A Regularization Scheme for Displacement Reconstruction
Using Acceleration Data Measured from Structures
Yun Hwa Hong
This paper presents a regularization scheme in time domain to estimate displacement history using measured acceleration from structures. Displacement estimation is redefined as an elliptic problem with boundary conditions to alleviate a constant drift, linear drift and nonlinear noise drift. Because of unknown boundary condition, this problem is a rank deficient problem. To solve this problem an optimization scheme is needed. An error function is defined as the least-squared error between measured accelerations and estimated accelerations. To alleviate the ill-posedness of an inverse problem the Tikhonov regularization technique are employed. The time window concept is proposed for real time system monitoring and real time displacement estimation. Generally, in Tikhonov regularization scheme, the regularization factor is determined by LCM(L-Curve Method), GCV (Generalized Cross Validation), GMS (Geometric Mean Scheme), VRFS (Variable Regularization Factor Scheme). In this paper, we select GCV method to determine the regularization factor because this method has been a popular method not only for determining the regularization factor but for estimating the noise amplitude of measurements. From parametric study using simple harmonic motions, GCV method can properly estimated the regularization factor. However, under severe noise condition, it has drawbacks such as over-fitting. To overcome the drawbacks, the fixed regularization technique is proposed. The validity of the proposed method is demonstrated by a numerical simulation study on five-story shear building and two-span bridge and presented by displacement estimation of a real cable free vibration.
Double Integration, Displacement Estimation, Regularization, Time Windowing Technique