Adaptive Bayesian Inference Framework for Joint Model and Noise Identification

Abstract

Model updating, the process of inferring a model from data, is prone to the adverse effects of modeling error, which is caused by simplification and idealization assumptions in the mathematical models. In this study, an adaptive recursive Bayesian inference framework is developed to jointly estimate model parameters and the statistical characteristics of the prediction error that includes the effects of modeling error and measurement noise. The prediction error is usually modeled as a Gaussian white noise process in a Bayesian model updating framework. In this study, the prediction error is assumed to be a nonstationary Gaussian process with an unknown and time-variant mean vector and covariance matrix to be estimated. This allows one to better account for the effects of time-variant model uncertainties in the model updating process. The proposed approach is verified numerically using a 3-story 1-bay nonlinear steel moment frame excited by an earthquake. Comparison of the results with those obtained from a classical nonadaptive recursive Bayesian model updating method shows the efficacy of the proposed approach in the estimation of the prediction error statistics and model parameters.