A Bayesian optimization approach for finite element model updating

Model updating aims at estimating unknown system properties, that are described by parameters in numerical models, when actual observations of the physical system response are available. Typically, besides plain model calibration purposes, model updating procedures are employed for non-destructive damage assessment of structures. In this framework, damage can be located and quantified by updating stiffness-related parameters: a local reduction of stiffness denotes localized structural damage. When iterative model updating methods that make use of a cost function are concerned, three major critical aspects may compromise the success of the whole updating procedure: the FE model validity, the reliability of the experimental data and the complexity of the optimization problem at the computational level. Usually, the insidious nature of the model updating problem along with the use of sophisticated FE models generate expensive and non-convex cost functions which minimization is a non-trivial task. To deal with such a challenging optimization problem, this work makes use of a Bayesian approach, which performance is compared to three well-established global optimization techniques, namely pattern search, Simulated annealing and Genetic Algorithm, by means of four numerical case studies. In Bayesian optimization methods, a prior is set over the objective function and combined with evidence (an observation) to get a posterior function. This enables the intelligent selection of the next point to be sampled from the objective function, taking into account both exploitation and exploration needs, resulting in a very efficient global optimization technique, that is best-suited for minimizing expensive black-box functions. Bayesian optimization is also deemed as a surrogate optimization technique, since the prior, usually a Gaussian Process (GP), can be seen as a probabilistic surrogate model of the underlying objective function. The last case study, the bell tower of Santa Maria Maggiore cathedral in Mirandola (Italy), served also as an experimental case study, allowing to evaluate the performance of this relatively new global optimization technique in a real-case model updating scenario.