Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines最新文献

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A universal algorithm for linear and quadratic programming in the problems of contact deformation of cable-stayed structures with one-way connections 单向连接斜拉结构接触变形问题线性规划和二次规划的通用算法
V. Grischenko
{"title":"A universal algorithm for linear and quadratic programming in the problems of contact deformation of cable-stayed structures with one-way connections","authors":"V. Grischenko","doi":"10.20998/2078-9130.2022.2.270862","DOIUrl":"https://doi.org/10.20998/2078-9130.2022.2.270862","url":null,"abstract":"Problems in production activities that require optimization problems are extremely numerous and very diverse. Optimization approaches are most often associated with the search for the best version of a structure or building. Mathematical methods for solving such problems are developing rapidly and are widely used. They actively and productively penetrate into many areas of scientific research, into engineering and design developments, are an important tool for improving design efficiency throughout the entire process of creating structures. The search for the best design solution is reduced to the selection of a set of parameters that provide a stationary value of the objective function. A wide range of extreme problems of practical orientation, as a rule, in mathematical models contains restrictions on design parameters of the equality-inequality type. In general, their set makes up the content of such a section of mathematics as Mathematical Programming. Due to the fact that there is no single solution method, diversity in research approaches has formed, which divides them into groups, classes, etc. Linear programming (LP), as one of the sections, with a linear objective function and constraints is well studied and successfully applied. Methods of solving problems of nonlinear programming, which includes quadratic programming, are more complex. Therefore, the development of convenient computational schemes is relevant. The essence of this work is that the statements of 2 optimization problems are formalized in a single and convenient form of a symmetric matrix dependence, which makes it possible to obtain an effective (in our opinion) algorithm for their implementation. Namely, a unified scheme for solving both LP and KP problems based on matrix algebra operations is proposed. Quadratic programming (QP), as the second section, also has wide possibilities, in particular, it allows considering the practical tasks of calculating VAT in the mechanics of a deformed solid body under the conditions of contact interaction. Such problems, in particular, include cable-stayed structures with one-way connections and span lengths that can reach tens or hundreds of meters. As an example, the behavior of a model cable-stayed span structure under varying wind loads is considered. The given results may be of interest.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129560674","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}
引用次数: 0
Non-stationary phenomena in technological systems of electromagnetic processing of materials 材料电磁加工工艺系统中的非平稳现象
G. Anischenko, Denys Lavinskyi
{"title":"Non-stationary phenomena in technological systems of electromagnetic processing of materials","authors":"G. Anischenko, Denys Lavinskyi","doi":"10.20998/2078-9130.2022.2.270863","DOIUrl":"https://doi.org/10.20998/2078-9130.2022.2.270863","url":null,"abstract":"A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary deformation of structural elements under the action of electromagnetic fields. Coupling of electromagnetic field and mechanical field is carried out with the help of local electromagnetic forces. Further made the transition to a variational formulation on the basis of the task of finding the minimum of the total energy of the system, which includes the energy of the electromagnetic field. For the numerical solution the finite element method is used. Nodal unknowns in this case are the magnetic vector potential and displacements. The proposed method is applied to non-stationary deformation of the \"inductor-billet\" technological operation of magnetic-pulse processing of metals. Some results of the deformation are  presented. \u0000A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary deformation of structural elements under the action of electromagnetic fields. Coupling of electromagnetic field and mechanical field is carried out with the help of local electromagnetic forces. Further made the transition to a variational formulation on the basis of the task of finding the minimum of the total energy of the system, which includes the energy of the electromagnetic field. For the numerical solution the finite element method is used. Nodal unknowns in this case are the magnetic vector potential and displacements. The proposed method is applied to non-stationary deformation of the \"inductor-billet\" technological operation of magnetic-pulse processing of metals. Some results of the deformation are  presented. \u0000A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary defor","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"704 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125664669","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}
引用次数: 0
STRESS ANALYSIS IN A CONVEYOR BELT FOR THE MAXWELL MODEL OF ELASTIC ELEMENT 传送带弹性单元麦克斯韦模型的应力分析
O. Pihnastyi, M. Sobol
{"title":"STRESS ANALYSIS IN A CONVEYOR BELT FOR THE MAXWELL MODEL OF ELASTIC ELEMENT","authors":"O. Pihnastyi, M. Sobol","doi":"10.20998/2078-9130.2022.1.265430","DOIUrl":"https://doi.org/10.20998/2078-9130.2022.1.265430","url":null,"abstract":"The mechanism of propagation of longitudinal dynamic stresses in a conveyor belt, the material of which corresponds to the Maxwell model of an elastic element, is considered. The features of the occurrence of longitudinal vibrations in the material of the conveyor belt for the section of the transport system equipped with asynchronous motors are considered. It is shown that the acceleration of the conveyor belt occurs as a result of an abrupt change in the traction moment of the asynchronous electric motor when the power consumption of the conveyor section changes. The process of acceleration/deceleration of the conveyor belt is periodic and is determined by the uneven distribution of material along the transport route. This imposes additional restrictions on the synthesis of algorithms for optimal control of the conveyor belt speed. Accounting for uneven distribution of material along the transport route is based on an analytical PiKh-model of the conveyor section. To analyze the longitudinal vibrations in the conveyor belt section of the transport system, the wave equation is written and the boundary conditions are substantiated. An estimate of the propagation velocity of longitudinal vibrations in the conveyor belt is given. A solution of the wave equation based on the method of successive approximations is obtained, which determines the dynamics of the propagation of dynamic stresses along the conveyor belt. An estimate of the value of the characteristic acceleration time of the belt, which determines the continuous mode of operation of the transport conveyor section, is given. The scientific novelty of the results obtained lies in the improvement of the control systems for the flow parameters of the transport system in the presence of restrictions associated with the occurrence of longitudinal vibrations in the conveyor belt. The practical significance of the results obtained lies in the construction of a methodology for calculating the limitations of the acceleration/deceleration mode of a conveyor belt unevenly loaded with material along the transport route.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121462298","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}
引用次数: 0
Mathematical and software software of automation application of testing process using Spring framework 测试过程自动化应用的数学和软件软件采用Spring框架
Maryna Pazushko, K. Ivanchenko, D. Ivanchenko
{"title":"Mathematical and software software of automation application of testing process using Spring framework","authors":"Maryna Pazushko, K. Ivanchenko, D. Ivanchenko","doi":"10.20998/2078-9130.2022.2.270129","DOIUrl":"https://doi.org/10.20998/2078-9130.2022.2.270129","url":null,"abstract":"The purpose of this work was to design and create an information system for evaluating and testing students' knowledge, which would simplify the process of forming tests and evaluating students' knowledge for teachers. The paper formed an idea about the concept of knowledge testing. The principles of implementation of this process are revealed. An overview of existing software solutions for computer training programs was conducted, the market of existing analogues was analyzed and, based on the analysis, functional and non-functional requirements for the software product being developed were formed. Based on the requirements, technical and software tools were chosen for the development of the program, namely the Java programming language and the Spring framework, the components of which allow to increase the productivity of the software product, as well as to simplify and speed up the setup, configuration and launch of the project. \u0000To achieve the goal, the following tasks are solved in the work: processing user data, creating a personal account, information about students and teachers, creating and passing a test, evaluating the quality of students' knowledge and teacher-created tests. A mathematical, information and software model of the system was built. The database was designed and built. The structural and functional scheme of the system has been developed. There are three user roles: teacher, student and unregistered user. Saving test results and the ability to obtain mathematical statistics of test results have been implemented. An important role is played by ensuring the ease and comfort of using the product for the user. Therefore, when developing the program, a lot of attention was paid to creating a friendly and ergonomic interface. \u0000The result was an information system of automated testing that fulfills the task, and also meets all the requirements and can be implemented in practice. The results of the work can be used both for the further introduction of the application into the educational process, and for students to acquire practical skills.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114780084","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}
引用次数: 0
Narrowing the Pareto set on the basis of fuzzy information about the ratio of ODA preferences 基于官方发展援助偏好比例的模糊信息,缩小帕累托集合
M. Nekrasova
{"title":"Narrowing the Pareto set on the basis of fuzzy information about the ratio of ODA preferences","authors":"M. Nekrasova","doi":"10.20998/2078-9130.2022.2.270911","DOIUrl":"https://doi.org/10.20998/2078-9130.2022.2.270911","url":null,"abstract":"A multi-criteria choice model is considered, which includes a set of possible options, a numerical vector criterion and a fuzzy binary preference relation of the decision-maker person (DPR). The task of multi-criteria selection is to choose one or more \"best\" options from the Pareto set, that is, to narrow this set taking into account the information about the preference ratio of the DPR. Narrowing is carried out according to the axiomatic approach. The paper considers the algorithm for narrowing the Pareto set based on an arbitrary finite set of \"quanta\" of fuzzy information about the preference ratio of the DPR. Accordingly, an algorithm is proposed that allows, on the basis of an arbitrary set of clear information, to construct an estimate from above for an unknown set of options to be chosen, that is, to narrow the Pareto set. The purpose of this paper is to extend this algorithm to the case of a fuzzy preference relation, where the DPR assigns different degrees of certainty to its reasoning. In the fuzzy case under consideration, the set of options to be chosen and the top estimate constructed for it are also fuzzy. In the first section of the article, the statement of the problem of multi-criteria selection is presented and the basic axioms are formulated. The second chapter is devoted to the description of the reduction of this task to the geometric problem of constructing a fuzzy double cone. In the third section, a generalization of the algorithm is given, which makes it possible to construct the generators of a fuzzy double cone. Based on these constituents, a new vector criterion is constructed, the Pareto set with respect to which is the desired narrowing of the original Pareto set. An illustrative example is considered in the fourth chapter.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126325986","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}
引用次数: 0
Implementation and use of the Levenberg-Marquard algorithm in the problems of calibration of robotic manipulators Levenberg-Marquard算法在机械臂标定问题中的实现与应用
Yuriy Mihailovich Andrjejev
{"title":"Implementation and use of the Levenberg-Marquard algorithm in the problems of calibration of robotic manipulators","authors":"Yuriy Mihailovich Andrjejev","doi":"10.20998/2078-9130.2021.2.249537","DOIUrl":"https://doi.org/10.20998/2078-9130.2021.2.249537","url":null,"abstract":"The well-known problem of calibration of an arbitrary robotic manipulator, which is formulated in the most general form, is considered. To solve the direct problem of kinematics, an alternative to the Denavit-Hartenberg method, a universal analytical description of the kinematic scheme, taking into account possible errors in the manufacture and assembly of robot parts, is proposed. At the same time, a universal description of the errors in the orientation of the axes of the articulated joints of the links is proposed. On the basis of such a description, the direct and inverse problem of kinematics of robots as spatial mechanisms can be solved, taking into account the distortions of dimensions, the position of the axes of the joints and the positions of the zeros of the angles of their rotation. The problem of calibration of manipulators is formulated as a problem of the least squares method. Analytical formulas of the objective function of the least squares method for solving the problem are obtained. Expressions for the gradient vector and the Hessian of the objective function for the direct algorithm, Newton-Gauss and Levenberg-Marquardt algorithms are obtained by analytical differentiation using a special computer algebra system KiDyM. The procedures in the C ++ language for calculating the elements of the gradient and hessian are automatically generated. On the example of a projected angular 6-degree robot-manipulator, the results of modeling the solution to the problem of its calibration, that is, determination of 36 unknown angular and linear errors, are presented. A comparison is made of the solution of the calibration problem for simulated 64 and 729 experiments, in which the generalized coordinates - the angles in the joints took the values ±90° and -90°, 0, +90°.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126051532","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}
引用次数: 0
Evaluation of permissible amplitudes of external impact on free-of-platform inertial navigation systems 对自由平台惯性导航系统的外部冲击允许幅值的评估
Sergii Pogorilov, Valerij Havin
{"title":"Evaluation of permissible amplitudes of external impact on free-of-platform inertial navigation systems","authors":"Sergii Pogorilov, Valerij Havin","doi":"10.20998/2078-9130.2021.1.232154","DOIUrl":"https://doi.org/10.20998/2078-9130.2021.1.232154","url":null,"abstract":"In modern aerospace technology, strapdown inertial navigation systems (SINS) are widely used, using fiber-optic (FOG) or ring laser (CLG) gyroscopes. During the operation of such systems, the sensitivity axes are rotated relative to the basic coordinate system. The resulting angles between the axes of the base coordinate system and the axes of sensitivity of the navigation system (non-orthogonality) are one of the factors leading to an increase in the measurement errors of the device, which affects the measurement accuracy. During operation, the system is affected by vibrations of various nature, the impact of which can contribute to the appearance of non-orthogonality. The purpose of this work is to determine the maximum permissible vibration amplitudes affecting the SINS body according to the permissible values ​​of the deviation of the FOG sensitivity axes for two variants of the SINS layout. An approach to determining the permissible amplitudes of an external harmonic impact on the unit of a strapdown inertial navigation system based on fiber-optic or ring laser gyroscopes is considered. A design scheme, mathematical and finite element models for calculating natural frequencies and forced oscillations of a strapdown inertial navigation system unit have been developed. In various frequency ranges, numerical calculations have determined the boundary values ​​of the amplitudes of the external harmonic impact on the base of specific configurations of the SINS assembly. It has been established that dangerous states take place in the region of the 1st natural frequency of the system, as well as near higher frequencies. Comparison of the results for design options 1 and 2 allows us to conclude that in order to weaken the effect of vibrations on the accuracy of the SINS unit, it is advisable that the lowest natural vibration frequencies for the SINS assembly be as high as possible (more than 1000 Hz). \u0000Key words: vibration; fiber optic gyroscope; strapdown inertial navigation system; finite element method; natural frequencies and modes of vibration.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126803437","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}
引用次数: 0
Investigation of problems in modeling critical loads on a composite model of a wind turbine blade 风力机叶片复合模型临界载荷建模问题研究
Oleksiy Domin, O. Larin
{"title":"Investigation of problems in modeling critical loads on a composite model of a wind turbine blade","authors":"Oleksiy Domin, O. Larin","doi":"10.20998/2078-9130.2021.2.249149","DOIUrl":"https://doi.org/10.20998/2078-9130.2021.2.249149","url":null,"abstract":"This article deals with the problems of designing and analysis of the deformed state of the wind turbine blade under critical loads. A three-dimensional shell simulation model is built, taking into account the complex curvilinear geometry and the presence of reinforcing internal parts. The determination of the parameters of the stress-strain state under the influence of wind load was carried out on the basis of the finite element method. A shell ten-node isoparametric finite element was used. The constructed finite element model of the blade allows taking into account the composite structure and reproduced the presence of a different number of composite layers along the thickness of the shell, the diversity of fibers on individual layers, in particular, the curvilinear orthotropy of mechanical properties was modeled. The procedure of multi-layer structure setting is presented, which provides for superimposition of layers of composite one on the other in places of joint, which ensures compliance of model with technological peculiarities. Static analysis of structural deformation calculation is carried out taking into account lifting force and air head force. The strength analysis was performed for each of the layers according to the criterion of maximum deformations. \u0000Key words: composite material, wind turbine blade, strength, finite-elemental analysis, orthotropy of characteristics.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115262583","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}
引用次数: 0
Heat generation in devices for magnetic-pulse processing of materials 材料磁脉冲加工装置中的热产生
Galina Ottovna Anishchenko, V. I. Konokhov, D. V. Lavinsky
{"title":"Heat generation in devices for magnetic-pulse processing of materials","authors":"Galina Ottovna Anishchenko, V. I. Konokhov, D. V. Lavinsky","doi":"10.20998/2078-9130.2021.2.249735","DOIUrl":"https://doi.org/10.20998/2078-9130.2021.2.249735","url":null,"abstract":"The problem of analysis of non-stationary heat generation due to the flow of electric current in devices for magnetic-pulse processing of materials is considered. An analysis of the available information sources led to the conclusion that a large number of studies in this area are devoted to the study of heat transfer processes during technological operations of induction heating. In other technological operations of magnetic-pulse processing of materials, heat release is also significant. In this case, a non-stationary inhomogeneous temperature field can lead to significant temperature deformations. This, in turn, can cause a loss in the performance of the device due to destruction or irreversible deformation. Adequate modeling of non-stationary temperature propagation in this case is an obligatory step in carrying out computational analysis in the process of designing technological devices. A general strategy is proposed for determining the propagation of a non-stationary temperature field in the presence of a non-stationary non-uniform electromagnetic field. The proposed strategy presupposes a general solution of the problems of the propagation of the electromagnetic field and the temperature field within the framework of a unified design scheme. The use of the finite element method is proposed as a numerical method. The finite element method, when used in such problems, allows one to draw up iterative procedures that can be used to take into account the nonlinear effects associated with the influence of temperature on the electro-physical properties of materials. The problem of sequential determination of a non-stationary, non-uniform electromagnetic field and a non-stationary temperature field in composite matrices intended for electromagnetic pressing of powders of super-strong refractory materials is considered. The distribution of some quantitative characteristics of the electromagnetic field, as well as the dependence of temperature on time are presented.    ","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128029352","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}
引用次数: 0
Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system 随机动力系统数值解谱统计特性评定误差的研究
Yaroslav Beskrovnii, Oleksii Larin
{"title":"Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system","authors":"Yaroslav Beskrovnii, Oleksii Larin","doi":"10.20998/2078-9130.2021.1.232387","DOIUrl":"https://doi.org/10.20998/2078-9130.2021.1.232387","url":null,"abstract":"In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.","PeriodicalId":186064,"journal":{"name":"Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines","volume":"170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133271920","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}
引用次数: 0
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