Applied Mathematics and Control Sciences

Applied Mathematics and Control Sciences is an open-access periodical scientific peer-reviewed journal.

Full Journal Title: Applied Mathematics and Control Sciences

Abbreviation: Appl. Math. Control Sci.

Publisher: Perm National Research Polytechnic University, Perm, Russian Federation

DOI: 10.15593/2499-9873

Languages: Russian, English

Editor-in-Chief: Professor, Dr. Sci. Valerii Yu. Stolbov

Executive Editor: C.Sci. Aleksandr O. Alekseev

Editorial Contact: 

Address: Editorial Board "Applied Mathematics and Control Sciences", Russian Federation, Perm, 614990, Komsomolsky ave., 29
Phone: +7 (342) 219-85-87; + 7 (909) 1000-150
E-mail: aoalekseev@pstu.ru  

Frequency: Quarterly

Applied Mathematics and Control Sciences has no article processing and/or article submission charges.

All Journal's Content, including articles,  is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Editorial of the Journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles and allows readers to use them for any other lawful purpose in accordance with Budapest Open Access Initiative's definition of Open Access.

Journal intended for researchers specializing in the field of applied mathematics, mathematical modeling, differential equations, dynamical systems, optimal control, organizational behavior control, automation, senior students of natural areas.

Since 2019 the journal included in the List of peer-reviewed scientific journals, formed by the Higher Attestation Commission under the Ministry of Science and Higher Education of the Russian Federation.

In 2022 the journal is categorized as category K1 (included in 25% leading Russian peer-reviewed scientific journals).

The years 2022-2031 have been declared the Decade of Science and Technology by decree of the president of the Russian Federation

Current Issue

No 4 (2024)

Mathematical approaches and software to solve the problem of sensitivity analysis by factors of tabularly specified mathematical models using remodeling concept
Sysoev A.S., Miroshnikov A.I., Saraev P.V.

Abstract

Sensitivity Analysis of mathematical models involves a large number of approaches, among which there are local methods (studying the influence of a factor on the response in the case of its isolated variation) and global methods (involving the study of simultaneous fluctuations in groups of factors). Classification of methods is also based on the applied mathematical tools. However, the known methods are approximate or allow using surrogate models approximating the original function, which is a source of error.Previously, the authors proposed an analytical method for analyzing the sensitivity by factors of mathematical models based on Analysis of Finite Fluctuations. In this case, the well-known Lagrange mean value theorem is used to study fluctuations of function responce. However, in some situations the process of finding partial derivatives can be a computationally labor-intensive task, and in some cases the function is given tabularly. In this case, it is possible to use numerical differentiation with further restoration of the analytical representation of the function. For this purpose it is suggested to use the approach of mathematical remodeling and to apply linear regression models with interaction effects as a remodeling class. This assumption is natural, as it models the presence of a linear relationship between the model factors.The paper presents a numerical example - the analysis of the Rosenbrock function, performed in two ways: analytical method and using remodeling to recover partial derivatives. The results obtained show the high quality of the obtained sensitivity estimates, which testifies to the validity of the remodeling approach in such problems. Promising aspects of the presented approach are: application of a wider set of classes of remodeling models (fully connected neural networks, approximating polynomials) and optimal choice of the numerical differentiation step.
Applied Mathematics and Control Sciences. 2024;(4):6-17
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Computer modeling of mechanical behavior of the Ilizarov apparatus modified by Bagirov
Lukina Y.S., Bionyshev-Abramov L.L., Sotin A.V., Suvarly P.N., Samborskij D.Y., Klokova A.N., Bagirov A.B.

Abstract

The development of computer models of orthopedic products allows adding to the arsenal of a trauma surgeon a digital toolkit that allows to calculate the biomechanical consequences of the chosen tactics of reconstructive and restorative treatment. Thus, when using percutaneous osteosynthesis systems with the help of a digital twin of the external fixation apparatus, the operating specialist at the preoperative stage can assess the influence of the choice of the apparatus layout on the risk of possible separation of bone fragments.Clinical indications for the use of the Ilizarov apparatus of the Bagirov modification are fractures of diaphyses of the tibia bones, which account for up to 45 % of all fractures of long bones of the human skeleton. Fracture healing is accompanied by a large number of complications, so the problem of improving the results of treatment of patients with this injury is still relevant for modern traumatology and orthopedics. The use of external fixation devices makes it possible to ensure stable functional osteosynthesis and eliminate the need for plaster immobilization of the segment or limb in the postoperative period. The use of compression-distraction devices allows us to expand the potential use of external fixation devices to solve the problems of distraction osteogenesis. Biomechanical relationships in the bone-apparatus system are a significant factor that allows objectifying the apparatus layout and the mode of motor rehabilitation in the early postoperative period.Within the framework of this study, a mathematical model of the Ilizarov apparatus of the Bagirov modification was constructed and the stress-strain state of the apparatus components under model loads was calculated using the finite element method. To validate the computer model, a field experiment was conducted on a Walter+Bai AG LFM-5 universal testing machine. The investigated structure was subjected to axial compression with a load up to 1000 N. As a result of the comparative analysis of the resistance of the device to axial compression, it was found that the results of finite element calculations describe the experimental results with sufficient accuracy. Comparison of the calculation results with experimental data allows us to state that the proposed computer model correctly describes the mechanical behavior of the studied medical device and can be used in computational experiments to assess the functionality of various device layouts.
Applied Mathematics and Control Sciences. 2024;(4):18–33
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Modeling of the process of manufacturing shells by the continuous wet winding method
Sahabutdinova L.R., Smetannikov O.Y.

Abstract

The article presents the main provisions of the developed complex calculation and experimental technique for describing the behavior and studying, on its basis, the stress-strain state of the "mandrel - composite shell" system during the shell manufacturing process, taking into account the thermoviscoelastic behavior of materials. The research was carried out using the results of an experimental study of the relaxation of the mandrel and shell materials at normal and elevated temperatures and the apparatus of mechanics of a deformed solid. Numerical modeling was carried out by the finite element method implemented in the ANSYS Mechanical environment by means of the APDL parametric programming language. Standard mechanical tests of mandrel material samples, binder and unidirectional PCM samples were carried out at the PNRPU Center for Experimental Mechanics on the certified Instron 5882 universal electromechanical system. The calculation and experimental technique includes: a numerical procedure for identifying thermomechanical parameters to describe the behavior of an isotropic mandrel material taking into account the rheology at normal and elevated temperatures; a model of thermoviscoelastic behavior of a composite material during winding and heat treatment that combines the anisotropy of the elastic behavior of the medium with one independent viscoelastic operator, implemented in the Ansys Mechanical APDL environment; an algorithm for constructing a three-dimensional finite element analogue of the "mandrel – shell" system with technological equipment that takes into account the distribution of initial forces in the shell and frictional contact with lubricant at the interface of the mandrel with the assembly shaft; an algorithm for determining the thermoviscoelastic behavior of the "mandrel – shell" system, implemented by sequentially solving the problem of non-stationary heat conductivity and the quasi-static boundary value problem of mechanics of a deformable solid. As a result of the studies, new data were obtained on the spatio-temporal distribution of stress intensities and normal pressure on the outer surface of the mandrel, established as a result of a comprehensive study based on computational experiments, including with deviations from the design parameters of the technological process.
Applied Mathematics and Control Sciences. 2024;(4):34-51
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Research and assessment of the indecomposable remainder in the degree of influence of each variable in factor analysis
Golovanov O.A., Tyrsin A.N.

Abstract

The least absolute deviation method is one of the most common alternatives to the least squares method in regression analysis. It allows obtaining stable estimates of coefficients when the probability density of random errors has more elongated tails compared to the normal distribution. However, when several violations of the Gauss-Markov conditions are combined, for example, with a one-sided nature of outliers and the presence of a correlation between explanatory variables and random errors, the least absolute deviation method also does not provide acceptable accuracy in estimating regression dependencies. One of the promising ways to solve this problem may be the weighted least absolute deviation method.The problem of determining the parameters of linear regression models based on the weighted least absolute deviation method is considered. Exact algorithms for solving it are described. The computational efficiency of exact algorithms for solving the problem of the weighted least absolute deviation method is investigated. It is proved that adding weight coefficients to the coordinate-wise and modified gradient descent algorithms did not cause changes in terms of computational complexity and accuracy of the solution. Nevertheless, a small increase in the execution time of computational experiments was recorded due to the addition of an additional operation to the descent algorithms. This dependence is more noticeable in the coordinate variant. This is due to the fact that the value of the objective function in it is determined at each nodal point of the nodal straight line up to finding the minimum, while in the gradient descent it is determined only at the point of extremum.As a result of the comparative analysis with the gradient projection method and solutions of direct and dual problems of linear programming using the simplex method, it was found that they are more than an order of magnitude inferior to the gradient descent along nodal straight lines in terms of computation time. It is shown that the gradient projection method does not guarantee finding an exact solution to problem.
Applied Mathematics and Control Sciences. 2024;(4):52-64
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Train the RASAT model that integrates the relational structure into the pre-trained Seq2Seq model to convert text into SQL
Xifei L.

Abstract

In this study the relational attention module is getting integrated into pre-trained Transformer Seq2Seq model and realize the conversion of natural language questions to Structured Query Language (SQL) retrieval commands by conducting experiments on the Spider dataset. The purpose of this scientific article is to improve the accuracy and efficiency of converting text into SQL queries by using the relational attention mechanism in the transformer model. The article presents the RASAT (Relational Attention-based SQL Transformation) model, which replaces the self-rotation module in the transformer encoder with a relational attention module for processing text-to-SQL tasks. this approach allows you to better take into account the semantic relationships between entities in the text and generate more accurate SQL queries. The research methods include the use of a pre-trained transformer model (T5-small) and training it on the Spider dataset with the introduction of a relational attention module. Experimental results show a significant improvement in accuracy indicators when converting text to SQL compared to the basic model without a relational component. The experimental results demonstrate that the RASAT model improves the Exact Match performance by 1.82% and the Execution Accuracy by 3.26%. These improvements are achieved despite the fact that the number of training epochs was limited to 500 instead of 3072 for the basic model, which emphasizes the effectiveness of the proposed approach even with limited computing resources. In conclusion, the prospects for further development of the relational model method to improve the quality of systems related to natural language processing and databases are emphasized.
Applied Mathematics and Control Sciences. 2024;(4):65-75
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Modelling the learning process in Petri net notation for effective managerial decision making
Fedoseev A.I., Ponomareva L.A., Zabolotnikova V.S.

Abstract

The authors propose a model of the testing process in the notation of colored Petri nets. Before starting the simulation, the information flows of the process of mastering the discipline «Informatics» in IDEF3 notation by students of the Department of Applied Information Technologies of the ION RANEPA were studied. In the process of building the model, the following task was solved:let's give a Petri net consisting of a set of positions P = {p1, p2, ..., pn} and a set of transitionsT = {t1, t2, ..., tm}. The network simulates the testing process. Then there are such states of positions P that the following conditions are met for each transition T in the network:1. ∀ti ∈ T: (∀pi' ∈ Pred(tj): pi'(pj) = 1) → T(P) = 1, where Pred(tj) is the set of all preceding transition positions ti. 2. ∀tj ∈ T: tj(pj) = 1 → (∀p' ∈ Succ(tj): pj'(pj) = 1), where Succ(tj) is the set of all the following transition positions tj.That is, it is necessary to formalize the educational process using a colored Petri net. Find a labeling that can be achieved in a given colored Petri net that satisfies the following condition: there is a sequence of transitions (transactions) starting from the initial labeling, such that each subsequent labeling is obtained by applying the corresponding transition to the previous labeling. I.e.: ∃ M0: (initial labeling) → M*, where → M* denotes the reflexive and transitive closure of the transition relation in the Petri net.Solving the problem of the reachability of network labeling gave the concept of an optimal scenario for monitoring the development of competencies in the discipline: Some tasks and questions do not have to be included in the testing. Various scenarios for monitoring student progress are presented using the example of discipline testing. For example, one of the variants of the test scenario assumed the presence of a common resource with questions and assignments on the five topics under study. There were 50 questions in the database. The answer to each question can be rated from zero to 10 points. The test is considered passed if the student scored at least 41 points. The numbers of completed tasks and questions with the correct answer were also recorded.Another test option: 10 questions for each topic and the response time to the question (task) was recorded.A matrix analysis of the model was carried out. The vector of the initial marking μ(pi) = {47,1,1,1,0,0,0,0} and μk = {30, 0, 0, 0, 0, 0, 0, 41} at the end of testing. The analysis of the reachability of the μk marking allowed us to obtain one of the sequences of triggering transitions U k-1 = (t1, t3, t4, t3, t3, t4). Where transitions t1 – t4 fix the beginning and end of an elementary process (for example, the beginning of testing – the end of testing).The analysis of the model allowed us to investigate the dynamics of studying the topics of the discipline « Informatics »: how many times the student returned to re-reading the module materials, how many times he turned to additional material. Monitors attached to the transitions made it possible to determine the time for each operation and draw up protocols for studying the discipline.
Applied Mathematics and Control Sciences. 2024;(4):76-87
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Hierarchical sensitivity analysis capacity models
Borovkova G.S., Pogodaev A.K., Klyavin V.E., Zhikhoreva S.V., Sysoev A.S.

Abstract

With the increasing number of private vehicles in urban agglomerations and growing freight traffic, there is a need to implement intelligent transportation systems to develop strategies to reduce congestion and prevent traffic accidents. One of the key indicators of the transportation system, reflecting the efficiency of using the available urban infrastructure, is the capacity of planned routes. The model for estimating the capacity of an urban route based on the capacity of its elements - runs and intersections - is multi-level, hierarchical, and multi-criteria. In addition, this model is dynamic because its parameters change over time. All this increases the computational complexity of analyzing such a model, and leads to the need to reduce the number of parameters under study. One approach to reducing model parameters is sensitivity analysis based on finite change analysis. In the case of the capacity model, this approach will allow to identify those parameters of the route elements, the change of which causes the greatest changes in the capacity of the route as a whole, and will give the opportunity to manage them in order to improve the overall efficiency of the system.The aim of the study is to develop a methodology for hierarchical sensitivity analysis of the capacity model of the street and road network based on finite change analysis, which makes it possible to identify critical points and assess the contribution of individual elements and groups of objects to the overall performance of the transportation system. The results obtained show that the proposed methodology allows to accurately identify the main factors affecting the capacity and to propose measures to optimize traffic flow management.
Applied Mathematics and Control Sciences. 2024;(4):88–98
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About one method of constructing a fuzzy classifier for evaluating the effectiveness of investment instruments
Nikitina S.A.

Abstract

The application of fuzzy modeling methods to analyze the effectiveness of investment instruments is considered. When choosing a financial strategy in a situation of uncertainty, such an analysis helps to evaluate and make a decision. Since the parameters of the financial system in conditions of uncertainty can be impossible to establish accurately, problems arise that are described by a number of characteristics of an indistinct nature. In the work, a system of indicators was set for evaluating the investment strategy. The significance of each indicator is determined using weighting coefficients, which are determined using the method of paired comparisons and the Saati scale. To describe financial instruments, special linguistic variables were introduced, for each of which term sets were set. Each term is a fuzzy trapezoidal number.After fixing the current values characterizing the financial system, a fuzzification procedure is performed, that is, the introduction of fuzziness. Then, in a certain way, the convolution operation is performed for all levels of the model indicators, taking into account the weighting coefficients of significance. As a result, we obtain a general aggregated characteristic of an investment instrument, according to which it is possible to draw a conclusion about the level of its effectiveness. The application of the obtained results is demonstrated by examples.
Applied Mathematics and Control Sciences. 2024;(4):99–111
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