Bayesian inversion in resin transfer molding

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 y, 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-y 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 and two-dimensional forward models for RTM. Based on the analytical solution for the one-dimensional case, we prove existence of the sequence of posteriors that arise from a sequential Bayesian formulation within the in_nite-dimensional framework. For the numerical characterisation of the Bayesian posteriors in the one-dimensional 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 one-dimensional and two-dimensional settings, practical aspects of REnKA relevant to RTM, which include the e_ect of pressure sensors con_guration 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.