Hierarchical Bayesian calibration of deck deflection models using distributed fiber optic strain data

A naval hovercraft was outfitted with a distributed fiber optic sensing system (FOSS) on its cargo deck in which two fibers were placed along orthogonal axes. A series of trucks were loaded onto the cargo deck to simulate operational loading conditions and the resulting strain profiles were measured by the distributed FOSS. The aim of this study is to quantify the deck deflections that correspond to the measured strains under different vehicular loads. This is accomplished by idealizing the cargo deck as a rectangular plate and using the data to estimate the associated plate model parameters. In order to account for measurement noise and model prediction error, as well as the inherent variability of inferences made with different data sets, a hierarchical Bayesian scheme that considers both the model parameter uncertainty and the prediction error variance is utilized to derive the posterior distributions of the model hyper-parameters, i.e., their mean and variance. Given the volume of FOSS strain data available, different approaches were taken for incorporating the data into the hierarchical approach in order to determine whether the inclusion of all available strain data meaningfully reduced the uncertainty compared to using only time-averaged strain. Comparisons between the different approaches are explored in the context of 95% confidence intervals for strain profiles, deck deflection envelopes, and reliability indices based on allowable deflections.