On the estimation of sorption isotherm coefficients using the optimal experiment design approach

Julien Berger (1, 2) , Thomas Busser (3, 1, 4) , Denys Dutykh (5) , Nathan Mendes (2)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 PUCPR - Pontifical Catholic University of Paraná
3 DTS - Département des Technologies Solaires
4 INES - Institut National de L'Energie Solaire
5 LAMA - Laboratoire de Mathématiques

This paper deals with an inverse problem applied to the field of building physics to experimentally estimate three sorption isotherm coefficients of a wood fiber material. First, the mathematical model, based on convective transport of moisture, the optimal experiment design (OED) and the experimental set-up are presented. Then measurements of relative humidity within the material are carried out, after searching the OED, which is based on the computation of the sensitivity functions and a priori values of the unknown parameters employed in the mathematical model. The OED enables to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs, ensuring the best accuracy for the identification method and, thus, for the estimated parameter. Two experimental procedures were identified: i) single step of relative humidity from 10% to 75% and ii) multiple steps of relative humidity 10-75-33-75% with an 8-day duration period for each step. For both experiment designs, it has been shown that the sensor has to be placed near the impermeable boundary. After the measurements, the parameter estimation problem is solved using an interior point algorithm to minimize the cost function. Several tests are performed for the definition of the cost function, by using the L_2 or L_infty norm and considering the experiments separately or in the same time. It has been found out that the residual between the experimental data and the numerical model is minimized when considering the discrete Euclidean norm and both experiments separately. It means that two parameters are estimated using one experiment while the third parameter is determined with the other experiments. Two cost functions are defined and minimized for this approach. Moreover, the algorithm requires less than 100 computations of the direct model to obtain the solution. In addition, the OED sensitivity functions allow to capture an approximation of the probability distribution function of the estimated parameters. The determined sorption isotherm coefficients enable to calibrate the numerical model and fit better the experimental data, reducing the discrepancies usually reported in the literature that underestimate the moisture adsorption and overestimate the desorption processes.

Mots clés: Optimal Experiment Design (OED); parameter estimation problem; convective moisture transfer; sensitivity functions; sorption moisture coefficients

Domaines: Mécanique des fluides [physics.class-ph]; Analyse classique [math.CA]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Physique Numérique [physics.comp-ph]; Mécanique des fluides [physics.class-ph]; Thermique [physics.class-ph]

Julien Berger, Thomas Busser, Denys Dutykh, Nathan Mendes. On the estimation of sorption isotherm coefficients using the optimal experiment design approach. 2017. ⟨hal-01509113v1⟩