Active learning Kriging methods for Bayesian updating

The paper studies the efficiency and the accuracy of active learning Kriging methods for Bayesian updating.Classical Bayesian updating is formulated as a reliability analysis problem using the Bayesian Updating with Structural reliability (BUS) methods, enabling active learning Kriging models to estimate the posterior distributions.The resulting structural reliability problem is handled with the aid of the quantified active learning Kriging (qAK) algorithm that was recently proposed by the authors.The accuracy of the BUS method depends strongly on the constant c, whose calculation using a surrogate Kriging model is a challenging problem.For this purpose, two approaches for calculating the constant c are compared: in the first approach, it is calculated during the active learning process, and in the second, c is calculated prior to the analysis, solving a global optimization problem.When the adaptive approach is chosen, emphasis is placed on strategies that leverage computational geometry algorithms for computing the convex hull of a set of sample points.In case of a nonadaptive scheme, the calculation of c is achieved by solving a global optimization problem, where an acquisition function guides the Design of Experiments of the Kriging model.The adopted methods are evaluated with the aid of a benchmark problem, demonstrating the advantages and disadvantages of each method.The work highlights the synergies between active learning and Bayesian inference, providing valuable insights for future research and practical applications in structural engineering.