Bayesian FE Model Updating in the Presence of Modeling Errors

Abstract

A new likelihood function is proposed for probabilistic damage identification of civil structures that are usually modeled with many simplifying assumptions and idealizations. Data from undamaged and damaged states of the structure are used in the likelihood function and damage is identified through a Bayesian finite element (FE) model updating process. The new likelihood function does not require calibration of an initial FE model to a baseline/reference model and is based on the difference between damaged and healthy state data. It is shown that the proposed likelihood function can identify structural damage as accurately as two other types of likelihood functions frequently used in the literature. The proposed likelihood is reasonably accurate in the presence of modeling error, measurement noise and data incompleteness (number of modes and number of sensors). The performance of FE model updating for damage identification using the proposed likelihood is evaluated numerically at multiple levels of modeling errors and structural damage. The effects of modeling errors are simulated by generating identified modal parameters from a model that is different from the FE model used in the updating process. It is observed that the accuracy of damage identifications can be improved by using the identified modes that are less affected by modeling errors and by assigning optimum weights between the eigen-frequency and mode shape errors.KeywordsProbabilistic damage identificationModeling errorBayesian FE model updatingUncertaintyquantificationLikelihood function