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Topicality. Control object model parameters calculation using its transient responses, which were obtained as a result of an active experiment, is widely used in engineering practice when adjusting the parameters of automatic control system controller. However, manual processing of transient responses graphs has certain disadvantages and, therefore, usage of special PC software is relevant. Goal. Is to consider the expediency of control object model parameters identification using the results of transient responses processing in MatLab’s System Identification Toolbox program and conduct control systems simulations with the controller’s parameters which were obtained based on the results of this identification. Method. Identification and simulation of control object model and automatic control system model using System Identification Toolbox and Simulink programs were chosen as a method of research. Results. Control object parameters determination examples with static and astatic properties using System Identification Toolbox were provided and correctness of their determination was verified by simulation of these control object models and control systems models in the Simulink program. Conclusions. Examples, which were given, confirmed the expediency of using System Identification Toolbox program to determine the control object model parameters based on its transient responses obtained in an active experiment through the control channel. This program can be recommended for the training of specialists in automation in acquiring of skills for identification of control object models. [ABSTRACT FROM AUTHOR]

New waves of the COVID-19 pandemic in Ukraine, which began in the summer of 2021, and after holidays in the middle of October 2021, were characterized by the almost exponential growth of smoothed daily numbers of new cases. This is a matter of great concern and the need to immediately predict the epidemic dynamics in order to assess the maximum possible values of new cases, the risk of infection, and the number of deaths. The generalized SIR-model and corresponding parameter identification procedure were used to simulate and predict the dynamics of two new epidemic waves in Ukraine and one worldwide. Results of calculations show that new cases in Ukraine will not stop appearing before November 2022. The pandemic can continue for another ten years if the global situation with vaccination, testing, and treatment does not change.

Background. The COVID-19 pandemic is of great interest to researchers due to high mortality and a very negative impact to the world economy. A detailed scientific analysis of the phenomenon is yet to come, but the public is already interested in the problems of duration of the epidemic, the expected number of patients, where and when the pandemic started. Correct simulation of the pandemic dynamics needs complicated mathematical models and many efforts for unknown parameters identification. In this article, preliminary estimates for many countries and world will be presented, summarized and discussed. Objective. We will estimate the epidemic characteristics for USA, Germany, UK, the Republic of Korea and in the world with the use of SIR simulations and compare them with the results obtained before for Italy, Spain, France, the Republic of Moldova, Ukraine and Kyiv. The hidden periods, epidemic durations, final numbers of cases and quarantine measures will be discussed. Methods. In this study we use the known SIR (susceptible-infected-removed) model for the dynamics of the epidemic, the known exact solution of the linear differential equations and statistical approach developed before. Results. The optimal values of the SIR model parameters were identified with the use of statistical approach for epidemic dynamics in USA, Germany, UK, the Republic of Korea, and in the world. The actual number of cases and the number of patients spreading the infection versus time were calculated. The hidden periods, durations and final sizes of the epidemic were evaluated. In particular, the pandemic began in China no later than October, 2019. If current trends continue, the end of the pandemic should be expected no earlier than March 2021, the global number of cases will exceed 5 million. A simple method for assessing the risk of premature weakening of quarantines is proposed. Conclusions. The SIR model and statistical approach to the parameter identification are helpful to make some reliable estimations for the epidemic dynamics, e.g., the real time of the outbreak, final size and duration of the epidemic and the number of persons spreading the infection versus time. This information will be useful to regulate the quarantine activities and to predict the medical and economic consequences of the pandemic.

Background. The epidemic outbreak caused by coronavirus COVID-19 is of great interest to researches because of the high rate of the infection spread and the significant number of fatalities. A detailed scientific analysis of the phenomenon is yet to come, but the public is already interested in the questions of the epidemic duration, the expected number of patients and deaths. Long-time predictions require complicated mathematical models that need a lot of effort to identify and calculate unknown parameters. This article will present some preliminary estimates. Objective. Since the long-time data are available only for mainland China, we will try to predict the epidemic characteristics only in this area. We will estimate some of the epidemic characteristics and present the dependen­cies for victim numbers, infected and removed persons versus time. Methods. In this study we use the known SIR model for the dynamics of an epidemic, the known exact solution of the linear differential equations and statistical approach developed before for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988–1989. Results. The optimal values of the SIR model parameters were identified with the use of statistical approach. The numbers of infected, susceptible and removed persons versus time were predicted and compared with the new data obtained after February 10, 2020, when the calculations were completed. Conclusions. The simple mathematical model was used to predict the characteristics of the epidemic caused by coronavirus in mainland China. Unfortunately, the number of coronavirus victims is expected to be much higher than that predicted on February 10, 2020, since 12289 new cases (not previously included in official counts) have been added two days later. Further research should focus on updating the predictions with the use of up-to-date data and using more complicated mathematical models.

Background. To simulate the COVID-19 pandemic dynamics, various data sets and different mathematical models can be used. In particular, previous simulations for Ukraine were based on smoothing of the dependence of the number of cases on time, classical and the generalized SIR (susceptible-infected-removed) models. Different simulation and comparison methods were based on official accumulated number of laboratory confirmed cases and the data reported by Johns Hopkins University. Since both datasets are incomplete (a very large percentage of infected persons are asymptomatic), the accuracy of calculations and predictions is limited. In this paper we will try to assess the degree of data incompleteness and correct the relevant forecasts. Objective. We aimed to estimate the real sizes of two new epidemic waves in Ukraine and compare them with visible dynamics based on the official number of laboratory confirmed cases. We also aimed to estimate the epidemic durations and final numbers of cases. Methods. In this study we use the generalized SIR model for the epidemic dynamics and its known exact solution. The known statistical approach is adopted in order to identify both the degree of data incompleteness and parameters of SIR model. Results. We have improved the method of estimating the unknown parameters of the generalized SIR model and calculated the optimal values ​​of the parameters. In particular, the visibility coefficients and the optimal values of the model parameters were estimated for two pandemic waves in Ukraine occurred in December 2020–March 2021. The real number of cases and the real number of patients spreading the infection versus time were calculated. Predictions of the real final sizes and durations of the pandemic in Ukraine are presented. If current trends continue, the end of the pandemic should be expected no earlier than in August 2022. Conclusions. New method of the unknown parameters identification for the generalized SIR model was proposed, which allows estimating the coefficients of data incompleteness as well. Its application for two pandemic waves in Ukraine has demonstrated that the real number of COVID-19 cases is approximately four times higher than those shown in official statistics. Probably, this situation is typical for other countries. The reassessments of the COVID-19 pandemic dynamics in other countries and clarification of world forecasts are necessary.

The widespread catalysts and nuclear fuel production are the sol-gel technology, including several stages, namely, the raw materials preparation, dispersing it into drops, the granules formation in gas and then in liquid media, granules removal with liquid separation. The vibration granulator is proposed to use on the dispersion stage. One of the problems in their development is determining the vibrational characteristics of a perforated bucket filled with liquid to a certain level. Considering that vibrations are transmitted from the emitter disk through the liquid melt and cause vibrations of the perforated shell, in research, it was decided to use the Fluent Flow and the Transient Structural modules of the ANSYS Workbench software. As a result, numerical simulation results of the emitter disk vibration effect on the cylindrical body are presented. Also, parameters of a discrete mathematical model are evaluated by the bucket vibrations characteristics. The corresponding model considers the inertial, stiffness, and damping properties of functional elements. Additionally, according to the modal analysis results of the priller body, it was determined the eigenfrequencies of the hydromechanical system. Finally, based on the numerical simulation results and their analysis using Fourier transformations, it was determined that the oscillations of the lower part of the bucket, consisting of two harmonic oscillations that equal 230 Hz and 520 Hz.

Various concentrated works have been done in the area of computational vision regarding the circle and texture detections. Detection of circles in images can be beneficial for PCB components industries for the detection of capacitors in printed circuit boards, also for medicine in the detection of red cells, white blood cells, and leukocytes, and for applications which requires precision and assignments regarding the detection of circles in a digital image. In this work is utilized a benchmarking of images to detection circle boards of different radio values for the comparison with the work [1] of this article. The benchmarking of images is composed of five main images that are tested in the algorithm of detection of circles in MATLAB with different values of radio for each image. The results appoint an enhancement of 300 % concerning the algorithm proposed in work [1] showed in this article. In this work also would be plotted graphs concerning the accuracy of the new proposed algorithm with relation to the algorithm proposed in work [1], indicating better results concerning the GUI interfaces and capacity of detection circles.

Topicality. Controlled disturbances channel identification remains topical problem when building ACS which provide high dynamic accuracy of controlled variable stabilization. This task requires knowledge of stochastic processes theory as well as utilization of MATLAB modern program packages, which provide analysis and synthesis of control systems.Goal. To provide examples of using such packages as Signal Processing Toolbox and System Identification Toolbox in the task of test control object’s controlled disturbances channel’s dynamic characteristics identification and establish an influence on accuracy of model parameters estimation and range of their change and also intensity and spectral composition of non-controllable disturbances. Means. Test control object modelling in Simulink environment was chosen as means of research.Results. Experimental data is provided which characterize the control object delay time change influence on its parameters identification accuracy as well as influence of varying spectral composition of non-controllable disturbances.Conclusions.If non-controllable disturbances are absent, test control object delay time change does not significantly affect the accuracy of identification of its model parameters. This accuracy depends more on the intensity of non-controllable disturbances then on its spectral composition. In general, software packages Signal Processing Toolbox and System Identification Toolbox can be recommended for training of specialists in automatic control for acquisition of skills in steady state processes analysis. [ABSTRACT FROM AUTHOR]

Background. Simple mathematical models of contamination and SIR-model of spreading an infection were used to simulate the time dynamics of the unknown before children disease, which occurred in Chernivtsi (Ukraine). The cause of many cases of alopecia, which began in this city in August 1988 is still not fully clarified. According to the official report of the governmental commission, the last new cases occurred in the middle of November 1988, and the reason of the illness was reported as chemical exogenous intoxication. Later this illness became the name “Chernivtsi chemical disease”. Nevertheless, the significantly increased number of new cases of the local alopecia was registered almost three years and is still not clarified. Objective. The comparison of two different versions of the disease: chemical exogenous intoxication and infection. Identification of the parameters of mathematical models and prediction of the disease development. Methods. Analytical solutions of the contamination models and SIR-model for an epidemic are obtained. The optimal values of parameters with the use of linear regression were found. Results. The optimal values of the models parameters with the use of statistical approach were identified. The calculations showed that the infectious version of the disease is more reliable in comparison with the popular contamination one. The possible date of the epidemic beginning was estimated. Conclusions. The optimal parameters of SIR-model allow calculating the realistic number of victims and other characteristics of possible epidemic. They also show that increased number of cases of local alopecia could be a part of the same epidemic as “Chernivtsi chemical disease”.