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We study a Bayesian inverse problem arising in the context of resin transfer molding (RTM), which is a process commonly used for the manufacturing of fiber-reinforced composite materials. The forward model is described by a moving boundary problem in a porous medium. During the injection of resin in RTM, our aim is to update, on the fly, our probabilistic knowledge of the permeability of the material as soon as pressure measurements and observations of the resin moving domain become available. A probabilistic on-the-fly characterisation of the material permeability via the inversion of those measurements/observations is crucial for optimal real-time control aimed at minimising both process duration and the risk of defects formation within RTM. We consider both one-dimensional (1D) and two-dimensional (2D) forward models for RTM. Based on the analytical solution for the 1D case, we prove existence of the sequence of posteriors that arise from a sequential Bayesian formulation within the infinite-dimensional framework. For the numerical characterisation of the Bayesian posteriors in the 1D case, we investigate the application of a fully-Bayesian sequential Monte Carlo method (SMC) for high-dimensional inverse problems. By means of SMC we construct a benchmark against which we compare performance of a novel regularizing ensemble Kalman algorithm (REnKA) that we propose to approximate the posteriors in a computationally efficient manner under practical scenarios. We investigate the robustness of the proposed REnKA with respect to tuneable parameters and computational cost. We demonstrate advantages of REnKA compared with SMC with a small number of particles. We further investigate, in both the 1D and 2D settings, practical aspects of REnKA relevant to RTM, which include the effect of pressure sensors configuration and the observational noise level in the uncertainty in the log-permeability quantified via the sequence of Bayesian posteriors. The results of this work are also useful for other applications than RTM, which can be modelled by a random moving boundary problem. [ABSTRACT FROM AUTHOR]

In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach (Ruggeri et al 2017 Bayesian Anal. 12 407–33, Iglesias et al 2018 Int. J. Heat Mass Transfer116 417–31), for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified ensemble Kalman filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time. [ABSTRACT FROM AUTHOR]