Bayesian model updating and nonlinear response estimation of structures subjected to unknown loads via FE-aided Kalman Filtering

This paper proposes a novel methodology for updating the parameters and estimating the full response of a nonlinear structural system subjected to unknown loads and with sparsely measured responses. The proposed methodology is based on the combination of an FE-aided Kalman Filter framework for nonlinear joint input-state estimation with a Bayesian model updating framework. A new explicit formulation of the Newmark-beta method in state space form is introduced for the joint input-state estimation in the Kalman Filter-based estimation, which avoids the need for an invertible mass matrix and the computation of the matrix exponential. The unknown parameters are updated on the basis of the maximum a posteriori (MAP) estimate combined with Laplace’s approximation to obtain a probability distribution. The optimization problem to find the MAP estimate is performed by means of a surrogate-based optimization. The methodology is illustrated through a numerical example consisting of a 2D steel frame subjected to a strong ground motion and responding in the nonlinear regime. The obtained results are compared with a state-of-the-art method, showing a clear superiority in terms of computational efficiency and equally accurate results. • Joint input-state-parameter estimation via FE-aided KF and Bayesian model updating. • New explicit Newmark-beta formulation for joint input-state estimation. • Validated on numerical example of nonlinear 2D steel frame under ground motion. • Accurate estimation and faster than state-of-the-art method on nonlinear frame.