結構系統採用逆向方法估測外力之研究

Using the Inverse Method for Estimating External Forces from Structural System

本文模擬加速計數據在不同時域，探討結構系統位移及外力估測量。特別是處理在外力是未知的情況。結構的系統是由加速計與樑（桁架）所構在，整理系統成統御方程式。接著，運用有限元素法，將統御方程式離散成為矩陣式，然後利用平均加速度法將矩陣式，建構成卡爾曼濾波器的狀態方程式與量測方程式。卡爾曼濾波器對於外力趨勢主要採用預測、更新與濾波的步驟。最後，採用遞迴最小平方法去降低介於量測與估測外力的誤差，以求出未知外力，同時藉由不同時域，外力作用在樑（桁架）特定的位置，進行數值模擬探討與分析，可以展現目前方法正確性。 This paper investigates to predict the non-measurable displacement and forces of the structural system in time histories from accelerometer simulated records. It deals specifically with the situation where the external forces are unknown. The accelerometer and beam (truss) were modeled as a structural system in order to get a system governing equation. The matrix representation of governing equation of the structural system was constructed by the finite element method. Then the matrix representation was transformed to state equation and measurement equation of the Kalman filter by using the average acceleration method. The Kalman filter was adopted to predict, innovate and filter for the estimable displacement without external forces. Then using the recursive least square algorithm to decrease error between measurement and estimable of the external forces, therefore this paper finally got the estimable external forces. The accuracy of the current method is demonstrated by the numerical simulations for the external forces applied at the specific location of the beam (truss) in time histories.