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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
Stochastic subspace identification operational modal analysis
Predictive filter
Monte Carlo simulation
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摘要: 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。 分析發現,正交投影可以以預測濾波器表示,正交投影的結果受到預測濾波器之相關性及波德圖中的假象與波瓣的寬度影響。當I等於3/4+1/2N_SL個Toeplitz矩陣的週期時,波德圖中主瓣的位子不會發生偏移,因此會有較佳的投影結果。然而,當訊號的取樣頻率上升時,Toeplitz會隨之增加,在電腦記憶體有限的情形下,建議降低訊號的取樣頻率以降低需要的I值。此外,分析發現當N值增加時,預測濾波器會逐漸收斂並趨於理想投影下的預測濾波器。 隨機子空間辨識法求得之模態參數也會受激振力的變化影響,為了評估隨機子空間辨識法之強健性,本論文使用蒙地卡羅法對隨機子空間辨識法進行測試,結果顯示隨機子空間辨識法所辨識出之阻尼比容易受到激振力改變之影響且可能出現負值。最後,隨機子空間辨識法被應用於一個多自由度測試平台之模態分析,實驗結果用於驗證分析之趨勢。
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.
文章公開時間: 2021-08-23
Appears in Collections:機械工程學系所



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