Bayesian history matching for structural dynamics applications

Computer models provide useful tools in understanding and predicting quantities of interest for structural dynamics. Although computer models (simulators) are useful for a specific context, each will contain some level of model-form error. These model-form errors arise for several reasons e.g., numerical approximations to a solution, simplifications of known physics, an inability to model all relevant physics etc. These errors form part of model discrepancy; the difference between observational data and simulator outputs, given the ‘true’ parameters are known. If model discrepancy is not considered during calibration, any inferred parameters will be biased and predictive performance may be poor. Bayesian history matching (BHM) is a technique for calibrating simulators under the assumption that additive model discrepancy exists. This ‘likelihood-free’ approach iteratively assesses the input space using emulators of the simulator and identifies parameters that could have ‘plausibly’ produced target outputs given prior uncertainties. This paper presents, for the first time, the application of BHM in a structural dynamics context. Furthermore, a novel method is provided that utilises Gaussian Process (GP) regression in order to infer the missing model discrepancy functionally from the outputs of BHM. Finally, a demonstration of the effectiveness of the approach is provided for an experimental representative five storey building structure.