A novel constrained UKF method for both updating structural parameters and identifying excitations for nonlinear structures

Finite element-based model updating of civil structures has been attracting increasing attention in structural health assessment and fragility analysis since several decades ago. However, the previously proposed finite element (FE) model updating methods for structures are either primarily limit to linear models under given external excitation or unknown excitation which should satisfy some assumptions. In this regard, this study proposes a novel constrained unscented Kalman filter (UKF) method for both updating structural parameters and identifying unknown external excitations without any assumption for strongly nonlinear structures. The unknown excitation (e.g., ground acceleration) can be preliminarily extracted from the state and measurement equations and then can be estimated by a recursive nonlinear least-square algorithm. To implement the recursive nonlinear least-square algorithm, a combined Matlab-OpenSees recursion platform herein is specially developed. It should be noted that certain constraints are necessary to be imposed on the sigma points to guarantee the propagation of the sigma points at each recursion step when the recursive nonlinear least-square algorithm is running. A three-story three-span steel frame and a three-span continuous reinforced concrete (RC) bridge, as two examples, are investigated for verifying the applicability of the novel constrained UKF method. The parameters which are most sensitive to the dynamic responses of structures are determined for identification. Subsequently, these structural parameters and the unknown excitation (e.g., ground motion) are jointly identified using the novel constrained UKF method based on partially measured noise-contaminated responses. In such a way, the feasibility of the Matlab-OpenSees recursion platform for structural dynamic inverse problems and the effectiveness of the novel constrained UKF for nonlinear model updating of structures are both verified.