagation artificial neural network scheme and the binary coded genetic algorithm. Based on the identified damaged structural stiffness and mass matrices, the damage locations and the extent of damage of the beam structure were then determined.
　　In addition, the adaptive excitation method could also help to reduce the system parameters in a large structure. In this work, the adaptive excitation is also adopted to analyze the sensitivity when the structure has defect. This method belongs to the two stages identification process. By checking the sensitivities in different defect conditions, the defect location could be found first and the unknown system parameters will then be reduced to three (i.e. mass, damping coefficient, and stiffness ratios) or two (i.e. mass, and stiffness ratios) parameters. These unknown parameters can then be determined by using gene or neural networks identification methods.
　　In this thesis, rotation angle identification of a beam structure based on a laser displacement sensor tracked transverse displacement signal is also discussed. Finite element beam model was coded to compute the dynamic response of structure at the specified sensor locations. These numerically computed transverse displacements were then superimposed with a 20% noise-to-signal ratio random generated white noise signals and were used as the input for rotation angle identification. The orthogonal polynomial approach was used to expand the dynamic transverse displacement signal to the orthogonal functions and their associated coefficients. These coefficients can be used to identify the orthogonally expanded coefficients associated with the rotation angles of beam. The rotation angle response can finally be synthesized. In addition, a series of tests was conducted using the impact hammer to study the dynamic response of the cantilever metallic beam. Both the loading history and the transverse displacement history were recorded. After the displacement signal was measured, either a wavelet filter with the Daubechies scaling function or the cubic moving least square error method were used to reduce the noise from test. Similar to the numerical synthesis process mentioned above, the rotation angle of the beam can be determined.
　　Through numerical validation, current identification process is capable of monitoring the structural health condition by using specified time domain input and output signals. And the rotation angle identification discussed in this thesis is also useful through numerical and experiment validations.

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