935 research outputs found
Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence
We study Gaussian approximations to the distribution of a diffusion. The
approximations are easy to compute: they are defined by two simple ordinary
differential equations for the mean and the covariance. Time correlations can
also be computed via solution of a linear stochastic differential equation. We
show, using the Kullback-Leibler divergence, that the approximations are
accurate in the small noise regime. An analogous discrete time setting is also
studied. The results provide both theoretical support for the use of Gaussian
processes in the approximation of diffusions, and methodological guidance in
the construction of Gaussian approximations in applications
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly initialized signals that evolve according to a deterministic map Ψ. The observations are assumed to comprise a low-dimensional projection of the signal, given by an operator P, subject to additive noise. We address the question of whether these observations contain sufficient information to accurately reconstruct the signal. In a general framework, we establish conditions on Ψ and P under which the filtering distributions concentrate around the signal in the small-noise, long-time asymptotic regime. Linear systems, the Lorenz ’63 and ’96 models, and the Navier–Stokes equation on a two-dimensional torus are within the scope of the theory. Our main findings come as a by-product of computable bounds, of independent interest, for suboptimal filters based on new variants of the 3DVAR filtering algorith
Estudio de una apiladora en procesos cerámicos
La cerámica española es una de las industrias más importantes en el ámbito nacional además de ser sinónimo de liderazgo internacional, y como bien dice el organismo marca España, “la industria española de fabricantes de baldosas cerámicas, piezas planas de poco espesor fabricadas con arcillas, sílice, fundentes, colorantes y otras materias primas es una de las más dinámicas e innovadoras de nuestro país y, dentro del sector cerámico mundial, se posiciona como líder en cuanto a desarrollo tecnológico, diseño y calidad del producto y del servicio”1
El siguiente proyecto tiene como objetivo el diseño y la implementación de una nueva etapa automática en un proceso de producción industrial del sector cerámico.
En este sentido, la función de esta nueva etapa será realizar lo que actualmente es un proceso manual sencillo realizado por un operario, el cual podrá tener otra función más productiva y menos monótona.
La etapa en cuestión forma parte de la cadena de producción de baldosas cerámicas y realizará el apilado de 2 en 2, adaptándose a los productos que salen de la extrusora (baldosas de 20x20 y vierteaguas principalmente).
Además, la implementación de esta etapa podrá desarrollar una futura función de control de calidad y de contabilización de producción diaria, y así poder obtener una mejor información de los productos que se están fabricando ya que se implementará un controlador programable tipo PLC.
Para ello, se realizará un estudio in-situ del proceso actual, analizando las características de los productos a manipular. A continuación, se plantearán diferentes alternativas en función del nivel de automatización posible, y de factores económicos y ambientales.
Para finalizar, se elegirá la solución más adecuada y se llevará a cabo su implementación real en el proceso productivo
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