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

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Investigation of the chaotic dynamics of the vertical strance of a human body on the model of an inverted pendulum 基于倒立摆模型的人体垂直距离混沌动力学研究
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.
医学和生物学研究人体的不同姿态,用于定量估计和临床诊断肌肉骨骼、神经、前庭系统和功能的损伤和疾病。人体由约200块骨骼和约600块肌肉组成,由于系统及其控制机制的高度复杂性,其直立位置是不稳定的。在不同的身体摇摆记录技术中,稳定记录技术是最简单、最廉价的一种。它由一个力平台组成,可以测量两脚与平台之间接触区域的反作用力。前者是便携式的,可以通过USB接口连接到任何笔记本电脑。本文研究了人体质心(CM)在水平面上的投影(XC,YC)振荡的非线性动力学,研究了控制人体垂直姿态的函数。对28名健康志愿者(年龄21 ~ 42岁,身高156 ~ 182 cm,体重48 ~ 84.8 kg)的时间序列{XC(t),YC(t)}进行了测量。志愿者被要求保持安静的双脚站立,类似的姿势是身体重心移到左腿,然后移到右腿。每个姿势重复30秒,先睁开眼睛,然后闭上眼睛。短暂休息后,先用左腿平衡,然后用右腿平衡。对于每种情况,根据倒立摆的数学模型,计算出的控制函数u(t)的形式为u(t)=k1(r(t)-r0)+ k2(r/(t)-r/0),其中r(t)为CM的半径矢量,r0为其随时间的平均值,(.)/为时间导数。通过统计分析,显示了不同受试者和同一志愿者身体不同位置的控制功能之间缺乏相关性。根据李雅普诺夫指数的计算,将个体分为对身体垂直位置控制稳定、弱和高度不稳定的三组。在非线性控制的不确定性混沌模型框架下,讨论了这类系统的建模问题。
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引用次数: 0
Empirical probability distribution validity based on accumulating statistics of observations by controlling the moving average and root-mean-square deviation 经验概率分布的有效性是通过控制移动平均和均方根偏差来积累观测值的统计量
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.
在工程实践和其他领域中,总是需要知道概率分布来计算期望值。通常,概率分布并不总是可用的。此外,分布类型可能无法可靠地确定。在这种情况下,经验分布应该直接从观察中建立。因此,目标是发展一种积累和处理观测数据的方法,使各自的经验分布足够接近未知的实际分布。为此,关于观察的充分性和分布有效性的标准必须得到证实。因此,提出了一种方法О.М。Мелкозьорова1,СГ。Рассомахінd,它考虑相对于参数期望值的经验概率分布有效性。参数的值是在对参数进行一段时间的观测或测量期间登记的。在此基础上,计算经验概率,其中每个下一个时期也使用以前的注册数据。每个周期使用这些经验概率给出参数期望值的近似值。使用移动平均线和均方根偏差的方法断言,如果参数的期望值近似值在三个连续窗口的至少三个窗口的2倍宽度中变得很少分散,则各自的经验分布是有效的(即,它与未知的实际分布足够接近)。这一标准也意味着观察期的充分性,尽管没有要求每一观察期的充分性。有效性很大程度上取决于每个周期的观测量。
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引用次数: 0
A method for solving a boundary value problem in a multilayered area 求解多层区域边值问题的一种方法
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.
以电机热过程的数学模型为例,提出了一个三层圆柱结构,其中一层内部热源工作,热量通过热传导的方式传递给另外两层。本文提出了一种求解复杂区域——多层圆柱体,其中一部分是内部热源,另一部分是外部热源的热传导方程边值问题的方法。讨论了在层间热传导的层间界面边界条件不确定的情况下问题的求解方法。该方法的原理在于对内层的径向温度分布进行平均。由于层间界面处的变换,出现了阻抗型共轭的边界条件。得到了简化问题的解析解和数值解析解。
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引用次数: 0
Analysis of existing parallel programs verification technologies 分析了现有的并行程序验证技术
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.
在过去的几十年里,人们对并行计算的认知价值出现了很大的波动。有时,并行计算被乐观地视为解决我们所有计算限制的方法。分析了传统验证方法的划分。最后得出结论:软件验证的综合方法是最相关、最有用和最有生产力的方法。本文指出,计算机系统软件的形式化验证方法的实施是对传统的测试和调试方法的补充,可以提高程序的正常运行时间和安全性。计算机系统软件形式验证方法可以保证系统模型对被验证属性的检验。如今,这些方法正朝着减少形式验证总成本、支持现代编程概念和最小化从系统模型到其实现过渡中的“手工”工作的方向积极发展。它们的主要特点是能够使用数学模型查找错误,而不依赖于现有的软件实现。这是非常方便和经济的。有几种特定的技术用于正式模型分析,如演绎分析,模型和一致性检查。每一种验证方法都是在特定情况下使用的,这取决于目标。软件验证的综合方法被认为是最实际、最有用和最有效的方法,因为它们以某种方式试图结合不同验证方法的优点,从而消除它们的缺点。目前,这些方法的开发及其在工业软件开发实践中的实现已经取得了重大进展。
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引用次数: 0
Flow modelling in a straight hard-walled duct with two rectangular axisymmetric narrowings 具有两个矩形轴对称变窄的直硬壁管道的流动模拟
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.
本文提出了一种具有两个狭缝的刚性壁管道内流动的模拟方法。该方法在空间坐标上具有二阶精度,在时间坐标上具有一阶精度,具有较高的解稳定性,与同类方法相比,计算时间大大减少。根据该方法,首先引入流函数和涡量,然后从控制方程、初始条件和边界条件过渡到所引入变量的适当关系。将得到的关系重写为无量纲形式。然后选择计算域和均匀计算网格,对无量纲关系进行离散化处理。最后,对离散化后得到的线性代数方程进行了求解。
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引用次数: 1
Hybrid adaptive method for finding the roots of a nonsmooth function in the problem of determining the natural frequencies of fluid vibrations in reservoirs 求解储层流体振动固有频率问题中非光滑函数根的混合自适应方法
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.
本文提出了一种求单变量非光滑函数根的混合自适应方法。提出了非光滑函数的自适应根搜索算法。它假设自适应缩减搜索步骤,并改变搜索方向。发现所提出的方法使我们能够在存在拐点的情况下检测到词根。例如,这对于牛顿法来说是不可能的。该算法的求根精度不依赖于函数的类型、初始近似的选择;在任何情况下,该方法都会以给定的精度找到根。采用二分法、“3/5”法和本文提出的算法对根计算结果进行了比较。结果表明,该方法在单独应用时的有效性超过了两种混合方法的有效性。将该方法应用于确定旋转壳形刚体中液体振荡固有频率问题特征方程的求解。假定罐内流体为完全不可压缩流体,其在外部载荷作用下的运动为涡流。在这些假设下,存在一个速度势来描述流体运动。给出了该问题的表述,并给出了将其化为非线性方程解的方法。这个方程是对应特征值问题的特征方程。应用积分奇异方程的方法和边界元法对其进行数值求解。研究了刚性圆柱形储罐内流体的振荡问题。比较了不同方法对不同节点直径数下流体振荡频率的数值模拟结果。值得注意的是,如果特征方程的根使用近似方法进行局部化,则可以使用所提出的方法进行其细化。
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引用次数: 0
Identification of fingers on the basis of Hamiltonian cycles of local features 基于局部特征哈密顿循环的手指识别
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.
研究了复图上哈密顿环长度的求解问题。该任务具有确定最优路线(推销员任务)、识别图结构(识别生物特征物体的局部特征)等实际应用。在解决生物特征样品的验证任务时,会出现参考点的增加或消失、参考点之间距离的变形、整个样品的线位移和角位移的出现等问题。使用文中描述的方法,可以消除位移问题,因为当存在点的洗牌时解是稳定的。此外,还可以获得具有相同稳定性的参考方案。获得它们需要较少的计算复杂度,并提供更高的识别精度。基于描述指纹图像局部特征分布的对称图矩阵的分支和边界方法,给出了问题求解的详细描述。已知对于任意平面点分布的哈密顿循环长度的保证解只有用穷举搜索才有可能。然而,这种搜索的计算复杂度是不可接受的。分支和边界的方法,像所有现有的定向搜索方法一样,不能保证找到任意大维图的解。因此,提出了一种分解图的方法,可以将一个复杂的问题简化为一组更简单的问题。这样可以显著降低计算复杂度。哈密顿循环的度量对概率位移的相对不变性,这是生物特征模式识别问题的特征,已经被证明。
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引用次数: 1
The impact of usage of post object-oriented technologies on defect reduction in software maintenance 使用后面向对象技术对减少软件维护中的缺陷的影响
K. Nagornyi, I. Martinkus, M. Tkachuk
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.
本文致力于基于后面向对象技术的维护阶段的软件质量改进研究。研究了维护阶段的一个重要问题,即横切功能问题。对后面向对象技术的机制进行了回顾,并制定了需要解决的基本任务,以达到研究的最终目标:在维护阶段减少缺陷。介绍了基于4个启发式假设集合的后面向对象技术用于软件质量改进的框架。提出了该框架的概念方案。描述了基于定量横切功能和缺陷度量的缺陷减少评估的应用的2步程序。给出并分析了12个残余缺陷数计算的实验结果。
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引用次数: 0
Forced liquid vibrations in prismatic tanks under vertical and horizontal loads 垂直和水平载荷作用下柱体槽内液体的强迫振动
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.
提出了一种研究液体在部分注入的刚性棱柱形容器中受迫振动的方法。假定液体是一种理想的不可压缩液体,它的运动是由外部影响引起的,是无旋的。在这些假设中,存在一个满足拉普拉斯方程的速度势。给出了该势的边值问题。在水箱的湿润表面选择非渗透条件。在液体的自由表面上,指定了运动和静态条件。静力条件是指自由表面的压力与大气表面的压力相等。液体压力由柯西-拉格朗日积分确定。为了表述运动条件,引入了一个描述自由曲面运动的附加未知函数。运动条件是液体的速度,用速度势来描述,和自由表面本身的速度相等。这些自由振动模态被用作解决油藏中受迫流体振动问题的基本函数系统。未知函数表示为一系列基本函数。这些级数的系数是广义坐标。考虑了作用在垂直和水平方向上的周期性激振力。如果研究垂直激励,这将导致额外加速度的出现。在这里,我们得到了一个无界的Mathieu型微分方程组。这使我们能够研究参数共振现象。当垂直激励频率等于液体振动自身频率的两倍时,考虑了参数共振的影响,得到了在水平力和垂直力的单独作用和相互作用下,自由表面水平随时间变化的依赖关系。给出了带共振指示的动态系统的相位图。该方法允许我们在油藏开采的设计阶段对不期望的激励频率进行调整,以防止稳定性的损失。
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引用次数: 0
Computer modeling system for the numerical solution of the one-dimensional non-stationary Burgers’ equation 一维非平稳Burgers方程数值解的计算机模拟系统
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.
介绍了非线性一维非平稳Burgers方程数值解的计算机模拟系统。采用部分解法和径向基函数法,采用无网格格式得到了Burgers方程的数值解。采用广义梯形法(θ-格式)得到一维Burgers方程的时间离散化。在计算机建模系统中,采用逆多重函数作为径向基函数。计算机建模系统允许设置初始条件和边界条件以及将源函数设置为与坐标和时间相关的函数来求解偏微分方程。计算机建模系统允许设置边值问题的域、插值节点数、非平稳边值问题的时间间隔、时间步长、径向基函数的形状参数和Burgers方程的系数等参数。非线性一维非平稳Burgers方程的解在计算机建模系统中被可视化为三维曲面。计算机建模系统允许在选定的时间步长将边值问题的解可视化为三维图。通过求解两个基准问题,验证了计算机建模系统的计算效率。对于已解决的基准问题,计算了平均相对误差、平均绝对误差和最大误差。
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引用次数: 3
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Visnik Kharkivs''kogo natsional''nogo universitetu imeni VN Karazina Seriia Matematichne modeliuvannia informatsiini tekhnologiyi avtomatizovani sistemi upravlinnia
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