# Aliona DregleaIrkutsk State Technical University · Baikal School of BRICS

Aliona Dreglea

PhD

## About

43

Publications

4,063

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311

Citations

Citations since 2017

Introduction

Education

September 1994 - September 1999

## Publications

Publications (43)

The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of block operators on normed spaces. A system of linear equations with the block operator acting in Banac...

Dear Colleagues, A series of applications of the Lyapunov-Schmidt method, Conley index theory, and the central manifold methods in the conditions of group symmetry were reported in many seminal works in recent decades. Various critical processes in plasma physics, fluid dynamics, and thermodynamics are modeled using the branching theory of nonlinea...

In the case of microgrid (MG) systems, the choice of the right configuration plays a vital role to meet grid/load necessities when integrating low voltage, non-linear and highly sensitive (to environmental conditions) power sources such as solar PV modules, batteries and supercapacitors (SCs), etc. In the case of MG systems, the choice of the right...

Objective of the study: development of mathematical models to assess the method of formation of the intestinal anastomosis with a comparison of the effectiveness of these models. Materials and methods of research: from January 2012 to December 2019, 204 operations were performed to restore the continuity of the intestinal lumen, of which 126 were p...

The nonlinear Volterra integral equations with loads on the desired solution are studied. Loads are given using the Stieltjes integrals. The equations contain a parameter, for any value of which the equation has a trivial solution. The necessary and sufficient conditions on the values of the parameter are derived in the neighborhood where theequati...

Biodegradable elastic scaffolds have attracted more and more attention in the field of soft tissue repair and tissue engineering. These scaffolds made of porous bioelastomers support tissue ingrowth along with their own degradation. It is necessary to develop a computer-aided analyzing method based on ultrasound images to identify the degradation p...

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central
nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain ti...

The researchers aimed to study the nonlinear fractional order model of malaria infection based on the Caputo-Fabrizio fractional derivative. The homotopy analysis transform method (HATM) is applied based on the floating-point arithmetic (FPA) and the discrete stochastic arithmetic (DSA). In the FPA, to show the accuracy of the method we use the abs...

This chapter gives the brief introduction to the management of energy in smart grids focusing on the hybrid renewable energy systems, load and generation forecasting, new grids structure, and smart technologies. The classification of smart infrastructure systems and smart energy management systems is provided and discussed with focus on both demand...

The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estim...

The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Also, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estimatio...

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of...

The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical me...

The necessary and sufficient conditions of existence of the nonlinear operator equations’ branches of solutions in the neighbourhood of branching points are derived. The approach is based on the reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory...

Energy storage systems will play a key role in the power system of the twenty first century considering the large penetrations of variable renewable energy, growth in transport electrification and decentralisation of heating loads. Therefore reliable real time methods to optimise energy storage, demand response and generation are vital for power sy...

Bubble detection is a challenging problem in automatic process control in the power and energy industry, medical and pharmaceutical industry and many other fields. Computer vision methods applications for bubble detection and measurement is the principal step of robust bubbles monitoring systems development. In various applications the input image...

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory bas...

Tourism development in ecologically vulnerable areas like the lake Baikal region in Eastern Siberia is a challenging problem. To this end, the dynamical models of AC/DC hybrid isolated power system consisting of four power grids with renewable generation units and energy storage systems are proposed using the advanced methods based on deep reinforc...

Tourism development in ecologically vulnerable areas like the lake Baikal region in Eastern Siberia is a challenging problem. To this end, the dynamical models of AC/DC hybrid isolated power system consisting of four power grids with renewable generation units and energy storage systems are proposed using the advanced methods based on deep reinforc...

Исследованы дифференциальные уравнения с неклассическими начальными условиями в случае необратимости оператора в главной части уравнения. Приведены необходимые и достаточные условия существования неограниченных решений с полюсом $p$-го порядка в точках, в которых оператор, стоящий в главной части дифференциального уравнения, не имеет обратного. На...

The paper presents a brief overview of the main areas of research and educational activities of the founder of the Irkutsk school on the theory of differential operator equations with the irreversible operator in the main part, the professor of the Institute of Mathematics and Information Technologies of Irkutsk State University N. A. Sidorov.

Accurate wind power and wind speed forecasting remains a critical challenge in wind power systems management. This paper proposes an ultra short-time forecasting method based on the Takagi–Sugeno (T–S) fuzzy model for wind power and wind speed. The model does not rely on a large amount of historical data and can obtain accurate forecasting results...

Energy storage systems will play a key role in the power system of the twenty first century considering the large penetrations of variable renewable energy, growth in transport electrification and decentralisation of heating loads. Therefore reliable real time methods to optimise energy storage, demand response and generation are vital for power sy...

Renewable-energy-based grids development needs new methods to maintain the balance between the load and generation using the efficient energy storages models. Most of the available energy storages models do not take into account such important features as the nonlinear dependence of efficiency on lifetime and changes in capacity over time horizon,...

We consider a linear inhomogeneous wave equation and linear inhomo-geneous heat equation with initial and boundary conditions. It is assumed that the inhomogeneous terms describing the external force and heat source in the model are decomposed into Fourier series uniformly convergent together with the derivatives up to the second order. In this cas...

Bubbles detection is important in various applications in areas including medicine, process control, geochemistry. The application of computer vision methods enables robust bubbles detection and classification even in complex image registration environments. Complex image background is one of the key issues we studied. Proposed method uses image se...

The novel approach for automatic detection and classification of road defects is proposed based on shape and texture features analysis. The system includes three main steps: defects position detection, feature contour extraction followed by classification of defects. The proposed approach is implemented in Matlab for automatic detection and classif...

The linear homogeneous wave equations with initial and boundary conditions are considered. It is assumed that the non-uniform terms describing an external force, are expanded into Fourier series, and the objective is to determine its N time depending coefficients. In order to determine these coefficients uniquely, N non-local boundary conditions ar...

We consider the nonlinear operator equation B(λ)x + R(x, λ) = 0 with parameter λ, which is an element of a linear normed space Λ. The linear operator B(λ) has no bounded inverse for λ = 0. The range of the operator B(0) can be nonclosed. The nonlinear operator R(x, λ) is continuous in a neighborhood of zero and R(0, 0) = 0. We obtain sufficient con...

Рассматривается нелинейное операторное уравнение B(λ)x+R(x,λ)=0 с параметром λ, являющимся элементом линейного нормированного пространства Λ. Линейный оператор B(λ) не имеет ограниченного обратного при λ=0. Область значений оператора B(0) может быть незамкнутой. Нелинейный оператор R(x,λ) непрерывен в окрестности нуля, R(0,0)=0. Получены достаточны...

Ключевую роль в теории формования волокон занимают гидродинамические модели, описываемые нелинейными краевыми задачами пограничного слоя. Настоящая монография ставит своей целью рассмотрение таких краевых задач с привлечением современных методов функционального анализа, гидродинамики и вычислительной математики. Разработан аналитический метод постр...

An analytical solutions of Glauert and Lighthill nonlinear systems with partial derivatives have been constructed. The nonlinear system introduced by Blasius for plane model of polymers has been addressed. For such system the resolving equation with respect to the stream function and three exact solutions have been constructed.

The continuous solutions for BVP of third order nonlinear differential equations appears in [1] mathematical model of the melt spinning process. The existence theorem is proved for such BVP. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The continuous solutions for BVP of third order nonlinear differential equations appears in [1] mathematical model of the melt spinning process. The existence theorem is proved for such BVP. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Paper addresses generalized solution of the Volterra inte-gral equations of the first kind. The explicit structure of the solution is derived. Applications of the proposed ap-proach include blind identification of nonlinear dynamic systems from time domain input-output data in heat and power engineering. The resluts will be also of interest to biom...

## Projects

Projects (2)

The influence of heliogeophysical phenomena, such as magnetic storms, on the functioning of modern electric power systems (EPS) is one of the well-known and, at the same time, poorly studied, factors of EPS vulnerability for major systemic accidents due to the influence of geomagnetically induced induced currents. All over the world, there are trends both in increasing the load and in the various energy systems integration, including the renewable energy sources, primarily the sun and wind. The connection of local EPSs to a unified power system on the one hand allows to reduce the risks of local threats, but at the same time increases the integral risks of the EPS blackouts, which in modern conditions often operate in modes close to the design limit. The most serious systemic accident in the world, due to a powerful magnetic storm, is the blackout in the province of Quebec (Canada) in 1989. There was no electricity for almost six hours for 6 million people there. The threat of a future extreme geomagnetic storm in the US is declared a threat to national security. According to the estimates of the National Academy of Sciences of the United States, the weather cataclysm could lead to the failure of several hundred key transformers of the US power system within just one and a half minutes, which would mean stopping access to electricity for more than 130 million people. It is obvious that theoretical and applied interdisciplinary studies of the influence of heliogeophysical phenomena on the reliability of the functioning of the Unified Energy System (EEC) of Russia is the to topic to get studied. Especially in the light of the fact that until recently such surveys and assessments of the consequences of such threats for domestic power plants have not been carried out in our country. At the present time, research is being conducted on a broad front in the development of effective predictive propagation models and the degree of influence of space weather on the surface layer of the atmosphere. A large-scale interdisciplinary study of the effect of geomagnetically induced induced currents on the reliability of the operation of the UES of Russia is planned in the project on the basis of the ISTP SB RAS infrastructure object (IO Angara). The project proposes a new system approach for assessing the risk and preventing the occurrence of EPS accidents in various geomagnetic conditions, at various latitudes and the geoelectric structure of the lithosphere of the location of the EPS. Depending on the degree of threat for early detection of pre-emergency states and their prevention, preventive measures will be proposed to manage EPS regimes. Thus, the proposed approach solves the inverse problem of the effect of space weather on the reliability of EPS. Based on measurements of the IO Angara and analyse the retrospective data of the UES of Russia accidents, it is proposed to develop mathematical forecast models of risk assessment and classification of EPS states based on machine learning methods. The second stage involves modeling the effects of induced currents on both autonomous and large power systems. With the use of test schemes and modern author software and software, an analysis of the risks of the most characteristic types of accidents due to geomagnetically induced induced currents and the development of a preventive system for eliminating the consequences of system failures are planned.