Analysis and improvement of the VTT mold growth model: application to bamboo fiberboard

Julien Berger (1) , Hervé Le Meur (2) , Denys Dutykh (3, 4, 5) , Dang Mao Nguyen (1) , A.-C. Grillet (1)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 LAMA - Laboratoire de Mathématiques
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
5 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

The reliability of a model is its accuracy in predicting the physical phenomena using the known input parameters. It also depends on the model's ability to estimate relevant parameters using observations of the physical phenomena. In this paper, the reliability of the VTT model is investigated under these two criteria for various given temperature and relative humidity constant in time. First of all, experiments are conducted on bamboo fiberboard. Using these data, five parameters of the VTT model, defining the mold vulnerability class of a material, are identified. The results highlight that the determined parameters are not within the range of the classes defined in the VTT model. In addition, the quality of the parameter estimation is not satisfactory. Then the sensitivity of the numerical results of the VTT model is analyzed by varying an input parameter. These investigations show that the VTT mathematical formulation of the physical model of mold growth is not reliable. An improved model is proposed with a new mathematical formulation. It is inspired by the logistic equation whose parameters are estimated using the experimental data obtained. The parameter estimation is very satisfactory. In the last parts of the paper, the numerical predictions of the improved model are compared to experimental data from the literature to prove its reliability.

Mots clés: VTT model; Mold growth prediction models; Fisher matrix; Structural identifiability; Parameter estimation problem; Model reliability

Domaines: Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]; Analyse numérique [cs.NA]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Physique Numérique [physics.comp-ph]; Matériaux; Construction durable; Eco-conception

Julien Berger, Hervé Le Meur, Denys Dutykh, Dang Mao Nguyen, A.-C. Grillet. Analysis and improvement of the VTT mold growth model: application to bamboo fiberboard. Building and Environment, 2018, 138, pp.262-274. ⟨10.1016/j.buildenv.2018.03.031⟩. ⟨hal-01759837v2⟩