370 research outputs found
A method of characteristics for solving population balance equations (PBE) describing the adsorption of impurities during crystallization processes
International audiencePossible hindering effects of impurities on the crystal growth were shown to take place because of the adsorption of impurity species on the crystal surface. Transient features of this adsorption were observed, such that the growth of a given crystal does not depend on supersaturation only, but also on the time a given particle spent in contact with impurities present in the mother liquor. Meanwhile, few kinetic models describe the effect of impurities on the growth of crystals in solution, and published models are usually derived from data obtained, thanks to specific experiments based on the evaluation of the growth rate of single crystals. Such models are obviously questionable because, in the industrial practice, distributed properties of crystals are actually involved. Considering the “time of contamination” of particles as a new internal variable is thus made necessary. This is the reason why a specific PBE resolution algorithm is presented in this paper. The numerical scheme for the resolution of PBEs is based on the method of characteristics and shown to allow fast and accurate simulation of transient features of the crystal size distribution in the particular case when the growth or nucleation rates are assumed to exhibit unsteady-state dynamics. The algorithm is finally used to simulate the isothermal desupersaturation crystallization of citric acid in water
Algorithms for nonnegative matrix factorization with the beta-divergence
This paper describes algorithms for nonnegative matrix factorization (NMF)
with the beta-divergence (beta-NMF). The beta-divergence is a family of cost
functions parametrized by a single shape parameter beta that takes the
Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito
divergence as special cases (beta = 2,1,0, respectively). The proposed
algorithms are based on a surrogate auxiliary function (a local majorization of
the criterion function). We first describe a majorization-minimization (MM)
algorithm that leads to multiplicative updates, which differ from standard
heuristic multiplicative updates by a beta-dependent power exponent. The
monotonicity of the heuristic algorithm can however be proven for beta in (0,1)
using the proposed auxiliary function. Then we introduce the concept of
majorization-equalization (ME) algorithm which produces updates that move along
constant level sets of the auxiliary function and lead to larger steps than MM.
Simulations on synthetic and real data illustrate the faster convergence of the
ME approach. The paper also describes how the proposed algorithms can be
adapted to two common variants of NMF : penalized NMF (i.e., when a penalty
function of the factors is added to the criterion function) and convex-NMF
(when the dictionary is assumed to belong to a known subspace).Comment: \`a para\^itre dans Neural Computatio
Nonlinear Hyperspectral Unmixing With Robust Nonnegative Matrix Factorization
International audienceWe introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. The new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects, that are treated as sparsely distributed additive outliers.With the standard nonnegativity and sum-to-one constraints inherent to spectral unmixing, our model leads to a new form of robust nonnegative matrix factorization with a group-sparse outlier term. The factorization is posed as an optimization problem which is addressed with a block-coordinate descent algorithm involving majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods
Hybrid sparse and low-rank time-frequency signal decomposition
International audienceWe propose a new hybrid (or morphological) generative model that decomposes a signal into two (and possibly more) layers. Each layer is a linear combination of localised atoms from a time-frequency dictionary. One layer has a low-rank time-frequency structure while the other as a sparse structure. The time-frequency resolutions of the dictionaries describing each layer may be different. Our contribution builds on the recently introduced Low-Rank Time-Frequency Synthesis (LRTFS) model and proposes an iterative algorithm similar to the popular iterative shrinkage/thresholding algorithm. We illustrate the capacities of the proposed model and estimation procedure on a tonal + transient audio decomposition example. Index Terms— Low-rank time-frequency synthesis, sparse component analysis, hybrid/morphological decom-positions, non-negative matrix factorisation
Goal-based h-adaptivity of the 1-D diamond difference discrete ordinate method.
The quantity of interest (QoI) associated with a solution of a partial differential equation (PDE) is not, in general, the solution itself, but a functional of the solution. Dual weighted residual (DWR) error estimators are one way of providing an estimate of the error in the QoI resulting from the discretisation of the PDE. This paper aims to provide an estimate of the error in the QoI due to the spatial discretisation, where the discretisation scheme being used is the diamond difference (DD) method in space and discrete ordinate (SNSN) method in angle. The QoI are reaction rates in detectors and the value of the eigenvalue (Keff)(Keff) for 1-D fixed source and eigenvalue (KeffKeff criticality) neutron transport problems respectively. Local values of the DWR over individual cells are used as error indicators for goal-based mesh refinement, which aims to give an optimal mesh for a given QoI
Acoustic Emission: a new in-line and non-intrusive sensor for monitoring batch solution crystallization operations
International audienceAcoustic emission (AE) is shown to provide complex and in-depth information on both the liquid and the dispersed phases during batch cooling solution crystallization processes. Despite its complexity, such information might be highly valuable for process monitoring and control purposes owing to its non-intrusive features, its relative cheapness, and the very wide scope of its potential applications. Basic crystallization phenomena such as the onset of nucleation and the development of crystal growth, several key-process variables like the concentration of solid in suspension, and overall data describing the average particle size and the content in impurities of the crystallization medium are evaluated from real experimental data obtained at the lab-scale. AE is not claimed here to allow replacing "usual" particle sizes sensing technologies like image analysis or FBRM; it is rather suggested that the large amount of information contained in the acoustic data is quite interesting and deserves further investigation
Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images
International audienceThis paper introduces a robust linear model to describe hyperspectral data arising from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model but also allows for possible nonlinear effects to be handled, relying on mild assumptions regarding these nonlinearities. Based on this model, a nonlinear unmixing procedure is proposed. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. The resulting objective function is minimized using a multiplicative algorithm. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods
A majorization-minimization algorithm for nonnegative binary matrix factorization
This paper tackles the problem of decomposing binary data using matrix
factorization. We consider the family of mean-parametrized Bernoulli models, a
class of generative models that are well suited for modeling binary data and
enables interpretability of the factors. We factorize the Bernoulli parameter
and consider an additional Beta prior on one of the factors to further improve
the model's expressive power. While similar models have been proposed in the
literature, they only exploit the Beta prior as a proxy to ensure a valid
Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform
or uninformative prior. Besides, estimation in these models has focused on
costly Bayesian inference. In this paper, we propose a simple yet very
efficient majorization-minimization algorithm for maximum a posteriori
estimation. Our approach leverages the Beta prior whose parameters can be tuned
to improve performance in matrix completion tasks. Experiments conducted on
three public binary datasets show that our approach offers an excellent
trade-off between prediction performance, computational complexity, and
interpretability
- …