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

摘要

This paper deals with an inverse problem applied to the field of buildingphysics to experimentally estimate three sorption isotherm coefficients of awood fiber material. First, the mathematical model, based on convectivetransport of moisture, the optimal experiment design (OED) and the experimentalset-up are presented. Then measurements of relative humidity within thematerial are carried out, after searching the OED, which is based on thecomputation of the sensitivity functions and a priori values of the unknownparameters employed in the mathematical model. The OED enables to plan theexperimental conditions in terms of sensor positioning and boundary conditionsout of 20 possible designs, ensuring the best accuracy for the identificationmethod and, thus, for the estimated parameter. Two experimental procedures wereidentified: 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 periodfor each step. For both experiment designs, it has been shown that the sensorhas to be placed near the impermeable boundary. After the measurements, theparameter estimation problem is solved using an interior point algorithm tominimize the cost function. Several tests are performed for the definition ofthe cost function, by using the L\_2 or L\_infty norm and considering theexperiments separately or in the same time. It has been found out that theresidual between the experimental data and the numerical model is minimizedwhen considering the discrete Euclidean norm and both experiments separately.It means that two parameters are estimated using one experiment while the thirdparameter is determined with the other experiments. Two cost functions aredefined and minimized for this approach. Moreover, the algorithm requires lessthan 100 computations of the direct model to obtain the solution. In addition,the OED sensitivity functions allow to capture an approximation of theprobability distribution function of the estimated parameters. The determinedsorption isotherm coefficients enable to calibrate the numerical model and fitbetter the experimental data, reducing the discrepancies usually reported inthe literature that underestimate the moisture adsorption and overestimate thedesorption processes.