Utiliser des machines à vecteurs de support pour approcher les contours d'une fonction valeur dans des problèmes d'atteinte de cible

Nous proposons d'utiliser un algorithme d'apprentissage particulier, les SVMs, pour résoudre des problèmes d'atteinte de cible en temps minimal. La cible correspond à un état souhaité, en sachant que le système se détériore dans une certaine région de l'espace (lorsqu'il transgresse un ensemble de contraintes de viabilité). Le bassin de capture au temps t correspond à l'ensemble des états qui peuvent atteindre la cible en un temps inférieur ou égal à t, sans quitter l'ensemble des contrainte de viabilité. Les frontières d'un bassin de capture au temps t correspondent alors aux contours d'une fonction valeur au temps t. Les bassins de capture peuvent alors être utilisés pour définir une fonction de contrôle qui permet au système d'atteindre la cible en un temps minimal. Nous proposons une nouvelle approche, basée sur les SVMs, qui permettent d'approcher les bassins de capture successifs et définissons une procédure de contrôle qui permet de contrôler le système afin qu'il atteigne la cible. Nous illustrons cette méthode sur un exemple simple : le problème de la voiture sur la colline

Approximation of reachable sets using optimal control and support vector machines

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples

Anomaly Detection Based on Sensor Data in Petroleum Industry Applications

Anomaly detection is the problem of finding patterns in data that do not conform to an a priori expected behavior. This is related to the problem in which some samples are distant, in terms of a given metric, from the rest of the dataset, where these anomalous samples are indicated as outliers. Anomaly detection has recently attracted the attention of the research community, because of its relevance in real-world applications, like intrusion detection, fraud detection, fault detection and system health monitoring, among many others. Anomalies themselves can have a positive or negative nature, depending on their context and interpretation. However, in either case, it is important for decision makers to be able to detect them in order to take appropriate actions. The petroleum industry is one of the application contexts where these problems are present. The correct detection of such types of unusual information empowers the decision maker with the capacity to act on the system in order to correctly avoid, correct or react to the situations associated with them. In that application context, heavy extraction machines for pumping and generation operations, like turbomachines, are intensively monitored by hundreds of sensors each that send measurements with a high frequency for damage prevention. In this paper, we propose a combination of yet another segmentation algorithm (YASA), a novel fast and high quality segmentation algorithm, with a one-class support vector machine approach for efficient anomaly detection in turbomachines. The proposal is meant for dealing with the aforementioned task and to cope with the lack of labeled training data. As a result, we perform a series of empirical studies comparing our approach to other methods applied to benchmark problems and a real-life application related to oil platform turbomachinery anomaly detection.This work was partially funded by the Brazilian National Council for Scientific and Technological Development projects CNPq BJT 407851/2012-7 and CNPq PVE 314017/2013-5 and projects MINECO TEC 2012-37832-C02-01, CICYT TEC 2011-28626-C02-02.Publicad

Viabilitree: A kd-tree Framework for Viability-based Decision

The mathematical viability theory offers concepts and methods that are suitable to study the compatibility between a dynamical system described by a set of differential equations and constraints in the state space. The result sets built during the viability analysis can give very useful information regarding management issues in fields where it is easier to discuss constraints than objective functions. However, computational problems arise very quickly with the number of state variables, and the practical implementation of the method is difficult, although there exists a convergent numerical scheme and several approaches to bypass the computational problems. In order to popularize the use of viability analysis we propose a framework in which the viability sets are represented and approximated with particular kd-trees. The computation of the viability kernel is seen as an active learning problem. We prove the convergence of the algorithm and assess the approximation it produces for known problems with analytical solution. This framework aims at simplifying the declaration of the viability problem and provides useful methods to assist further use of viability sets produced by the computation

Sample dispersion is better than sample discrepancy for classification

We want to generate learning data within the context of active learning. First, we recall theoretical results proposing discrepancy as a criterion for generating sample in regression. We show surprisingly that theoretical results about low discrepancy sequences in regression problems are not adequate for classification problems. Secondly we propose dispersion as a criterion for generating data. Then, we present numerical experiments which have a good degree of adequacy with theory