Кафедра прикладної математики (ПМ)

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About one class of the problems of optimal stochastic control of hybrid dynamical systems
(Econtechmod. An International Quarterly Journal, 2016) Тевяшев, А. Д.; Матвиенко, О. И.
A new class of the problems of optimal stochastic control of hybrid dynamical systems different from well-known ones by the introduction of additional extreme and probabilistic constraints on the phase variables is studied in the present work. The mathematical formulation and approximate method of solution of the examined class of the problems are presented in this work. The effectiveness of the use of this class of the problems is illustrated on the example of one of the largest water main of Ukraine.
About one problem of optimal stochastic control of the modes of operation of water mains
(Econtechmod. An International Quarterly Journal, 2015) Tevyashev, A.; Matviyenko, O.
The problem of increasing of the efficiency of operation of the water mains in modern conditions while the transition to a three-tier tariff for the electricity is examined in the present work. An effective method for solving this problem, based on the use of specific features of the water mains as stochastic objects operating in the stochastic environment is offered. The mathematical formulation of the problems of optimal stochastic control of the modes of operation of the water main with probabilistic constraints on the phase variables is presented. A new strategy for the optimal stochastic control of the modes of operation of the water main, the use of which has allowed to develop an effective method for solving the examined problem is proposed in the present work. It is shown that the transition from the classical deterministic problems of control of the modes of operation of the water mains to stochastic ones, provides a significant (up 9%) decrease of financial expenses for the electricity.
Air object recognition by the normalized contour descriptors
(ХНУРЕ, 2021) Єсілевський, В. С.; Тевяшев, А. Д.; Колядін, А. В.
This paper consider research into the methods for recognizing the type of an air object on a digital image acquired from video monitoring system. A method has been proposed that is applied on a feature vector built on the basis of a Fourier transform for the sequence of coordinates of its two-dimensional contour. This makes it easier to solve the classification problem owing to a more compact arrangement of the multidimensional feature vectors for similar air objects. The architecture of an air situation video monitoring system has been suggested, which includes an image preprocessing module and a module of neural network. Preprocessing makes it possible to identify an object’s contour and build a sequence of normalized descriptors, which are partially independent of the spatial position of the object and the contour processing technique. Proposal method is easy in realization and do not require significant computational resources due take into consideration the specificity of recognizing objects in 3 dimensional. This research has shown that the reported results make it easier to train a neural network and reduce the hardware requirements for solve the task of air situation video monitoring.
Air Objects Recognition by the Phase Correlation Method
(Друкарня Мадрид, 2020) Yesilevskyi, V. S.; Tevyashev, A. D.; Koliadin, A.
The article considers a method for determining the type of an air object on a digital image by comparing it with standard images using the phase correlation method.
Analysis of the properties of ordinary levy motion based on the estimation of stability index
(Sofia : ITHEA, 2014) Kirichenko, L.; Shergin, V.
The work proposes a method for estimating the stability index of alpha-stable distributions by using moments of fractional order. Provided numerical modeling has fully justified all of the results. Comparative analysis of the efficiency among the proposed method of estimating the stability index and widely used methods was performed. Proposal method is much simpler, far more faster and substantially less memory required. Estimation of generalized Hurst exponent from time series of the ordinary Lévy process was performed. Multifractal fluctuation analysis method and evaluation based on stability index estimation were compared. The results of numerical modelling showed that proposed method for estimating the fractal properties of the ordinary Lévy process, based on stability index estimation via fractional order moments is a much more accurate.
Classification of Multifractal Time Series by Decision Tree Methods
(КНУ, 2018) Булах, В. А.; Кіріченко, Л. О.; Радівілова, Т. А.
The article considers classification task of model fractal time series by the methods of machine learning. To classify the series, it is proposed to use the meta algorithms based on decision trees. To modeling the fractal time series, binomial stochastic cascade processes are used. Classification of time series by the ensembles of decision trees models is carried out. The analysis indicates that the best results are obtained by the methods of bagging and random forest which use regression trees.
Classification of time realizations using machine learning recognition of recurrence plots
(AISC, 2021) Кіріченко, Л. О.; Радівілова, Т. А.; Зінченко, П. П.
In the article,the machine learning classification of time realizations using the recurrence plot visualization is considered. Every time realization is converted intoa matrix of recurrence states and it is presented as a black-and-white image. The resulting images of realizations are classified using deep neural networks. A deep residual neural network is used as an image classifier. The binary classifi-cation of EEG realizationsis carried out. The result of the binary classification is the detection of an epileptic seizure. The data for the experiment are records of brain activity containing 178 values. The results of the studyshow that the consi-dered method has a high classification accuracy. The proposed classification ap-proach can be readily used in practice.
Comparative Analysis of Noisy Time Series Clustering
(2019) Кіріченко, Л. О.; Радівілова, Т. А.; Ткаченко, А. Є.
A comparative analysis of the clustering of sample time series was performed. The clustering sample contained time series of various types, among which atypical objects were present. In the numerical experiment, white noise with different variance was added to the time series. Clustering was performed by k-means and DBSCAN methods using various similarity functions of time series. The values of the quality functionals were quantitative measures of the quality of clustering. The best results were shown by the DBSCAN method using the Euclidean metric with a Complexity Invariant Distance. The method allows to separate a cluster with atypical series at different levels of additive noise. The results of the clustering of real time series confirmed the applicability of the DBSCAN method for detecting anomaly.
Comparative analysis of the complexity of chaotic and stochastic time series
(Zaporizhzhia National Technical University, 2014) Kirichenko, L. O.; Kobitskaya, Yu. A.; Habacheva, A. Yu.
The new approach to the recognition mechanism of the time series generating process based on the results of the entropy and the recurrent analysis is proposed. The comparative analysis of the realizations properties of chaotic and stochastic processes with different correlation structure was carried out. It is shown that the derived set of information characteristics allows to distinguish the realizations of deterministic chaotic and fractal random processes. Depending on complexity measures of time series of process parameters were obtained. The information characteristics dependencies from the process parameters were obtained. The results of bioelectric signals and financial time series study are presented. Предложен новый подход к распознаванию механизма процесса, породившего временной ряд, базирующийся на результатах энтропийного и рекуррентного анализа. Проведен сравнительный анализ свойств реализаций хаотических и стохастических процессов, имеющих различную корреляционную структуру. Показано, что полученное множество характеристик информационной сложности позволяет различать реализации детерминированных хаотических и фрактальных случайных процессов. Получены зависимости информационных характеристик от параметров процессов. Приведены результаты исследования биоэлектрических сигналов и финансовых рядов.
Comparison of classifiers based on the decision tree
(ХНУРЕ, 2021) Федоров, Д. П.
The main purpose of this work is to compare classifiers. Random Forest and XGBoost are two popular machine learning algorithms. In this paper, we looked at how they work, compared their features, and obtained accurate results from their robots.
Construction of a Stochastic Model for a Water Supply Network with Hidden Leaks and a Method for Detecting and Calculating the Leaks
(Eastern-European Journal of Enterprise Technologies, 2019) Тевяшев, А. Д.; Матвієнко, О. І.; Никитенко, Г. В.
Розроблена стохастична модель водопровідної мережі з витоками, яка в порівнянні із запропонованими раніше моделями (без урахування витоків) більш адекватно описує процеси транспорту і розподілу води в системах водопостачання. При математичному моделюванні водопровідних мереж виникають труднощі, пов'язані з величезною розмірністю реальних водопровідних мереж, обмеженістю інформаційних ресурсів і оперативних даних, що не дозволяє досить адекватно оцінити параметри технологічного обладнання і структуру водопровідної мережі. Тому для реальної водопровідної мережі по її диктуючих точках будується еквівалентна схема, для якої проводяться всі подальші розрахунки. Задача побудови схеми еквівалентної водопровідної мережі складається з трьох задач: ідентифікації структури, параметрів і стану водопровідної мережі. Запропонований метод виявлення витоків заснований на порівнянні зміни величини напору на насосних станціях і в диктуючих точках водопровідної мережі. На базі стохастичної моделі водопровідної мережі з витоками розроблений метод розрахунку величини витоків, який полягає в наступному: знаючи напір води у вузлах еквівалентної водопровідної мережі і приблизні діаметри витоків у вузлах проводиться розрахунок нових значень напорів у вузлах еквівалентної водопровідної мережі. Далі знову розраховується величина витоку, знаючи новий напір у вузлі і діаметр витоків. Зробивши кілька таких ітерацій приходимо до висновку, що починаючи з деякого кроку величина витоків і напори у вузлах еквівалентної водопровідної мережі перестають змінюватися. Знаючи величину витоку і напір у кожному вузлі еквівалентної водопровідної мережі, визначаємо дійсний діаметр свищів у кожному вузлі. Запропонований метод виявлення розрахунку величини витоків не вимагає фінансових витрат або використання додаткового обладнання, він може застосовуватися у Водоканалах для виявлення і розрахунку величини витоків.
Data Mining methods for detection of collective anomalies in time series
(Національна академія Національної гвардії України, 2021) Кіріченко, Л. О.; Кобзєв, В. Г.; Федоренко, Є. Д.
The paper considers the approach to the detection of collective anomalies in time series, based on the use of clustering methods, in particular the method of k-means, as well as the effectiveness of their application.
Development of QoS Methods in the Information Networks with Fractal Traffic
(International Journal of Electronics and Telecommunications, 2018) Кіріченко, Л. О.; Радівілова, Т. А.; Daradkeh Yousef Ibrahim
The paper discusses actual task of ensuring the quality of services in information networks with fractal traffic. The generalized approach to traffic management and quality of service based on the account of multifractal properties of the network traffic is proposed. To describe the multifractal traffic properties, it is proposed to use the Hurst exponent, the range of generalized Hurst exponent and coefficient of variation. Methods of preventing of network overload in communication node, routing cost calculation and load balancing, which based on fractal properties of traffic are presented. The results of simulation have shown that the joint use of the proposed methods can significantly improve the quality of service network.
Dynamic Bayesian Networks for State- and Action-Space Modelling in Reinforcement Learning
(ХНУРЕ, 2018) Леховицький, Д. І.; Ховрат, А. В.
In recent years Reinforcement Learning has proven its efficiency in solving problems of sequential decision making, formalized with a concept called Markov Decision Process. Though, there is a lot of problems: high computational complexity for multivariate state- and action-space problems, needs to handle missing data and hidden variables, lack of both good model and a sufficient number of episodes for constructing an optimal policy. In this work we suggest Dynamic Bayesian networks (DBNs) as a solution. These models provide an elegant and compact representation of joint state-action space, efficient inference algorithms, which include Monte-Carlo methods and Belief Propagation, and can be used in Dyna-Q Algorithm for integrating real-world and simulated experience.
Dynamic load balancing algorithm of distributed systems
(2016) Ivanisenko, I.; Kirichenko, L.; Radivilova, T.
The dynamic load balancing algorithm based on the monitoring server load, self-similar characteristics of passing traffic have to provide a statistically uniform load distribution on servers, high performance, fault tolerance and capacity, low response time, the amount of overhead and losses was propose in work. Integrated measurement for the total imbalance level of the system were entered.
Generalized approach to Hurst exponent estimating
(IAPGOŚ, 2018) Булах, В. А.; Кіріченко, Л. О.; Радивилова, Т. А.
This paper presents a generalized approach to the fractal analysis of self-similar random processes by short time series. Several stages of the fractal analysis are proposed. Preliminary time series analysis includes the removal of short-term dependence, the identification of true long-term dependence and hypothesis test on the existence of a self-similarity property. Methods of unbiased interval estimation of the Hurst exponent in cases of stationary and non-stationary time series are discussed. Methods of estimate refinement are proposed. This approach is applicable to the study of selfsimilar time series of different nature
Information and Analytical System for Monitoring the Energy Resources of the Enterprise
(Друкарня Мадрид, 2020) Tevyashev, A. D.; Tkachenko, V. F.; Sizova, N.; Kostarev, D.
The issues of creation and functioning of the Ekoflex Information Monitoring System intended for accounting and forecasting values the consumption of energy resources of the enterprise, have been considered. A description of the system architecture and its software content has been given. A common digital network for centralized data collection and processing has been developed. The energy consumption of the enterprise can be monitored from any device anywhere in the world through a cloud web interface and a mobile interface. The gas (flow) consumption forecasting module takes into account several external factors (exogenous variables) and the structural specifics of the enterprise.
Interfaces and Software Control Models of Multipoint Aerial Objects Trajectory Measurements System
(Друкарня Мадрид, 2020) Tevyashev, A. D.; Koliadin, A.
This paper is devoted to the development of the software interfaces for multipoint air objects trajectory measurements system.
Investigation of multifractal properties of additive data stream
(Publishing House of Lviv Polytechnic National University, 2016) Radivilova, T.; Ivanisenko, I.; Kirichenko, L.
The work presents results of a numerical study of fractal characteristics of multifractal stream at addition of stream, which does not have multifractal properties. They showed that the generalized Hurst exponent of total stream tends to one of original multifractal stream with increase in signal/noise ratio.
Investigation of Self-similar Properties of Additive Data Traffic
(Lviv, 2015) Radivilova, T.; Ivanisenko, I.; Kirichenko, L.

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