Nonlinear Structural Finite Element Model Updating Using Batch Bayesian Estimation

Abstract

This paper proposes framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation (MLE) method to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. Using the MLE as a parameter estimation tool results in a nonlinear optimization problem, which can be efficiently solved using gradient-based optimization algorithms such as the interior-point method. Gradient-based optimization algorithms require the FE response sensitivities with respect to the material parameters to be identified, which are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to validate the proposed nonlinear FE model updating framework. The simulated responses of this bridge pier to an earthquake ground motion is polluted with artificial output measurement noise and used to estimate the unknown parameters of the material constitutive model. The example illustrates the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise.