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標題: 隨機子空間辨識之強健性與參數選擇
Robustness and parameter selection in Stochastic Subspace Identification
作者: 蔡淳宇
Chun-Yu Tsai
關鍵字: 隨機子空間辨識操作模態分析;正交投影;預測濾波器;強健性;蒙地卡羅法;Stochastic subspace identification operational modal analysis;Projection;Predictive filter;Robustness;Monte Carlo simulation
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隨機子空間辨識操作模態分析(SSI-OMA)是一種新型的模態分析方法,此方法中決定Hankel矩陣的維度(分別為I與N值)是一個重要步驟,不同Hankel 矩陣的維度下的辨識可能導致模態參數變異。為了找出在不同Hankel 矩陣維度下正交投影結果的變化,本論文透過機率與數位訊號處理理論,對隨機子空間辨識法中的正交投影進行分析。



Stochastic subspace identification operational modal analysis (SSI-OMA) is a recent method in modal testing. In this method, determining the size of the Hankel matrix, demoted I and N, is an important step. Different sizes of the Hankel matrix may lead to variations in identified modal parameters. In this thesis, the projection procedure is analyzed using probability and digital signal processing theory, and the variation of the projection result under Hankel matrix sizes is sought.

It is found that the projection can be seen as a predictive filter and the projection quality is influenced by the location of passband if I=(3/4+1/2N_SL) T_Toep, the location of passband in Bode diagram would be located at the signal frequency. Also, the optimal value of I increases with sampling frequency. Therefore, under limited computer memory, it is beneficial to use low sampling frequency and a reduced value of I. In addition, it is found when the value of N is increased, the predictive filter would converge gradually

The identified modal parameters are also influenced by variation of excitation force. Using Monte Carlo simulation, it is found that identified damping ratios are sensitive to the variation of excitation force and negative values may emerge on a system with positive damping loss factors. Finally, the SSI is applied to a multi-degrees-of-freedom test rig and the trends shown in simulations are validated.
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