Comparison between Bayesian updating and approximate Bayesian computation for model identification of masonry towers through dynamic data

Abstract

Model updating procedures based on experimental data are commonly used in case of historic buildings to identify numerical models that are subsequently employed to assess their structural behaviour. The reliability of these models is closely related to their ability to account for all the uncertainties that are involved in the knowledge process. In this regard, to handle these uncertainties and quantify their propagation, Bayesian inference is frequently employed being able to deal with the effects of parameter uncertainty, observation errors and model inadequacy. The computation of the posterior distribution through Bayesian inference needs–however–the evaluation of the likelihood function, which requires solving complex multi-dimensional integration problems. To bridge this shortcoming, the paper compares two Bayesian inference approaches to show how different approximations affect the results of simulated inference: a discrete approach for the likelihood computation in the Bayesian Model Updating (BMU) and a Monte Carlo likelihood-free method known as Approximate Bayesian Computation (ABC) are reported. As reference, the typology of historic masonry towers was considered by using their natural frequencies as experimental data for model updating. The two procedures provide very similar results supporting the validity of both methods despite ABC turns out to be a more flexible approach.

Bayesian Updating for Random Tensile Force Identification of Ancient Tie Rods Using Modal Data

“…where c = p(Θ)p(x)p(D|Θ, x)dxdΘ is the normalizing constant. Further details about this mathematical formulations can be found in [38]. The primary objective of using latent random variables in this study is to expansively augment the parameter space, thereby facilitating the tractable treatment of distributions that would otherwise be deemed intractable.…”

“…At its core, Bayesian inference uses the well known Bayes' theorem [28] to calculate the probability over an hypothesis or a parameter space given observed data. The use of dynamic data to update the initial hypotheses over the input parameter of a computational structural model was firstly introduced in [29,30], becoming an actual research topic to solve the structural inverse problems (i.e., numerical model updating) of different types of structure (i.e., steel structures, masonry buildings, timber buildings, dams, wind turbines) [31][32][33][34][35][36][37][38][39].…”