INVESTIGATION OF A TWO-FACTOR FULLY CONNECTED LINEAR REGRESSION MODEL
This paper is devoted to the study of a fully connected linear regression model, which is a synthesis of the pairing linear regression model and the Deming regression model. If multiple regression is based on the principle “independent variables influence dependent”, then the principle of fully connected regression is “all variables influence each other”. A fully connected regression is fairly simply estimated, devoid of multicollinearity effect, has a much more diverse interpretation than multiple regression, and is suitable for prediction. However, when building a fully connected regression, the ratio of error variances of independent variables remains unknown. In this paper, we find the ratio of error variances of independent variables that provides the best approximation qualities of the secondary fully connected regression model. The research results are presented in the form of a theorem. It follows from the theorem that the value of the coefficient of determination of the secondary model of a fully connected regression will be greatest either when it takes the form of a two-factor linear regression or the best one in the coefficient of determination of a single-factor linear regression. Thus, the selection of informative regressors in the regression model is carried out. It is established that the basis of such a selection is the complete consistency of the signs of the coefficients with independent variable signs of the corresponding correlation coefficients.
Keywords: :fully connected regression, multiple regression, Deming regression, EIV-model, coefficient of determination, multicollinearity, subset selection in regression
MATHEMATICAL SUPPORT THE PROCESS OF MANAGING DIAGRAM OF RELATIONAL DATABASES IN HORIZONTAL SCALING TASKS
D.D. Gromey, E.V. Lebedenko
The article proposes an approach to the development of mathematical support system for the relational database (database control system) schematic control process, allowing to take into account the statistics of competitive access to the data query flow in the memory used by the database control system engine by hierarchy. The articles notes shortcomings of existing approaches based on the conditional costs of the query plan and the issue of ignoring the costs related to cooperative access to the data contained in a shared computer memory. There is a set-theoretic presentation of the query flow processing, which also takes into consideration the shortcomings of the existing set-theoretic models. The proposed approach ensures the actual time costs calculations for the flow of concurrently executed queries. High-level query language operations are provided through a variety of typical access operations to the In-Memory Data. The article presents a classification of the memory access operations, which allows to calculate the degree of competition during the cooperative query execution. This study also introduces a formal presentation of competitive queries and the conditions for choosing the optimal data distribution method during the database operation in a given period of time. The proposed set-theoretic model allows us to calculate the memory segments, access to which leads to a competitive query. The results obtained in this paper can be used in the development of mathematical support systems and other software for the Autonomous database control systems that automate the management of the physical database scheme.
Keywords: :database management system, query optimization, parallel data processing, competitive queries.
OPENMP PARALLEL CALCULATIONS IN ALGORITHMS FOR SOLVING SHORTEST PATHS PROBLEM
O.Y. Lavlinskaya, V.V. Bernikov, O.N. Grigorova
The relevance of the study is due to the need to solve the problems of parallelization of calculations for the class of NP-complete problems, since computing power allows the use of parallel flows and reduce the computation time and energy consumption to obtain a complex computational result using software technologies of parallelization of calculations. In this regard, this article aims to publish the results of the study, based on the analysis of empirical data, proving the effectiveness of parallel calculations for the class of NP-complete problems. The article compares the work of a single-threaded application and multithreaded applications using OpenMP technology, on the example of the Floyd-Warshall Algorithm for finding the shortest path. During the experiment, data on the speed of serial and parallel algorithms were obtained. It is concluded that the parallel algorithm is more efficient than the serial one. With the growth of the computational power of the algorithm, the efficiency of parallel computing increases. The experiment was carried out for calculations at different power of a set of initial data, the data are presented in the form of tables and graphs. Evaluate the effectiveness of the use of standard parallelization and OpenMP. The materials of the article are of practical importance for master’s students studying the course “Computer systems”, can be used to solve applied optimization problems.
Keywords: :OpenMP, parallelization, search of ways, Floyd- Warshall algorithm.
METHOD OF THE SOLUTION OF SOME CLASSES OPTIMISING TASKS
The relevance of this work is caused by wide circulation in all spheres of activity of important practical tasks which can be solved by methods of linear programming. The main difficulty at application of a universal way of the solution of such tasks (a simplex – a method) is its computing complexity. For the solution of this problem special methods of the solution of private problems of linear programming, for example, are developed for positive or limited basic data. These special cases are proved by economic, social, technical, technological sense. In this article the method maximizing linear function at one linear restriction with positive coefficients is developed. This method is generalized on a case of maximizing linear function at several linear restrictions. The received theoretical results are proved by the proof of the corresponding theorems. For an illustration of the received results numerical examples are given. The algorithmic complexity of the developed method is estimated for solvable tasks by calculation of number of the used operations and comparison with their quantity when using a simplex – a method. The received results allow to solve applied optimizing problems in various areas, including in problems of planning of production, a balanced diet and a diet, management of educational process, etc.
Keywords: a problem of linear programming, function, restriction, coefficient, a simplex – a method, an optimal solution.
RESEARCH ABSTRACT CELLULAR AUTOMAT INDEPENDENT OF TIME
The relevance of the study is due to the increasing number of computing cores from a single computing device, and the total number of such devices. At the same time, many algorithms are designed to work in a strictly defined sequence, as a result, either part of the computing power is idle, or additional logic is added on top of the main calculations, which not only complicates the development, but also requires additional calculations, the only purpose of which is synchronization between nodes / cores / threads. In this regard, this article aims to identify how to perform calculations without the need for synchronization as such, using the example of the cellular automaton. The leading method for the study of this problem is the mathematical and computer simulation of the cellular automaton, which allows to comprehensively consider the root cause of the need to perform synchronization – time. The article presents a method of describing a cellular automaton, in which all unnecessary entities are excluded, one of which was time, as a result of which synchronization was no longer necessary. Key entities that are sufficient for a full description of the operation of an arbitrary cellular automaton are identified. The applicability of the minimum set of entities is justified by the example of an elementary one-dimensional cellular automaton. The materials of the article are of practical value for specialists in the field of mathematical modeling and information technology.
Keywords: :cellular automaton, rule, state, superposition, space, time, matrix.
SYNTHESIS OF LINEAR REGRESSION MODEL AND EIV-MODEL
M. P. Bazilevskiy
This paper is devoted to a synthesis of pair-wise linear regression model and simplest EiV-model (Errors-In-Variables model), better known as the Deming regression. The EIV model is a regression in which all variables contain random errors. Such models have a number of significant drawbacks, which makes it difficult to work with them. The synthesis proposed in the paper, called the two-factor model of a fully connected linear regression, is not only devoid of these shortcomings, but also has certain advantages. The main stages of the construction and analysis of two-factor models of fully connected linear regression are considered. The proposed fully connected linear regression model has much in common with the classical multiple regression model; however, these two types are based on completely different approaches. If multiple regression is based on the principle “independent variables affect the dependent one”, then the principle of fully connected regression is “all variables influence each other”. It is established that the approximation abilities of fully connected models do not exceed the capabilities of multiple regressions, but the former have a much more diverse interpretation. The developed synthesis can be used in the construction of multiple models as a tool for solving problems of reducing the dimensionality of data, eliminating multicollinearity and selecting informative regressors.
Keywords: :regression model, ordinary least squares, total least squares, Deming regression, EIV-model, fully connected linear regression model.
METHOD OF AUTONOMOUS CORRECTION OF INERTIAL NAVIGATION SYSTEM OF UNMANNED AIRCRAFT ON THE BASIS OF MODERN GEOINFORMATION TECHNOLOGIES
A.V. Sizov, S.V. Ippolitov, A.Y. Savchenko, V.A. Malyshev
The method of correction of inertial navigation system based on modern geoinformation technologies with the use of optical-electronic system and electronic terrain map, allowing determining the coordinates of the location of the unmanned aircraft in offline mode without the use of satellite and radio navigation, is developed. In this case, the current coordinates of the unmanned aircraft are determined with the help of inertial navigation system. Then these coordinates, taking into account the error accumulated after the last correction of the inertial navigation system, are entered into an electronic terrain map. Thus, the boundaries of the working area of the electronic terrain map are determined, which significantly reduces the computational cost. The correction of the current coordinates of the location of the unmanned aircraft from the optical-electronic system is carried out by two types of data – the geographical coordinates of the three known landmarks (identical points) of the area and the coordinates of the position of the unmanned aircraft relative to these landmarks (relative coordinates – range, height and lateral deviation). Determination of geographical coordinates of three identical points is made in the electronic terrain map on the basis of recognition of the received by the optical-electronic system image. The calculation of the relative coordinates of the unmanned aircraft is carried out by the triangle method with the circumscribed (inscribed) circle (sphere), the vertices of which are three identical points, with the determination of their coordinates in the associated coordinate system of the unmanned aircraft as a result of the corresponding image processing by the optical-electronic system.
Keywords: :inertial navigation system, optical-electronic system, electronic terrain map.
THE ALGORITHM OF CORRECTION OF THE INERTIAL NAVIGATION SYSTEM OF THE UNMANNED AIRCRAFT ON THE BASIS OF THE OPTICAL-ELECTRONIC SYSTEM AND THE ELECTRONIC TERRAIN MAP
A.V. Sizov, S.V. Ippolitov, A.Y. Savchenko, V.A. Malyshev
The paper presents an algorithm of correction of the inertial navigation system of an unmanned aircraft based on the usage of an optical-electronic system and an electronic terrain map, which will provide high accuracy of determining of the navigation parameters, the speed of the correction system, small size, cost and also autonomy of work. This algorithm implements a new method of correction of the inertial navigation system based on the developed mathematical model describing the procedures for solving navigation problems: determining the relative coordinates of three identical points (landmarks on the ground) in the coordinate system of the optical-electronic system associated with the unmanned aircraft; recalculating of the obtained relative coordinates with the help of the matrix of guide cosines into the geographic coordinate system; determining the geographical coordinates of identical points from the electronic terrain map; calculation of the current geographical coordinates of the unmanned aircraft on the basis of its relative coordinates and geographical coordinates of identical points. The solution of the described problems is carried out by the developed algorithm, the final step of which is the input of the current geographical coordinates of the unmanned aircraft into the inertial navigation system for its correction.
Keywords: :inertial navigation system, optical-electronic system, electronic terrain map, unmanned aircraft.
ALGORITHM FOR ADDING TURBOVINET EFFECT
The article discusses the occurrence of noise components from rotating structural elements of the aircraft or turboprop components and the effect of these components on the radio signal tracking aerodynamic object. The masking effect of signals from rotating elements affects the observation of the glider component, which interferes with the tracking of the object. The need to suppress the turboprop components in the radio signal is noted. To solve the problem, it is proposed to use fractal signal processing methods. An algorithm for suppressing turboprop spectral components in an echo signal of an aerodynamic object, based on the definition of the similarity function, is proposed. The article describes the steps of the algorithm and its block diagram. An example of a signal from a bank of temporal functions of micro-movements of an object’s structural elements, used as a basis for approximating the initial echo signal, is given. A simulation was performed for a single aerodynamic object, confirming the suppression of the turboprop component of the echo signal. The proposed algorithm is proposed to be used to classify the number of objects in a swarm of unmanned aerial vehicles. The necessity of decreasing the interval of discreteness of the parameters describing the kinematics of the object’s micro-movements is noted. The materials are of practical value in radiolocation when accompanied by unmanned aerial vehicles to eliminate interfering components in the far-Doppler portrait of the object, automatic coordination, navigation, and increased flight safety.
Keywords: :turboprop component, glider component, micromovement, echo signal, spectrum, radar, Doppler.
APPLICATION OF ANN IN HUMAN-MACHINE INTERFACES
The article continues the cycle of the author’s works on the subject of HIL-simulation. The article proposes an algorithm for the decomposition of any radio system and the subsequent coupling of its parts by adjusting only one of the two stabilizing parameters of the coupling scheme. In addition, the possibility of using a coupling scheme as a matching device between fragments of the system through the aspect of system stability was analyzed. All this makes it possible to significantly reduce the amount of debugging work performed in HIL-simulation of radio systems, both in the field of research of elementary systems and in working out options for creating complex multisystems. As a proof of the correctness of the proposed method, an analytical calculation was performed, in general, showing the possibility of adjusting only one stabilizing parameter in the coupling scheme of a decomposed system, while convergence of the parameters of the divided system to the parameters of the original system can be achieved in several iterations. In some cases, this convergence can be achieved in one iteration. In the conclusion of the article, the calculation was performed using a numerical example for practical confirmation of the proposed method. For clarity and correct understanding of the described actions, illustrations are given of both the operations performed and the results of the calculations..
Keywords: :stabilizing parameter, system decomposition, coupling scheme, HIL-modeling, radio system, Cramer’s rule, Schur complement.