利用李群微分代數方程法即時重建作用於非線性結構之外力

Abstract

在土木領域裡，對結構的保護及控制來說，能夠即時地重建施於系統的外力向來是個不可忽視的研究議題。 過去雖有許多重建外力的方案提出，但因運算求解費時，故欲達到「即時」重建的方法仍舊有限。本論文中，將過去已廣泛應用的強健微分器及追蹤微分器，自常微分方程轉換為一微分代數方程組，透過控制力加以調配控制，並利用結合隱格式李群法和牛頓迭代法的新數值方法——李群微分代數方程法進行運算求解，內外迴圈雙重迭代增加穩定性。此方法可利用於設計線上偵測器，意為可在僅有已受噪音干擾的位移訊號資料下，即時重建施於系統的未知外力。隨著線性結構、杜芬方程式、范德波爾方程式及地震力作用下的線性結構等四個數值算例顯示，此方法呈現的效果有相當不錯的精度與效率，且簡單易於使用，未來發展應用的機會極大。

For structure protection and control, it is utmost to immediately detect the external force being imposed on the structure currently in civil engineering. In this thesis, we remodel the famous robust exact differentiator and tracking differentiator into a type of differential algebraic equations (DAEs), and then we solve the resultant DAEs by a Lie-group method, which can be used as an on-line estimator to detect unknown external force by using only a real-time measurement of the structural displacement under random noise in time. The estimated results obtained by the novel methods are quite promising.