應用整體經驗模態分解法及含外變數的自我迴歸模型識別結構系統之特徵參數之研究

近年來結構系統識別已經發展的非常完善，在模擬方面透過適當的數學模型都可以得到良好的識別成果。但在實際識別上，雜訊對訊號之影響是無法避免的，因為它充斥著量測環境，有時會以提高數學模型之階數來增加識別的精確度，使得挑選特徵根的過程較為麻煩，運算的時間也較長。為了降低雜訊在系統識別上的影響，本文應用希爾伯特－黃轉換中的一個重要步驟：整體經驗模態分解法來做為結構系統訊號前處理的工具。透過其特性將訊號分解成數個本質模態函數，並將高頻的雜訊濾除之，配合含外變數的自我迴歸模型與狀態空間系統識別理論，識別出結構系統的模態參數。本文使用的訊號處理及系統識別之方法，將透過電腦模擬加入雜訊後的自由振動及強迫振動輸出入響應進行識別，由單自由度進程至三自由度，並與正解做比較。最後應用於兩個實際結構物系統：一個為直立式懸臂鋼樑結構之衝擊測試，其結構簡單且具有理論解供識別結果對照比較；另一個為由國家地震工程研究中心提供之地震波測試五層樓縮尺鋼架結構。由模擬的結果顯示，本文所使用的方法有效的提高了在含有雜訊情況下的識別結果。

關鍵字

系統識別；希爾伯特－黃轉換；整體經驗模態分解法；含外變數的自我迴歸模型；模態參數

並列摘要

Structural system identification has been well-developed recently, mature enough to yield an effective result in simulation through proper mathematics modeling. However, the identification in practice encounters signal interference that dampens the result. For better precision, mathematics modeling order would be lifted, yet the process of selecting eigenvalue becomes longer. This thesis applies one of the most important step in HHT – EEMD. EEMD as a preset uses its properties to decompose signal into IMF and filters out high-frequency signal. In addition, along with ARX model and state-space system identification theorem, the structural characteristic parameters can be identified. The EEMD method will be tested through computer simulation that includes interfered free vibration and forced vibration signal under either single or three-degrees-of-freedom. The method will later be applied onto two virtual systems: a simple and efficient virtual perpendicular beam structure crash test and seismic waves to test five-story steel frame structure of NCREE. As the result reveals, the method in the thesis provides an effective result against signal interference.

並列關鍵字

System Identification ； Hilbert-Huang Transform (HHT) ； Ensemble Empirical Mode Decomposition (EEMD) ； ARX model ； characteristic parameters

參考文獻

[32] 吳季學，應用含外變數的非線性自我迴歸模型估算結構系統之線性及非線性特徵參數之研究，碩士論文，工程科學及海洋工程研究所，國立臺灣大學，台北，2011。

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應用整體經驗模態分解法及含外變數的自我迴歸模型識別結構系統之特徵參數之研究

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