Identifying structural variability using Bayesian inference

A stochastic approach is proposed for estimating the variability in structural parameters present in a large set of metal-frame structures, given only measurements of modal frequency performed on a subset of the structures. The key step is a new statistical model relating simulation and experiment, including terms representing not only the measurement noise, but also the unknown structural variability. This latter is modelled by random variables whose hyper-parameters are themselves stochastic, and these hyper-parameters are estimated by Bayes' theorem. The evaluation of the posterior distribution is efficiently performed by combining a number of modern numerical tools: kriging surrogates for the finite-element analysis, probabilistic collocation uncertainty quantification, and Markov chain Monte-Carlo. The method is demonstrated for a metal-frame model with two uncertain parameters, using data from specially designed experiments with controlled variability. The output probability densities on the structural parameters are useful for input to subsequent uncertainty quantification.