Bayesian updating of complex nonlinear FE models with high-dimensional parameter space using heterogeneous measurements and a batch-recursive approach

Abstract

Finite element (FE) model updating aims to minimize the discrepancy between measured and FE-predicted responses of instrumented structural systems. In the last decades, significant efforts have focused on linear FE models, including recent studies investigating applications with large models (i.e., models with many degrees-of-freedom) and/or models with a large number of parameters to be estimated (i.e., high-dimensional parameter space). Recently, increasing interests have been attracted to the calibration of nonlinear FE models, which has emerged as an attractive approach for damage diagnosis and prognosis, chiefly if Bayesian methods are employed to solve the inverse parameter estimation problem. A crucial step towards the application of damage identification methods based on nonlinear FE model updating in the real-world, is the validation for cases involving large and complex nonlinear FE models requiring the estimation of a high number of parameters. In this paper, the performance of the unscented Kalman filter (UKF) in updating these types of models is investigated and a batch-recursive variant to reduce the computational cost is proposed. In addition, the effects of considering heterogeneous response measurements are studied. Two application examples of large and complex FE models involving strong nonlinearities, including a two-dimensional steel frame building and a three-dimensional isolated bridge, with high number of unknown model parameters are examined. Significant computational time savings of the presented batch-recursive approach, without sacrificing the estimation performance, are found. This confirms the feasibility of using Bayesian techniques to calibrate large and complex hysteretic FE models of real-world systems with high-dimensional parameter space. The successful results obtained here show that the presented approach represents a novel and promising tool to update large nonlinear structural FE models involving a great number of parameters whose calibration might become prohibitive by means of conventional updating techniques.