Vol 30, No 3 (2022)


On the application of the Fourier method to solve the problem of correction of thermographic images

Baaj O.


The work is devoted to the construction of computational algorithms implementing the method of correction of thermographic images. The correction is carried out on the basis of solving some ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. This problem corresponds to the problem of the analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The cylindrical region is bounded by an arbitrary surface and plane. On an arbitrary surface, a temperature distribution is measured (and thus is known). It is called a thermogram and reproduces an image of the internal heat-generating structure. On this surface, which is the boundary of the object under study, convective heat exchange with the external environment of a given temperature takes place, which is described by Newton’s law. This is the third boundary condition, which together with the first boundary condition corresponds to the Cauchy conditions - the boundary values of the desired function and its normal derivative. The problem is ill-posed. In this paper, using the Tikhonov regularization method, an approximate solution of the problem was obtained, stable with respect to the error in the Cauchy data, and which can be used to build effective computational algorithms. The paper considers algorithms that can significantly reduce the amount of calculations.

Discrete and Continuous Models and Applied Computational Science. 2022;30(3):205-216
pages 205-216 views

Numerical simulation of cold emission in coaxial diode with magnetic isolation

Belov A.A., Loza O.T., Lovetskiy K.P., Karnilovich S.P., Sevastianov L.A.


Due to the emergence and active development of new areas of application of powerful and super-powerful microwave vacuum devices, interest in studying the behavior of ensembles of charged particles moving in the interaction space has increased. An example is an electron beam formed in a coaxial diode with magnetic isolation. Numerical simulation of emission in such a diode is traditionally carried out using particle-in-cell methods. They are based on the simultaneous calculation of the equations of motion of particles and the Maxwell’s equations for the electromagnetic field. In the present work, a new computational approach called the point macroparticle method is proposed. In it, the motion of particles is described by the equations of relativistic mechanics, and explicit expressions are written out for fields in a quasi-static approximation. Calculations of the formation of a relativistic electron beam in a coaxial diode with magnetic isolation are performed and a comparison is made with the known theoretical relations for the electron velocity in the beam and for the beam current. Excellent agreement of calculation results with theoretical formulas is obtained.

Discrete and Continuous Models and Applied Computational Science. 2022;30(3):217-230
pages 217-230 views

Application of the method of continued boundary conditions to the solution of the problems of wave diffraction on various types of scatterers with complex structure

Krysanov D.V.


The article considers the application of the method of continued boundary conditions to the two-dimensional problem of diffraction of electromagnetic waves by a dielectric body with a cross section of complex geometry and to the problem of diffraction by a Janus sphere in the form of a permeable sphere partially covered by an absolutely soft or an absolutely rigid spherical screen. The results of calculating the scattering pattern for a large set of bodies of different geometry, including fractal-like scatterers, are obtained. It is illustrated that in the case of a smooth body boundary, the algorithm based on the Fredholm equations of the 1st kind makes it possible to obtain results with greater accuracy than for equations of the 2nd kind. The correctness of the method was confirmed by verifying the implementation of the optical theorem for various bodies and by comparing with the results of calculations obtained by other methods.

Discrete and Continuous Models and Applied Computational Science. 2022;30(3):231-243
pages 231-243 views

Development and analysis of models for service migration to the MEC server based on hysteresis approach

Poluektov D.S., Khakimov A.A.


Online video services are among the most popular ways of content consumption. Video hosting servers have a very high load every day, which we propose to reduce by migrating the application with the video content in demand to the local Multi-access Edge Computing (MEC) server of the target. This makes it possible to improve the quality of services (QoS) provided to users by reducing the transmission delay. Therefore, an architecture has been proposed that allows, at times of increased demand for the same video content, to migrate the video service application to the edge servers of the network operator. To evaluate the performance of this approach, a mathematical model was developed in the form of a queuing system. The results of the numerical experiment make it possible to optimize the time of using local MEC servers to provide video content.

Discrete and Continuous Models and Applied Computational Science. 2022;30(3):244-257
pages 244-257 views

Detection of cyber-attacks on the power smart grids using semi-supervised deep learning models

Shchetinin E.Y., Velieva T.R.


Modern smart energy grids combine advanced information and communication technologies into traditional energy systems for a more efficient and sustainable supply of electricity, which creates vulnerabilities in their security systems that can be used by attackers to conduct cyber-attacks that cause serious consequences, such as massive power outages and infrastructure damage. Existing machine learning methods for detecting cyber-attacks in intelligent energy networks mainly use classical classification algorithms, which require data markup, which is sometimes difficult, if not impossible. This article presents a new method for detecting cyber-attacks in intelligent energy networks based on weak machine learning methods for detecting anomalies. Semi-supervised anomaly detection uses only instances of normal events to train detection models, which makes it suitable for searching for unknown attack events. A number of popular methods for detecting anomalies with semisupervised algorithms were investigated in study using publicly available data sets on cyber-attacks on power systems to determine the most effective ones. A performance comparison with popular controlled algorithms shows that semi-controlled algorithms are more capable of detecting attack events than controlled algorithms. Our results also show that the performance of semi-supervised anomaly detection algorithms can be further improved by enhancing deep autoencoder model.

Discrete and Continuous Models and Applied Computational Science. 2022;30(3):258-268
pages 258-268 views

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