Bayesian updating using multi-fidelity active learning Kriging models

• An active learning Kriging methodology for Bayesian updating is presented. • The BUS method recasts the updating problem into an equivalent reliability problem, solved with a Kriging metamodel. • A multi-fidelity approach is employed in the active learning Kriging model, where models of different accuracy are adopted. • Multi-fidelity Bayesian optimization is used for calculating the constant c of the BUS method. • An improved version of the Quantified Active learning Subset Simulation method is proposed to define the posterior samples. The paper presents a multi-fidelity framework for efficient Bayesian updating using active learning Kriging models. The updating problem is solved as an equivalent probabilistic problem using the Bayesian updating with Structural reliability (BUS) method. The proposed approach leverages an ensemble surrogate modeling strategy that combines two Kriging models of multiple fidelities, thereby enhancing predictive capacity while reducing computational cost by exploiting information from models of different fidelity levels. A key contribution is the integration of multi-fidelity Bayesian optimization in order to determine the optimal BUS constant, ensuring accurate transformation of the posterior into a reliability problem. Furthermore, an improved version of the Quantified Active Learning Subset Simulation (qAK-SuS) method, previously proposed by the authors, is proposed in order to efficiently estimate small failure probabilities and obtain the posterior distribution. The proposed framework, called qAK-BUS, offers a robust solution for Bayesian inference in engineering systems by smartly balancing model fidelity, prediction variance, and learning efficiency. Three numerical examples and an engineering application that involves the updating of a reinforced concrete bridge are examined for demonstrating and validating the proposed framework.