Impact of the number and sampling time of water content measurements on the identifiability of a concentration-dependent water diffusivity

Abstract

The aim of this work was to determine the impact of the experimental conditions (number and sampling time) of measurements of the water content on the identifiability of a concentration-dependent water diffusivity. Water contents simulating a drying process were generated from a diffusion model with the addition of Gaussian noise. An infinite slab with Dirichlet boundary conditions was considered. The coefficients describing a concentration-dependent water diffusivity were estimated from the water content by least-squares minimization. The identifiability of the coefficients was investigated from the model sensitivity functions and using the asymptotic method, the profile likelihood method, and Monte Carlo simulation. The inner product sensitivity matrix was full rank, indicating that the coefficients were locally structurally identifiable. The coefficients were estimated more accurately from water content obtained over the whole drying process, because sampling times concentrated in a short period increased the correlation between the coefficients and increased their uncertainty. The coefficients were practically identifiable from the water content for noise intensity below 0.4%. Above that threshold, the number of measurements of the water content required for the practical identifiability of the coefficients increased linearly with the noise intensity of the water content.