Characterization of image sets: the Galois Lattice approach

This paper presents a new method for supervised image classification. One or several landmarks are attached to each class, with the intention of characterizing it and discriminating it from the other classes. The different features, deduced from image primitives, and their relationships with the sets of images are structured and organized into a hierarchy thanks to an original method relying on a mathematical formalism called Galois (or Concept) Lattices. Such lattices allow us to select features as landmarks of specific classes. This paper details the feature selection process and illustrates this through a robotic example in a structured environment. The class of any image is the room from which the image is shot by the robot camera. In the discussion, we compare this approach with decision trees and we give some issues for future research

Random Recurrent Neural Networks Dynamics

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using an averaging principle. After a first introductory section, the section 1 reviews the various models from the points of view of the single neuron dynamics and of the global network dynamics. A summary of notations is presented, which is quite helpful for the sequel. In section 2, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 3, some applications of mean-field theory to the prediction of chaotic regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The case of AFRRNN with an homogeneous population of neurons is studied in section 4. Then, a two-population model is studied in section 5. The occurrence of a cyclo-stationary chaos is displayed using the results of \cite{Dauce01}. In section 6, an insight of the application of mean-field theory to IF networks is given using the results of \cite{BrunelHakim99}.Comment: Review paper, 36 pages, 5 figure

Topological visual localization using decentralized galois lattices

This paper presents a new decentralized method for selecting visual landmarks in a structured environment. Different images, issued from the different places, are analyzed, and primitives are extracted to determine whether or not features are present in the images. Subsequently, landmarks are selected as a combination of these features with a mathematical formalism called Galois - or concept - lattices. The main drawback of the general approach is the exponential complexity of lattice building algorithms. A decentralized approach is therefore defined and detailed here: it leads to smaller lattices, and thus to better performance as well as an improved legibility

Application of response surface methodology to stiffened panel optimization

In a multilevel optimization frame, the use of surrogate models to approximate optimization constraints allows great time saving. Among available metamodelling techniques we chose to use Neural Networks to perform regression of static mechanical criteria, namely buckling and collapse reserve factors of a stiffened panel, which are constraints of our subsystem optimization problem. Due to the highly non linear behaviour of these functions with respect to loading and design variables, we encountered some difficulties to obtain an approximation of sufficient quality on the whole design space. In particular, variations of the approximated function can be very different according to the value of loading variables. We show how a prior knowledge of the influence of the variables allows us to build an efficient Mixture of Expert model, leading to a good approximation of constraints. Optimization benchmark processes are computed to measure time saving, effects on optimum feasibility and objective value due to the use of the surrogate models as constraints. Finally we see that, while efficient, this mixture of expert model could be still improved by some additional learning techniques

Galois lattice theory for probabilistic visual landmarks

This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera. First, visual landmarks have to be selected in order to characterize a structural environment. Second, such landmarks have to be detected and updated for localization. These landmarks are combinations of attributes, and the selection process is done through a Galois lattice. This paper exposes the landmark selection process and focuses on probabilistic landmarks, which give the robot thorough information on how to locate itself. As a result, landmarks are no longer binary, but probabilistic. The full process of using such landmarks is described in this paper and validated through a robotics experiment

Surrogate modeling approximation using a mixture of experts based on EM joint estimation

An automatic method to combine several local surrogate models is presented. This method is intended to build accurate and smooth approximation of discontinuous functions that are to be used in structural optimization problems. It strongly relies on the Expectation-Maximization (EM) algorithm for Gaussian mixture models (GMM). To the end of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, artificial neural network, moving least squares) on each cluster. Lastly, the local experts are combined using the Gaussian mixture model parameters found by the EM algorithm to obtain a global model. This method is tested over both mathematical test cases and an engineering optimization problem from aeronautics and is found to improve the accuracy of the approximation

A physics-based approach to flow control using system identification

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A modelbased approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based systemidentification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only timesequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure

Approche en paramètres de stratification pour l’optimisation biniveau de structures de fuselage composite

On présente ici une méthode d’optimisation biniveau de grandes structures de fuselage composite. Ce schéma biniveau est inspiré de la formulation Quasi Separable Decomposition (QSD)récemment développée par Haftka et Watson. Le comportement membrane et hors-plan des stratifiés est représenté au moyen des paramètres de stratification. La boucle d’optimisation supérieure fait intervenir la redistribution des efforts et a pour contraintes des quantités calculées par des problèmes d’optimisation locale en stabilité où les facteurs critiques de flambage sont approchés par des modèles réduits

Modèles réduits en optimisation multiniveau de structures aéronautiques

Le dimensionnement de grandes structures aéronautiques s’appuie sur des heuristiques qui garantissent l’admissibilité de la structure par rapport aux contraintes de tenue mais pas nécessairement l’optimalité en masse. On se propose ici de formaliser le problème d’optimisation de structures en l’incluant dans la catégorie des problèmes d’optimisation multiniveau. On montre comment l’utilisation de modèles réduits peut simplifier et améliorer les méthodes directes. On présente les premiers résultats obtenus sur un cas test pour les différentes méthodes