Information-driven modeling of structures using a Bayesian framework

Abstract

This work presents a comprehensive Bayesian framework for integrating information from data and models of civil infrastructure systems. In the proposed framework, modeling uncertainties are quantified and propagated through simulations using probability tools. Bayes theorem is used to select the most appropriate model among alternative competing ones, to estimate the parameters of a model and the uncertainties in the parameters, and to propagate the uncertainties in output quantities of interest that are important for evaluating structural performance and safety. The framework is developed using as data the modal characteristics estimated from response time history measurements. Theoretical challenges associated with the selection of the model prediction error equation introduced to build up the likelihood are pointed out. Bayesian tools such as Laplace asymptotic approximations and sampling algorithms require a moderate to very large number of system re-analyses to be performed, often resulting in excessive computational demands. Computationally efficient techniques are presented to drastically speed up computations within the Bayesian uncertainty quantification framework. These techniques include model reduction techniques based on component mode synthesis, surrogate models and parallelized Bayesian algorithms to exploit HPC environments. Bayesian optimal experimental design methods constitute a major component of the proposed framework for cost-effectively selecting the most informative data. A computationally efficient asymptotic approximation is proposed to simplify information-based utility functions used for optimizing the placement of sensors in a structure. The structure of the approximation provides insight into the use of the prediction error spatial correlation to avoid sensor clustering, as well as the effect of the prior uncertainty on the optimal sensor configuration. The framework is illustrated by integrating vibration measurements and high fidelity models for (a) a reinforced concrete bridge to update stiffness related model parameters, and (b) a circular hanger to estimate the axial tension required in structural safety evaluations.