Batch and Recursive Bayesian Estimation Methods for Nonlinear Structural System Identification

This chapter presents a framework for the identification of nonlinear finite element (FE) structural models using Bayesian inference methods. Using the input-output dynamic data recorded during an earthquake event, batch and recursive Bayesian estimation methods are employed to update a mechanics-based nonlinear FE model of the structure of interest (building, bridge, dam, etc.). Unknown parameters of the nonlinear FE model characterizing material constitutive models, inertia, geometric, and/or constraint properties of the structure can be estimated using limited response data recorded through accelerometers or heterogeneous sensor arrays. The updated nonlinear FE model can be used to identify the damage in the structure following a damage-inducing event. This framework, therefore, can provide an advanced tool for post-disaster damage identification and structural health monitoring. The batch estimation method is based on a maximum a posteriori estimation (MAP) approach, where the time history of the input and output measurements are used as a single batch of data for estimating the FE model parameters. This method results in a nonlinear optimization problem that can be solved using gradient-based and non-gradient-based optimization algorithms. In contrast, the recursive Bayesian estimation method processes the information from the measured data recursively, and updates the estimation of the FE model parameters progressively over the time history of the event. The recursive Bayesian estimation method results in a nonlinear Kalman filtering approach. The Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) are employed as recursive Bayesian estimation methods herein. For those estimation methods that require the computation of structural FE response sensitivities (total partial derivatives) with respect to the unknown FE model parameters, the direct differentiation method (DDM) is used. Response data numerically simulated from a nonlinear FE model (with unknown material model parameters) of a five-story two-by-one bay reinforced concrete frame building subjected to bi-directional horizontal seismic excitation are used to illustrate the performance of the proposed framework.