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題名 | 含外力參數之向量後向自我回歸模型之系統識別方法=System Identification with VBARX Model |
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作者 | 洪振發; 柯文俊; 彭彥惇; 藍凱祺; | 書刊名 | 國立臺灣大學工程學刊 |
卷期 | 86 2002.10[民91.10] |
頁次 | 頁83-94 |
專輯 | 「工科海洋」專輯 |
分類號 | 312.1 |
關鍵詞 | 系統識別; 狀態空間; 模態參數; VBARX; System identification; State space model; Modal parameters; |
語文 | 中文(Chinese) |
中文摘要 | 本文提出一個應用於系統模態識別方法的模型,稱為含外力參數向量型後向自我回歸模型(Vector Backward Auto-Regressive with eXogenous, 簡稱VBARX)。此模型所應用的系統識別方法適用於同時具有輸出及輸入資訊的條件下。其特色為資料點排列方式與一般前向模型不同。一般習慣會將資料點由先而後順序排列,而將目前時步資訊由先前的時步資訊來預估。但在此後向模型中,將資料點由後而先排列,以後續時步出現的資訊來推算當前時步。此排列順序將在系統與非系統特徵根判別上有很大的方便,從特徵根的表徵即可判別系統與非系統模態。 本文採用狀態空間(state space)模型,由量測資料所建立的狀態方程式中萃取等效系統狀態方程式的系統矩陣與系統模態參數,如模態振頻、阻尼比、模態振形等。另外透過轉換的技巧,進一步從等效狀態方程式的系統矩陣,擷取運動方程式的等效質量、阻尼和勁度三個參數矩陣。本文中,以一個三自由度的質量彈簧系統將用來說明本文所提的計算程序,另以一個十八自由度的剛架模型的數值模擬來驗證此法的實用性。 |
英文摘要 | A system identification model, vector backward auto-regressive with exogenous (VBARX), is proposed in this paper. This model deals properly with the case of multiple input/output data. The characteristic of this model is the arrangement of data. In common cases, the data are arranged from past to future, and the information of current step is predicted by the past time steps. On the contrary, data are arranged from future to past in the proposed model. Although it is not a common way, the system eigen-values and non-system eigen-values can be distinguished automatically during the identification process. In this paper, the state space model is employed to identify the equivalent system matrices of state equation and the model parameters of system, which are the natural frequencies, damping ratios, and the relative mode shapes related to measured points. Furthermore, the equivalent mass, damping, and stiffness matrices of equation of motion can be extracted from the equivalent state space system by using a transformation technique. One numerical example, a 3-DOFs lumped-mass model, is selected to illustrate the procedure availability and the effectiveness of the proposed method. Another numerical example, a 18-DOFs frame structure model, is selected to validate its practicability. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。