| ||Balance and characteristics chemes with staggered conservative and fluxes variables on picewise-constant initial dates (preprint IBRAE-2002-16)|
Goloviznin V.M., Karabasov S.A.
It is shown, that the “balance and characteristics” approach to construction of numerical algorithms for hyperbolic conservation laws gives on set piecewise – constant initial functions the exact decision of the elementary equation of convective transport. Two different realizations of the corresponding algorithm named as algorithm « jumping transport » are described. The new algorithm possesses the following properties: is explicit – does not demand procedures of the decision of systems of the linear equations, including procedure of “the running account”; – it is determined on constant minimally possible computing stencil – operates with grid function from two times layers within of one computational cell; – is conservative and monotonous at CFL numbers , smaller units; – on smooth function does not approximate the original equation in classical sense. Generalization of algorithm jumping transport on a case of non-uniform computational grids and on the convection – diffusion equation is given. Examples of test calculations are considered.
Goloviznin V.M., Karabasov S.A. BALANCE AND CHARACTERISTICS CHEMES WITH STAGGERED CONSERVATIVE AND FLUXES VARIABLES ON PICEWISE-CONSTANT INITIAL DATES. (In Russian). Preprint IBRAE-2002-16. Moscow: Nuclear Safety Institute, July 2002. 19 p. — Refs.: 22 items.
| ||Balance-characteristic schemes with separated conservative and flux variables (preprint IBRAE-2002-15)|
Goloviznin V.M., Karabasov S.A., Kobrinsky I.M.
The new approach is suggested for the development of difference methods with high resolution for the equation of convection with regard to diffusion. It is based on the introduction of two different types of variables – “conservative” and “flux”, corresponding to the realization of the conservation law and correct calculation of characteristic region of influence respectively. The process of creation of new algorithms consists of two stages. At the first stage, linear uniform conservative difference schemes with improved dissipative and dispertion characteristics are constructed on the minimal computing stencil. At the second stage, conservative algorithm of minimal correction of the calculated values is used for the realization of the sufficient conditions of the principle of maximum. Explicit monotone algorithms were developed, that are stable in the case of the Courant number is less then unity and have the second order of accuracy on the smooth solutions. It is shown that new algorithms have noticeable advantages in comparison with the well-known TVD-schemes, based on the limitation of fluxes.
Goloviznin V.M., Karabasov S.A., Kobrinsky I.M. BALANCE-CHARACTERISTIC SCHEMES WITH SEPARATED CONSERVATIVE AND FLUX VARIABLES. (In Russian). Preprint IBRAE-2002-15. Moscow: Nuclear Safety Institute RAS, July 2002. 25 p. — Refs.: 15 items.
| ||Modelling of grain face diffusion transport and swelling in UO2 fuel (preprint IBRAE-2002-14)|
Berdyshev A.V., Veshchunov M.S.
An advanced model for the grain face transport based on the self-consistent consideration of gas atoms diffusion, sinking to and resolution from bubbles on grain faces, is developed. An important role of grain boundary diffusion of gas atoms to edges before interlinking of inter-granular bubbles, is outlined. The coalescence of face bubbles due to their random migration is considered as the main mechanism of grain face bubbles relaxation. Implementation in the MFPR code of the new model and numerical treatment of various available data on gas release from irradiated fuel, fuel swelling and grain face microstructure, show a satisfactory agreement of the code predictions with measurements.
Berdyshev A.V., Veshchunov M.S. Modelling of grain face diffusion transport and swelling in UO2 fuel. Preprint IBRAE-2002-14. Moscow: Nuclear Safety Institute RAS, June 2002. 19 p. — Refs.: 29 items.
| ||Environmental data mining and modelling based on machine learning algorithms and geostatistics (preprint IBRAE-2002-13)|
Parkin R., Kanevski M., Pozdnukhov A., Timonin V., Maignan M., Yatsalo B., Canu S.
The paper presents some contemporary approaches to the spatial environmental data analysis, processing and presentation. The main topics are concentrated on the decision–oriented problems of environmental and pollution spatial data mining and modelling. The set of tools used consists of machine learning algorithms (MLA) – Multilayer Perceptron and Support Vector Regression, and recently developed geostatistical predictive and simulation models. The innovative part of the report deals with integrated/hybrid models, including ML Residuals Kriging predictions and ML Residuals Sequential Gaussian simulations. ML algorithms efficiently solve problems of spatial non-stationarity, which are difficult for geostatistical approach, but geostatistical tools are widely and successfully applied to characterise the performance of the ML algorithms, analysing the quality and quantity of the spatially structured information extracted from data by ML. Moreover, mixture of ML data driven and geostatistical model based approaches are attractive for decision-making process..
Parkin R., Kanevski M., Pozdnukhov A., Timonin V., Maignan M., Yatsalo B., Canu S. ENVIRONMENTAL DATA MINING AND MODELLING BASED ON MACHINE LEARNING ALGORITHMS AND GEOSTATISTICS. Preprint IBRAE-2002-13. Moscow: Nuclear Safety Institute RAS, 2002. 13p. — Refs.: 9 items.
| ||Reseach of opportunities of practical use neural networks for identification of the basic parameters of the fractional diffusion (preprint IBRAE-2002-12)|
Goloviznin V., Kiselev V., Korotkin I., Semenov V., Hromov A., Yurkov Y.
The inverse problem of identification of fractional diffusion parameters is considered according to practical measurements. For the decision of this problem it is offered to use neural networks. The brief review neural networks is given The various ways of representation of the information on an input in a neural network are considered. Results of research of noise influence and quantity of training examples on accuracy of definition of parameters fractional diffusion also are given. As results of practical measurements it is used numerical decisions of a direct problem.
Goloviznin V., Kiselev V., Korotkin I., Semenov V., Hromov A., Yurkov Y. RESEACH OF OPPORTUNITIES OF PRACTICAL USE NEURAL NETWORKS FOR IDENTIFICATION OF THE BASIC PARAMETERS OF THE FRACTIONAL DIFFUSION. (In Russian). Preprint ¹ IBRAE-2002-12. Moscow: Nuclear Safety Institute RAS, 2002. 37 p. — Refs.: 6 items.
| ||Stochastic approximation ratio’s property for oscillating processes (preprint IBRAE-2002-11)|
Visochansckiy V.B., Islamov R.T.
Results of stochastic approximation ratio’s property analysis for oscillating processes are presented in this paper. Determination of stochastic approximation ratio’s property in the variation of oscillating function parameters is a purpose of the research. Dependence of stochastic approximation ratio’s on such parameters as, function’s mean value, magnitude and phase is carried out for standard function. Additional investigation of dependence of stochastic approximation ratio’s on range of definition of is developed.
Visochansckiy V.B., Islamov R.T. Stochastic approximation ratio’s property for oscillating processes. (In Russian). Preprint IBRAE-2002-11. Moscow: Nuclear Safety Institute RAS, 2002. 21 p. — Refs.: 3 items.
| ||Computational methods for one-dimensional fractional diffusion equations (preprint IBRAE-2002-10)|
Goloviznin V.M., Kiselev V.P., Korotkin I.A.
In the work the computing algorithms for the numerical decision of a fractional diffusion primal problem in a one-dimensional case have been developed and analyzed. Fractional diffusion essentially differs from classical diffusion by behavior of substance concentration on large distances from the initial data source. In the publication the review of basic definitions of fractional derivatives is given. On the basis of this definitions difference methods of the first and second orders of approximation have been constructed. Explicit, partially implicit unconditionally stable schemes and a method based on Fourior transform are also given. The numerous examples of calculations represent computing properties of new algorithms, their detailed comparison is carried out, the second order of convergence of the decision of stationary boundary value problem by a method of an establishment is shown. The given algorithms are supposed to be used first of all for the adjustment of methodical questions of an inverse problem decision — estimation of unknown values of fractional diffusion parameters by the results of experiments on location.
Goloviznin V.M., Kiselev V.P., Korotkin I.A. COMPUTATIONAL METHODS FOR ONE-DIMENSIONAL FRACTIONAL DIFFUSION EQUATIONS. Preprint IBRAE-2002-10. Moscow: Nuclear Safety Institute, May 2002. 35 p. — Refs.: 14 items.
| ||Classification of environmental data with kernel based algorithms (preprint IBRAE-2002-09)|
Pozdnukhov A., Timonin V., Kanevski M., Savelieva E., Chernov S.
Soil type classification is an important problem from different points of view. Vertical migration of radio-nuclides in soils can be mentioned as an example. The process of migration depends on a number of different properties corresponding both to radio-nuclides and soils. All soil properties are strongly connected with a soil type. Official soil type maps are not good enough to be used for migration problems. Real soil type is more variable value, than it is usually presented in official maps. Soil type mapping can be improved by using additional information obtained during radio-nuclide concentration measurement.
In this work the classification problem is solved by machine learning methods such as probabilistic neural networks PNN (supervised learning algorithm) and Support Vector Machines SVM. The advantages of both methods are general non-linear modelling that avoids the direct modelling of spatial correlation structure. The methods are compared with the nearest neighbour method, the simplest approach to spatial classification.
Pozdnukhov A., Timonin V., Kanevski M., Savelieva E., Chernov S. CLASSIFICATION OF ENVIRONMENTAL DATA WITH KERNEL BASED ALGORITHMS. Preprint IBRAE-2002-09. Moscow: Nuclear Safety Institute RAS, 2002. 23 p. — Refs.: 10 items.
| ||Science-based modelling of Chernobyl fallout trend (preprint IBRAE-2002-08)|
Kanevski M., Savelieva E., Demyanov V., Chernov S., Sorokovikova O., Belikov V.
This work is devoted to the science based modeling of 137Cs contamination due toChernobyl fallout, this fallout is an example of data with non-linear trend and high local variability and that’s why they are very efficient for testing non-linear estimators. Science based atmospheric dispersion modeling is performed on the base of the Lagrange model atmospheric transport model and with the help of software NOSTRADAMUS, developed at IBRAE. Nevertheless of detailed preliminary preparation of model parameters the final result shows only the main orientation of the trace. It does not reproduce the spotted structure presented in measured data. Such situation is caused by not exact knowledge of parameters important for atmospheric modeling – Chernobyl example seems to be too difficult for pure science-based modeling. The residuals of science-based model were studied using Artificial Neural Networks (ANN). Such hybridization allows to improve the results by introducing some “hot spots” distributed not in the main trace.
Kanevski M., Savelieva E., Demyanov V., Chernov S., Sorokovikova O., Belikov V. SCIENCE-BASED MODELLING OF CHERNOBYL FALLOUT TREND. Preprint IBRAE-2002-08. Moscow: Nuclear Safety Institute RAS, 2002. 23 p. — Refs.: 15 items.
| ||GEOSOM application for data analysis using the self-organizing maps (preprint IBRAE-2002-07)|
Kanevski M., Chernov S., Demianov V., Savelieva E., Timonin V., Trouttse A.
In this work the program application GeoSOM described which was developed and realized to data analyze using Self-Organizing Kohonen’s Maps. The paper contains the theory of SOM method which had been realized. There is given the example of data analysis using GeoSOM application.
Kanevski M., Chernov S., Demianov V., Savelieva E., Timonin V., Trouttse A. GEOSOM APPLICATION FOR DATA ANALYSIS USING THE SELF-ORGANIZING MAPS. Preprint IBRAE-2002-07. Moscow: Nuclear Safety Institute RAS, 2002. 16 p. — Refs.: 2 items.