Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

Algorithmes bio-mimétiques pour la reconnaissance de formes et l'apprentissage

Dans cette thèse, nous appliquons deux algorithmes bio-mimétiques à la résolution d un problème de biologie marine : la détection de structures rétentives en eaux côtières. Nous confrontons ces deux méthodes, à savoir un algorithme à colonies de fourmis et la programmation génétique, avec des méthodes dites classiques (analyse physique, streamlines ) et mettons en évidence les difficultés de ces dernières à traiter ce problème, rendu difficile par la proximité des côtes induisant de fortes perturbations de courant. Pour pallier ce problème, nous proposons tout d abord une adaptation de l algorithme à colonies de fourmis tel que défini par Marco Dorigo, introduisant les notions de biais, de multiples colonies et d évaporation instantanée de la phéromone. Cette méthode se révèle performante et ses détections sont d une qualité satisfaisant les exigences des biologistes. Nous proposons ensuite une adaptation de la programmation génétique inspirée des travaux de Jason Daida sur la détection de crêtes de pressions sur la croûte glaciaire. Nous introduisons le concept de génération de filtres itératifs, technique permettant la prise en compte et la propagation d informations globales. Cette méthode se révèle, elle aussi performante, mais n est pas directement utilisable car elle ne permet pas d identifier les enveloppes des structures rétentives. Elle met plutôt en évidence des zones rétentives.In this thesis, we apply two bio-mimetic algorithms to solve a marine biology problem : retentive structures detection in coastal waters. We compare these two methods (an ant based algorithm and genetic programming) to classical methods (physical analysis, streamlines...) and we draw out their difficulties to solve this problem, made difficult by the proximity of the coast inducing strong stream perturbations. To solve this problem, we present an adaptation of the ant based algorithm defined by Marco Dorigo, introducing the notion of bias, several colonies and instantaneous pheromone evaporation. This method appears to be efficient and its detections are good enough to satisfy biologists. We also propose an adaptation of genetic programming inspired of the work of Jason Daida about detection of peaks of pressure. We introduce the concept of oterative filters generation which allows to take into account and propagate global informations. This method appears to be also very efficient, but is not directly usable because it is not able to detect the envelops of retentive structures, but it rather draws out retentive zones.CALAIS-BU Sciences (621932101) / SudocSudocFranceF

"Le syndrome de Cockett" (analyse d'une population de 10 patients symptomatiques)

LILLE2-BU Santé-Recherche (593502101) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF