Mixmod - Développement, diffusion, valorisation d’un ensemble logiciel de classification de données quantitatives et qualitatives par modèles de mélanges

International audienceClassification des donnéesMixmod et les modèles de mélnagesComment est développé Mixmod

Clustering "optimal" dans des espaces fonctionnels

International audienceComputer codes used in support of nuclear industry are more and more complex, and consequently more and more CPU time consuming. We are here interested in such code, in the special case of functional output : the code output represents the evolutions of some physical parameters in time. Those last curves are functions from an interval $I \subset \R$ to $\R$, which will be preprocessed in order to cluster them in a few meaningful groups (clustering, or unsupervised classification). The aim of our work is the estimation of the convergence speed of clustering error estimates. After finding bounds on convergence speeds, we will illustrate this on an example with six distinct groups of curves

Projection-based curve clustering

This paper focuses on unsupervised curve classification in the context of nuclear industry. At the Commissariat à l'Energie Atomique (CEA), Cadarache (France), the thermal-hydraulic computer code CATHARE is used to study the reliability of reactor vessels. The code inputs are physical parameters and the outputs are time evolution curves of a few other physical quantities. As the CATHARE code is quite complex and CPU-time consuming, it has to be approximated by a regression model. This regression process involves a clustering step. In the present paper, CATHARE output curves are clustered using a k-means scheme, with a projection onto a lower dimensional space. We study the properties of the empirically optimal cluster centers found by the clustering method based on projections, compared to the “true” ones. The choice of the projection basis is discussed, and an algorithm is implemented to select the best projection basis among a library of orthonormal bases. The approach is illustrated on a simulated example and then applied to the industrial problem

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps

Classification et modélisation de sorties fonctionnelles de codes de calcul (application aux calculs thermo-hydrauliques accidentels dans les réacteurs à eau pressurisés (REP))

Compte-tenu de la complexité des systèmes industriels actuels et des progrès en calcul scientifique, les codes utilisés pour modéliser des phénomènes physiques en ingénierie nucléaire sont souvent coûteux en temps. Il est cependant nécessaire de réaliser des analyses statistiques sur certains événements, et ces analyses demandent de multiples applications du code pour être précises. C'est pourquoi le temps de simulation doit être réduit, en modélisant le code de calcul par une fonction de coût CPU négligeable. Cette modélisation s'effectue sur la base d'un échantillon de quelques centaines de résultats de calculs physiques. Ce travail s'inscrit dans le cadre relativement peu étudié des codes de calcul à réponses fonctionnelles 1D. Ces dernières modélisent l'évolution de paramètres physiques dans le temps, pour un état initial. Différents types d'évolution peuvent se dégager ; c'est pourquoi les (entrées-)sorties sont d'abord divisées en K groupes, une méthode basée sur l'erreur de classification supervisée permettant de sélectionner ce dernier nombre automatiquement. Afin de contourner la difficulté liée aux réponses fonctionnelles, l'idée principale consiste à représenter ces dernières en dimension réduite pour effectuer la régression dans le cadre vectoriel. Pour cela nous proposons une alternative non linéaire à la décomposition sur une base, accompagnée de sa justification théorique. Nous montrons que l'application ainsi construite permet d'approximer une large classe de codes, et est complémentaire de l'approche classique (utilisant une base de fonctions) sur les jeux de données CEA.PARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

Mixture of experts for sequential PM10 forecasting in Normandy (France)

Within the framework of air quality monitoring in Normandy, we experiment the methods of sequential aggregation for forecasting concentrations of PM10 of the next day. Besides the field of application and the adaptation to the special context of the work of the forecaster, the main originality of this contribution is that the set of experts contains at the same time statistical models built by means of various methods and different sets of predictors, as well as experts which are deterministic chemical models of prediction modeling pollution, weather and atmosphere. Numerical results on recent data from April 2013 until March 2014, on three monitoring stations, illustrate and compare various methods of aggregation. The obtained results show that such a strategy improves clearly the performances of the best expert both in errors and in alerts and reaches an unbiased observed-forecasted scatterplot, difficult to obtain by usual methods

Planning 3D Task Demonstrations of a Teleoperated Space Robot Arm

We present an automated planning application for generating 3D tasks demonstrations involving a teleoperated robot arm on the International Space Station (ISS). A typical task demonstration involves moving the robot arm from one configuration to another. Our objective is to automatically plan the position of virtual cameras to film the arm in a manner that conveys the best awareness of the robot trajectory to the user. Given a new task, or given changes to a task previously planned, our system automatically and efficiently generates 3D demonstrations of the task without the intervention of a computer graphics programmer. For a given task, the robot trajectory is generated using a path planner. Then we consider the filming of the trajectory as a sequence of shots satisfying some temporally extended goal conveying constraints on the desirable positioning of virtual cameras. Then a temporallogic based planning system (TLPlan) is used to generate a 3D movie satisfying the goal. One motivation for this application is to eventually use it to support ground operators in planning mission tasks for the ISS. Another motivation is to eventually use automatically generated demonstrations in a 3D training simulator to provide feedback to student astronauts learning to manipulate the robot arm. Although motivated by the ISS application, the key ideas underlying our system are potentially useful for automatically filming other kinds of complex animated scenes