Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • GENETIC ALGORITHM OF DEFINITION OF OPTIMAL ELECTRIC POWER SYSTEM CONFIGURATION

      pg(s) 57-60

      This paper presents, general formulation and new solution to actual scientific and applied task of developing new methods of the high voltage distribution networks reconfiguration based on mathematical devices of genetic algorithms, that provide additional reduction of electricity losses and its quality improvements, when increasing 6 (10 ) kV networks to 20 kV voltage class. New method of the electrical power distribution network reconfiguration at normal mode was developed using of genetic algorithms, which on the basis of electrical power network modes enables determination of an optimal scheme configuration so that losses of power transportation were minimal provided that standard quality of electric power with voltage at consumers’ connection points assured and minimum connectedness of electrical power network  scheme and minimal economic losses from power underproduction maintained.

    • THE METHOD OF NUMERICAL MODELING OF HYDRODYNAMICS AND HEAT EXCHANGE IN A CHANNEL WITH DISCRETE ROUGHNESS

      pg(s) 61-64

      Basic methodology has been developed for a numerical modeling and heat exchange in a smooth channel and in a channel with a discrete roughness in the form of semispherical dimples. The methodology provides a possibility of computerized parametric calculations that adequately enough model the examined physical phenomena and allow to determine their characteristics being of practical interest. The efficiency of the examined discretely rough surface was estimated based on the coefficients of heat transfer and hydraulic resistance.

    • CALIBRATION OF AN ARTICULATED VEHICLE MODEL

      pg(s) 65-68

      A model of an articulated vehicle (tractor with a trailer and/or semitrailer) formulated using joint coordinates and homogenous transformations is presented. Experimental measurements of yawing velocities of the vehicle units have been carried out for a sharp turn manoeuvre. These results are used to calibrate the mathematical models. Using optimisation methods the parameters of tires for the Dugoff-Uffelman model are chosen in such a way that the results of calculations and measurements are compatible.

    • THE THEORETICAL ESTIMATION OF THE TRACTOR DRIVE WHEELS SLIPPAGE WITH THE VARIABLE TIRE INFLATION PRESSURE.

      pg(s) 69-72

      The main tractor parameters that defy suitability of tractors to perform traction work is traction power and driven axle wheel-slide. Different mass tractors wheel-slide on the same soil differs and depends on the vertical load (G), which falls on the driven axle wheels. When choosing tractors and agriculture implements it is needed to foresee the formed implements traction and economical parameters. To achieve this goal mathematical modeling methods are used. The purpose of mathematical modeling is to
      determine traction characteristics of the tractor, taking into account various factors. At this moment there are tractor traction models created, that describe various agriculture and field tasks. Most Mathematical models mainly assess the hardness of the soil and driven wheel geometrical parameters. However, one of the most important parameters in assessing the suitability of a tractor unit is the tractors driven wheels slide. To decrease wheel-slide and to increase the driving wheels grip with soil there are different methods being used: Ballast weights, use of twin wheels and changeable air pressure in the tires. However current mathematical models do not consider the change of air pressure in tires. A mathematical module was created, which takes into calculations the driven wheels wheel-slide having different air pressure in the tires.

    • MODELLING AND SIMULATION OF HIGH-FREQUENCY AUTONOMOUS PUBLIC-TRANSPORT SERVICE

      pg(s) 73-80

      In this paper, a simulation model of the novel concept of autonomous vehicles is developed for public transport (PT) service. The model aims to serve PT planners as a tool enabling the simulation of a metro-like, high-frequency service with punctual autonomous vehicles running on exclusive lanes. The model was applied in a numerical example of a passenger bus, with different scenarios employed. The outcome of the simulation shows that characteristics of the modelled system are reproduced, with the following results: (i) highfrequency, metro-like PT service, with reduced passenger waiting time, (ii) reduced vehicle capacity with reduced average dwell time; (iii) the least number of unserved passengers, across all scenarios, and (iv) better utilisation of vehicle capacity (with fewer unserved passengers) achieved through a small decrease in vehicle frequency, which led to a negligible increase of the average passenger waiting times. In addition, the model allows us to examine the system’s behaviour under uncertainty, considering passenger arrivals and vehicle headways as random input variables with predefined probability distributions. The proposed model enables modellers not only to evaluate a system’s performance, but also to examine different working conditions and possible future scenarios.

    • INTERDISCIPLINARY TASKS AS A MEANS FOR FORMING TECHNICAL COMPETENCE OF THE FUTURE TEACHERS OF INFORMATICS

      pg(s) 81-83

      The article describes the possibilities of realization of interdisciplinary links in the process of forming the technical competence of future computer science teachers in the study of general computer disciplines. The author offered content and integrated tasks of an interdisciplinary nature, which make it possible to form the technical competence of specialists.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • COMPLEX SYSTEM, UTILITY AND DECISION CONTROL: A RISK PORTFOLIO OPTIMIZATION CASE

      pg(s) 84-87

      The decision making is based on the objective preferences and starting from this position the incorporation of human preferences in complex systems is a contemporary trend in scientific investigations. In Complex system where a human participation is decisive for the final decision the human thinking, notions and preferences have cardinal significance and need analytical representation. Mathematical modeling of complex „human – process” systems and build mathematically well-founded control solution need analytical representation of quantitative information like preferences. This could be made by utility theory and stochastic approximation theory. The objective of the paper is to present a strict logical mathematical approach for modeling and estimation of human preferences as machine learning in the process of building of mathematical models of complex systems with human participation. The approach is demonstrated on a case study in the area of risk portfolios optimization and financial risk management with color noise. The objective of the paper is to present a mathematical approach for modeling and estimation of human preferences as machine learning in the process of building of mathematical models of complex systems with human participation.