Bayesian model updating with controlled Gaussian process predictive uncertainty

Abstract Bayesian model updating is widely used in engineering for the identification of unknown parameters of computational models based on noisy experimental measurements. In practical applications, however, the repeated evaluation of computational models may be demanding, which renders direct Bayesian inference prohibitive as it relies often on extensive sampling procedures. Surrogate models, particularly Gaussian process regression, are therefore frequently employed due to their capability to provide both predictions of the model response and a probabilistic characterization of the approximation uncertainty. Nevertheless, the uncertainty introduced by the surrogate model is not always treated consistently within the Bayesian inference procedure. This contribution proposes a framework for Bayesian model updating that explicitly propagates the predictive uncertainty induced by Gaussian process surrogates into the likelihood function via analytical marginalization. In addition, the proposed framework allows the simultaneous identification of the measurement noise characteristics. Moreover, an active learning strategy is developed in order to adaptively refine the surrogate model while controlling the uncertainty in the estimation of the model evidence. The resulting formulation provides a unified framework in which surrogate uncertainty, measurement noise, and adaptive learning are treated in a consistent probabilistic manner within Bayesian inference. The approach is illustrated by means of a simple dynamical system.