Estimation of a semi-physical GLBE model using dual EnKF learning algorithm coupled with a sensor network design strategy: application to air field monitoring

International audienceIn this paper, we present the fusion of two complementary approaches for modeling and monitoring the spatio-temporal behavior of a fluid flow system. We also propose a mobile sensor deployment strategy to produce the most accurate estimate of the true system state. For this purpose, deterministic and statistical information was used. We adopted a filtering method based on a semi-physical model which derives from a fluid flow numerical model known as lattice Boltzmann model (LBM). The a priori physical knowledge was introduced by the Navier-Stokes equations which were discretized by the lattice Boltzmann approach. Moreover, its multiple-relaxation-time (MRT) variant not only improved the stability, but also enabled the introduction of additional degrees of freedom to be estimated like the synaptic weights of a neural network. The statistical knowledge was then introduced into the model by performing a sequential learning of these parameters and an estimation of the speed field of the fluid flow starting from measurements. The low spatial density of measurements, the large amount of data inherent to environmental issues and the nonlinearity of the generalized lattice Boltzmann equations (GLBE) enjoined us to use the ensemble Kalman filter (EnKF) for the recursive estimation procedure. A dual state-parameter estimation which results in a significantly reduced computation time was used by combining two filters consecutively activated in the same iteration. Finally, we proposed to complete the lack of spatial information of the sparse-observation network by adding a mobile sensor, which was routed to the location where the cell-by-cell output estimation error was the highest. Experimental results in the context of the standard lid-driven cavity problem revealed the presence of few zones of interest, where fixed sensors can be deployed to increase performances in terms of convergence speed and estimation quality. Finally, the study showed the feasibility of introducing some additional parameters which act as degrees of freedom, to perform large-eddy simulation of turbulent flows without numerical instabilities

Kullback-leibler NMF under linear equality constraints. Application to pollution source apportionment

International audienceNon negative matrix factorisation (NMF) coupled to divergence measure has been investigated in the frame of an application to polluant source identification. It relies on receptor modelling which considers the data matrix as the result of cumulative effects of p sources. NMF aims at finding a contribution matrix G and a profile matrix F by minimizing a specific cost function. The focus is made here on the Kullback-Leibler divergence (KL) cost function. Linear equality constraints are incorporated into parts of the decomposition and general mu-tiplicative like expressions, which take into account these constraints, are derived. This method is applied in the frame of source apportion-ment of particulate matter

Méthode de démélange et dématriçage conjoints fondée sur la complétion de rang un pour les images multispectrales « snapshot »

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Do random projections fasten an already fast NMF technique using Nesterov optimal gradient?

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