A Regularization Scheme for Displacement Reconstruction Using Acceleration Data Measured from Structures

摘要

This paper present a new displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second-order central finite difference of displacement. The displacement is reconstructed by minimizing the least squared errors between measured and approximated acceleration within a finite time interval referred to as a time window. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill-posed because the boundary conditions at both ends of each time window are not known a priori. Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement similar to the conventional time integration schemes. A Tikhonov regularization scheme is adopted to alleviate the ill-posedness. The validity of the proposed method is demonstrated through two laboratory experiments.