協方差型亞伯拉罕時域法於非定常唯輸出系統模態估測

Nonstationary Output-Only Modal Estimation of Structures from Using Covariance-Driven Ibrahim Time Domain Algorithm

吳益修(Yi-Xiu Wu) ； 林章生(Chang-Sheng Lin)

《應用聲學與振動學刊》 14卷1&2期 (2022/12) Pp. 1-12

https://doi.org/10.6282/JASV.202212_14(1_2).0001

摘要

傳統的模態測試係藉由結構的脈衝響應與激勵信號，計算頻率響應函數以估測系統模態參數。實際情況下，大尺寸結構較難進行模態測試且所費不貲，因此往往需藉由環境振動直接得到系統響應，從而衍生出唯輸出模態識別的相關研究。在唯輸出模態識別領域中，傳統協方差型隨機子空間法是結合奇異值分解，藉由奇異譜判定系統最小階數進而估測模態參數，此法藉由奇異譜判定時，其可能會因模態激發不良或系統階數選定不佳，導致影響識別有效性。本文針對受非定常激勵過程引入乘積模型之激勵及緩慢變化條件，將協方差矩陣計算推廣至非定常響應，並將協方差型隨機子空間法中數據相關矩陣引入亞伯拉罕時域法的模態識別過程，利用數據相關矩陣獲得不同時序所對應數據矩陣間之關係，減少系統階數的判定，進而提升模態參數估測的有效性。

關鍵字

非定常激勵 ； 模態估測 ； 亞伯拉罕時域法 ； 協方差型隨機子空間法

並列摘要

Conventional modal testing uses the response and excitation signal of structures to evaluate the frequency response function to estimate the modal parameters of systems. However, it is difficult and expensive to perform the modal testing for large-scale structures, and therefore the ambient response data directly for output-only modal identification is considered. In the output-only modal identification the conventional covariance-driven stochastic subspace identification (SSI-COV) method is combined with singular value decomposition to estimate the modal parameters by determining the minimum order of the system through the singular spectrum analysis. This method may affect the effectiveness of the identification due to the improper selection of the system order and incomplete modal information from poor frequency content around the structure modes of interest. The data correlation matrix is constructed by covariance matrix in state space form composed of the nonstationary response in the form of the product model with the slowly-time-varying function. The concept of Ibrahim time domain (ITD) algorithm is introduced to the data correlation matrix constructed by covariance matrix. Then, without the determination of the system order in SSI-COV method, the data correlation matrix is introduced into the modal identification process of the ITD algorithm. Numerical simulations and experimental verification confirm the effectiveness of the proposed method for response-only modal identification.

並列關鍵字

Nonstationary Excitation ； Modal Estimation ； Ibrahim Time Domain Algorithm ； Covariance-Driven Stochastic Subspace Identification Method