Model updating and model selection for structural structures via Approximate Bayesian Computation

Approximate Bayesian methods, or “likelihood-free” methods, have become a key component of modern statistical methodology, providing a framework for inference, prediction, and decision-making. Their versatility lies in their ability to handle parameter estimation, model selection, and uncertainty quantification within a unified probabilistic framework. In this work, Approximate Bayesian Computation (ABC) using an ellipsoidal Nested Sampling (NS) approach is employed to deal with model updating and model comparison issues applied to structural health monitoring. ABC methods rely essentially on the ability to simulate data from a simulator/forward model, bypassing the need to write down an explicit likelihood function, which is always far from trivial. These methods are particularly captivating because of the modelling freedom they provide; in addition, they are flexible in the sense that different discrepancy functions measuring the similarity between the observed modal data and the corresponding model output can be used. However, Bayesian inference methods usually require numerous forward model simulations to generate converged samples. To enhance the computational efficiency of the sampler, the minimum-volume enclosing ellipsoid (MVEE) is incorporated to better enclose the accepted particles and to guide the sampler more efficiently towards the highest probability region. The performance and the robustness of the novel sampler in structural model updating and model selection is demonstrated here via different numerical studies using modal data.