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, IX. Annexes ANNEXE

A. F. Monnet, S. Berland, C. ;. Michon, K. Monnet, C. Laleg et al., novembre 2016legume flour, which differs in composition, has an impact on the balance of the components in the formula. Legume flours contain less starch, more protein and more fiber than wheat flour and semolina, at an equal or higher lipid content. Starch content accounts for between 60% and 80% db of soft and durum wheat, whereas it ranges from 40% to 65% for legumes except for lupin (less than 1% db, Approche intégrée Filières. A.F. Monnet, M.H. Jeuffroy, C. Michon, Journée atelier-échange Nestlé. Paris, 7 novembre 2016. -Association céréale-légumineuse : Caractériser les farines pour mieux les transformer. A.F. Monnet, S. Berland, C. Michon. Poster présenté dans le cadre des Journée Techniques des Industries Céréalières, vol.1, pp.32-33, 1987.

, Protein contents (N x 6.25) vary between 20% and 30% db in legume flours (D'Appolonia, 1977.

N. Wang, 2009) except in faba and lupin flours in which protein can reach almost 40% db, wheat flour and semolina, protein content usually varies between 9% and 18% db, 2000.

. Abou-zaid, Fiber contents are around 2% db in wheat flour and semolina while it can reach 10% db in pea and faba flours, and even 20% to 40% db in chickpea, lentil and lupin flours, 2011.

. Osorio-díaz, , 2008.

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, Annexe 3 : Démarche de plan d'expériences pour la modélisation et l'optimisation de la fabrication

, Ces démarches s'opposent aux méthodes classiques d'essai-erreur (« one-variable-at-a-time » en anglais) consistant à faire varier un seul facteur X à la fois en conservant les niveaux des autres facteurs constants, rendant ainsi impossibles l'étude des interactions entre facteurs et ne permettant pas d'identifier à coup sûr des optimums globaux. Correctement employées, ces méthodes de planification expérimentale permettent : i) d'établir la modélisation du phénomène étudié, c'està-dire d'établir la relation entre les facteurs X, leurs interactions et les réponses Y ; ii) d'identifier la ou les solutions optimales, c'est-à-dire de déterminer les niveaux des facteurs X (les conditions opératoires) à adopter pour cibler une valeur de Y ou un ensemble de valeurs de Y ; iii) de parvenir à ces finalités en, Les démarches de plan d'expériences sont des processus codifiés permettant d'organiser les expériences à réaliser dans le but de répondre à une question scientifique ou technique concernant l'effet de plusieurs facteurs expérimentaux X sur une ou plusieurs réponses mesurées Y, 2006.

. Dans-le-domaine-de-l-;-turabi, Cependant une démarche de plan d'expériences complète se compose d'un nombre important d'étapes et les études ne les exécutent pas toutes, ou pas de la même façon. La partie qui suit a pour objectif de présenter brièvement les étapes qui composent classiquement une démarche de plan d'expériences à partir d'informations issues des ouvrages de Jacques Goupy (Goupy, 1982.

, A l'issue de ce résumé, une schématisation de la démarche de plan d'expériences dans son ensemble est présentée en guise de conclusion

, Définition de l'objectif

, Il s'agit selon les articles de (Tableau 66): -modéliser les effets de plusieurs facteurs X sur les propriétés des produits Y. Ceci fait référence à la capacité d

, -et/ou trouver les niveaux des facteurs X (les conditions opératoires) pour optimiser les propriétés des produits Y. Ceci fait référence à la capacité de prédiction du modèle

, La modélisation des Y par les X est réalisée sous la forme d'un modèle polynomial du premier ou du second degré, avec ou sans interactions. Voici l'expression de ces modèles dans le cas d'un plan à deux facteurs : Modèle

, Avec 0 la constante du modèle ; 1 et 2 les coefficients des effets simples des facteurs X1 et X2 ; 12 le coefficient de l'interaction des facteurs X1 et X2 qui est incluse dans l'analyse ou pas

, Pour la résolution du système d'équations du modèle, les variables X sont normalisées (centrées et réduites) de façon à gommer les différences d'unités et de gamme de variation entre chaque facteur. Chaque facteur X varie de façon discrète entre des niveaux dont le nombre et les valeurs

, ensemble des coefficients : effets simples, interactions et effets quadratiques. Ces coefficients ont un signe de variation qui traduit le sens de variation de la variable X associée lorsque celle-ci passe d

, Lorsqu'on parle des « termes » du modèle, on fait cette fois-ci référence à l'ensemble des

, Les interactions expriment le fait que l'effet d'un facteur Xi peut dépendre du niveau adopté par un autre facteur Xj. Le nombre d'interactions envisageables augmente avec le nombre de facteurs inclus dans le plan : interactions doubles (deuxième ordre) pour un plan à deux facteurs

, Recherche des facteurs X influents

, En effet, lors de la réalisation des expériences, ces facteurs sont des sources de variation de la réponse qu'il vaut mieux connaître afin de pouvoir les maîtriser, qu'ils soient choisis comme facteurs étudiés ou pas. Trois catégories de facteurs sont ainsi définies : les facteurs étudiés, les facteurs non étudiés mais maîtrisés, Dans une démarche de plans d'expériences complète, tous les facteurs rentrant dans le champ de la problématique et susceptibles d'influer sur les réponses mesurées doivent être recherchés

, Une façon efficace de déterminer les facteurs influents est de réaliser un plan de criblage, généralement exécuté sous la forme d'un plan factoriel fractionnaire. C'est un type de plan pour lequel l'effet des facteurs est étudié sur deux niveaux sans considérer l'effet de leurs interactions d'utiliser un facteur de blocking

, Exécution du plan d'expériences

C. , Elle doit être menée avec soin. Deux points d'attention peuvent être mis en avant : i) la maîtrise d'un maximum de facteurs non étudiés à des niveaux constants afin de limiter au maximum l'erreur expérimentale ; ii) l'attention portée au réglage du niveau de chaque facteur à chaque essai, qui est plus délicate lorsque le nombre de facteurs est important, et qui est pourtant limitante pour l'analyse du modèle si un de ces réglages est faussé

. Étude-de-ferrari, Un présupposé à l'analyse des résultats est que les distributions des réponses pour chaque réponse Y suivent une loi normale. C'est une condition qui peut être vérifiée comme cela est mentionné dans l, 2013.

. Gergely, Il y a donc création d'autant de modèles que de variables Y. Ce mode d'analyse est le plus classique, il correspond à celui employé par l'ensemble des études du Tableau 66 (« modèle mono Y »). La seconde possibilité est de réaliser un seul modèle expliquant la variation de toutes les réponses Y par l'ensemble des facteurs X : on parle alors de modèle multicritère (les Y) multi-contraintes (les X), Lorsque plusieurs réponses Y ont été mesurées deux modes d'analyse sont possibles, 2003.

, Leur significativité est indiquée par leur p-value ainsi que par leur « LogWorth » qui correspond à une transformation de la p-value pour obtenir une forme qui soit graphiquement représentable sous la forme de bâtons d'histogramme

Y. Vaisey-genser and . Johnston, Il s'agit d'une étape réellement discriminante entre une approche basée sur l'utilisation de modèles à une réponse et une approche de modèle multicritère multicontraintes. En effet dans le cas d'un modèle multicritère multi-contraintes le tri des effets a lieu sur la liste des LogWorth générale et s'applique donc de façon identique sur chaque modèle composant. Dans le cas de modèles à une réponse, le tri est réalisé de façon spécifique pour chaque modèle. Une différence supplémentaire entre ces deux approches est le nombre d'effets retenus dans le modèle final ; il est généralement plus important dans le cas d'un modèle multicritère multi-contraintes que pour chaque modèle mono Y car l, La seconde étape d'analyse consiste à effectuer un tri parmi les effets de façon à ne conserver que ceux qui sont statistiquement significatifs, 1982.