Bayesian finite element model updating

Abstract

In this chapter, the implementation of the reduced-order models within Bayesian finite element model updating is explored. The Bayesian framework for model parameter estimation, model selection, and robust predictions of output quantities of interest is first presented. Bayesian asymptotic approximations and sampling algorithms are then outlined. The framework is implemented for updating linear and nonlinear finite element models in structural dynamics using vibration measurements consisting of either identified modal frequencies or measured response time histories. For asymptotic approximations based on modal properties, the formulation for the posterior distribution is presented with respect to the modal properties of the reduced-order model. In addition, analytical expressions for the required gradients with respect to the model parameters are provided using adjoint methods. Two applications demonstrate that drastic reductions in computational demands can be achieved without compromising the accuracy of the model updating results. In the first application, a high-fidelity linear finite element model of a full-scale bridge with hundreds of thousands of degrees-of-freedom (DOFs) is updated using experimentally identified modal properties. In the second application, a nonlinear model of a base-isolated building is updated using acceleration response time histories. © 2019, Springer Nature Switzerland AG.