This work presents a framework for updating an estimate of a probability distribution, arising from an uncertainty propagation using Non-intrusive Polynomial Chaos (NIPC), with scarce experimental measurements of a Quantity of Interest (QoI). In recent years much work has been directed towards developing methods of combining models of different accuracies in order to propagate uncertainty, but the problem of improving uncertainty propagations by considering evidence from both computational models and experiments has received less attention.

The framework described here uses the Maximum Entropy Principle (MEP) to find an updated, least biased estimate of a probability distribution by maximising the entropy between the original and updated estimates. A constrained optimisation is performed to find the coefficients of a Polynomial Chaos Expansion (PCE) that minimise the Kullback–Leibler (KL) divergence between estimates, while ensuring that the new estimate conforms to constraints imposed by the available experimental measurements of the QoI. In this work a novel constraint is used, based upon the Dvoretzky–Kiefer–Wolfowitz inequality and the Massart bound (DKWM), as opposed to the more commonly used moment-based constraints. Such a constraint allows scarce experimental data to be used in informing the updated estimate of the probability distribution.