Parameter estimation and model selection for water sorption in a wood fibre material
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Parameter estimation and model selection for water sorption in a wood fibre material Julien Berger1 · Thibaut Colinart2 · Bruna R. Loiola3 · Helcio R. B. Orlande4 Received: 21 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The sorption curve is an essential feature for the modelling of heat and mass transfer in porous building materials. Several models have been proposed in the literature to represent the amount of moisture content in the material according to the water activity (or capillary pressure) level. These models are based on analytical expressions and few parameters that need to be estimated by inverse analysis. This article investigates the reliability of eight models through the accuracy of the estimated parameters. For this, experimental data for a wood fibre material are generated with special attention to the stop criterion to capture long time kinetic constants. Among five sets of measurements, the best estimate is computed. The reliability of the models is then discussed. After proving the theoretical identifiability of the unknown parameters for each model, the primary identifiability is analysed. It evaluates whether the parameters influence on the model output is sufficient to proceed the parameter estimation with accuracy. For this, a continuous derivative-based approach is adopted. Seven models have a low primary identifiability for at least one parameter. Indeed, when estimating the unknown parameters using the experimental observations, the parameters with low primary identifiability exhibit large uncertainties. Finally, an Approximation Bayesian Computation algorithm is used to simultaneously select the best model and estimate the parameters that best represent the experimental data. The GAB and Fredlund-Xing models, together with a proposed model in this work, were the best ones selected by this algorithm. List of symbols Physical parameters: Latin letters a, â Water activity (–) K Slope of the sorption model (–) Electronic supplementary material The online version of this article (https://doi.org/10.1007/s0022 6-020-01206-0) contains supplementary material, which is available to authorized users. * Julien Berger julien.berger@univ‑lr.fr Extended author information available on the last page of the article
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Wood Science and Technology
m, m0 Mass (kg) p Parameter of a model (–) R1 Water vapour gas constant (J kg−1 K−1 ) T Temperature (K) u, u0 , û , um Moisture content dry basis (–) Physical parameters: Greek letters 𝛿 Measurement uncertainty (–) 𝛿∼ Random component of measurement uncertainty (–) 𝛿𝜎 Systematic component of measurement uncertainty (–) 𝛹 Capillary pressure (Pa) 𝜌 Material dry density (kg m−3 ) 𝜌2 Liquid water specific mass (kg m−3 ) Mathematical notations: Latin letters d Distance function i 𝔇i Polynomial of order i f Sorption model function F Fisher matrix K Kernel perturbation N Number of parameters of a model Na Number of measurement points for a population Ne Number of carried o
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