Experimental validation of the Kalman-type filters for online and real-time state and input estimation

Abstract

In this study, a novel dual implementation of the Kalman filter proposed by Eftekhar Azam et al. (2014, 2015) is experimentally validated for simultaneous estimation of the states and input of structural systems. By means of numerical simulations, it has been shown that the proposed method outperforms existing techniques in terms of robustness and accuracy for the estimated displacement and velocity time histories. Herein, dynamic response measurements, in the form of displacement and acceleration time histories from a small-scale laboratory building structure excited at the base by a shake table, are considered for evaluating the performance of the proposed Dual Kalman filter and in order to compare this with available alternatives, such as the augmented Kalman filter (Lourens et al., 2012b) and the Gillijn De Moore filter (GDF) (2007b). The suggested Bayesian approach requires the availability of a physical model of the system in addition to output-only measurements from limited degrees of freedom. Two categories of such physical models are herein studied to evaluate the effect of model error on the filter performances; the first, is a model that comprises identified modal parameters, i.e., natural frequencies, mode shapes, modal damping ratios and modal participation factors; the second, is a model that is extracted from a recently developed subspace identification procedure, namely the transformed stochastic subspace identification method. The results are encouraging for the further use of the dual Kalman filter and its available alternatives for addressing the important problems of full response reconstruction and fatigue estimation in the entire body of linear structures, using a limited number of output-only vibration measurements.