Bayesian inference of structural model parameters in an uncertainty quantification framework

In structural engineering, modeling fulfills a key role to simulate the behavior of structures, but even very detailed models may fail to represent critical mechanisms. The uniqueness and uncertainties associated with civil structures make the prediction of the actual mechanical characteristics and the structural performance, a difficult task. Reliable estimates require calibration of system parameters based on measured experimental response data. To date, several different approaches have been adopted in literature. Generally, these ones try to minimize the difference between the model output and the experimental data. However, inverse problems (such as the estimate of mechanical parameters) when treated deterministically, are typically ill-conditioned and often ill-posed, since the values of parameters used to predict the structural behavior are uncertain owing to simplifying and approximate assumptions on model. As consequence, these modeling uncertainties suggest that a single optimal parameter vector is not sufficient to specify the structural model, but rather a family of all plausible values of the model parameters consistent with observations needs to be identified. A common accepted approach to deal with model uncertainties and experimental errors is to consider the identification problem from a statistical perspective. In the last decade, Bayesian model updating techniques became the standard tool for the identification of nonlinear dynamical systems. These techniques provide a robust and rigorous framework due to their ability to account model uncertainties and other sources of errors intrinsic in any system identification method as result of noise-measurements, as well as the partial model capacity to replicate the real physics of the system of interest. This understanding has resulted in the need to model a discrepancy term to connect model prediction to the observations. The goal of this thesis work is to provide a fuller treatment of the posterior uncertainty linked to the discrepancy. Specifically, the Bayesian inference has been applied to the system identification of nonlinear hysteretic systems not only to provide the most plausible model parameters and their probability distribution in uncertainty framework, but also to estimate the probability of the model discrepancy, i.e. a probabilistic estimate of the influence of the effects of measurement error and model inaccuracy on the prediction of system parameters. This Bayesian approach is illustrated first for parameters estimation of a basic nonlinear model using simulated data, and then applied to an experimental case study for the system identification of a planar masonry facade system with the application of the hybrid simulation/testing procedure for seismic response history. The effectiveness of the proposed Bayesian inference of system identification in uncertainty framework lies in providing probabilistic information of the estimated parameters and on their error, which can be useful at the moment of making decisions with respect to the selection of parameters and/or the assessment of mathematical models that simulate the nonlinear behavior experienced by the system.