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Model of geophysical fields representation in problems of complex correlation-extreme navigation

Kharchenko V., Mukhina M.

Transport Problems

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2015

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T. 10, z. 3

35--41

EN

A model of the optimal representation of spatial data for the task of complex correlation-extreme navigation is developed based on the criterion of minimum deviation of the correlation functions of the original and the resulting fields. Calculations are presented for one-dimensional case using the approximation of the correlation function by Fourier series. It is shown that in the presence of different geophysical map data fields their representation is possible by single template with optimal sampling without distorting the form of the correlation functions.

RU

Разработана модель оптимального представления пространственных данных для задач комплексной корреляционно-экстремальной навигации на основе критерия минимального отклонения корреляционных функций исходного и полученного полей. Представлены расчеты для одномерного случая с использованием аппроксимации корреляционной функции рядом Фурье. Показано, что при наличии картографических данных разных геофизических полей возможно их представление единым эталоном с оптимальной дискретизацией без искажения вида корреляционных функций.

2

Bizon K.

Chemical and Process Engineering

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2015

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Vol. 36, nr 3

365--376

EN

Over the last decades the method of proper orthogonal decomposition (POD) has been successfully employed for reduced order modelling (ROM) in many applications, including distributed parameter models of chemical reactors. Nevertheless, there are still a number of issues that need further investigation. Among them, the policy of the collection of representative ensemble of experimental or simulation data, being a starting and perhaps most crucial point of the POD-based model reduction procedure. This paper summarises the theoretical background of the POD method and briefly discusses the sampling issue. Next, the reduction procedure is applied to an idealised model of circulating fluidised bed combustor (CFBC). Results obtained confirm that a proper choice of the sampling strategy is essential for the modes convergence however, even low number of observations can be sufficient for the determination of the faithful dynamical ROM.

3

Optimal random sampling for spectrum estimation in DASP applications

Tarczyński A., Qu D.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

463-469

EN

In this paper we analyse a class of DASP (Digital Alias-free Signal Processing) methods for spectrum estimation of sampled signals. These methods consist in sampling the processed signals at randomly selected time instants. We construct estimators of Fourier transforms of the analysed signals. The estimators are unbiased inside arbitrarily wide frequency ranges, regardless of how sparsely the signal samples are collected. In order to facilitate quality assessment of the estimators, we calculate their standard deviations. The optimal sampling scheme that minimises the variance of the resulting estimator is derived. The further analysis presented in this paper shows how sampling instant jitter deteriorates the quality of spectrum estimation. A couple of numerical examples illustrate the main thesis of the paper