Effect of the water content measurements on the estimation and identifiability of water diffusion and convection mass transfer coefficients

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

“…For the profile likelihood method, confidence intervals were calculated following Mercier et al [9]. Briefly, the method consisted of modifying the value of one coefficient, starting from its least-squares value, by increments of 5% in the increasing and decreasing directions and minimizing SSE (Eq.…”

“…Minimization of SSE was performed using the Nelder-Mead simplex search algorithm following Mercier et al [9]. The coefficients minimizing SSE were denoted byD 0 andÂ.…”

“…Analysis of the least-squares objective function by Mercier et al [9] showed the structural identifiability of the water diffusivity and the convection mass transfer coefficient from local or global measurements of the water content. However, a high number of measurements is required for the practical identifiability of the coefficients if the measurement noise is above 2% for global water content and above 5% for local water content.…”

“…However, a high number of measurements is required for the practical identifiability of the coefficients if the measurement noise is above 2% for global water content and above 5% for local water content. Mercier et al [9] also showed that the confidence intervals of the water diffusivity and the convection mass transfer coefficient need to be calculated using a systematic method, such http as the profile likelihood method, because the local asymptotic method assumes symmetric confidence intervals and underestimates the uncertainty of the coefficients. In accordance with Mercier et al [9], Martinez-Lopez et al [10] showed that local measurements of the output variable provide more accurate estimates of the coefficients than global measurements do and that local measurements hence promote the coefficients' practical identifiability.…”

“…Mercier et al [9] also showed that the confidence intervals of the water diffusivity and the convection mass transfer coefficient need to be calculated using a systematic method, such http as the profile likelihood method, because the local asymptotic method assumes symmetric confidence intervals and underestimates the uncertainty of the coefficients. In accordance with Mercier et al [9], Martinez-Lopez et al [10] showed that local measurements of the output variable provide more accurate estimates of the coefficients than global measurements do and that local measurements hence promote the coefficients' practical identifiability. Wan et al [11] studied the impact of the number of measurements of the output variable on the practical identifiability of the coefficients for different geometries and showed that the coefficients are practically identifiable if the ratio of noise to the number of measurements is low and if the Biot number (dimensionless ratio between the internal and external resistances) is close to unity.…”