Chapter12 Bayesian FE Model Updating in the Presence of Modeling Errors Iman Behmanesh and Babak Moaveni 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. Keywords Probabilistic damage identification • Modeling error • Bayesian FE model updating • Uncertainty quantification • Likelihood function 12.1 Introduction In the structural health monitoring research community, damage identification is defined as the process of determining: (1) existence of damage; (2) location of damage; (3) severity of damage; and (4) remaining useful life of structures [1]. Among many methods that have been proposed in the past two decades [2–4], finite element (FE) model updating methods are popular for damage identification [5–9] because they directly provide information about the existence, location, and extent of damage, and because in some cases the updated FE model can also be used for damage prognosis. These methods have been successfully applied for damage identification of civil structures in recent years [10–14]. In the FE model updating methods, a set of structural model parameters, usually stiffness of finite elements, is adjusted so that the model predicted quantities of interest, modal parameters in this study, best match those obtained from the test data. Damage identification through FE model updating is usually performed in two steps: a baseline/reference model is calibrated in the first step to match the data at the undamaged state of the structure, and in the second step, another model is fitted to the data of the damaged structure. The difference between the two models indicates the location and extent of damage. The baseline model parameters are expected to be close to their corresponding values assigned in the initial FE model, as the initial model and its parameters are created based on the best level of engineer’s knowledge and based on the experimental test data. This expectation is not fulfilled when large modeling errors exist. In this case, the model parameters of the initial model usually need large and in many cases unrealistic modifications to fit to the undamaged state data. These unrealistic modifications often try to compensate for different sources of modeling errors. Moreover, our previous studies [14, 15] I. Behmanesh • B. Moaveni ( ) Department of Civil and Environmental Engineering, Tufts University, Medford, MA, USA e-mail: iman.behmanesh@tufts.edu; babak.moaveni@tufts.edu H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__12, © The Society for Experimental Mechanics, Inc. 2014 119
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