2020 № 2(47)

CONTENTS

Kalney A. M., Rodionov A. S. Reliability analysis of multilevel networks with unreliable Vertices
Zabinyakova O. B., Sklyar S. N.Results of numerical experiments on magnetotelluric eld modeling in a vertically gradient medium
Yakimenko A. A., Makfuzova A. I., Mikhailenko D. A. Software for border detection on example of seismic wave eld images
Zagorulko G. B. Software environment and development METHODOLOGY OF INTELLIGENT DSS

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

RELIABILITY ANALYSIS OF MULTILEVEL NETWORKS WITH UNRELIABLE VERTICES

DOI: 10.24411/2073-0667-2020-10005

Random graphs and hypergraphs are commonly used to analyze untrusted networks. At the same time, in the case of hierarchical networks, modeling a network with a random graph may be insu cient. You can nd various examples of such models: bigographs, sandwich graphs, graphs with di erent types of edges, application-level descriptions, multi-level complex networks (LCN), but they are not universal. Nevertheless, for more than 30 years, the hypernet model has been successfully used to model multilevel networks in several Russian, Kyrgyz and Kazakh universities. A hypernet allows you to adequately describe multilevel networks with an arbitrary number of levels. In this article, we will discuss the simplest case of two-level networks. Particular attention will be paid to obtaining indicators of the connectivity of secondary networks of two-level hypernets, depending on the probability of the presence of vertices in the primary network. We selected indicators based on the probability of the connectivity of a pair of nodes of the secondary network with possible damage to the primary network: the arithmetic probability of the connectivity of a pair of nodes of the network (APC), the average size of the connected subgraph containing the selected vertex (ASCS). It is assumed that the sets of vertices of the primary and secondary networks coincide. The article gives an example of the algorithm for the ASCS indicator, which shows the possibility of using it to optimize the placement of environmental monitoring sensors of a part of the Novosibirsk transport network.

The task of accurately calculating the connectivity probability of a random network with unreliable elements belongs to the class of NP-hard ones; therefore, various approximate methods were previously used in practice, while exact calculation methods were mostly of purely academic interest. However, the development of computer technology has led to a revival of interest in the use of exact methods in practice, since it became possible in a reasonable time to calculate the reliability of small and medium-sized networks (up to tens of nodes). Of the exact methods for determining the probability of a network being connected with unreliable elements, the factorization or Moore-Shannon method is most widely known. This method consists in recursively breaking a hypernet into several simpler branches, respectively, where the vertex is reliable“ (the probability of presence becomes equal to one) and where it is removed. Recursion continues until a reliable path connecting the selected vertices is obtained, or until an unconnected secondary network is obtained; the recursion also ends when a two- vertex hypernet is received. Due to the fact that the number of recursions grows exponentially with the number of vertices, additional techniques are required to accelerate this method. The following methods are used: before calling a recursion, edges in hanging trees and in connected components that do not contain selected vertices in the secondary network are deleted, when the vertex is deleted, the network connectivity is checked and if both selected vertices are in the same connected component, then the reliability is calculated in this component, if the selected vertices lie in di erent components, then we get a disconnected network. In both of the above methods, the number of elements of the hypernet decreases, the reliability indicator does not change.

The article considers the reliability analysis of multilevel networks represented by hypernets. Indicators were selected based on the connectivity probability of a pair of nodes of the secondary network with possible destruction of the primary network. A program was written, methods were developed to accelerate the calculation of the value of reliability indicators of a hypernet, which are derivatives of pair reliability. As a result of numerical experiments, it was concluded that it is possible to use the proposed algorithms to optimize the reliability of networks of medium (up to tens of nodes) dimensions. Further research is related to the consideration of more complex structures of hypernets, new indicators of their reliability and the development of parallel algorithms.

Key words: multilevel networks, modeling, Hypernets, reliability analysis.

References

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Bibliographic reference: Kalney A. M., Rodionov A. S. Reliability analysis of multilevel networks with unreliable //journal “Problems of informatics”. 2020, № 2. P.5-14. DOI: 10.24411/2073-0667-2020-10005

O. B. Zabinyakova, S. N. Sklyar∗

Federal State Budgetary Institution of Science Research Station of the Russian Academy of Sciences in Bishkek city,720049, Bishkek, Kyrgyz Republic

^∗American University of Central Asia, 720060, Bishkek, Kyrgyz Republic

RESULTS OF NUMERICAL EXPERIMENTS ON MAGNETOTELLURIC FIELD MODELING IN A VERTICALLY GRADIENT MEDIUM

DOI: 10.24411/2073-0667-2020-10006

The Magnetotelluric Sounding Method (MTS) is one of the passive electrical exploration methods which associated with the studying of the Earth's natural electromagnetic eld variations. It is commonly used to get information about lithosphere structure and about geodynamic processes occurring in it. It's known that the mathematical model which describes the magnetotelluric eld behavior inside a horizontally homogeneous medium is Maxwell's system of equations under some standard simplifying assumptions such as quasi-stationarity and harmonic time-dependence, geological environment homogeneity in horizontal directions, constancy of permeability and permittivity, independence of the electrical conductivity of the medium from the frequency of the electromagnetic eld. The unknown functions of this system are mutually orthogonal complex components of the magnetic and electric elds. Usually, this system of di erential equations is supplemented by the Cauchy boundary conditions, thereby obtaining a one-dimensional forward magnetotelluric sounding (MTS) problem. The model which forms the basis of this problem is called Tikhonov Cagniard model and assumes that a plane electromagnetic wave falls vertically downward on the surface of a horizontally layered geological medium represented by electrical conductivity piecewise constant function. Moreover, actually, geophysical practical interest is also related to gradient medium models in which electrical conductivity is represented by continuous function with respect to the depth (vertically gradient function). Analytical solutions of such problems are known just only for a limited number of the electrical conductivity gradient functions types. Therefore, the particular interest lies in the development of numerical methods which would make it possible to solve the one-dimensional forward problem of magnetotelluric sounding for any vertically gradient medium.

In previous investigations of other authors, the forward one-dimensional problem of magnetotelluric sounding was mainly solved by reducing the system of Maxwell's equations to the one-dimensional Helmholtz equation by eliminating one of the unknown functions. After that, this equation was solved numerically, for example, by nite di erence approximation method or by nite volume method.

Earlier, authors of this paper have constructed special view di erence schemes for the one- dimensional forward MTS problem solving for the general case of the electrical conductivity function. The method which was used for constructing of di erence schemes, interpolations of approximate solutions and proving of convergence estimates is conditionally named by authors like local integral equations“ the method of ”. Due to the fact that the description of the obtained di erence schemes and their properties are currently in the process of publication, in this paper we are presenting these results in a short form and without evidences. Also, this paper presents the results of the proposed numerical methods testing. The Kato-Kikuchi powered model is used here as a test model because for such model correspondent analytical solutions of the Maxwell's system of equations are known. Various options of boundary conditions setting and algorithms for solving the one-dimensional forward MTS problem for these boundary conditions are considered. Di erent cases of tested di erence schemes convergence (depending on variations of problem parameters and alterations of computational grid used for solving) are demonstrated. The issue of the optimal computational grid choosing (i.e. building a computational grid of a special view) is considered by authors like topical question and will be discussed in the future papers. Formulae of approximate solutions natural interpolation are also tested in this paper: according to the visual evaluation results it is established that interpolants' errors are not exceed the corresponding di erence schemes' errors in most cases.

Constructed di erence schemes are possible to be applied for the one-dimensional inverse magnetotelluric sounding problems solving or for determining of the boundary conditions for the two- dimensional forward MTS problem.

The results presented in this paper have been obtained and will be used in the framework of the ful llment of RS RAS State Assignment (research topic No. AAAA-A19-119020190063-2).

Key words: one-dimensional forward problem of magnetotelluric sounding, vertically gradient medium, method of local integral equations, numerical experiments.

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Bibliographic reference: Zabinyakova O. B., Sklyar S. N.Results of numerical experiments on magnetotelluric eld modeling in a vertically gradient medium //journal “Problems of informatics”. 2020, № 2. P. 15-36. DOI: 10.24411/2073-0667-2020-10006

A. A. Yakimenko, A. I. Makfuzova, D. A. Mikhailenko

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

SOFTWARE FOR BORDER DETECTION ON EXAMPLE OF SEISMIC WAVE FIELD IMAGES

DOI: 10.24411/2073-0667-2020-10007

This work was supported by the RFBR grant No. 19-07-00170.

The article evaluates the e ectiveness of software for detecting boundaries using the example of images of seismic wave- eld patterns. Sobel lters are used to detect borders on images. Prewitt, Roberts, Gabor and the Canny algorithm. Software evaluation is performed by quantitative and qualitative characteristics. The results will be used in the study of the neocognitron neural network for the recognition of geological and physical models of media (GPMM). There are currently no quick and accurate tools allowing to solve the inverse problem of geophysics, including in terms of obtaining the structure structure of the studied medium. Under the inverse problem we understand the problem of determining the structure and parameters of the medium under study from existing picture of wave eld propagation. One of the existing approaches to solving inverse problems is an iterative method: by gradually changing the environmental parameters speci ed in a special program, the propagation picture is synthesized wave eld for a given environment and is compared with the existing one. Then the parameters change in the direction of the assumed optimum a set of environmental parameters corresponding to the captured eld picture. As a result of repeated repetition of a given operation, one can approach the desired parameter values. This approach is time consuming for modeling and comparison of eld patterns. Simulation time, depending on the accuracy and detail of the model, can reach several days even on powerful supercomputers. To solve the problem of determining the position and geometric properties of objects, we propose the use of neural networks that have proven themselves in various elds from image recognition to time series processing. The use of properly trained neural network structures will allow us to obtain models that require small processing time and allow you to fairly accurately determine the location and shape of the desired inclusion (hereinafter, we consider the example of cavernous media) - caverns. The input data for a neural network is the pattern of wave eld propagation through a given medium in the form of a sequence of color two-dimensional images. Pictures taken at regular intervals. The output data for the network should be the proposed GFMS, presented in the form of a color two-dimensional image, on which the direct problem was solved. Currently, there is a neural network LSTM for determining the structure of the studied GFMS, given in the form of a two-dimensional image. The image shows a homogeneous medium with a cavity available at an arbitrary point ?a cavity of round or oval shape with arbitrary sizes. This is the main drawback of the neural network. In our study, it is proposed not to recognize the entire GFMS, but to recognize only objects of the geological and physical model of the environment. The neocognitron arti cial neural network was used to perform the task of object recognition, since its recognition ability in the ideal case is insensitive to shifts, resizing, or other distortions. The task of pattern recognition is to partition multidimensional space into areas corresponding to given categories or classes.

One of the important tasks in the system for recognizing objects in an image is the problem of image segmentation. Segmentation divides the image into many disjoint areas that are visually di erent, uniform and signi cant in relation to several qualities or processed properties. Erroneous recognition of segments in the image a ects its quality. The method of nding boundaries on the brightness di erence is the main tool for high-quality image segmentation. Borders are curves in the image along which there is a sharp change in brightness or its derivatives with respect to spatial variables. The GFMS model of a previously unknown shape of brightness and background brightness, therefore, by the distinguishable di erence in brightness, one can judge its presence in the image. The article evaluates the e ectiveness of software (software) for detecting boundaries using the example of images of seismic wave eld patterns. To detect borders on images, Sobel lters are used. Prewitt, Roberts, Gabor and the Canny algorithm. A feature of this program is the con gurability of the parameters of each lter. The program automatically prepares the image for recognition: processing in grayscale, sharpening. It is possible to save images in three di erent formats: jpg, bmp, png.

Software evaluation is performed by quantitative and qualitative characteristics. The results will be used in the study of the neocognitron neural network for recognition of geological and physical models of media (GPMM).

Key words: boundary detection, image recognition, neural network, neocognitron.

References

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Bibliographic reference: Yakimenko A. A., Makfuzova A. I., Mikhailenko D. A. Software for border detection on example of seismic wave eld images//journal “Problems of informatics”. 2020, № 2. P. 37-47. DOI: 10.24411/2073-0667-2020-10007

G. B. Zagorulko

A. P. Ershov Institute of Informatics Systems Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

SOFTWARE ENVIRONMENT AND DEVELOPMENT METHODOLOGY OF INTELLIGENT DSS

DOI: 10.24411/2073-0667-2020-10008

The development of intelligent decision support systems is an important actual problem, which is complicated by the lack of universal, accessible tools. Modern applied intelligent DSS usually consists of several interconnected subsystems such as analytical, expert, information, modeling, and evaluating subsystems. These subsystems solve di erent tasks and use di erent methods for this purpose. To develop intelligent DSS the shells which are ready-made systems with an empty or partially lled knowledge base are often used. The utilization of shells allows to reduce the development of such systems to the re nement of the knowledge base, the creation of base of facts and the development of the solving problems models. Another tool class of software systems used in the development of intelligent DSS is frameworks, which are specialized software platforms comprising tools for building a knowledge base and models of problem, as well as solvers that interpret these models. Both shells and frameworks usually work within the same knowledge representation model. The solvers included in them are focused on a speci c class of problems and implement a single method. However, frameworks usually have means for connecting third-party solvers and data stores. They are often used for shells building.

The paper discusses the most well-known available frameworks used for building intelligent DSS such as CLIPS and jColibri, analyzes their purpose and functionality. The SPORA+ framework created at the A.P. Ershov Institute of Informatics Systems of Siberian Branch of the Russian Academy of Sciences is considered in detail. This framework is a software environment intended to provide comprehensive support for the development of intelligent DSS at all stages of their creation. SPORA+ is based on a model that considers comprehensive support as a process that meets the needs of intelligent DSS developers and is running in parallel with DSS development process. It o ers methods to meet needs and means to implement these methods. Developers of intelligent DSS need conceptual, informational, component, and methodological support. The main methods that meet the needs of developers are ways to work with information about methods and aspects of decision support. They are systematization and provision of content-based access to such information, implementations of decision support methods and intelligent DSS design methods. The facility for conceptual support isthe ontology of

Decision support“ knowledge area. Information support is provided by an information and analytical Internet resource based on this ontology. The resource is a system that has a webinterface, contains systematized information related to the knowledge area

Decision support“ androvides content-based access to this information, methods of its processing and methods for solving typical problems in this eld. The facility for component support is the repository of decision support methods which is a software library integrated with the information and analytical Internet resource and providing access to implementations of methods represented in the form of services. The methodology for developing intelligent DSS includes the architecture and algorithm for development of such systems It suggests to use the information and analytical Internet resource of the modeled subject area as theframework of the created system and provide its functionality by including services from the repository in its structure. The proposed comprehensive support tools are based on principles and approaches that have proven themselves well in the development of systems of this class. The most important principles are maximum use of ready-made solutions, scalability, openness, accessibility, ease of use, independence from the subject area, and informativity. The main approaches are ontological, framework-based, fractal-strati ed, service-oriented, rapid prototyping and agile development approaches. SPORA+ uses technologies for developing intelligent scienti c Internet resources and Semantic Web. These approaches and technologies provide compliance with these principles, simplify and accelerate the development of intelligent DSS, and determine the properties and functionality of the intelligent DSS that will be developed within the framework of the SPORA+.

Key words: development of intelligent DSS, ontology, DSS shell, framework, information- analytical internet-resource.

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Bibliographic reference: Zagorulko G. B. Software environment and development METHODOLOGY OF INTELLIGENT DSS //journal “Problems of informatics”. 2020, № 2. P. 48-67. DOI: 10.24411/2073-0667-2020-10008

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