Flexible polyurethane foam (PUF) is a very versatile material ever created. The material is used for various applications and consumer end-use products such as upholstered furniture and mattresses. The increased use of these polymeric materials causes fire safety concerns. This has led to the development of various regulations and flammability test standards aimed at addressing the hazards associated with polyurethane foam fires. Several fire protection engineering correlations and thermal models have also been developed for the simulation of fire growth behaviour of polyurethane foams. Thus, the overall objective of this research project is to investigate the laboratory test behaviour of this material and then use finer modeling techniques to predict the heat release rate of the specimens, based on information obtained from cone calorimeter tests.<p> Full-scale fire tests of 10 cm thick polyurethane foams of different sizes were conducted using center and edge-ignition locations. Flame spread and heat release rates were compared. For specimens of the same size, center-ignition tests produced flame areas and peak heat release rates which were respectively 10 and 20% larger compared to edge-ignition tests. Average flame spread rates for horizontal and vertical spread were determined, and results showed excellent agreement with literature. Cone calorimeter tests of the specimens were performed using steel edge frame and open durarock board. Results indicate that different test arrangements and heat sources have significant effects on the fire behaviour of the specimens.<p> Predictions using the integral convolution model and other fire protection engineering correlations were compared with the full-scale tests results. Results show that the model was more efficient in predicting the heat release rates for edge-ignition tests than the center-ignition tests. The model also was more successful in predicting the heat release rates during the early part of the growth phase than during the later stages of the fire. The predicted and measured peak heat release rates and total heat release were within 10-15% of one another. Flame spread and t-squared fire models also gave satisfactory predictions of the full-scale fire behaviour of the specimens.

Flexible polyurethane foam (PUF) is a very versatile material ever created. The material is used for various applications and consumer end-use products such as upholstered furniture and mattresses. The increased use of these polymeric materials causes fire safety concerns. This has led to the development of various regulations and flammability test standards aimed at addressing the hazards associated with polyurethane foam fires. Several fire protection engineering correlations and thermal models have also been developed for the simulation of fire growth behaviour of polyurethane foams. Thus, the overall objective of this research project is to investigate the laboratory test behaviour of this material and then use finer modeling techniques to predict the heat release rate of the specimens, based on information obtained from cone calorimeter tests.<p> Full-scale fire tests of 10 cm thick polyurethane foams of different sizes were conducted using center and edge-ignition locations. Flame spread and heat release rates were compared. For specimens of the same size, center-ignition tests produced flame areas and peak heat release rates which were respectively 10 and 20% larger compared to edge-ignition tests. Average flame spread rates for horizontal and vertical spread were determined, and results showed excellent agreement with literature. Cone calorimeter tests of the specimens were performed using steel edge frame and open durarock board. Results indicate that different test arrangements and heat sources have significant effects on the fire behaviour of the specimens.<p> Predictions using the integral convolution model and other fire protection engineering correlations were compared with the full-scale tests results. Results show that the model was more efficient in predicting the heat release rates for edge-ignition tests than the center-ignition tests. The model also was more successful in predicting the heat release rates during the early part of the growth phase than during the later stages of the fire. The predicted and measured peak heat release rates and total heat release were within 10-15% of one another. Flame spread and t-squared fire models also gave satisfactory predictions of the full-scale fire behaviour of the specimens.

L'Analyse des Données Fonctionnelles (ADF) est une branche de la statistique qui est de plus en plus utilisée dans de nombreux domaines scientifiques appliqués tels que l'expérimentation biologique, la finance, la physique, etc. Une raison à cela est l'utilisation des nouvelles technologies de collecte de données qui augmentent le nombre d'observations dans un intervalle de temps.Les jeux de données fonctionnelles sont des échantillons de réalisations de fonctions aléatoires qui sont des fonctions mesurables définies sur un espace de probabilité à valeurs dans un espace fonctionnel de dimension infinie.Parmi les nombreuses questions étudiées par l'ADF, la régression linéaire fonctionnelle est l'une des plus étudiées, aussi bien dans les applications que dans le développement méthodologique.L'objectif de cette thèse est l'étude de modèles de régression linéaire fonctionnels lorsque la covariable X et la réponse Y sont des fonctions aléatoires et les deux dépendent du temps. En particulier, nous abordons la question de l'influence de l'histoire d'une fonction aléatoire X sur la valeur actuelle d'une autre fonction aléatoire Y à un instant donné t.Pour ce faire, nous sommes surtout intéressés par trois modèles: le modèle fonctionnel de concurrence (Functional Concurrent Model: FCCM), le modèle fonctionnel de convolution (Functional Convolution Model: FCVM) et le modèle linéaire fonctionnel historique. En particulier pour le FCVM et FCCM nous avons proposé des estimateurs qui sont consistants, robustes et plus rapides à calculer par rapport à d'autres estimateurs déjà proposés dans la littérature.Notre méthode d'estimation dans le FCCM étend la méthode de régression Ridge développée dans le cas linéaire classique au cadre de données fonctionnelles. Nous avons montré la convergence en probabilité de cet estimateur, obtenu une vitesse de convergence et développé une méthode de choix optimal du paramètre de régularisation.Le FCVM permet d'étudier l'influence de l'histoire de X sur Y d'une manière simple par la convolution. Dans ce cas, nous utilisons la transformée de Fourier continue pour définir un estimateur du coefficient fonctionnel. Cet opérateur transforme le modèle de convolution en un FCCM associé dans le domaine des fréquences. La consistance et la vitesse de convergence de l'estimateur sont obtenues à partir du FCCM.Le FCVM peut être généralisé au modèle linéaire fonctionnel historique, qui est lui-même un cas particulier du modèle linéaire entièrement fonctionnel. Grâce à cela, nous avons utilisé l'estimateur de Karhunen-Loève du noyau historique. La question connexe de l'estimation de l'opérateur de covariance du bruit dans le modèle linéaire entièrement fonctionnel est également traitée. Finalement nous utilisons tous les modèles mentionnés ci-dessus pour étudier l'interaction entre le déficit de pression de vapeur (Vapour Pressure Deficit: VPD) et vitesse d'élongation foliaire (Leaf Elongation Rate: LER) courbes. Ce type de données est obtenu avec phénotypage végétal haut débit. L'étude est bien adaptée aux méthodes de l'ADF. / Functional data analysis (FDA) is a statistical branch that is increasingly being used in many applied scientific fields such as biological experimentation, finance, physics, etc. A reason for this is the use of new data collection technologies that increase the number of observations during a time interval.Functional datasets are realization samples of some random functions which are measurable functions defined on some probability space with values in an infinite dimensional functional space.There are many questions that FDA studies, among which functional linear regression is one of the most studied, both in applications and in methodological development.The objective of this thesis is the study of functional linear regression models when both the covariate X and the response Y are random functions and both of them are time-dependent. In particular we want to address the question of how the history of a random function X influences the current value of another random function Y at any given time t.In order to do this we are mainly interested in three models: the functional concurrent model (FCCM), the functional convolution model (FCVM) and the historical functional linear model. In particular for the FCVM and FCCM we have proposed estimators which are consistent, robust and which are faster to compute compared to others already proposed in the literature.Our estimation method in the FCCM extends the Ridge Regression method developed in the classical linear case to the functional data framework. We prove the probability convergence of this estimator, obtain a rate of convergence and develop an optimal selection procedure of theregularization parameter.The FCVM allows to study the influence of the history of X on Y in a simple way through the convolution. In this case we use the continuous Fourier transform operator to define an estimator of the functional coefficient. This operator transforms the convolution model into a FCCM associated in the frequency domain. The consistency and rate of convergence of the estimator are derived from the FCCM.The FCVM can be generalized to the historical functional linear model, which is itself a particular case of the fully functional linear model. Thanks to this we have used the Karhunen–Loève estimator of the historical kernel. The related question about the estimation of the covariance operator of the noise in the fully functional linear model is also treated.Finally we use all the aforementioned models to study the interaction between Vapour Pressure Deficit (VPD) and Leaf Elongation Rate (LER) curves. This kind of data is obtained with high-throughput plant phenotyping platform and is well suited to be studied with FDA methods.