Pub Date : 2022-09-29DOI: 10.17212/2782-2001-2022-3-59-74
A. Kler, Danil V. Apanovich
The calculations of dynamic processes in the pipeline are necessary for modeling the processes of fluid movement in the pipeline, for example, for predicting loads on the pipeline when compression and rarefaction waves move in it. These tasks are reduced to solving systems of partial differential equations. The calculation of the phenomenon excluding hydraulic friction can be carried out by the method of characteristics, however, the calculation, taking into account the friction forces, is complicated for known methods, such as the finite difference method and the final element method. The article provides a brief description and an example of using the control point method for the task of modeling the water hammer phenomenon, taking into account the hydraulic friction forces of the pipeline. The main idea of the proposed method is to reduce the solution of these systems of equations to solving linear programming problems. The purpose of this work is to solve the problem of water hammerwith friction by the control point method. This method, developed jointly with A.S. Maksimov by the authors of this article at the Melentiev Energy Systems Institute, has shown good results in solving systems of partial differential equations of a periodic heat exchanger with ceramic ball filling. Moreover, heat transfer inside these elements was taken into account. With large values of thermal conductivity coefficients, this system is also rigid, which complicates its solution by the control volume method, but the control point method has shown good results. This gives reason to consider it promising in calculations of hydraulic friction. The results of modeling a hydraulic shock to a pipe filled with an incompressible liquid at different friction coefficients have been obtained. The results make it possible to make a numerical assessment of the effect of the o hydraulic friction coefficient on the attenuation of oscillatory processes during a hydraulic shock.
{"title":"Numerical simulation of the water hammer phenomenon taking into account the hydraulic friction of the pipeline by the control point method","authors":"A. Kler, Danil V. Apanovich","doi":"10.17212/2782-2001-2022-3-59-74","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-3-59-74","url":null,"abstract":"The calculations of dynamic processes in the pipeline are necessary for modeling the processes of fluid movement in the pipeline, for example, for predicting loads on the pipeline when compression and rarefaction waves move in it. These tasks are reduced to solving systems of partial differential equations. The calculation of the phenomenon excluding hydraulic friction can be carried out by the method of characteristics, however, the calculation, taking into account the friction forces, is complicated for known methods, such as the finite difference method and the final element method. The article provides a brief description and an example of using the control point method for the task of modeling the water hammer phenomenon, taking into account the hydraulic friction forces of the pipeline. The main idea of the proposed method is to reduce the solution of these systems of equations to solving linear programming problems. The purpose of this work is to solve the problem of water hammerwith friction by the control point method. This method, developed jointly with A.S. Maksimov by the authors of this article at the Melentiev Energy Systems Institute, has shown good results in solving systems of partial differential equations of a periodic heat exchanger with ceramic ball filling. Moreover, heat transfer inside these elements was taken into account. With large values of thermal conductivity coefficients, this system is also rigid, which complicates its solution by the control volume method, but the control point method has shown good results. This gives reason to consider it promising in calculations of hydraulic friction. The results of modeling a hydraulic shock to a pipe filled with an incompressible liquid at different friction coefficients have been obtained. The results make it possible to make a numerical assessment of the effect of the o hydraulic friction coefficient on the attenuation of oscillatory processes during a hydraulic shock.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116010470","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-21-38
B. Lemeshko, S. Lemeshko
When analyzing measurement series in various applications, the verification of whether measurement errors belong to the normal law is considered as a mandatory procedure. For this purpose, various special tests for testing hypotheses about normality can be used; non-parametric tests of goodness or chi-square tests can be used. When using nonparametric goodness-of-fit tests to test normality, it must be taken into account that a complex hypothesis is being tested. When testing a complex hypothesis, the distributions of the statistics of the goodness-of-fit tests differ significantly from the classical ones that occur when testing simple hypotheses. It is known that the presence of rounding errors can significantly change the distribution of test statistics. In such situations, ignoring the fact of influence can lead to incorrect conclusions about the results of the normality test. In metrology, when carrying out high-precision measurements, as a rule, scientists do not even allow thoughts about the possible influence of D rounding errors on the results of statistical analysis. This allows the possibility of incorrect conclusions since there is no influence not only at small D, but at values of D much less than the standard deviation s of the measurement error distribution law and sample sizes n not exceeding some maximum values. For sample sizes larger than these maximum values, the real distributions of the test statistics deviate from the asymptotic ones towards larger statistics values. In this work, based on real and well-known data, using statistical modeling methods, we demonstrate the dependence of the distributions of statistics of nonparametric goodness-of-fit tests when testing normality on the ratio of D and s for specific n. The possibility of correct application of the tests under the influence of rounding errors on the conclusions is shown and implemented.
{"title":"Nonparametric goodness-of-fit tests for normality testing under rounding-off measurements","authors":"B. Lemeshko, S. Lemeshko","doi":"10.17212/2782-2001-2022-2-21-38","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-21-38","url":null,"abstract":"When analyzing measurement series in various applications, the verification of whether measurement errors belong to the normal law is considered as a mandatory procedure. For this purpose, various special tests for testing hypotheses about normality can be used; non-parametric tests of goodness or chi-square tests can be used. When using nonparametric goodness-of-fit tests to test normality, it must be taken into account that a complex hypothesis is being tested. When testing a complex hypothesis, the distributions of the statistics of the goodness-of-fit tests differ significantly from the classical ones that occur when testing simple hypotheses. It is known that the presence of rounding errors can significantly change the distribution of test statistics. In such situations, ignoring the fact of influence can lead to incorrect conclusions about the results of the normality test. In metrology, when carrying out high-precision measurements, as a rule, scientists do not even allow thoughts about the possible influence of D rounding errors on the results of statistical analysis. This allows the possibility of incorrect conclusions since there is no influence not only at small D, but at values of D much less than the standard deviation s of the measurement error distribution law and sample sizes n not exceeding some maximum values. For sample sizes larger than these maximum values, the real distributions of the test statistics deviate from the asymptotic ones towards larger statistics values. In this work, based on real and well-known data, using statistical modeling methods, we demonstrate the dependence of the distributions of statistics of nonparametric goodness-of-fit tests when testing normality on the ratio of D and s for specific n. The possibility of correct application of the tests under the influence of rounding errors on the conclusions is shown and implemented.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134253719","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-121-132
N. Golovin, A. Dmitriev
In non-linear optical processes, such as obtaining attosecond pulses, it is extremely important to control the carrier envelope phase. To do this, various periodic trains of identical femtosecond pulses with a controlled phase can be created. In addition, since there is no frequency comb offset in such sequences, the process of measuring optical frequencies is greatly simplified. The pulse selector has been developed to obtain a sequence of identical femtosecond pulses with a controlled carrier – envelope phase. The selector makes it possible to obtain a “pure” sequence of identical femtosecond pulses at the modulator output (when every 125th pulse is selected from the original sequence with a repetition rate of 250 MHz) in a fairly wide range of control signal phase tuning. This range is 1.3 degrees. The phase tuning of the pulse selector provides the possibility of obtaining one hundred twenty-five such sequences with a phase tuning discreteness of 2π/125. The simplest way to reduce discreteness is to increase the ratio of the pulse repetition rate of a femtosecond laser to the shift of its frequency comb. The phase characteristic of the pulse selector was obtained by registering the time dependence of the synthesized sequence with a selector phase tuning step of 0.1 degrees. We measured the spectra of the sequences at different phases of the pulse selector, as well as the emission spectrum of the master laser at the minimum transmission of the modulator in the absence of modulation. The spectrum with the maximum amplitude corresponded to the case when identical pulses with the highest amplitude were selected from the original sequence. The difference between these spectra made it possible to isolate the spectrum of a pure sequence of identical femtosecond pulses without taking into account the "background" that occurs due to the modulator has a finite attenuation of –20 dB.
{"title":"Pulse selector for obtaining femtosecond radiation with a controlled carrier-envelope phase","authors":"N. Golovin, A. Dmitriev","doi":"10.17212/2782-2001-2022-2-121-132","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-121-132","url":null,"abstract":"In non-linear optical processes, such as obtaining attosecond pulses, it is extremely important to control the carrier envelope phase. To do this, various periodic trains of identical femtosecond pulses with a controlled phase can be created. In addition, since there is no frequency comb offset in such sequences, the process of measuring optical frequencies is greatly simplified. The pulse selector has been developed to obtain a sequence of identical femtosecond pulses with a controlled carrier – envelope phase. The selector makes it possible to obtain a “pure” sequence of identical femtosecond pulses at the modulator output (when every 125th pulse is selected from the original sequence with a repetition rate of 250 MHz) in a fairly wide range of control signal phase tuning. This range is 1.3 degrees. The phase tuning of the pulse selector provides the possibility of obtaining one hundred twenty-five such sequences with a phase tuning discreteness of 2π/125. The simplest way to reduce discreteness is to increase the ratio of the pulse repetition rate of a femtosecond laser to the shift of its frequency comb. The phase characteristic of the pulse selector was obtained by registering the time dependence of the synthesized sequence with a selector phase tuning step of 0.1 degrees. We measured the spectra of the sequences at different phases of the pulse selector, as well as the emission spectrum of the master laser at the minimum transmission of the modulator in the absence of modulation. The spectrum with the maximum amplitude corresponded to the case when identical pulses with the highest amplitude were selected from the original sequence. The difference between these spectra made it possible to isolate the spectrum of a pure sequence of identical femtosecond pulses without taking into account the \"background\" that occurs due to the modulator has a finite attenuation of –20 dB.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132728935","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-39-54
A. A. Popov
To solve the problem of effective identification of regression models of multifactor systems, as a rule, they resort to using the concept of optimal experiment design. The synthesis of experimental designs involves the use of an a priori chosen optimality criterion. Quite a few criteria have been proposed. Most often, criteria are used that are associated with the accuracy of estimating the parameters of regression models. We can name such well-known criteria as: the D-optimality criterion, the A-optimality, criterion and the E-optimality criterion. It should be noted that most of the theoretical and applied research is associated with the use of the D-optimality criterion. It is noted in the paper that often plans built according to the A-optimality criterion show good performance for a number of other optimality criteria. At the same time, the criterion itself characterizes an average variance of estimates of the parameters of the regression model and, for A-optimal designs the dispersion ellipsoid has the smallest overall dimensions. The use of the D-optimality criterion makes it possible to obtain an ellipsoid of dispersion of parameter estimates of the smallest volume, which does not exclude the possibility of obtaining an ellipsoid elongated along one or more principal axes. The paper proposes and describes two algorithms for the synthesis of discrete A-optimal designs. The first of them is based on the concept of the consistent completion of the experiment design to the required volume developed by the author. It can be successfully used in a situation where the researcher needs to increase the number of experiments to achieve the required accuracy of the resulting model. The second algorithm, which makes it possible to build plans for a given number of observations, consists of iterations in which points are added and removed from the plan according to certain rules.
{"title":"Algorithms for constructing discrete A-optimal experiment designs in active identification of regression models of multifactor systems","authors":"A. A. Popov","doi":"10.17212/2782-2001-2022-2-39-54","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-39-54","url":null,"abstract":"To solve the problem of effective identification of regression models of multifactor systems, as a rule, they resort to using the concept of optimal experiment design. The synthesis of experimental designs involves the use of an a priori chosen optimality criterion. Quite a few criteria have been proposed. Most often, criteria are used that are associated with the accuracy of estimating the parameters of regression models. We can name such well-known criteria as: the D-optimality criterion, the A-optimality, criterion and the E-optimality criterion. It should be noted that most of the theoretical and applied research is associated with the use of the D-optimality criterion. It is noted in the paper that often plans built according to the A-optimality criterion show good performance for a number of other optimality criteria. At the same time, the criterion itself characterizes an average variance of estimates of the parameters of the regression model and, for A-optimal designs the dispersion ellipsoid has the smallest overall dimensions. The use of the D-optimality criterion makes it possible to obtain an ellipsoid of dispersion of parameter estimates of the smallest volume, which does not exclude the possibility of obtaining an ellipsoid elongated along one or more principal axes. The paper proposes and describes two algorithms for the synthesis of discrete A-optimal designs. The first of them is based on the concept of the consistent completion of the experiment design to the required volume developed by the author. It can be successfully used in a situation where the researcher needs to increase the number of experiments to achieve the required accuracy of the resulting model. The second algorithm, which makes it possible to build plans for a given number of observations, consists of iterations in which points are added and removed from the plan according to certain rules.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"82 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132968347","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-95-104
G. P. Chikildin, Anna A. Mizyukanova
Problems formulation for modern industrial systems is completely or partially reduced to the problem of parametric identification of dynamic objects. Success of solving such problems largely depends on the availability and volume of a priori information, such as input and output signals of the control object measured with noise. However, the solution of identification problem also requires derivatives of measured signals, and the obtaining of its values by numerical differentiation is an ill-posed problem. This paper considers the parametric identification problem, in which parameters estimation of a mathematical model of a linear dynamic object from experimentally obtained values of input and output signals is reduced to solving a linear algebraic system formed by integral convolution operators with analytically given forming functions. An approach to solve the numerical differentiation problem by using integration by parts in a system of linear algebraic equations forming is proposed. However, for this operation to be correct from the point of view of identification it is necessary that the forming functions should satisfy certain requirements of behavior in both the time and frequency domains. Thus, key task in the formation of a linear algebraic equation system is the choice of linearly independent functions that form this system. The paper proposes such a forming function. A detailed analysis of its properties and properties of its derivatives is presented. Experimental results obtained illustrate the correctness of using an operation of integration by parts instead of numerical differentiation of measured signals relating to the identification problem. The aim of the work is to study features of the formation of an algebraic system of equations, to analyze properties of the functions that form this system in detail, including the impact of correcting parameters of these functions and also to produce recommendations for their choice in parametric identification.
{"title":"Analysis of the function that forms an algebraic system in parametric identification","authors":"G. P. Chikildin, Anna A. Mizyukanova","doi":"10.17212/2782-2001-2022-2-95-104","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-95-104","url":null,"abstract":"Problems formulation for modern industrial systems is completely or partially reduced to the problem of parametric identification of dynamic objects. Success of solving such problems largely depends on the availability and volume of a priori information, such as input and output signals of the control object measured with noise. However, the solution of identification problem also requires derivatives of measured signals, and the obtaining of its values by numerical differentiation is an ill-posed problem. This paper considers the parametric identification problem, in which parameters estimation of a mathematical model of a linear dynamic object from experimentally obtained values of input and output signals is reduced to solving a linear algebraic system formed by integral convolution operators with analytically given forming functions. An approach to solve the numerical differentiation problem by using integration by parts in a system of linear algebraic equations forming is proposed. However, for this operation to be correct from the point of view of identification it is necessary that the forming functions should satisfy certain requirements of behavior in both the time and frequency domains. Thus, key task in the formation of a linear algebraic equation system is the choice of linearly independent functions that form this system. The paper proposes such a forming function. A detailed analysis of its properties and properties of its derivatives is presented. Experimental results obtained illustrate the correctness of using an operation of integration by parts instead of numerical differentiation of measured signals relating to the identification problem. The aim of the work is to study features of the formation of an algebraic system of equations, to analyze properties of the functions that form this system in detail, including the impact of correcting parameters of these functions and also to produce recommendations for their choice in parametric identification.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116564386","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-7-20
V. Voronin, S. V. Shalobanov, S. Shalobanov
The paper considers an algorithm for searching for single defects of structural blocks of a diagnostic object in the form of an arbitrary change in the parameters of one dynamic block as part of a continuous dynamic system. This approach corresponds to the real picture of the manifestation of a specific structural defect in the unit and its influence on the dynamics of the system. The use of known algorithms of this kind is complicated by the need to use models with trial deviations of parameters, or by the need to analyze the signs of signal transmissions. The algorithm based on trial deviations of model parameters uses the specification of these changes in the model, which is a laborious task. The algorithm for analyzing transmission signs using a normalized diagnostic feature, as well as using a binary diagnostic feature, requires additional calculations of the signs of signal transmissions from block outputs to checkpoints. An algorithm for searching for single defects in the form of changes in the parameters of dynamic blocks is considered, based on the use of a model of the structural sensitivity of integral estimates of the output signals of an object to changes in the dynamic properties of a block. The algorithm allows you to move from the analysis of time functions to the analysis of the numerical values of their integral estimates. This approach allows you to identify a faulty dynamic unit without determining the actual parameters of its transfer function. The procedure for obtaining normalized diagnostic features and calculating a quantitative measure of the distinguishability of defects has been determined. The results of the implementation of the algorithm for the gas pressure stabilization system at a straight-tube furnace for heating oil products of an oil refinery are presented. The implementation of the algorithm shows that the considered algorithm gives acceptable values of the distinguishability of all single defects.
{"title":"Diagnostics of continuous dynamic systems using structure sensitivity functions","authors":"V. Voronin, S. V. Shalobanov, S. Shalobanov","doi":"10.17212/2782-2001-2022-2-7-20","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-7-20","url":null,"abstract":"The paper considers an algorithm for searching for single defects of structural blocks of a diagnostic object in the form of an arbitrary change in the parameters of one dynamic block as part of a continuous dynamic system. This approach corresponds to the real picture of the manifestation of a specific structural defect in the unit and its influence on the dynamics of the system. The use of known algorithms of this kind is complicated by the need to use models with trial deviations of parameters, or by the need to analyze the signs of signal transmissions. The algorithm based on trial deviations of model parameters uses the specification of these changes in the model, which is a laborious task. The algorithm for analyzing transmission signs using a normalized diagnostic feature, as well as using a binary diagnostic feature, requires additional calculations of the signs of signal transmissions from block outputs to checkpoints. An algorithm for searching for single defects in the form of changes in the parameters of dynamic blocks is considered, based on the use of a model of the structural sensitivity of integral estimates of the output signals of an object to changes in the dynamic properties of a block. The algorithm allows you to move from the analysis of time functions to the analysis of the numerical values of their integral estimates. This approach allows you to identify a faulty dynamic unit without determining the actual parameters of its transfer function. The procedure for obtaining normalized diagnostic features and calculating a quantitative measure of the distinguishability of defects has been determined. The results of the implementation of the algorithm for the gas pressure stabilization system at a straight-tube furnace for heating oil products of an oil refinery are presented. The implementation of the algorithm shows that the considered algorithm gives acceptable values of the distinguishability of all single defects.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130682139","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-105-120
D. Ozerkin
Modern approaches to the electronic means design include modeling of thermophysical processes occurring in the apparatus being developed. At the same time, a common task in thermophysical modeling is the problem of determining the temperature field of the supporting structure of an electronic device (board, substrate). Knowledge of the quantitative indicators of the supporting structure temperature field directly affects the prediction of the entire electronic device reliability. The load-bearing structures of electronic devices are increasingly made in the form of multilayer structures where conductive, insulating and semiconductor layers can be present. These features impose new requirements on the development of mathematical models, algorithms, application software packages for calculating the temperature fields of the supporting structures of electronic means. The article considers the process of modeling the temperature field for the supporting structures of electronic means using common software systems MathCAD and SolidWorks. The whole variety of supporting structures of electronic means is divided into three categories: conditionally one-dimensional, conditionally two-dimensional and three-dimensional. It is shown that the temperature fields of conditionally one-dimensional (rods) and conditionally two-dimensional (single-layer boards and substrates) structures should be calculated by the finite difference method in the MathCAD software package. Temperature fields of three-dimensional load-bearing structures, including complex geometric configurations, should be calculated using the finite element method in the SolidWorks software package. The developed algorithms for calculating temperature fields are verified by solving a test problem. Comparative analysis has shown that the discrepancy between the calculation results relative to the test problem does not exceed 0.8%. The developed algorithms for calculating the temperature field can be practically useful in the engineering activities of the developer of electronic equipment.
{"title":"Computation of the temperature field of multilayer load-bearing structures by numerical methods","authors":"D. Ozerkin","doi":"10.17212/2782-2001-2022-2-105-120","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-105-120","url":null,"abstract":"Modern approaches to the electronic means design include modeling of thermophysical processes occurring in the apparatus being developed. At the same time, a common task in thermophysical modeling is the problem of determining the temperature field of the supporting structure of an electronic device (board, substrate). Knowledge of the quantitative indicators of the supporting structure temperature field directly affects the prediction of the entire electronic device reliability. The load-bearing structures of electronic devices are increasingly made in the form of multilayer structures where conductive, insulating and semiconductor layers can be present. These features impose new requirements on the development of mathematical models, algorithms, application software packages for calculating the temperature fields of the supporting structures of electronic means. The article considers the process of modeling the temperature field for the supporting structures of electronic means using common software systems MathCAD and SolidWorks. The whole variety of supporting structures of electronic means is divided into three categories: conditionally one-dimensional, conditionally two-dimensional and three-dimensional. It is shown that the temperature fields of conditionally one-dimensional (rods) and conditionally two-dimensional (single-layer boards and substrates) structures should be calculated by the finite difference method in the MathCAD software package. Temperature fields of three-dimensional load-bearing structures, including complex geometric configurations, should be calculated using the finite element method in the SolidWorks software package. The developed algorithms for calculating temperature fields are verified by solving a test problem. Comparative analysis has shown that the discrepancy between the calculation results relative to the test problem does not exceed 0.8%. The developed algorithms for calculating the temperature field can be practically useful in the engineering activities of the developer of electronic equipment.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133622107","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-81-94
A. Chekhonadskikh
We study the stabilizing problem for a multidimensional vibration system using a gyroscopic stabilizer. A vibration system is given by a second order differential equation with symmetrical matrix coefficients: a positive definite stiffness matrix and an indefinite damping matrix; in general, such a system is unstable. We need find an optimal gyroscopic stabilizer for it represented by a skew-symmetric matrix coefficient in a speed term. The choice of this control type is dictated by the tendency to avoid additional vibrations caused by slip-slide friction. Its feature is a reduced order of the controller, regardless of the dimension of the system and the number of tunable parameter. Our goal is to elucidate the most important properties of the gyroscopic stabilizers variety. It is described by a polynomial equations system. The dimension of the general solution variety in the regular case is easily found and some of its points can be calculated numerically. We start with an example of dimension 3, which leads to a system of 6th order ordinary differential equations (ODE) and then a system of five polynomial equations with regard to six unknowns. Its general solution turns out to be a one-dimensional algebraic variety presented in a table form. The second example has dimension 5; it corresponds to a tenth-order system of differential equations and nine polynomial equations in fifteen unknowns. The dimension of the solution manifold is equal to six; we find a one-dimensional subvariety and some singular points. The main difficulty is the divergence of numerical calculations near the multiple poles of a closed system. One of the important properties, that manifested itself in both examples, was the presence of complex conjugate poles and occasionally multiples of real ones; thus, almost all solutions for an optimal gyroscopic stabilizer are made up of relatively rapidly decaying oscillations. In both examples, the variety of solutions consists mostly of simple poles and allows one to choose a stabilizer that does not create resonant effects.
{"title":"An optimal gyroscopic stabilizer of a multidimensional vibration system","authors":"A. Chekhonadskikh","doi":"10.17212/2782-2001-2022-2-81-94","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-81-94","url":null,"abstract":"We study the stabilizing problem for a multidimensional vibration system using a gyroscopic stabilizer. A vibration system is given by a second order differential equation with symmetrical matrix coefficients: a positive definite stiffness matrix and an indefinite damping matrix; in general, such a system is unstable. We need find an optimal gyroscopic stabilizer for it represented by a skew-symmetric matrix coefficient in a speed term. The choice of this control type is dictated by the tendency to avoid additional vibrations caused by slip-slide friction. Its feature is a reduced order of the controller, regardless of the dimension of the system and the number of tunable parameter. Our goal is to elucidate the most important properties of the gyroscopic stabilizers variety. It is described by a polynomial equations system. The dimension of the general solution variety in the regular case is easily found and some of its points can be calculated numerically. We start with an example of dimension 3, which leads to a system of 6th order ordinary differential equations (ODE) and then a system of five polynomial equations with regard to six unknowns. Its general solution turns out to be a one-dimensional algebraic variety presented in a table form. The second example has dimension 5; it corresponds to a tenth-order system of differential equations and nine polynomial equations in fifteen unknowns. The dimension of the solution manifold is equal to six; we find a one-dimensional subvariety and some singular points. The main difficulty is the divergence of numerical calculations near the multiple poles of a closed system. One of the important properties, that manifested itself in both examples, was the presence of complex conjugate poles and occasionally multiples of real ones; thus, almost all solutions for an optimal gyroscopic stabilizer are made up of relatively rapidly decaying oscillations. In both examples, the variety of solutions consists mostly of simple poles and allows one to choose a stabilizer that does not create resonant effects.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126955206","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-55-68
I. Reva, A. V. Ivanov, M. Medvedev, I. Ognev
To date, in matters of processing and managing network traffic, there is no single approach applicable to a wide pool of practical and applied tasks that would allow solving traffic management issues. Published works in this area are aimed at solving highly specialized problems: when applying complex solutions, these problems require the introduction of many additional parameters that increase computational complexity or solve only narrowly focused problems. This article provides a comparative analysis of classical network traffic models and reveals the possibility of practical application of such models in real-life problems. Classical traffic models are considered in detail, namely the Poisson model, heavy-tail traffic models, models based on Markov chains, traffic models based on the fractal theory and models based on stochastic time series. A mathematical description of each traffic model is also presented. Based on the results of the comparative analysis, the applicability of mathematical models to real projects was assessed. Based on it, two main problems were identified: first, the lack of consideration of the previous results of network traffic processing; secondly, the narrowly focused applicability of each of the models, given the rigid binding to subject areas, which allows solving only a narrow range of problems. The following indicators were taken as the criteria for evaluating network traffic models: the ability to scale the analyzed traffic, the ability to consider previous traffic data, computational complexity and the absence of some random features that could affect the operation of the model. A detailed study of the problem of traffic scaling revealed the main patterns, dependencies, dimensions of the traffic packet by the time it was processed.
{"title":"Comparative analysis of modern trends in the field of traffic models of data transmission networks","authors":"I. Reva, A. V. Ivanov, M. Medvedev, I. Ognev","doi":"10.17212/2782-2001-2022-2-55-68","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-55-68","url":null,"abstract":"To date, in matters of processing and managing network traffic, there is no single approach applicable to a wide pool of practical and applied tasks that would allow solving traffic management issues. Published works in this area are aimed at solving highly specialized problems: when applying complex solutions, these problems require the introduction of many additional parameters that increase computational complexity or solve only narrowly focused problems. This article provides a comparative analysis of classical network traffic models and reveals the possibility of practical application of such models in real-life problems. Classical traffic models are considered in detail, namely the Poisson model, heavy-tail traffic models, models based on Markov chains, traffic models based on the fractal theory and models based on stochastic time series. A mathematical description of each traffic model is also presented. Based on the results of the comparative analysis, the applicability of mathematical models to real projects was assessed. Based on it, two main problems were identified: first, the lack of consideration of the previous results of network traffic processing; secondly, the narrowly focused applicability of each of the models, given the rigid binding to subject areas, which allows solving only a narrow range of problems. The following indicators were taken as the criteria for evaluating network traffic models: the ability to scale the analyzed traffic, the ability to consider previous traffic data, computational complexity and the absence of some random features that could affect the operation of the model. A detailed study of the problem of traffic scaling revealed the main patterns, dependencies, dimensions of the traffic packet by the time it was processed.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122532369","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}
Pub Date : 2022-06-28DOI: 10.17212/2782-2001-2022-2-69-80
Dmitry S. Khudyakov
In many fields of science and technology there is a need to record fast running processes and phenomena, often occurring in low light conditions. In such cases, there is a need to use highly sensitive image sensors. Such sensors can be constructed on the basis of photon avalanche diodes capable of capturing even single photons. However, creating this type of sensor with high performance, in particular, with high resolution, presents a number of technological challenges, as they are more complex than traditional CMOS (Complementary Metal–Oxide–Semiconductor) and CCD (Charge-Coupled Device) sensors. Using recent advances and new circuitry, Canon created the first megapixel image sensor with a photon avalanche diode (Single Photon Avalanche Diode, SPAD). In this article, in addition to general issues related to image sensors with photon avalanche diode, the design, operation, characteristics, features and possible applications of Canon’s SPAD megapixel sensor are discussed. In particular, the methods of photon counting and time-of-flight are discussed, as well as the dynamic range of the sensor, the possibilities of sensor application for imaging in the infrared range, and the prospects for wide application of SPAD sensors in the near future. As a result, it can be noted that in addition to direct use for obtaining high-quality 2D-images of fast processes running in low light conditions, such a sensor can be used for taking images in the infrared range, to obtain 3D-images for xReality, measuring the distance to objects, obtaining a depth map, as well as in areas of science and technology that are new for such devices, including, for example, quantum computing.
{"title":"Capabilities of image sensors with a photonic avalanche diode","authors":"Dmitry S. Khudyakov","doi":"10.17212/2782-2001-2022-2-69-80","DOIUrl":"https://doi.org/10.17212/2782-2001-2022-2-69-80","url":null,"abstract":"In many fields of science and technology there is a need to record fast running processes and phenomena, often occurring in low light conditions. In such cases, there is a need to use highly sensitive image sensors. Such sensors can be constructed on the basis of photon avalanche diodes capable of capturing even single photons. However, creating this type of sensor with high performance, in particular, with high resolution, presents a number of technological challenges, as they are more complex than traditional CMOS (Complementary Metal–Oxide–Semiconductor) and CCD (Charge-Coupled Device) sensors. Using recent advances and new circuitry, Canon created the first megapixel image sensor with a photon avalanche diode (Single Photon Avalanche Diode, SPAD). In this article, in addition to general issues related to image sensors with photon avalanche diode, the design, operation, characteristics, features and possible applications of Canon’s SPAD megapixel sensor are discussed. In particular, the methods of photon counting and time-of-flight are discussed, as well as the dynamic range of the sensor, the possibilities of sensor application for imaging in the infrared range, and the prospects for wide application of SPAD sensors in the near future. As a result, it can be noted that in addition to direct use for obtaining high-quality 2D-images of fast processes running in low light conditions, such a sensor can be used for taking images in the infrared range, to obtain 3D-images for xReality, measuring the distance to objects, obtaining a depth map, as well as in areas of science and technology that are new for such devices, including, for example, quantum computing.","PeriodicalId":292298,"journal":{"name":"Analysis and data processing systems","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131277468","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}
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