Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia最新文献

{"title":"Investigation of the chaotic dynamics of the vertical strance of a human body on the model of an inverted pendulum","authors":"","doi":"10.26565/2304-6201-2020-45-04","DOIUrl":"https://doi.org/10.26565/2304-6201-2020-45-04","url":null,"abstract":"Different stances of human body are studied in medicine and biology for quantitative estimation and clinical diagnostics of impairments and diseases of the musculoskeletal, nervous, vestibular systems and functions. Human body is composed of ~200 bones and ~600 muscles, and its upright position is unstable due to high complexity of the system and its control mechanisms. Among different techniques of the body sway recording the stabilography is one of the most simple and cheap unit. It is composed by a force platform that can measure the reaction forces over the contact areas between two feet and the platform. The former is portable and can be connected to any laptop via USB port. In this study the functions controlling the vertical stance of a person are studied accounting for the nonlinear dynamics of oscillations of the projection (XC,YC) of center of mass (CM) of the body on the horizontal plane. The time series {XC(t),YC(t)} have been measured on 28 healthy volunteers (age 21-42, height 156-182 cm, body mass 48-84.8 kg). The volunteers were asked to keep a quiet stance on two feet, similar stances with body mass shifted onto the left and then onto the right leg. Each stance has been repeated during 30 s with open and then with closed eyes. After a short break a test with balancing on the left and then on the right leg has been perfrmed. For each case, based on the mathematical model of the inverted pendulum, the calculated control functions u(t) in the form u(t)=k1(r(t)-r0)+ k2(r/(t)-r/0), where r(t) is the radius-vector of the CM, r0 is its averaged value over time, (.)/ means the time derivative. Using statistical analysis, the absence of correlations between the control functions for both different subjects and for different positions of the body of the same volunteer was shown. Based on the calculations of the Lyapunov exponent, the individuals have been classified into groups with stable, weakly and highly unstable control of the vertical position of the body. The modeling of such systems in the framework of nondeterministic chaos models with nonlinear control is discussed.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Empirical probability distribution validity based on accumulating statistics of observations by controlling the moving average and root-mean-square deviation","authors":"","doi":"10.26565/2304-6201-2020-45-08","DOIUrl":"https://doi.org/10.26565/2304-6201-2020-45-08","url":null,"abstract":"Knowing probability distributions for calculating expected values is always required in the engineering practice and other fields. Commonly, probability distributions are not always available. Moreover, the distribution type may not be reliably determined. In this case, an empirical distribution should be built directly from the observations. Therefore, the goal is to develop a methodology of accumulating and processing observation data so that the respective empirical distribution would be close enough to the unknown real distribution. For this, criteria regarding sufficiency of observations and the distribution validity are to be substantiated. As a result, a methodology is presente О.М. Мелкозьорова1, С.Г. Рассомахінd that considers the empirical probability distribution validity with respect to the parameter’s expected value. Values of the parameter are registered during a period of observations or measurements of the parameter. On this basis, empirical probabilities are calculated, where every next period the previous registration data are used as well. Every period gives an approximation to the parameter’s expected value using those empirical probabilities. The methodology using the moving averages and root-mean-square deviations asserts that the respective empirical distribution is valid (i.e., it is sufficiently close to the unknown real distribution) if the parameter’s expected value approximations become scattered very little for at least the three window multiple-of-2 widths by three successive windows. This criterion also implies the sufficiency of observation periods, although the sufficiency of observations per period is not claimed. The validity strongly depends on the volume of observations per period.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A method for solving a boundary value problem in a multilayered area","authors":"","doi":"10.26565/2304-6201-2020-46-03","DOIUrl":"https://doi.org/10.26565/2304-6201-2020-46-03","url":null,"abstract":"A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area – a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69004012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of existing parallel programs verification technologies","authors":"","doi":"10.26565/2304-6201-2020-46-07","DOIUrl":"https://doi.org/10.26565/2304-6201-2020-46-07","url":null,"abstract":"The past few decades have seen large fluctuations in the perceived value of parallel computing. At times, parallel computation has optimistically been viewed as the solution to all of our computational limitations. The conventional division of verification methods is analyzed. It is concluded that synthetic methods of software verification can be considered as the most relevant, most useful and productive ones. It is noted that the implementation of the methods of formal verification of software of computer systems, which supplement the traditional methods of testing and debugging, and make it possible to improve the uptime and security of programs, is relevant. Methods of computer systems software formal verification can guarantee the check that verified properties are performed by system model. Nowadays, these methods are actively being developed in the direction of reducing the formal verification total cost, support of modern programming concepts and minimization of \"manual\" work in the transition from the system model to its implementation. Their main feature is an ability to search for errors using mathematical model, without recourse to existing realization of software. It is very convenient and economical. There are several specific techniques used for formal models analysis, such as deductive analysis, model and consistence check. Every verification method is been used in particular cases, depending on the goal. Synthetic methods of software verification are considered the most actual, useful and efficient, as they somehow try to combine the advantages of different verification approaches, getting rid of their drawbacks. Currently, there has been made significant progress in the development of such methods and their implementation in the practice of industrial software development.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow modelling in a straight hard-walled duct with two rectangular axisymmetric narrowings","authors":"","doi":"10.26565/2304-6201-2019-44-01","DOIUrl":"https://doi.org/10.26565/2304-6201-2019-44-01","url":null,"abstract":"A method for modelling the flow in a rigid-walled duct with two narrowings has been developed. It has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of the solution, and compared to the similar methods requires much less computational time to obtain a result. According to the method, the stream function and the vorticity are introduced initially, and consequently the transition from the governing equations, as well as the initial and boundary conditions to the proper relationships for the introduced variables is performed. The obtained relationships are rewritten in a non-dimensional form. After that a computational domain and a uniform computational mesh are chosen, and the corresponding discretization of the non-dimensional relationships is performed. Finally, the linear algebraic equations obtained as a result of the discretization are solved.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid adaptive method for finding the roots of a nonsmooth function in the problem of determining the natural frequencies of fluid vibrations in reservoirs","authors":"","doi":"10.26565/2304-6201-2020-46-05","DOIUrl":"https://doi.org/10.26565/2304-6201-2020-46-05","url":null,"abstract":"The article proposes a hybrid adaptive method for finding the roots of a non-smooth function of a single variable. The algorithm of adaptive root search method for non-smooth functions is presented. It assumes both adaptive reduction of a search step, and changing the search direction. It is found that the proposed approach allows us to detect the root even in the presence of a point of inflection. That is, for example, is impossible for the Newton method. The accuracy of finding the root using the proposed algorithm does not depend on the type of functions, the choice of the initial approximation; the method in any case will find the root with the given accuracy. Comparison of the results of the root calculations is performed using the dichotomy method, the \"3/5\" method and the proposed algorithm. It is established that the effectiveness of the developed method exceeds the efficiency of both methods - hybrids, when they have applied separately. The developed method is applied to the solution of the characteristic equation in the problem of determining the natural frequencies of oscillations of a liquid in a rigid tank having the form of a shell of revolution. The fluid in the tank is assumed to be perfect and incompressible, and its motion caused by the action of external loads is eddy. Under these assumptions, there exists a velocity potential to describe the fluid motion. The formulation of the problem is given and the method of its reducing to the solution of a nonlinear equation is given. This equation is a characteristic one for the corresponding problem of eigenvalues. The methods of integral singular equations and the boundary element method for their numerical solution are applied. The problem of fluid oscillation in a rigid cylindrical tank is considered. The results of numerical simulation of the fluid oscillation frequencies obtained by different methods for different number of nodal diameters are compared. It is noted that if the root of the characteristic equation is localized using approximate methods, then its refinement can be carried out using the proposed approach.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69004131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Identification of fingers on the basis of Hamiltonian cycles of local features","authors":"","doi":"10.26565/2304-6201-2019-44-06","DOIUrl":"https://doi.org/10.26565/2304-6201-2019-44-06","url":null,"abstract":"The problem of finding the lengths of Hamiltonian cycles on complex graphs is considered. The task has such practical applications as determining the optimal routes (salesman's task), identifying graph structures (recognizing the characteristics of local features of biometric objects), etc. When solving the task of verification of biometric samples, the problems of addition or disappearance of reference points, deformation of the distances between them, the appearance of linear and angular displacements of the whole sample emerges. Using the method described in the article, the problem of displacements can be eliminated, as the solution is stable when shuffling of the points is present. Moreover, it is possible to obtain reference plans with the same stability. Obtaining them requires less computational complexity and provides greater recognition accuracy. A detailed description of the problem solution based on the application of the method of branches and boundaries for symmetric matrices of graphs, which describe the distribution of local features in the images of fingerprints, has been proposed. It is known that a guaranteed solution for finding the length of the Hamiltonian cycle for an arbitrary graph of the planar distribution of points is possible only by using an exhaustive search. However, the computational complexity of such a search is not acceptable. The method of branches and boundaries, like all existing methods of directional search, does not guarantee finding a solution with an arbitrarily large dimension of the graph. Therefore, a method of decomposing graphs is proposed, which allows reducing a complex problem to a set of simpler ones. That allows for a significant reduction in computational complexity. The relative invariance of the metrics of Hamiltonian cycles to probabilistic shifts, which are characteristic of biometric pattern recognition problems, has been shown.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The impact of usage of post object-oriented technologies on defect reduction in software maintenance","authors":"K. Nagornyi, I. Martinkus, M. Tkachuk","doi":"10.26565/2304-6201-2019-41-06","DOIUrl":"https://doi.org/10.26565/2304-6201-2019-41-06","url":null,"abstract":"The article is dedicated to software quality improvement research within the maintenance phase based on post-object-oriented technologies. An important problem of the maintenance phase is surveyed, namely, the crosscutting functionality problem. Mechanisms of post-object-oriented technologies have been reviewed and basic tasks to be resolved have been formulated in order to reach the final goal of the research: defect reduction during the maintenance phase. The post object-oriented technologies utilization framework for software quality improvement based on a collection of 4 heuristic assumptions has been introduced. The conceptual scheme of the framework has been presented. An applied 2-steps procedure for defect reduction assessment based on quantitative crosscutting-functionality and defect metrics has been described. Twelve results of the experiments concerning calculation of the residual defect number have been presented and analyzed.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Forced liquid vibrations in prismatic tanks under vertical and horizontal loads","authors":"","doi":"10.26565/2304-6201-2019-42-07","DOIUrl":"https://doi.org/10.26565/2304-6201-2019-42-07","url":null,"abstract":"The method of studying forced vibrations of a liquid in rigid prismatic tanks partially filed by a liquid is offered. It is supposed that the liquid is an ideal and incompressible one, and its motion, caused by the action of external influences, is irrotational. In these assumptions, there exists a velocity potential that satisfies the Laplace equation. The boundary value problem for this potential is formulated. On the wetted surfaces of the tank the non-penetration conditions are chosen. On the free surface of the liquid, the kinematic and static conditions are specified. The static condition consists in the equality of pressure on the free surface to atmospheric one. The liquid pressure is determined from the Cauchy-Lagrange integral. To formulate the kinematic condition, an additional unknown function is introduced, which describes the motion of the free surface. The kinematic condition is the equality of the velocity of the liquid, which is described by the velocity potential, and the velocity of the free surface itself. These modes of free vibrations are used as a system of basic functions in solving problems of forced fluid vibrations in reservoirs. Unknown functions are presented as series of the basic functions. The coefficients of these series are generalized coordinates. Periodic excitation forces acting in the vertical and horizontal directions are considered. If vertical excitation is studied, this leads to appearance of additional acceleration. Here we obtain a system of unbounded differential equations of the Mathieu type. This allows us to investigate the phenomena of parametric resonance. The effect of parametrical resonance is considered when the vertical excitation frequency is equal to double own frequency of liquid vibrations Dependences of change in the level of free surface via time under both separate and mutual action of horizontal and, vertical forces of are obtained. The phase portraits of a dynamic system with indication of resonances are presented. The method allows us to carry out the adjustment of undesired excitation frequencies at the design stage at reservoir producing in order to prevent the loss of stability.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computer modeling system for the numerical solution of the one-dimensional non-stationary Burgers’ equation","authors":"","doi":"10.26565/2304-6201-2019-43-02","DOIUrl":"https://doi.org/10.26565/2304-6201-2019-43-02","url":null,"abstract":"The computer modeling system for numerical solution of the nonlinear one-dimensional non-stationary Burgers’ equation is described. The numerical solution of the Burgers’ equation is obtained by a meshless scheme using the method of partial solutions and radial basis functions. Time discretization of the one-dimensional Burgers’ equation is obtained by the generalized trapezoidal method (θ-scheme). The inverse multiquadric function is used as radial basis functions in the computer modeling system. The computer modeling system allows setting the initial conditions and boundary conditions as well as setting the source function as a coordinate- and time-dependent function for solving partial differential equation. A computer modeling system allows setting such parameters as the domain of the boundary-value problem, number of interpolation nodes, the time interval of non-stationary boundary-value problem, the time step size, the shape parameter of the radial basis function, and coefficients in the Burgers’ equation. The solution of the nonlinear one-dimensional non-stationary Burgers’ equation is visualized as a three-dimensional surface plot in the computer modeling system. The computer modeling system allows visualizing the solution of the boundary-value problem at chosen time steps as three-dimensional plots. The computational effectiveness of the computer modeling system is demonstrated by solving two benchmark problems. For solved benchmark problems, the average relative error, the average absolute error, and the maximum error have been calculated.","PeriodicalId":33695,"journal":{"name":"Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69003278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}