Statistical Regularization for Identification of Structural Parameters and External Loadings Using State Space Models

A novel numerical approach is presented, in the time domain, to simultaneously identify structural parameters and unmeasured input loadings using incomplete output measurement only. The identification problem is formulated as an optimization process, wherein the objective function is defined as the discrepancy between the measured and the predicted data, and is solved by a damped Gauss-Newton method. Because the proposed algorithm is a time domain technique, forward analyses are required to obtain predicted system responses so as to compute the discrepancy. Therefore, we propose an input force estimation scheme in the identification process to complete the task of input-output forward analyses, for the case of output-only measurement. The relationship between the unknown input loadings and the output measurement is established through a state space model, which basically formulates an ill-posed least squares problem. A statistical Bayesian inferencebased regularization technique is presented to solve such a least squares problem. Finally, the proposed approach is illustrated by both numerical and experimental examples using output-only measurements of either acceleration or strain time histories. The results clearly show the robustness and the applicability of the proposed algorithm to simultaneously identify structural parameters and unmeasured input loadings with a high accuracy.