Model Order Reduction based on Proper Generalized Decomposition for the Propagation of Uncertainties in Structural Dynamics

International audienceA priori model reduction methods based on separated representations are introduced for the prediction of the low frequency response of uncertain structures within a parametric stochastic framework. The Proper Generalized Decomposition method is used to construct a quasi-optimal separated representation of the random solution at some frequency samples. At each frequency, an accurate representation of the solution is obtained on reduced bases of spatial functions and stochastic functions. An extraction of the deterministic bases allows for the generation of a global reduced basis yielding a reduced order model of the uncertain structure which appears to be accurate on the whole frequency band under study and for all values of input random parameters. This strategy can be seen as an alternative to traditional constructions of reduced order models in structural dynamics in the presence of parametric uncertainties. This reduced order model can then be used for further analyses such as the computation of the response at unresolved frequencies or the computation of more accurate stochastic approximations at some frequencies of interest. The dynamic response being highly nonlinear with respect to the input random parameters, a second level of separation of variables is introduced for the representation of functions of multiple random parameters, thus allowing the introduction of very fine approximations in each parametric dimension even when dealing with high parametric dimension

Blind Signal Separation for Digital Communication Data

to appear in EURASIP E-reference in Signal Processing, invited paper.International audienceBlind source separation, often called independent component analysis , is a main field of research in signal processing since the eightees. It consists in retrieving the components, up to certain indeterminacies, of a mixture involving statistically independent signals. Solid theoretical results are known; besides, they have given rise to performent algorithms. There are numerous applications of blind source separation. In this contribution, we particularize the separation of telecommunication sources. In this context, the sources stem from telecommunication devices transmitting at the same time in a given band of frequencies. The received data is a mixed version of all these sources. The aim of the receiver is to isolate (separate) the different contributions prior to estimating the unknown parameters associated with a transmitter. The context of telecommunication signals has the particularity that the sources are not stationary but cyclo-stationary. Now, in general, the standard methods of blind source separation assume the stationarity of the sources. In this contribution , we hence make a survey of the well-known methods and show how the results extend to cyclo-stationary sources

A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties

International audienceWe here propose a multiscale numerical method for the solution of stochastic partial di erential equations with localized uncertainties. It is based on a multiscale domain decomposition method that exploits the localized side of uncertainties and incidentally improves the conditioning of the problem by operating a separation of scales. An efficient iterative algorithm is proposed that requires the solution of a sequence of simple global problems at a macro scale, involving a deterministic operator, and local problems at a micro scale for which we have the possibility to use ne approximation spaces. Global and local problems are solved using tensor approximation methods allowing the representation of high dimensional stochastic parametric solutions. Convergence properties of these tensor based methods, which are closely related to spectral decompositions, benefit from the separation of scales. Different types of uncertainties are considered at the micro level. They may be associated with some variability in the operator or source terms, or even with some geometrical variability. In the latter case, specific reformulations of local problems using fictitious domain methods are introduced

Separation of instantaneous mixtures of cyclostationary sources and application to digital communication signals

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

Blind source separation of convolutive mixtures of non circular linearly modulated signals with unknown baud rates

International audienceThis paper addresses the problem of blind separation of convolutive mixtures of BPSK and circular linearly modulated signals with unknown (and possibly different) baud rates and carrier frequencies. In previous works, we established that the Constant Modulus Algorithm (CMA) is able to extract a source from a convolutive mixture of circular linearly modulated signals. We extend the analysis of the extraction capabilities of the CMA when the mixing also contains BPSK signals. We prove that if the various source signals do not share any non zero cyclic frequency nor any non conjugate cyclic frequencies, the local minima of the constant modulus cost function are separating filters. Unfortunately, the minimization of the Godard cost function generally fails when considering BPSK signals that have the same rates and the same carrier frequencies. This failure is due to the existence of non-separating local minima of the Godard cost function. In order to achieve the separation, we propose a simple modification of the Godard cost function which only requires knowledge of the BPSK sources frequency offsets at the receiver side. We provide various simulations of realistic digital communications scenarios that support our theoretical statements

Modalités du transport des PCB dans la rivière Seine (France)

L'évolution de la pollution et les modalités du transport des P.C.B. en rivière ont été étudiées en Seine à Paris en relation avec les épisodes du cycle hydrologique durant un an.Les résultats analytiques montrent que la pollution occasionnée par les P.C.B. est supérieure à celle produite par les autres résidus de pesticides organochlorés, et ceci malgré la limitation réglementaire d'emploi des P.C.B. aux systèmes clos depuis 1975.Pour 88 % des échantillons analysés, les concentrations en P.C.B. dissous sont supérieures aux teneurs en P.C.B. adsorbés sur M.E.S. et atteignent jusqu'à 170 ng.l-1.Le transport se fait en solution pour 73 %, en moyenne, de la teneur totale, contrairement aux idées admises fondées sur la faible solubilité du polluant, mais qui ne prennent pas en compte le rapport en masse M.E.S./eau voisin de 25 x 10-6 en rivière.L'étude de la capacité d'adsorption des particules démontre qu'elle subit une évolution inverse de celle de la charge solide et du débit, ce qui explique la dominance des P.C.B. en phase aqueuse quelle que soit la teneur en M.E.S. Il en résulte que les valeurs élevées du coefficient de partage ne correspondent pas aux fortes teneurs en M.E.S. Les valeurs sont faibles pour la moitié d'entre elles et comprises entre 2 x 103 et 12 x 103 l.kg-1.The evolution of pollution by PCBs and their transport state in rivers was studied in the River Seine in Paris, in relation to the yearly hydrological cycle.Sampling took place just upstream of main waste waters (output) in the Paris area, and downstream from the junction of the Marne and the Seine, in order to establish the mean quality of water pumped upstream of these two rivers for drinking water production.Micropollutant concentrations were measured on 500 ml of raw water and 500 ml of water centrifuged at 6 000 G. Three extractions were carried out on these samples with a solvent mixture (85 % hexane, 15 % dichloromethane).In some cases extracts were purified on unactivated Florisil. After concentration down to 1 ml, extracts were measured through GC (falling needle injector; fused silica capillry column I.D. 0.25 mm, stationary phase SPB5; E.C.D. ni 63; vector gas He, make up Ar + 10 % CH4).Identification and quantification were carried out using an integrator and commercial Aroclor : 1242, 1254 and 1268 standards. In natural samples, the isomer composition is generally close to that of Aroclor 1254.Analytical data show that pollution linked to PCBs is higher than that due to other organochlorinated products, in spite of the official PCBs use limitation for closed systems since 1975.Except for a pollution peak of 990 ng.l-1, concentrations in raw water are irregular and vary from 25 to 250 ng.l-1.For 88 % of analyzed samples, dissolved PCB concentrations are higher than the concentrations of PCBs adsorbed onto suspended matter and reach 170 ng.1-1. The main transport (73 %) of the total flux is by solution, in contradiction with commonly accepted views based on the low solubility of PCBs.The study of adsorption capacity of solid particles demonstrates that its evolution is negatively correlated with the water flux and the solid load, which explains the prevalence of PCBs transport through solution, whatever the suspended matter concentration. Thereafter, it appears that high values of the partition coefficient are not linked to the concentration of suspended matter. For about half of them, values are low, between 2.102 and 12.101 l.kg-1

Estimation of the symbol period: the frequency offset case

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 200

Méthode multi-échelle avec patchs pour la propagation d'incertitudes localisées dans les modèles stochastiques

National audienceNous présentons une stratégie basée sur une méthode multiéchelle avec patch afin de traiter des problèmes stochastiques où les sources d'incertitudes sont nombreuses et dont les modèles associés sont des modèles multiéchelles complexes de grande dimension stochastique. La méthode exploite l'aspect localisé des incertitudes en séparant les échelles ce qui permet d'améliorer à la fois le conditionnement du problème et la convergence des méthodes d'approximation de tenseur utilisées pour résoudre les problèmes stochastiques de grande dimension aux niveaux local et global

On a conjecture about Dirac's delta representation using q-exponentials

A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid