A Hellinger Distance-Based Stochastic Model Updating Framework for the Accreditation Validation of a Material Thermal Property Under Limited Data

The paper presents a distance-based Approximate Bayesian Computation framework involving the use of the Hellinger distance to perform stochastic model updating, and to subsequently perform an accreditation validation procedure based on the 2008 Sandia thermal problem. In computing the Hellinger distance, the adaptive-binning algorithm is implemented to adaptively select an appropriate bin number to approximate the probability density of the experimental data and the model prediction. The distance function subsequently quantifies the difference in the distribution between the two statistical objects. To verify the proposed stochastic model updating framework, the approach is implemented to perform a model calibration on the aleatory input variables of a dynamic temperature model of a slab material based on limited experimental data. This involves the use of the Staircase Density Function to calibrate and characterise the distribution over the input variables based on limited data, thereby providing for a distribution-free approach and eliminating the element of model uncertainty. A stochastic validation of the calibrated model is then performed against a set of accreditation validation experiment data. The results showed that using the mean estimates on the inferred shape parameters of the Staircase Density Function yields a better validation performance by the resulting calibrated model, in contrast to the case where the Maximum A-posteriori estimate on the inferred parameters is used.

Keywords: Stochastic model updating, Approximate Bayesian computation, Hellinger distance, Transitional Ensemble Markov chain Monte Carlo, Area metric, Model validation, Solid mechanics, Physics-guided machine-learning.