Gilles Delmaire

PM2.5 source apportionment in a French urban coastal site under steelworks emission influences using constrained non-negative matrix factorization receptor model

The constrained weighted-non-negative matrix factorization (CW-NMF) hybrid receptor model was applied to study the influence of steelmaking activities on PM2.5 (particulate matter with equivalent aerodynamic diameter less than 2.5 μm) composition in Dunkerque, Northern France. Semi-diurnal PM2.5 samples were collected using a high volume sampler in winter 2010 and spring 2011 and were analyzed for trace metals, water-soluble ions, and total carbon using inductively coupled plasma--atomic emission spectrometry (ICP-AES), ICP--mass spectrometry (ICP-MS), ionic chromatography and micro elemental carbon analyzer. The elemental composition shows that NO3(-), SO4(2-), NH4(+) and total carbon are the main PM2.5 constituents. Trace metals data were interpreted using concentration roses and both influences of integrated steelworks and electric steel plant were evidenced. The distinction between the two sources is made possible by the use Zn/Fe and Zn/Mn diagnostic ratios. Moreover Rb/Cr, Pb/Cr and Cu/Cd combination ratio are proposed to distinguish the ISW-sintering stack from the ISW-fugitive emissions. The a priori knowledge on the influencing source was introduced in the CW-NMF to guide the calculation. Eleven source profiles with various contributions were identified: 8 are characteristics of coastal urban background site profiles and 3 are related to the steelmaking activities. Between them, secondary nitrates, secondary sulfates and combustion profiles give the highest contributions and account for 93% of the PM2.5 concentration. The steelwork facilities contribute in about 2% of the total PM2.5 concentration and appear to be the main source of Cr, Cu, Fe, Mn, Zn.

Blind Calibration of Mobile Sensors Using Informed Nonnegative Matrix Factorization

In this paper, we assume several heterogeneous, geolocalized, and time-stamped sensors to observe an area over time. We also assume that most of them are uncalibrated and we propose a novel formulation of the blind calibration problem as a Nonnegative Matrix Factorization NMF with missing entries. Our proposed approach is generalizing our previous informed and weighted NMF method, which is shown to be accurate for the considered application and to outperform blind calibration based on matrix completion and nonnegative least squares.

Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model

In this paper, we consider the problem of blindly calibrating a mobile sensor network-i.e., determining the gain and the offset of each sensor-from heterogeneous observations on a defined spatial area over time. For that purpose, we previously proposed a blind sensor calibration method based on Weighted Informed Nonnegative Matrix Factorization with missing entries. It required a minimum number of rendezvous-i.e., data sensed by different sensors at almost the same time and place-which might be difficult to satisfy in practice. In this paper we relax the rendezvous requirement by using a sparse decomposition of the signal of interest with respect to a known dictionary. The calibration can thus be performed if sensors share some common support in the dictionary, and provides a consistent performance even if no sensors are in exact rendezvous.

Non-negative Matrix Factorization using weighted beta divergence and equality constraints for industrial source apportionment

In this paper, we propose two weighted Non-negative Matrix Factorization (NMF) methods using a β-divergence cost function. This divergence is used as a dissimilarity measure which can be tuned by the parameter β. The weights allow to deal with the uncertainty associated to each data sample. Our first approach consists of generalizing weighted NMF methods proposed with specific divergences or norms to the β-divergence. In our second approach, we assume that some components of the factorization are known and we use them to inform our NMF algorithm. We thus consider a specific parameterization which involves these constraints. In particular, we propose specific multiplicative update rules for the minimization of this parameterization with a weighted divergence. Lastly, some experiments on simulated mixtures of particulate matter sources show the relevance of these approaches.

Bound constrained weighted NMF for industrial source apportionment

In our recent work, we introduced a constrained weighted Non-negative Matrix Factorization (NMF) method using a β-divergence cost function. We assumed that some components of the factorization were known and were used to inform our NMF algorithm. In this paper, we are provided some intervals of possible values for some factorization components. We thus introduce an extended version of our previous work combining an improved divergence expression and some matrix normalizationswhile using the known / bounded information. Some experiments on simulated mixtures of particulate matter sources show the relevance of these approaches.

Separation problem of industrial particles emissions using a stationary scattering model

Abstract This paper deals with some methods used to separate and to evaluate emission of dust particles coming from various industrial origins. Locations of all sources are supposed to be known by their 3D-Cartesian coordinates and steady-state dispersion is assumed to be reached. Our main contribution is to combine a particular stationary dispersion model with some efficient separation methods. The estimation of particles flow for the case of point sources over flat terrain is first addressed and then it is extended to line or area sources. Anyway, the approach is divided into two specific steps: the stationary model presentation and the separation techniques applied to the previous model. Finally, simulation results show the performances of the different methods in case of point. It turns out that small variations on the wind angle lead to large errors on flows estimate. Robust techniques with respect to model uncertainties appear to be of prime interest.

Nonlinear mobile sensor calibration using informed semi-nonnegative matrix factorization with a Vandermonde factor

In this paper we aim to blindly calibrate a mobile sensor network whose sensor outputs and the sensed phenomenon are linked by a polynomial relationship. The proposed approach is based on a novel informed semi-nonnegative matrix factorization with a Vandermonde factor matrix. The proposed approach outperforms a matrix-completion-based method in a crowdsensing-like simulation of particulate matter sensing.

Robust informed split gradient NMF using αβ-divergence for source apportionment

Source apportionment is a very challenging topic for which non-negative source separation is well-suited. Recently, we proposed several informed Non-negative Matrix Factorization (NMF) for which some expert knowledge was introduced. These methods were all dealing with some set values of one factor together with the row sum-to-one property by either processing each constraint alternatingly or using a new parameterization which involves all of them. However, this last method was sensitive to the presence of outliers. In this paper, we thus propose a new robust informed Split Gradient NMF method which is based on a weighted αβ-divergence cost function. Experiments conducted for several input SNR with and without outliers on simulated mixtures of particulate matter sources show the relevance of the new approach.

The Use of a Non Negative Matrix Factorization Method Combined to PM2.5 Chemical Data for a Source Apportionment Study in Different Environments

This study revolves around the use of a Non Negative Matrix Factorization method under constraints for the identification sources profiles as well as their respective contributions in three sites in northern France. Using PM2.5 chemical analysis data, the model identified eight background and four local industrial sources profiles. In addition, the contributions of these profiles showed that secondary aerosols and combustion sources are the major constituents of the analyzed PM2.5, whereas industrial contributions were found majorly responsible for the elemental enrichments.

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

In 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 (GLBEs) 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.