2 research outputs found
Evolving Takagi-Sugeno-Kang fuzzy systems using multi-population grammar guided genetic programming
This work proposes a novel approach for the automatic generation and tuning of complete Takagi-Sugeno-Kang fuzzy rule based systems. The examined system aims to explore the effects of a reduced search space for a genetic programming framework by means of grammar guidance that describes candidate structures of fuzzy rule based systems. The presented approach applies context-free grammars to generate individuals and evolve solutions through the search process of the algorithm. A multi-population approach is adopted for the genetic programming system, in order to increase the depth of the search process. Two candidate grammars are examined in one regression problem and one system identification task. Preliminary results are included and discussion proposes further research directions
Type-2 Takagi-Sugeno-Kang Fuzzy Logic System and Uncertainty in Machining
RĂSUMĂ: Plusieurs mĂ©thodes permettent aujourdâhui dâanalyser le comportement des Ă©coulements
qui rĂ©gissent le fonctionnement de systĂšmes rencontrĂ©s dans lâindustrie (vĂ©hicules aĂ©riens,
marins et terrestres, gĂ©nĂ©ration dâĂ©nergie, etc.). Pour les Ă©coulements transitoires ou
turbulents, les méthodes expérimentales sont utilisées conjointement avec les simulations
numĂ©riques (simulation directe ou faisant appel Ă des modĂšles) afin dâextraire le plus
dâinformation possible. Dans les deux cas, les mĂ©thodes gĂ©nĂšrent des quantitĂ©s de donnĂ©es
importantes qui doivent ensuite ĂȘtre traitĂ©es et analysĂ©es. Ce projet de recherche vise Ă
amĂ©liorer notre capacitĂ© dâanalyse pour lâĂ©tude des Ă©coulements simulĂ©s numĂ©riquement
et les Ă©coulements obtenus Ă lâaide de mĂ©thodes de mesure (par exemple la vĂ©locimĂ©trie
par image de particules PIV ).
Lâabsence, jusquâĂ aujourdâhui, dâune dĂ©finition objective dâune structure tourbillonnaire
a conduit Ă lâutilisation de plusieurs mĂ©thodes eulĂ©riennes (vorticitĂ©, critĂšre Q,
Lambda-2, etc.), souvent inadaptées, pour extraire les structures cohérentes des écoulements.
Lâexposant de Lyapunov, calculĂ© sur un temps fini (appelĂ© le FTLE), sâest rĂ©vĂ©lĂ©
comme une alternative lagrangienne efficace à ces méthodes classiques. Cependant, la
mĂ©thodologie de calcul actuelle du FTLE exige lâĂ©valuation numĂ©rique dâun 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
dâun Ă©coulement 3D instationnaire atteint facilement plusieurs millions, ce qui nĂ©cessite
des ressources informatiques importantes pour une analyse adéquate.
Dans ce projet, nous visons Ă amĂ©liorer lâefficacitĂ© du calcul du champ FTLE en
proposant une méthode alternative au calcul classique des composantes du tenseur de
dĂ©formation de Cauchy-Green. Un ensemble dâĂ©quations diffĂ©rentielles ordinaires (EDOs)
est utilisé pour calculer simultanément les trajectoires des particules et les dérivées premiÚres
et secondes du champ de déplacement, ce qui se traduit par une amélioration de
la précision nodale des composantes du tenseur. Les dérivées premiÚres sont utilisées
pour le calcul de lâexposant de Lyapunov et les dĂ©rivĂ©es secondes pour lâestimation de
lâerreur dâinterpolation. Les matrices hessiennes du champ de dĂ©placement (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 Ă minimiser lâerreur dâinterpolation.----------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