45,811 research outputs found
Modelling of radionuclide migration through the geosphere with radial basis function method and geostatistics
The modelling of radionuclide transport through the geosphere is necessary in the safety assessment of repositories for radioactive waste. A number of key geosphere processes need to be considered when predicting the movement of radionuclides through the geosphere. The most important input data are obtained from field measurements, which are not available for all regions of interest. For example, the hydraulic conductivity, as input parameter, varies from place to place. In such cases geostatistical science offers a variety of spatial estimation procedures. To assess the a long term safety of a radioactive waste disposal system, mathematical models are used to describe the complicated groundwater flow, chemistry and potential radionuclide migration through geological formations. The numerical solution of partial differential equations (PDEs) has usually been obtained by finite difference methods (FDM), finite element methods (FEM), or finite volume methods (FVM). Kansa introduced the concept of solving PDEs using radial basis functions (RBFs) for hyperbolic, parabolic and elliptic PDEs. The aim of this study was to present a relatively new approach to the modelling of radionuclide migration through the geosphere using radial basis functions methods and to determine the average and sample variance of radionuclide concentration with regard to spatial variability of hydraulic conductivity modelled by a geostatistical approach. We will also explore residual errors and their influence on optimal shape parameters
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation
We investigate the influence of the shape parameter in the meshless Gaussian RBF finite difference method with irregular centres on the quality of the approximation of the Dirichlet problem for the Poisson equation with smooth solution. Numerical experiments show that the optimal shape parameter strongly depends on the problem, but insignificantly on the density of the centres. Therefore, we suggest a multilevel algorithm that effectively finds near-optimal shape parameter, which helps to significantly reduce the error. Comparison to the finite element method and to the generalised finite differences obtained in the flat limits of the Gaussian RBF is provided
A radial basis function neural network based approach for the electrical characteristics estimation of a photovoltaic module
The design process of photovoltaic (PV) modules can be greatly enhanced by
using advanced and accurate models in order to predict accurately their
electrical output behavior. The main aim of this paper is to investigate the
application of an advanced neural network based model of a module to improve
the accuracy of the predicted output I--V and P--V curves and to keep in
account the change of all the parameters at different operating conditions.
Radial basis function neural networks (RBFNN) are here utilized to predict the
output characteristic of a commercial PV module, by reading only the data of
solar irradiation and temperature. A lot of available experimental data were
used for the training of the RBFNN, and a backpropagation algorithm was
employed. Simulation and experimental validation is reported
Increasing the density of available pareto optimal solutions
The set of available multi-objective optimization
algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due
to the computational cost - to use a population large enough
to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem
A new code for orbit analysis and Schwarzschild modelling of triaxial stellar systems
We review the methods used to study the orbital structure and chaotic
properties of various galactic models and to construct self-consistent
equilibrium solutions by Schwarzschild's orbit superposition technique. These
methods are implemented in a new publicly available software tool, SMILE, which
is intended to be a convenient and interactive instrument for studying a
variety of 2D and 3D models, including arbitrary potentials represented by a
basis-set expansion, a spherical-harmonic expansion with coefficients being
smooth functions of radius (splines), or a set of fixed point masses. We also
propose two new variants of Schwarzschild modelling, in which the density of
each orbit is represented by the coefficients of the basis-set or spline
spherical-harmonic expansion, and the orbit weights are assigned in such a way
as to reproduce the coefficients of the underlying density model. We explore
the accuracy of these general-purpose potential expansions and show that they
may be efficiently used to approximate a wide range of analytic density models
and serve as smooth representations of discrete particle sets (e.g. snapshots
from an N-body simulation), for instance, for the purpose of orbit analysis of
the snapshot. For the variants of Schwarzschild modelling, we use two test
cases - a triaxial Dehnen model containing a central black hole, and a model
re-created from an N-body snapshot obtained by a cold collapse. These tests
demonstrate that all modelling approaches are capable of creating equilibrium
models.Comment: MNRAS, 24 pages, 18 figures. Software is available at
http://td.lpi.ru/~eugvas/smile
Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario
A variety of methods is available to quantify uncertainties arising with\-in
the modeling of flow and transport in carbon dioxide storage, but there is a
lack of thorough comparisons. Usually, raw data from such storage sites can
hardly be described by theoretical statistical distributions since only very
limited data is available. Hence, exact information on distribution shapes for
all uncertain parameters is very rare in realistic applications. We discuss and
compare four different methods tested for data-driven uncertainty
quantification based on a benchmark scenario of carbon dioxide storage. In the
benchmark, for which we provide data and code, carbon dioxide is injected into
a saline aquifer modeled by the nonlinear capillarity-free fractional flow
formulation for two incompressible fluid phases, namely carbon dioxide and
brine. To cover different aspects of uncertainty quantification, we incorporate
various sources of uncertainty such as uncertainty of boundary conditions, of
conceptual model definitions and of material properties. We consider recent
versions of the following non-intrusive and intrusive uncertainty
quantification methods: arbitary polynomial chaos, spatially adaptive sparse
grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The
performance of each approach is demonstrated assessing expectation value and
standard deviation of the carbon dioxide saturation against a reference
statistic based on Monte Carlo sampling. We compare the convergence of all
methods reporting on accuracy with respect to the number of model runs and
resolution. Finally we offer suggestions about the methods' advantages and
disadvantages that can guide the modeler for uncertainty quantification in
carbon dioxide storage and beyond
Reliability assessment of cutting tool life based on surrogate approximation methods
A novel reliability estimation approach to the cutting tools based on advanced approximation methods is proposed. Methods such as the stochastic response surface and surrogate modeling are tested, starting from a few sample points obtained through fundamental experiments and extending them to models able to estimate the tool wear as a function of the key process parameters. Subsequently, different reliability analysis methods are employed such as Monte Carlo simulations and first- and second-order reliability methods. In the present study, these reliability analysis methods are assessed for estimating the reliability of cutting tools. The results show that the proposed method is an efficient method for assessing the reliability of the cutting tool based on the minimum number of experimental results. Experimental verification for the case of high-speed turning confirms the findings of the present study for cutting tools under flank wear
On fundamental diffraction limitation of finesse of a Fabry-Perot cavity
We perform a theoretical study of finesse limitations of a Fabry-Perot (FP)
cavity occurring due to finite size, asymmetry, as well as imperfections of the
cavity mirrors. A method of numerical simulations of the eigenvalue problem
applicable for both the fundamental and high order cavity modes is suggested.
Using this technique we find spatial profile of the modes and their round-trip
diffraction loss. The results of the numerical simulations and analytical
calculations are nearly identical when we consider a conventional FP cavity.
The proposed numerical technique has much broader applicability range and is
valid for any FP cavity with arbitrary non-spherical mirrors which have
cylindrical symmetry but disturbed in an asymmetric way, for example, by tilt
or roughness of their mirrors.Comment: 15 pages, 10 figure
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