Кафедра "Комп'ютерна математика і аналіз даних"

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https://repository.kpi.kharkov.ua/handle/KhPI-Press/7570

Офіційний сайт кафедри http://web.kpi.kharkov.ua/kmmm

Кафедра "Комп'ютерна математика і аналіз даних" заснована в 2002 році.

Кафедра входить до складу Навчально-наукового інституту комп'ютерних наук та інформаційних технологій Національного технічного університету "Харківський політехнічний інститут", забезпечує підготовку бакалаврів і магістрів за проектно-орієнтованою освітньою програмою за напрямом науки про дані "DataScience".

У складі науково-педагогічного колективу кафедри працюють: 3 доктора наук: 1 – технічних, 1 – фізико-математичних, 1 – педагогічних; 15 кандидатів наук: 10 – технічних, 4 – фізико-математичних, 1 – педагогічних; 3 співробітників мають звання професора, 9 – доцента.

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Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes
(Технологический центр, 2019) Panchenko, Sergii; Prykhodko, Sergii; Kozelkov, Sergii; Shtompel, Mykola; Kosenko, Viktor; Shefer, Oleksandr; Dunaievska, O. I.
It has been shown that convolutional codes are widely used, along with various decoding methods, to improve the reliability of information transmission in wireless telecommunication systems. The general principles of synthesis and the parameters and algebraic non-systematic convolutional codes with arbitrary coding rate and maximum achievable code distance have been shown. The basic stages of the bioinspired method for decoding algebraic convolutional codes using a random shift mechanism have been presented. It has been shown that the essence of the presented decoding method implies applying the procedure of differential evolution with the heuristically determined parameters. In addition, this method uses information about the reliability of the adopted symbols to find the most reliable basis for the generalized generator matrix. The mechanism of random shift for the modification of the accepted sequence is additionally applied for the bioinspired search based on various most reliable bases of a generalized generator matrix. The research results established that the bioinspired method for decoding algebraic convolutional codes ensures greater efficiency compared with the algebraic decoding method in the communication channel with additive white Gaussian noise. Depending on the parameters of the algebraic convolutional code and the necessary error coefficient, the energy gain from encoding ranges from 1.6 dB to 3 dB. It was shown that the presented bioinspired decoding method can be used for convolutional codes with a large code constraint length. In doing so, the presented method for decoding algebraic convolutional codes is less efficient than the Viterbi decoding method and turbo codes at a sufficient number of decoding iterations.
Analysis of operating modes of single-phase current source rectifier with rectangular-stepped pulse-width modulation
(Технологический центр, 2018) Krasnov, Oleksii; Liubarskyi, Borys; Bozhko, Vladimir; Petrenko, Оleksandr; Dubinina, Oksana; Nuriiev, Ramil
The operating modes of the single-phase active current-source rectifier in the case of rectangular-stepped pulse-width modulation and load in the form of DC traction motor are investigated. The single-phase bridge rectifier circuit with a discharge diode is considered. The mathematical model of the rectifier is developed and the main ratios for pulse-width modulation with rectangular-stepped modulating signal are determined. On the computer model, electromagnetic processes at three modulation frequencies (900, 1,200, 1,800 Hz) are studied. The features of the effect of the modulation depth and frequency on the rectifier power factor and the total harmonic voltage and current distortion in the mains supply are determined. The DC motor for today remains the main type of the traction motor of the 25 kV, 50 Hz AC mainline electric locomotives of alternating current in Ukraine and in some other countries. To power such motors, diode or thyristor rectifiers are used. At the same time, it is known that converters on fully controlled semiconductor devices provide higher power efficiency. The studies allow determining what values of modulation frequency and depth provide a high power factor (more than 0.9) and minimum total harmonic voltage and current distortion distortions in the mains supply. This allows finding rational approaches to the selection of power circuits and control algorithms for active converters in the traction electric drive of electric locomotives. The efficiency of increasing the power factor and reducing the total harmonic voltage and current distortion can be achieved, first of all, by reducing the power consumption for traction of trains. According to the set of selected comparison criteria, the active current-source rectifier with a modulation frequency of 1,200 Hz is the most suitable for implementation in the traction electric drive of the electric locomotive. Provision of high power characteristics in a wide range of traction loads can be achieved in the multi-zone circuit of such a converter.
Determining parameters of electromagnetic radiation for energoinformational disinfection of wool in its pretreatment
(Технологический центр, 2017) Kosulina, N.; Cherenkov, A.; Pirotti, E.; Moroz, S.; Chorna, M.
Угнетение инфекционных микроорганизмов в кипах шерсти возможно при помощи электромагнитного излучения (ЭМИ) с параметрами: частота 36 ГГц, мощность 0,5 кВт, экспозиция 3 мин. Энергоинформационные параметры были определены в результате теоретических и экспериментальных исследований процесс взаимодействия ЭМИ с инфекционными микроорганизмами.
Effect of deformation degree under quasihydroextrusion at 77K on the structure and properties of CuCrZr alloy
(Харківський національний університет імені В. Н. Каразіна, 2019) Belyaeva, A. I.; Khaimovich, P. A.; Galuza, A. A.; Kolenov, I. V.; Savchenko, Alla Aleksandrovna; Shul`gin, N. A.
Influence of the parallelepiped form localized defects on ellipsometry data: scale modeling
(Institute of Nuclear Physics, 2021) Galuza, A. A.; Kolenov, I.; Savchenko, Alla Aleksandrovna
Ця стаття присвячена проблемі аналізу еліпсометричних даних поверхні з локалізованими дефектами (різні фази, пухирі, зерна тощо).
Influence of the parallelepiped form localized defects on ellipsometry data: scale modeling
(Institute of Nuclear Physics Polish Academy of Sciences, 2021) Galuza, A. A.; Kolenov, I.; Savchenko, A.
Mathematical model of the development of a single twin layer inmetal crystals
(Національний технічний університет "Харківський політехнічний інститут", 2021) Bosin, Mark Yevgenovych; Gomozov, Yevgen Pavlovych; Drygach, Tetyana Grygorivna
By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a singletwin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only inrelation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in thesense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.
Matlab модель генератора ЭКГ сигнала на основе частотного преобразования
(НТУ "ХПИ", 2018) Шишкин, Михаил Анатольевич; Бутова, Ольга Анатольевна; Фетюхина, Людмила Викторовна; Ахиезер, Елена Борисовна; Дунаевская, Ольга Игоревна
Предложен метод построения Matlab/Simulink модели генератора электрокардиографического сигнала на основе анализа частотного спектра и формирования соответствующих компонент, реализующих суперпозицию сигналов необходимых гармонических составляющих. Целью работы является синтез такого блока с изменяемыми параметрами, который бы мог использоваться в качестве источника сигнала при имитационном моделировании различных кардиологических систем. В ходе работы были получены решения, позволяющие генерировать кардиографический сигнал наиболее часто встречающихся патологий, моделировать вариабельность сердечного ритма и влияние наиболее распространённых помех.
On eigenvalues of banded matrices
(Інститут математики НАН України, 2019) Akhiiezer, O. B.; Dunaievska, О. I.
In the paper, asymptotics for eigenvalues of Hermitian, compact operators, generated by infinite, banded matrices is obtained in terms of the asymptotics of their matrix entries. Analogues for banded matrices of Gershgorin’s disks theory are discussed.
Optimization of thermal modes and cooling systems of the induction traction engines of trams
(Технологический центр, 2017) Liubarskyi, Borys; Petrenko, Оleksandr; Iakunin, Dmytro; Dubinina, Oksana
We developed a procedure for the optimization of thermal modes and parameters of the cooling system of induction traction engines of tram carriages. The procedure includes the following basic steps. The optimization of operating modes of an induction traction drive by the criterion of effectiveness of its work under different modes. The optimization of motion modes of a tram carriage along a track section with the assigned motion schedule and profile based on the curves of the motion of a tram carriage, optimal by the criterion of energy consumption, using the method of Hamilton-Jacobi-Bellman. The optimization of parameters of the cooling fan of traction engines by the criterion of efficiency of a cooling system using the Weyl method by the generalized golden section. It is proposed to conduct determining of operating modes of a traction drive in advance based on the solution to the problem of conditional optimization of its modes. In order to determine the optimal operating modes of a traction drive, we selected a combined method: global search is executed by genetic algorithm with a one-point crossover and by selection on the principle of roulette. At the final stage of an optimization procedure, optimum refining is carried out using the Nelder-Mead method. When a tram carriage moved along a track section, we defined the following. We determined the optimal modes of motion of the tram carriage T-3 VPA with induction traction engines for a track section with the assigned motion schedule. It was found that, compared with the basic design, efficiency of the cooling system increased by 27.6 %, which corresponds to a reduction in the proposed criterion of efficiency. Based on the results of modeling a traction engine with an optimal fan, it was established that the largest overheating is observed in the frontal part of the stator winding. The temperature is 139.6 °C at second 3363 from starting the motion and it does not exceed a permissible value of 140 °C.
Pedagogical acme-technology of formation of responsibility among leader-professionals during the process of professional education
(Національний технічний університет "Харківський політехнічний інститут", 2020) Dubinina, Oksana; Ignatyuk, Olha; Sereda, Nataliia V.
The article is devoted to the problem of formation of responsibility among leader-professionals during the process of professional education at the university. The authors note that the solution to this problem is possible by developing a special pedagogical acme-technology. The paper presents characteristics of structural components of proposed technology (concept, content, procedural parts, software and methodology). In the course of this study, the pedagogical conditions for the formation of responsibility among leaderprofessionals were determined. The results of this study on the establishment of the influence of factor units on the responsibility formation of future leader-professionals in the process of their professional education at the university are discussed.
Probabilistic estimation of stability of solutions of optimization problems
(Research and Scientific Group, Poland, 2018) Dunaievska, О. I.
The issues of stability of solution of optimization problems are considered on the example of transportation problem of linear programming, in which the transportation costs are random variables with a known distribution density. The complexity of solving such optimization problems by classical methods is substantiated. It is proved that the problem of estimating stability admits an analytic solution if the optimal solution of the problem is sought using the matrix minimum method. This solution is based on the search for the probability that characterizes the level of stability of solving the optimization problem. The corresponding computational procedure is described. An example is considered that illustrates it graphically.
Robust model predictive control of constrained supply networks via invariant ellipsoids technique
(2013) Lyubchyk, Leonid; Dorofieiev, Yuri; Nikulchenko, Artem
The problem of robust control strategy synthesis for distributed supply network under demand uncertainty, time delays and state and control constraints is considered. An invariant ellipsoids approach is used for robust control problem solving, since the uncertain demands are regarded as an external disturbance. On the base Model Predictive Control approach, the designed control law implements in the form of linear feedback signal based on mismatch between the current state and safety stock level and provides external disturbances effect suppression with simultaneous robust stabilization of closed-loop system. Via invariant ellipsoids technique the considered problem was presented in the terms of Linear Matrix Inequalities and a solution of corresponding semi-definite optimization problem was also obtained. As an example, the three-tier supply network with ve nodes robust control problem is considered.
Selective invariant multivariable control system design based on inverse model approach
(Consulting Company Consilium Sp. z o.o. Warsaw, Poland, 2015) Lyubchyk, Leonid; Kostyuk, Olga
The problem of disturbance rejection in multivariable control systems is considered. It has been shown that different two-degree-of-freedom control structures used for immeasurable disturbance estimation and compensation may be treated as a particular case of a general Inverse Model Control approach. The decomposition of the problem into the separate disturbance estimation and compensation is suggested. Moreover the connection between inverse model design problems and unknown input observer theory has been established in order to give a practical way to inverse model parameterization and design. The properties of closed-loop selective invariant control system with model-based controllers have been also investigated with the aim of attainable accuracy estimation.
Simulation of the formation of innovative engineering industry cluster
(Publishing House "Education and Science", 2015) Akhiezer, Elena; Dunaievska, О. I.; Mekhovich, Sergey; Heliarovska, Oksana
Teaching and Learning Math Behind Computer Science with the Help of GeoGebra and Python
(2016) Pikalova, Valentyna
The paper is focused on topics where mathematics and computing are most relevant to each other, emphasizing the bridges between theory and practice. Topics include sets, relations, elementary graph theory, asymptotic notation and growth of functions, permutations and combinations, discrete probability. The main tools in order to support and compare problem-solving technique are GeoGebra and Python. The main goal is not only to combine an appreciation of mathematical reasoning with an understanding of computing but enrich both of them through interdisciplinary approach.
Use of triangular models of non-stationary processes in modeling variability of heart rhythm
(Харківський національний університет радіоелектроніки, 2019) Akhiiezer, O. B.; Dunaievska, О. I.; Shyshkin, Mykhailo; Butova, Olha; Rohovyi, Anton
The subject matter is a mathematical model describing the process of heart rhythm variability, which is based on the use of triangular models of non-stationary random processes in the Hilbert space. The goal of the research is to develop a mathematical model of nonstationary processes of cardiac activity based on a triangular model. This research was the basis for the development of a Matlab model that implements the proposed method for analyzing heart rate variability. Tasks are: to give a description of the variability heart rate as a non-stationary process in Hilbert space in terms of correlation functions; to research the possibility of constructing a correlation and spectral theory of a non-stationary process using triangular models; to synthesize the mathematical model of nonstationary process on the basis of correlation theory for solving mathematical processing and forecasting tasks on the basis of ECG data. Using the proposed mathematical method, we implemented the Matlab model of a heart signal generator, which allowed us to synthesize an ECG with different variability parameters in noisy conditions. Methods of mathematical statistics, simulation modeling, theory of random processes and control theory are used in this work. Results of this research are as follows: 1) It has been shown that the new approach to the description of the HRV as a random process in the application of the triangular model in the Hilbert space made it possible to obtain expressions for the correlation function. 2) The imitation simulation showed the sensitivity of the method within the 5% error rate under the conditions of different types of influence on HRV. The qualitative assessment of the possibilities of the proposed models to generate artificial ECG provided the possibility of visual analysis by the cardiologist of the identity of the interpretation of real ECG records. The identities of modeling results were checked on time samples of electrocardiographs of 7 patients from open PhysioNet cardiographic libraries on samples with the duration T = 10 s. 3) The standard low-frequency oscillations and "white noise" barrier are clearly differentiated on the applied correlation function by the distribution of spectral density power within the frequency range of 0,15-0,3 Hz. Conclusion. The simulation results confirmed the correctness of the theoretical conclusions about the possibility of using models based on the representation of non-stationary processes in a triangular Hilbert space.
Адміністрування баз даних і управління версіями з теорії і практики циклу математичних дисциплін
(Українська інженерно-педагогічна академія, 2014) Дубініна, Оксана Миколаївна
В статті викладено результати розробки та особливості практичної реалізації педагогічної технології, яка стосується адміністрування баз даних і управління версіями з теорії і практики циклу математичних дисциплін студентами, що навчаються за напрямом професійної підготовки "Програмна інженерія". Визначено дидактичні можливості технології по інтенсифікації самостійної роботи студентів. Запропонована технологія є складовою частиною акме-технології формування математичної культури майбутніх фахівців галузі виробництва програмної продукції.
Акмеологічні засади розвитку математичної культури майбутніх інженерів індустрії програмної продукції
(Society for Cultural and Scientific Progress in Central and Eastern Europe, 2013) Дубініна, Оксана Миколаївна
Стаття присвячена проблемі пошуку ефективного шляху формування та наповнення математичної культури майбутніх інженерів індустрії програмної продукції, яка є однією з важливих умов стійкості професійної компетентності цих фахівців. Обґрунтовано доцільність акмеологічного підходу формування і розвитку математичної культури студентів за напрямом підготовки "програмна інженерія". Зазначено, що професія інженера з програмного забезпечення та, взагалі, ІТ-фахівця, стає не тільки однією з наймасовіших, але й однією з найважливіших за ступенем впливу інженерної праці на суспільство. По великому рахунку, особистісно-професійні якості цих фахівців впливають на мільйони людей. А підвищення якості підготовки спеціаліста галузі програмної інженерії істотно залежить від організації навчального процесу у вищих технічних навчальних закладах системи освіти. В роботі наведені ті технологічні зміни, які у рамках акмеологічного підходу, під час вивчення доволі великого за об'ємом та зазвичай складного для студентів циклу математичних дисциплін, покликані наряду з одночасним формуванням математичної культури фахівця, готувати його до майбутньої професійної діяльності, допомогти досягти наукового та інженерного способу мислення. Отримавши міцні знання з математичної мови при подальшому отриманні професійної освіти майбутній фахівець вже використовуватиме їх в своїй проектно-конструктивній діяльності, що є основною в області програмної інженерії. Опираючись на акмеологічне підґрунтя визначено, що математична культура майбутнього інженера індустрії програмної продукції – це система, яка має домінуючу акмео-синергетичну основу, спирається на певні визначені компоненти, а саме: виховний, діяльнісний, дослідницький, евристичний, компетентніснокогнітивний, мотиваційний, творчий, що дозволяє забезпечити стійку професійну компетентність, відповідно до вимог інноваційного сталого розвитку суспільства та економіки, можливість самоосвіти та самовдосконалення впродовж усього життя.
Алгоритм расчета формы временных видеоимпульсов, искаженных рассеивающим каналом передачи информации
(Харьковский национальный университет радиоэлектроники, 2013) Галуза, А. А.; Тевяшева, Ольга Андреевна; Ахиезер, Елена Борисовна
В настоящей работе показана методика получения временной формы ЭМ сигнала, прошедшего однородный поглощающий рассеивающий канал передачи. Результаты могут быть использованы для анализа предельных возможностей передающих трактов, а так же при решении обратных задач(восстановление исходного сигнала, определение параметров среды).

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