Bayesian inversion in resin transfer molding

TL;DR

This paper develops Bayesian methods to infer the permeability of porous media in Resin Transfer Molding, comparing a novel ensemble Kalman algorithm with Sequential Monte Carlo, and analyzing their robustness and practical implications.

Contribution

It introduces a computationally efficient ensemble Kalman method for Bayesian inversion in RTM and compares it with existing SMC techniques, including theoretical analysis and practical applications.

Findings

REnKA is robust to parameter tuning and computationally efficient.

REnKA outperforms SMC with fewer particles in accuracy.

Bayesian posteriors effectively quantify uncertainty in permeability.

Abstract

We study the Bayesian inverse problem of inferring the permeability of a porous medium within the context of a moving boundary framework motivated by Resin Transfer Molding (RTM), one of the most commonly used processes for manufacturing fiber-reinforced composite materials. During the injection of resin in RTM, our aim is to update our probabilistic knowledge of the per- meability of the material by inverting pressure measurements as well as observations of the resin moving domain. 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 infinite-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 param- eters and computational cost, and display advantages of REnKA compared with SMC with a small number of particles. We further apply REnKA to investigate, in both the one-dimensional and two-dimensional settings, practical aspects 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.