Information Theory Filters for Wavelet Packet Coefficient Selection with Application to Corrosion Type Identification from Acoustic Emission Signals

The damage caused by corrosion in chemical process installations can lead to unexpected plant shutdowns and the leakage of potentially toxic chemicals into the environment. When subjected to corrosion, structural changes in the material occur, leading to energy releases as acoustic waves. This acoustic activity can in turn be used for corrosion monitoring, and even for predicting the type of corrosion. Here we apply wavelet packet decomposition to extract features from acoustic emission signals. We then use the extracted wavelet packet coefficients for distinguishing between the most important types of corrosion processes in the chemical process industry: uniform corrosion, pitting and stress corrosion cracking. The local discriminant basis selection algorithm can be considered as a standard for the selection of the most discriminative wavelet coefficients. However, it does not take the statistical dependencies between wavelet coefficients into account. We show that, when these dependencies are ignored, a lower accuracy is obtained in predicting the corrosion type. We compare several mutual information filters to take these dependencies into account in order to arrive at a more accurate prediction

Type-2 Takagi-Sugeno-Kang Fuzzy Logic System and Uncertainty in Machining

RÉSUMÉ: Plusieurs méthodes permettent aujourd’hui d’analyser le comportement des écoulements qui régissent le fonctionnement de systèmes rencontrés dans l’industrie (véhicules aériens, marins et terrestres, génération d’énergie, etc.). Pour les écoulements transitoires ou turbulents, les méthodes expérimentales sont utilisées conjointement avec les simulations numériques (simulation directe ou faisant appel à des modèles) afin d’extraire le plus d’information possible. Dans les deux cas, les méthodes génèrent des quantités de données importantes qui doivent ensuite être traitées et analysées. Ce projet de recherche vise à améliorer notre capacité d’analyse pour l’étude des écoulements simulés numériquement et les écoulements obtenus à l’aide de méthodes de mesure (par exemple la vélocimétrie par image de particules PIV ). L’absence, jusqu’à aujourd’hui, d’une définition objective d’une structure tourbillonnaire a conduit à l’utilisation de plusieurs méthodes eulériennes (vorticité, critère Q, Lambda-2, etc.), souvent inadaptées, pour extraire les structures cohérentes des écoulements. L’exposant de Lyapunov, calculé sur un temps fini (appelé le FTLE), s’est révélé comme une alternative lagrangienne efficace à ces méthodes classiques. Cependant, la méthodologie de calcul actuelle du FTLE exige l’évaluation numérique d’un grand nombre de trajectoires sur une grille cartésienne qui est superposée aux champs de vitesse simulés ou mesurés. Le nombre de noeuds nécessaire pour représenter un champ FTLE d’un écoulement 3D instationnaire atteint facilement plusieurs millions, ce qui nécessite des ressources informatiques importantes pour une analyse adéquate. Dans ce projet, nous visons à améliorer l’efficacité du calcul du champ FTLE en proposant une méthode alternative au calcul classique des composantes du tenseur de déformation de Cauchy-Green. Un ensemble d’équations différentielles ordinaires (EDOs) est utilisé pour calculer simultanément les trajectoires des particules et les dérivées premières et secondes du champ de déplacement, ce qui se traduit par une amélioration de la précision nodale des composantes du tenseur. Les dérivées premières sont utilisées pour le calcul de l’exposant de Lyapunov et les dérivées secondes pour l’estimation de l’erreur d’interpolation. Les matrices hessiennes du champ de déplacement (deux matrices en 2D et trois matrices en 3D) nous permettent de construire une métrique optimale multi-échelle et de générer un maillage anisotrope non structuré de façon à distribuer efficacement les noeuds et à minimiser l’erreur d’interpolation.----------ABSTRACT: Several methods can help us to analyse the behavior of flows that govern the operation of fluid flow systems encountered in the industry (aerospace, marine and terrestrial transportation, power generation, etc..). For transient or turbulent flows, experimental methods are used in conjunction with numerical simulations ( direct simulation or based on models) to extract as much information as possible. In both cases, these methods generate massive amounts of data which must then be processed and analyzed. This research project aims to improve the post-processing algorithms to facilitate the study of numerically simulated flows and those obtained using measurement techniques (e.g. particle image velocimetry PIV ). The absence, even until today, of an objective definition of a vortex has led to the use of several Eulerian methods (vorticity, the Q and the Lambda-2 criteria, etc..), often unsuitable to extract the flow characteristics. The Lyapunov exponent, calculated on a finite time (the so-called FTLE), is an effective Lagrangian alternative to these standard methods. However, the computation methodology currently used to obtain the FTLE requires numerical evaluation of a large number of fluid particle trajectories on a Cartesian grid that is superimposed on the simulated or measured velocity fields. The number of nodes required to visualize a FTLE field of an unsteady 3D flow can easily reach several millions, which requires significant computing resources for an adequate analysis. In this project, we aim to improve the computational efficiency of the FTLE field by providing an alternative to the conventional calculation of the components of the Cauchy-Green deformation tensor. A set of ordinary differential equations (ODEs) is used to calculate the particle trajectories and simultaneously the first and the second derivatives of the displacement field, resulting in a highly improved accuracy of nodal tensor components. The first derivatives are used to calculate the Lyapunov exponent and the second derivatives to estimate the interpolation error. Hessian matrices of the displacement field (two matrices in 2D and three matrices in 3D) allow us to build a multi-scale optimal metric and generate an unstructured anisotropic mesh to efficiently distribute nodes and to minimize the interpolation error. The flexibility of anisotropic meshes allows to add and align nodes near the structures of the flow and to remove those in areas of low interest. The mesh adaptation is based on the intersection of the Hessian matrices of the displacement field and not on the FTLE field

Wavelet packet decomposition for the identification of corrosion type from acoustic emission signals

Corrosion causes a degradation of the structural integrity of petrochemical plants, nu- clear power plants, ships, bridges and other constructions containing steel with the con- sequence that people and the environment may be exposed to dangerous situations. The detection of corrosion and the prediction of the type of corrosion is studied in this article by means of the acoustic emission technique. We use a wavelet packet decomposition to compute features from the acoustic emission signals. The basis functions with the high- est discriminative power are selected according to the highest pair-wise Kullback-Leibler divergence between distributions of wavelet coefficients. It is proven that the pair-wise Kullback-Leibler divergence used in the local discriminant basis algorithm requires class conditional independence of the wavelet coefficients. Several classification algorithms us- ing the most discriminative wavelet coefficients are compared for the prediction of three types of corrosion and the absence of corrosion.status: publishe