在模態分析的理論中，線性結構系統在自由振動下不受隨機外力的影響且包含了結構之動態特性，因此模態參數識別之理論通常以自由響應數據來識別模態參數。但在真實情況中，當線性結構系統受環境激勵產生振動時，環境響應訊號具有隨機性，因此如何去除環境響應中的隨機性，以進行模態參數識別為本研究之重點。本文考慮當線性結構系統在環境振動下，若激勵訊號可近似為乘積模型之非定常白訊，則此環境響應之自相關函數相當於系統自由振動之自相關函數，而環境響應訊號經由隨機遞減法處理後所得之隨機遞減訊號可證明為正比於環境響應之自相關函數與確定性函數之自相關函數的乘積，因此隨機遞減法可有效地去除環境響應中的隨機成分而得到自由響應。資料相關特徵系統實現法(ERA/DC)是利用建構資料相關矩陣來去除環境響應中的隨機成分，此資料相關矩陣與隨機遞減訊號皆為利用相關函數的概念消除環境響應中的隨機成分，因此本研究於ERA/DC之架構下將資料相關矩陣替換成隨機遞減訊號進而求得模態參數。最後並經由數值模擬驗證，說明此做法能有效識別出結構之模態參數。

In the theory of modal analysis, since the linear structure system is not affected by random external forces under free vibration, the theory of modal parameter identification is usually based on free response data to identify modal parameters. In the real situation, when the linear structural system is excited by the ambient force to produce ambient vibration, the ambient response signal is random. Therefore, how to remove the randomness in the ambient response and convert it into a free response is the focus of this study. This paper considers a linear structure system under ambient vibration. If the excitation signal can be approximated as nonstationary white noise, the autocorrelation function of the ambient response is equal to the autocorrelation function of the free vibration of the system. The ambient response is converted into a randomdec signature by the random decrement technique. The randomdec signature can be proved to be proportional to product of the autocorrelation function of the ambient response and the autocorrelation function of the deterministic function. Therefore, the random decrement technique can effectively remove the random component in the ambient response to obtain a free response. In this study, Eigensystem Realization Algorithm using Data Correlation (ERA/DC) construct a data-correlation matrix to remove random components in the ambient response. The data-correlation matrix and the randomdec signature both use the concept of correlation functions to eliminate randomness in the ambient response. Therefore, in the ERA/DC framework, the data correlation matrix is replaced with the randomdec signature to obtain the modal parameters. Through numerical simulation, this method can effectively identify the modal parameters of the structure.

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