scholarly journals Research of a mathematical model for designing a barge-towing complex for the Republic of the Union of Myanmar

2021 ◽  
pp. 82-87
Author(s):  
Т.А. Апалько ◽  
М.Х. Най
Keyword(s):  
Mathematical Model ◽  
Random Search ◽  
Computer Experiment ◽  
Functional Constraints ◽  
Criterion Function ◽  
Complex Technical System ◽  
The Republic ◽  
The Mathematical Model ◽  
Inland Water Transport ◽  
Program Modules

В статье описана математическая модель проектирования барже-буксирного комплекса с учётом особенности эксплуатации в условиях Республики Союз Мьянма. В статье исследуются особенности ББК как объекта оптимизации, описана математическая модель ББК, отображается его как сложную техническую систему. В рамках модели приведены математические зависимости и алгоритмы для определения элементов теоретического чертежа, мощности главных двигателей, для решения некоторых вопросов общего расположения с учетом расстояния главных водонепроницаемых переборок корпуса, для расчета нагрузки и устойчивости. Метод комплексной оценки эффективности применения барже-буксирного комплекса на стадии технико-экономического обоснования проекта в условиях развивающихся стран, в частности в условиях Республики Союз Мьянмы. В результате работы были полностью определены параметры основных типов барже-буксировочных комплексов для перспективной системы внутреннего водного транспорта Республики Союза Мьянма. На базе методов случайного поиска создан алгоритм оптимизации элементов ББК, решающий задачу математического программирования с процедурным характером функции критерия и функциональных ограничений. Математическая модель и алгоритм оптимизации реализованы в виде программы для обеспечения компьютерного эксперимента. Программа, реализующая математическую модель проектирования ББК, состоит из отдельных программных модулей, что облегчает ее совершенствование в анализе результатов решения задачи. Создан программный комплекс с использованием языка программирования Паскаль в среде Delphi для обеспечения автоматизирования проектирования. Указанные программы могут быть использованы в исследовательском проектировании на начальных стадиях проектирования. The article describes a mathematical models for designing a barge-towing complex, taking into account the peculiarities of operation in the conditions of the Republic of the Union of Myanmar. The article examines the features of the BBK as an object of optimization, describes the mathematical model of the BBK, displays it as a complex technical system. Within the framework of the model, mathematical dependencies and algorithms are given for determining the elements of the theoretical drawing, the power of the main engines, for solving some issues of the general location, taking into account the distance of the main watertight bulkheads of the hull, for calculating the load and stability. The method of comprehensive assessment of the effectiveness of the use of the barge-tow complex at the stage of the feasibility study of the project in the conditions of developing countries, in particular in the conditions of the Republic of the Union of Myanmar. As a result of the work, the parameters of the main types of barge-towing complexes for the prospective inland water transport system of the Republic of the Union of Myanmar were fully determined. On the basis of random search methods, an algorithm for optimizing the BBK elements is created, which solves the problem of mathematical programming with the procedural nature of the criterion function and functional constraints. The mathematical model and the optimization algorithm are implemented as a program to provide a computer experiment. The program that implements the mathematical model of the design of the BBK consists of separate program modules, which facilitates its improvement in the analysis of the results of solving the problem. A software package was created using the Pascal programming language in the Delphi environment to provide design automation. These programs can be used in research design at the initial stages of design.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Mathematical model of the dynamics of a hydrofoil vessel as a complex technical system

2021 ◽  
pp. 168-178
Author(s):  
Д.А. Скороходов ◽  
Ю.Е. Крылов ◽  
А.Л. Стариченков
Keyword(s):  
Mathematical Model ◽  
Unified Modeling ◽  
Modeling Environment ◽  
Phase Coordinates ◽  
Electrohydraulic Drive ◽  
Linearized System ◽  
Complex Technical System ◽  
The Mathematical Model ◽  
Output Indicators ◽  
Disturbed Motion

Определена структура единой среды моделирования, состоящая из трёх блоков: блок, где задаются или формируются значения исследуемых параметров, влияющие на выходные показатели судна, как объекта моделирования, блок представляющий собой ядро единой среды моделирования и блок, где формируется совокупность тех или иных показателей, подлежащих анализу. Определена математическая модель динамики возмущенного движения СПК, при этом использованы следующие системы координат: земная прямоугольная горизонтальная правая, связанная с судном прямоугольная правая и вспомогательная нецентральная прямоугольная правая. Определены основные допущения математической модели. Представлены уравнения динамики судна на подводных крыльях в общем виде и определены силы и моменты, действующие на судно на подводных крыльях в крыльевом режиме движения. Гидродинамические силы и моменты, возникающие на каждом из крыльевых устройств, определены расчетным путем. Работа движителей моделируется заданием среднего упора, направленного по оси вала движителя и параллельного диаметральной плоскости судна. В модели динамики предусмотрена возможность задания аэродинамических сил и моментов, действующие на СПК в крыльевом режиме. Разработана математическая модель электрогидравлического привода, состоящая из суммирующего устройства, электрогидроусилителя и силового интегрирующего привода, охваченных общей обратной связью по положению и скорости перемещения, а также модель системы управления движением, которая является одной из важнейших подсистем СПК, формирующей алгоритмы управления, поступающие на входы ЭГП соответствующих ИО, расположенных на несущих поверхностях КУ. При решении некоторых задач, связанных с проектированием СПК и его технических систем, особенно для получения оценочных значений фазовых координат судна на начальных этапах проектирования или решения специальных задач, разработана линеаризованная система дифференциальных уравнений объекта. The structure of a unified modeling environment has been determined, which consists of three blocks: a block where the values of the studied parameters are set or formed, which affect the output indicators of the vessel as an object of modeling, a block that is the core of a unified modeling environment and a block where a set of certain indicators is formed. analysis. A mathematical model of the dynamics of the disturbed motion of the SPK was determined, with the following coordinate systems used: earth rectangular horizontal right, rectangular right connected to the ship and auxiliary off-center rectangular right. The basic assumptions of the mathematical model are determined. The equations of the dynamics of a hydrofoil ship in general form are presented and the forces and moments acting on a hydrofoil ship in the wing mode of motion are determined. The hydrodynamic forces and moments arising on each of the wing devices are determined by calculation. The operation of the propellers is modeled by setting the middle stop directed along the axis of the propeller shaft and parallel to the diametral plane of the vessel. The dynamics model provides for the possibility of setting aerodynamic forces and moments acting on the HFV in the wing mode. A mathematical model of an electrohydraulic drive has been developed, consisting of a summing device, an electrohydraulic amplifier and a power integrating drive, covered by a general feedback on the JJposition and speed of movement, as well as a model of a motion control system, which is one of the most important subsystems of the SPC that forms control algorithms entering the EGP inputs of the corresponding EUT located on the bearing surfaces of the KU. When solving some problems related to the design of the HFV and its technical systems, especially for obtaining the estimated values of the phase coordinates of the vessel at the initial stages of design or solving special problems, a linearized system of differential equations of the object was developed.

scholarly journals Разработка и исследование математической модели проектирования патрульного катера для Союза Мьянма

2020 ◽  
Author(s):  
A.I. Gaikovich ◽  
N.V. Nikitin ◽  
S. Pyae
Keyword(s):  
Mathematical Model ◽  
Search Algorithm ◽  
Load Capacity ◽  
Random Search ◽  
Design Model ◽  
Modular Architecture ◽  
Efficiency Criterion ◽  
Design Problems ◽  
The Mathematical Model ◽  
Mathematical Design

В статье описывается математические модель проектирования для обоснования концепции патрульного катера, предназначенного для Союза Мьянма. Основные кораблестроительные элементы определяются как результаты решения задачи математического программирования (оптимизации). В состав математической модели входят расчеты нагрузки, вместимости, остойчивости, ходкости, запаса плавучести. Критерием эффективности взято отношение вероятности перехвата нарушителя к приведенным годовым затратам. Для решения оптимизационной задачи используется алгоритм случайного поиска. Для реализации разработанной математической модели проектирования создан программный комплекс модульной архитектуры в оболочке DELPHI. В рамках исследования математической модели оценивалась её адекватность, чувствительность и устойчивость. Результаты исследования оказались удовлетворительными, что доказывает возможность применения разработанной математической модели для решения проектных задач на начальных стадиях разработки проекта патрульного катера.The article describes a mathematical design model to substantiate the concept of a patrol boat intended for the Union of Myanmar. The main shipbuilding elements are defined as the results of solving the problem of mathematical programming (optimization). The mathematical model includes calculations of the load, capacity, stability, propulsion, stock of buoyancy. The efficiency criterion is the ratio of the probability of interception of the intruder to the given annual costs. To solve the optimization problem, a random search algorithm is used. To implement the developed mathematical design model, a software package of modular architecture in the DELPHI shell was created. As part of the study of the mathematical model, its adequacy, sensitivity, and stability were evaluated. The research results were satisfactory, which proves the possibility of using the developed mathematical model to solve design problems in the initial stages of the design of a patrol boat project.

scholarly journals DEVELOPING EXPANDED POWELL’S ALGORITHM TO IDENTIFY THE MATHEMATICAL MODEL PARAMETERS FOR TRANSESTERIFICATION OF FISH FAT INTO BIODIESEL FUEL

2011 ◽  
Vol 14 (3) ◽  
pp. 34-48
Author(s):  
Hai Xuan Le ◽  
Anh Huynh Tuyet Le
Keyword(s):  
Mathematical Model ◽  
Random Search ◽  
Equation System ◽  
Optimal Operation ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Biodiesel Fuel ◽  
Model Parameters ◽  
Operation Conditions ◽  
The Mathematical Model

By employing the system approach methodology, this research showed the expansion of Powell’s algorithm to solve the identification of kinetic parameters in the differential equation system which describes the transesterification of fish fat into biodiesel fuel. The expanded Powell’s method is developed on the basis of the algorithm that combines Taxi-Cab method with random search method and gradient method (steepest descent method). The obtained results allow us to simulate and optimize the biodiesel fuel production in order to assess the influence of technological factors on the effect of process and to determine the optimal operation conditions. The expanded Powell’s algorithm can also be advantageously applied to simulation or optimizzation in the cases when the mathematical model of the research object contains several parameters which must be identified.

scholarly journals LEARNING TO SOLVE LOGICAL PROBLEMS IN A SECONDARY SCHOOL

2020 ◽  
pp. 92-97
Author(s):  
М.Т. Iskakova ◽  
◽  
А.К. Orazbaeva ◽  
Keyword(s):  
Mathematical Model ◽  
Secondary School ◽  
Mathematical Knowledge ◽  
Venn Diagram ◽  
Modern World ◽  
Regional Characteristics ◽  
Problem Finding ◽  
The Republic ◽  
The Mathematical Model

The formation of pupils' mathematical knowledge by solving logical problems is one of the most popular in the modern world. Solving problems using a deep analysis of the set conditions of problems, without using memorable formulas for solving logical problems, helps to improve the thinking of. The tasks in this article are based on regional characteristics of some regions and cities of the Republic of Kazakhstan. The compiled tasks correspond to the content of education of the 6th grade of a secondary school. The mathematical model of a text problem, finding numbers by part, Euler-Venn diagram, proportion, calculation of the path, speed, and construction of the scheme contribute to the formation of navics for solving students ' problems. Tasks related to the nature of their land arouse the interest of students and contribute to being a patriot of their country.

Pruning operator for minimum deck wind in carrier aircraft launch

2019 ◽  
Vol 234 (3) ◽  
pp. 655-664
Author(s):  
Zeyang Zhou ◽  
Jun Huang ◽  
Mingxu Yi
Keyword(s):  
Mathematical Model ◽  
Search Algorithm ◽  
Random Search ◽  
Optimal Solution ◽  
Flight Safety ◽  
Problem Statement ◽  
Linear Problems ◽  
Random Search Algorithm ◽  
The Mathematical Model ◽  
Wind Resources

Launch resources and flight safety are important for carrier-based aircraft to takeoff. Aimed at making full use of marine wind resources, a pruning operator added to linear random search algorithm is developed to solve the minimum deck wind for carrier aircraft launch. On the basis of problem statement, the catapult safety criteria are quantified as the boundary condition of the critical solution. Then the mathematical model is established for the algorithm including pruning schematic. The influence of deck wind on aircraft catapult launch is analyzed. With the algorithm proceeding and the feedback results of aircraft catapult launch simulation, the optimal solution of the minimum deck wind is determined in a few simulation times. The main contribution of this research is the development of the pruning operator to greatly shorten the search times under permissible error for the discrete linear problems. And the minimum deck wind is solved in full takeoff weight range due to combining linear random search algorithm and simulation.

A General Method for Optimum Design of Gear Boxes Through Nonlinear Programming

1989 ◽  
Author(s):  
W. L. Cleghorn ◽  
R. G. Fenton ◽  
J.-F. Fu
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Optimum Design ◽  
Random Search ◽  
Optimization Methods ◽  
Search Method ◽  
Programming Technique ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
General Method

Abstract A general method for the optimum design of gear boxes is presented using a nonlinear programming technique. The mathematical model of the gear box is developed using a symbolic mathematical manipulator. Constraints of the feasible design have been included but reduced to be as few as possible. Identical optimum results were obtained through employing two different optimization methods, the flexible tolerance method and the random search method, for solving an example problem.

scholarly journals Developing a System to Support Banks in Making Investment Decisions when Organizing Project Financing

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Model ◽  
System Development ◽  
Investment Decision ◽  
Investment Decisions ◽  
Software Implementation ◽  
Practical Implementation ◽  
Project Financing ◽  
The Russian Federation ◽  
The Republic ◽  
The Mathematical Model

The article deals with the development of an information system providing support for making investment decisions by Ziraat Bank in organizing project financing of innovative projects implemented within the machinebuilding cluster of the Republic of Tatarstan and its affiliated entities in the Russian Federation. A set of requirements for such a system was formulated and an appropriate mathematical model developed. The software implementation of the mathematical model was carried out in the Ziraat Bank's investment decision support system. An algorithm for system development was proposed, the practical implementation of which was performed using the theory of oriented graphs along with the schedule theory.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

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