scholarly journals Development of the mathematical model of the problem of reengineering topological structures of large-scale monitoring systems

2015 ◽  
Vol 4 (4(76)) ◽  
pp. 49
Author(s):  
Владимир Валентинович Бескоровайный ◽  
Ксения Евгеньевна Подоляка
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Monitoring Systems ◽  
Topological Structures ◽  
The Mathematical Model

The envelope method in the problem of choosing a rational composition of measuring instruments

2021 ◽  
pp. 68-72
Author(s):  
Il'ya A. Meshchikhin ◽  
Sergej S. Gavryushin
Keyword(s):  
Mathematical Model ◽  
Monitoring Systems ◽  
Measuring Instruments ◽  
Key Points ◽  
Envelope Method ◽  
Loaded State ◽  
The Mathematical Model ◽  
Selection Of ◽  
Rational Composition

As part of the development of monitoring systems for the operation of technical objects, the problem of improving the quality of monitoring systems for the loaded state is considered. Based on the analysis of the mathematical model of the structure and its loading, a methodology for the selection of measuring instruments was developed. The urgency of the problem of calculating substantiation of the choice of key points of the structure is shown, at which it is possible to measure deformations for the subsequent restoration of the existing loads with maximum accuracy. An approach based on the envelope method for determining the rational composition of measuring instruments for restoring the loads acting on the structure is stated.

scholarly journals Approximation of potential-driven flow dynamics in large-scale self-similar tree networks

2011 ◽  
Vol 467 (2134) ◽  
pp. 2810-2824 ◽  
Author(s):  
Jason Mayes ◽  
Mihir Sen
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Large Scale ◽  
Differential Algebraic Equations ◽  
Flow Dynamics ◽  
Algebraic Equations ◽  
Tree Networks ◽  
Self Similar ◽  
Large Scale Flow ◽  
The Mathematical Model

Dynamic analysis of large-scale flow networks is made difficult by the large system of differential-algebraic equations resulting from its modelling. To simplify analysis, the mathematical model must be sufficiently reduced in complexity. For self-similar tree networks, this reduction can be made using the network’s structure in way that can allow simple, analytical solutions. For very large, but finite, networks, analytical solutions are more difficult to obtain. In the infinite limit, however, analysis is sometimes greatly simplified. It is shown that approximating large finite networks as infinite not only simplifies the analysis, but also provides an excellent approximate solution.

The Numerical Simulation of Directional Solidification Process Temperature Field for Large-Scale Frustum of a Cone Ingot

2011 ◽  
Vol 189-193 ◽  
pp. 1476-1481
Author(s):  
Kun Liu ◽  
Zhe Wang ◽  
Ren Zhi Han ◽  
Zi Ping Ren
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Temperature Field ◽  
Directional Solidification ◽  
Large Scale ◽  
Solidification Process ◽  
Directional Solidification Process ◽  
Ingot Quality ◽  
Fluent Software ◽  
The Mathematical Model

By using Fluent software, the mathematical model of temperature field is established on directional solidification process for large-scale frustum of a cone ingot, and the result is analyzed by Origin software, Tecplot. The influences of different width/thickness ratio to directional solidification process of cone ingot are discussed in order to provide basis for design optimization and ingot quality improvement.

scholarly journals EXISTING APPROACHES TO THE MATHEMATICAL MODEL"INSULIN-GLUCOSE"

2020 ◽  
Vol 1 (27(54)) ◽  
pp. 4-7
Author(s):  
S.I. Kisil ◽  
T.S. Zaletova
Keyword(s):  
Mathematical Model ◽  
Blood Glucose ◽  
Mathematical Models ◽  
Blood Sugar ◽  
Continuous Monitoring ◽  
Monitoring Systems ◽  
The Mathematical Model

Algorithms for predicting blood glucose based on the use of mathematical models that can be used in continuous monitoring systems for blood sugar are described.

scholarly journals OPTIMIZATION OF TOPOLOGICAL STRUCTURES OF CENTRALIZED LOGISTICS NETWORKS IN THE PROCESS OF REENGINEERING

2021 ◽  
pp. 23-31
Author(s):  
Vladimir Beskorovainyi ◽  
Antonii Sudik
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Time Complexity ◽  
Large Scale ◽  
System Optimization ◽  
Distributed Objects ◽  
Computational Point ◽  
Topological Structures ◽  
Logistics Networks ◽  
Current State

The subject of research in the article is the topological structures of closed logistics networks. The purpose of the work is to create a mathematical model and methods for solving problems of optimization of topological structures of centralized logistics networks in the process of reengineering, taking into account many topological and functional constraints. The article solves the following tasks: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; formalization of the problem of system optimization of logistics networks as territorially distributed objects; development of a mathematical model of the problem of optimization of centralized three-level topological structures of logistics networks at the stage of reengineering; development of a method for solving the problem of optimization of centralized three-level topological structures of logistics networks at the reengineering stage; estimation of time complexity of the method of optimization of centralized three-level topological structures of logistics networks. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; the problem of system optimization of logistics networks as territorially distributed objects has been formalized; developed a mathematical model of the problem of reengineering three-level topological structures of logistics networks in terms of cost and efficiency for the case of combined production and processing points; methods of directed search of variants of construction of a logistic network which use procedures of coordinate optimization and modeling of evolution on the basis of genetic algorithm are developed; estimates of the accuracy and time complexity of optimization methods of centralized three-level topological structures of logistics networks are obtained. Conclusions: Based on the results of the study of methods for solving the problem, an approximation of their accuracy and time complexity was performed. In practice, this will allow you to choose a more efficient method for solving large-scale practical problems, based on the required accuracy, available computing and time resources. The method based on the coordinate optimization procedure has a significantly higher accuracy, but it is more complex from a computational point of view. The accuracy of the evolutionary method based on a genetic algorithm can be increased by increasing the number of iterations. The practical use of the proposed mathematical model and methods of reengineering the topological structures of centralized closed logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of transport activities of companies. Keywords: closed logistics; logistics network; optimization; reengineering; structure; topology.

scholarly journals The calculation of specific heats for some important solid components in hydrogen production process based on CuCl cycle

2014 ◽  
Vol 18 (3) ◽  
pp. 823-831 ◽  
Author(s):  
Jurij Avsec
Keyword(s):  
Mathematical Model ◽  
Hydrogen Production ◽  
Thermodynamic Properties ◽  
Large Scale ◽  
Solid Phase ◽  
Statistical Thermodynamics ◽  
Thermochemical Cycle ◽  
Direct Production ◽  
Production Of Hydrogen ◽  
The Mathematical Model

Hydrogen is one of the most promising energy sources of the future enabling direct production of power and heat in fuel cells, hydrogen engines or furnaces with hydrogen burners. One of the last remainder problems in hydrogen technology is how to produce a sufficient amount of cheap hydrogen. One of the best options is large scale thermochemical production of hydrogen in combination with nuclear power plant. copper-chlorine (CuCl) cycle is the most promissible thermochemical cycle to produce cheap hydrogen.This paper focuses on a CuCl cycle, and the describes the models how to calculate thermodynamic properties. Unfortunately, for many components in CuCl cycle the thermochemical functions of state have never been measured. This is the reason that we have tried to calculate some very important thermophysical properties. This paper discusses the mathematical model for computing the thermodynamic properties for pure substances and their mixtures such as CuCl, HCl, Cu2OCl2 important in CuCl hydrogen production in their fluid and solid phase with an aid of statistical thermodynamics. For the solid phase, we have developed the mathematical model for the calculation of thermodynamic properties for polyatomic crystals. In this way, we have used Debye functions and Einstein function for acoustical modes and optical modes of vibrations to take into account vibration of atoms. The influence of intermolecular energy we have solved on the basis of Murnaghan equation of state and statistical thermodynamics.

The Mathematical Model of Naphtha Steam Cracking

1992 ◽  
Vol 57 (10) ◽  
pp. 2113-2124
Author(s):  
Zdeněk Bělohlav ◽  
Josef Horák
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Raw Materials ◽  
Reaction Model ◽  
Radical Reactions ◽  
Inlet Temperature ◽  
Outlet Temperature ◽  
Outlet Pressure ◽  
Steam Cracking ◽  
The Mathematical Model

The mathematical model of naphtha steam cracking has been developed to predict products yields. The feedstock composition, feedstock rate, steam-oil ration, inlet temperature, outlet temperature and outlet pressure are introduced as inputs. The reaction model consists of two parts: the radical reactions of higher alkanes, higher alkenes, naphthenes and alkylaromatics and the formal molecular reactions of lower alkanes and lower alkenes. The model was identified using a series of large-scale experiments including four naphtha raw materials. Eight experiments were carried out for each naphtha kind at two levels of the temperature profile, feed rate and steam-oil ratio.

Mathematical model of structural and topological optimization of logistics networks

2021 ◽  
pp. 178
Author(s):  
Volodymyr Bezkorovainyi ◽  
Leonid Nefedov ◽  
Vladimir Russkin
Keyword(s):  
Mathematical Model ◽  
Optimization Problem ◽  
System Optimization ◽  
Topological Optimization ◽  
Distributed Objects ◽  
Topological Structures ◽  
Logistics Networks ◽  
Current State ◽  
Geographically Distributed ◽  
The Mathematical Model

The subject of research in the article is the topological structures of closed-loop logistics networks. The goal of the article is to increase the efficiency of centralized logistics networks by developing a mathematical model for a two-criteria problem of optimizing topological structures in the process of their reengineering. The article solves the following tasks: analysis of the current state of the problem of structural and topological optimization of logistics networks; formalization of the problem of optimization of logistics networks as geographically distributed objects; synthesis of objective functions of the mathematical model of a two-criterion optimization problem for centralized three-level topological structures of closed logistics networks at the reengineering stage; development of a system of constraints of the mathematical model of the problem of optimizing centralized three-level topological structures of closed logistics networks; a function for evaluating the overall utility of options based on the Kolmogorov-Gabor polynomial is offered. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: the analysis of the current state of the problem of system optimization of logistics networks, mathematical models and methods for its solution was carried out; formalization of the problem of structural and topological optimization of logistics networks as geographically distributed objects; a mathematical model of a two-criterion task of reengineering of three-level topological structures of logistics networks in terms of costs and efficiency with integrated points of production and processing has been developed (originality). Conclusions: Based on the results of the analysis of the problem of optimizing the topological structures of logistics systems, it has been established that the problems of direct and reverse logistics are still considered as conditionally independent, which does not allow obtaining effective global solutions. In the context of expanding the network of consumers, changes in delivery volumes, the introduction of environmental restrictions, it is proposed to reengineer the networks, which provides for their radical redesign. The formulated statement and the developed mathematical model of a two-criterion (in terms of cost and efficiency) optimization problem for three-level topological structures for combined production and processing points will increase the efficiency of logistics networks with reverse flows by reducing the cost of reengineering (practical value).

scholarly journals Transient Phenomena Generated in Emptying Operations in Large-Scale Hydraulic Pipelines

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2313
Author(s):  
Guillermo Romero ◽  
Vicente S. Fuertes-Miquel ◽  
Óscar E. Coronado-Hernández ◽  
Román Ponz-Carcelén ◽  
Francisco Biel-Sanchis
Keyword(s):  
Mathematical Model ◽  
Hydraulic System ◽  
Large Scale ◽  
Hydraulic Systems ◽  
Transient Phenomena ◽  
Pressure Drops ◽  
Pipeline Route ◽  
Air Pockets ◽  
Pressure Changes ◽  
The Mathematical Model

Air pockets generated during emptying operations in pressurized hydraulic systems cause significant pressure drops inside pipes. To avoid these sudden pressure changes, one of the most widely used methods involves the installation of air valves along the pipeline route. These elements allow air exchange between the exterior and the interior of the pipe, which alleviates the pressure drops produced and thus prevents possible breaks or failures in the structure of the installation. This study uses a mathematical model previously validated by the authors in smaller installations to simulate all hydraulic variables involved in emptying processes over time. The purpose of these simulations is the validation of the mathematical model in real large-scale installations, and to do this, the results obtained with the mathematical model are compared with actual measurements made by the partner company. The hydraulic system selected for the study is a pipeline with a nominal diameter of 400 mm and a total length of 1020 m. The results obtained from the mathematical model show great similarity with the experimental measurements, thus validating the model for emptying large pipes.

Optimization Design of Large-Scale Cross-Roller Slewing Bearing Used in Special Propeller

2011 ◽  
Vol 48-49 ◽  
pp. 787-792 ◽  
Author(s):  
Gang Zhang ◽  
Xue Zhang ◽  
Kai Feng Zhou ◽  
Juan Ruan ◽  
De De Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Design Process ◽  
Optimization Design ◽  
Large Scale ◽  
Function Optimization ◽  
Design Model ◽  
Slewing Bearing ◽  
The Mathematical Model

According to the working requirement of large-scale cross roller slewing bearing used in special propeller, an optimal design model which includes objective function, optimization variables and constraints is established, and uses genetic toolbox of the Matlab software to solve the mathematical model. An example shows that the bearing’s life is improved significantly by the optimization. It indicates that the optimization design has some guidance significance in the design process of the slewing bearing.

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