scholarly journals Semi-Markov Model of the System of Repairs and Preventive Replacements by Age of City Buses

2021 ◽  
Vol 11 (21) ◽  
pp. 10411
Author(s):  
Klaudiusz Migawa ◽  
Sylwester Borowski ◽  
Andrzej Neubauer ◽  
Agnieszka Sołtysiak
Keyword(s):  
Mathematical Model ◽  
Markov Processes ◽  
Point Of View ◽  
Renewal Processes ◽  
Limited Extent ◽  
Preventive Replacement ◽  
City Bus ◽  
Criterion Functions ◽  
Semi Markov Processes ◽  
The Mathematical Model

The paper presents a mathematical model of the system of repairs and preventive replacements by age of city buses. The mathematical model was developed using the theory of semi-Markov processes. In the model developed, four types of city bus renewal processes are considered and three types of corrective repairs and preventive replacement. Corrective repairs are considered in two types: minimal repairs (repairs carried out by the Technical Service units) and perfect repairs (repairs carried out at the stations of the Service Station). The models of restoration systems that use semi-Markov processes in which minimal repairs, perfect repairs, and preventive replacements by age, have been examined in the literature to a limited extent. The system under consideration is analysed from the point of view of two criteria: profit per time unit and availability of city buses to carry out the assigned transport tasks. Conditions of criterion functions’ extremum (maximum) existence were formulated for the adopted assumptions. The considerations presented in the paper are illustrated by exemplary results of calculations.

The Properties of Two-Way Cartridge Valve in Water Hydraulic through Matlab/Simulink

2012 ◽  
Vol 271-272 ◽  
pp. 1073-1076
Author(s):  
Zhen Hua Duan ◽  
Zhang Yong Wu ◽  
Qing Hui Wang ◽  
Xi Wu ◽  
Cheng Zhuo Wen
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Point Of View ◽  
Matlab Simulink ◽  
Practical Point ◽  
Structure Characteristics ◽  
Water Hydraulic ◽  
The Mathematical Model

According to the requirements of hydraulic transmission to two-way cartridge valve, and from the practical point of view a water hydraulic two-way cartridge valve was designed. Then its structure characteristics was introduced and the mathematical model was established. The simulation analysis of the water hydraulic two-way cartridge valve has been carried out through Matlab/Simulink proving that its structure was reasonable and it had good performances.

NUMERICAL AND PROGRAM IMPLEMENTATION OF A ONE-DIMENSIONAL MATHEMATICAL MODEL OF HYDRAULIC FRACTURING

2021 ◽  
Vol 7 (1) ◽  
pp. 126-145
Author(s):  
Alexey S. SHLYAPKIN ◽  
Alexey V. TATOSOV
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Program Implementation ◽  
Software Package ◽  
Import Substitution ◽  
Point Of View ◽  
Growth Potential ◽  
Design Problems ◽  
Software Market ◽  
The Mathematical Model

At present, an active policy of import substitution is being pursued, dictated by the imposed international sanctions, which creates a need for finding optimal engineering solutions, in particular, in the field of creating Russian software. In the study and design of hydraulic fracturing, they often rely on the results of modeling in specialized simulators. The appearance of the Russian products on the software market, surely, sets the correct vector of development; however, some aspects are not implemented in the existing mathematical models. The authors of this article present a model that allows considering in detail the process of movement of proppant particles in a hydraulic fracture. The chosen direction is important from the point of view of calculating the fracture cavity and refining its productivity, since the behavior of the particles has a significant effect on both the growth potential of the crack and its shape. The research methodology includes a theoretical justification of the mathematical model presented by the authors in their previous works; a description of the basic principles of selecting and constructing a numerical calculation scheme and creating a software package. The main methods of research are the methods of mathematical modeling, formed from practical problems on the estimation of geometric parameters of the crack, including the areas of continuum mechanics and fracture of solids, underground hydrodynamics. The proposed and implemented numerically mathematical model forms the basis of the authors’ software package, which allows solving the main design problems when performing hydraulic fracturing operations.

Mathematical Model of the Servo Drive with Friction Wheals. Simulations and Real Object Examination Results

2013 ◽  
Vol 198 ◽  
pp. 15-20 ◽  
Author(s):  
Lukasz Fracczak
Keyword(s):  
Mathematical Model ◽  
Cardiac Surgery ◽  
Control System ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Real Object ◽  
Servo Drive ◽  
Two Degrees Of Freedom ◽  
The Mathematical Model

In this paper the servo drive with friction wheels is presented. The servo drive is designed to move the automatic laparoscope tool or laparoscope camera (thereinafter laparoscope sleeve or sleeve) in two Degrees of Freedom (DOF). The description of the drive mechanism, operating principle and mathematical model of this drive is presented. Based on this model, the Control System (CS) has been created, and used to the construction of a simulation model. The simulation illustrates the proper functionality of the mathematical model of the servo drive with the described CS. This paper also presents the servo drive test stand and the most important examination results from the point of view of using them in the cardiac surgery Robin Heart robot.

scholarly journals Optimisation of a clam bunk skidder from the emission production point of view

2012 ◽  
Vol 58 (No. 4) ◽  
pp. 136-141
Author(s):  
A. Janeček ◽  
R. Adamovský
Keyword(s):  
Mathematical Model ◽  
Production System ◽  
Operating Performance ◽  
Point Of View ◽  
Optimal Rate ◽  
Simple Mathematical Model ◽  
Operation Performance ◽  
The Mathematical Model

This article presents a proposal of a simple mathematical model for minimisation of the production of extraneous substances as a function of the rate of operation performance of a production system. The model is then verified by operation tests of the Terri 2040 clam bunk skidder and by determining the system&rsquo;s optimal rate of performance from the point of view of production of SO<sub>2</sub>, HC and NO<sub>x </sub>emissions. The operation tests conducted to verify the mathematical model have confirmed that conditions can be determined for the production system at which it produces minimum emissions. Min. values of SO<sub>2</sub>, and HC were achieved at approximately the same rate of performance of the clam bunk skidder. Minimum values of NO<sub>x </sub>were achieved at significantly higher rate of performance of the equipment. At the calculated optimal rate of operating performance of the Terri 2040 clam bunk skidder, the values of the produced emissions were determined per m<sup>3</sup> of timber: SO<sub>2</sub> = 1.00035 g/m<sup>3</sup>, HC = 7.796 g/m<sup>3</sup> and NO<sub>x</sub> = 0.277 g/m<sup>3</sup>.

Limit theorems for α-recurrent semi-Markov processes

1976 ◽  
Vol 8 (03) ◽  
pp. 531-547 ◽  
Author(s):  
Esa Nummelin
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transition Probabilities ◽  
Renewal Processes ◽  
Markov Renewal Processes ◽  
Semi Markov Process ◽  
Limit Behaviour ◽  
Semi Markov Processes ◽  
Special Case

In this paper the limit behaviour of α-recurrent Markov renewal processes and semi-Markov processes is studied by using the recent results on the concept of α-recurrence for Markov renewal processes. Section 1 contains the preliminary results, which are needed later in the paper. In Section 2 we consider the limit behaviour of the transition probabilities Pij (t) of an α-recurrent semi-Markov process. Section 4 deals with quasi-stationarity. Our results extend the results of Cheong (1968), (1970) and of Flaspohler and Holmes (1972) to the case in which the functions to be considered are directly Riemann integrable. We also try to correct the errors we have found in these papers. As a special case from our results we consider continuous-time Markov processes in Sections 3 and 5.

Simulation Model of the Thermodynamic Cycle of a Three-Cylinder Double-Acting Steam Engine

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
Evzen Thoendel
Keyword(s):  
Mathematical Model ◽  
Thermodynamic Cycle ◽  
Steam Pressure ◽  
Heat Energy ◽  
Point Of View ◽  
Steam Engine ◽  
Pressure Reduction ◽  
Software Environment ◽  
The Mathematical Model ◽  
Pressure Reduction Station

Today, steam engines are used for special purposes only, for example to reduce steam pressure in pressure reduction stations, where they replace the traditional and inefficient throttling process. Throttling is the most used way to control the pressure in steam reduction stations. This way is unsatisfactory from the economical point of view, because the exergy is lost uselessly. It is a part of heat energy that can perform a work. The better way of a pressure reduction is an expansion in a backpressure turbine or in a steam engine by simultaneous transformation of the heat energy into electricity (cogeneration). This article describes the design and implementation of the mathematical model of a steam engine used as pressure regulator in a pressure reduction station. The present model is a part of a comprehensive mathematical model of a cogeneration unit and also a part of the author's doctoral thesis. The model assumes detailed mathematical description of physical processes in a steam engine and implementation in an MATLAB-SIMULINK software environment.

Limit theorems for α-recurrent semi-Markov processes

1976 ◽  
Vol 8 (3) ◽  
pp. 531-547 ◽  
Author(s):  
Esa Nummelin
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transition Probabilities ◽  
Renewal Processes ◽  
Markov Renewal Processes ◽  
Semi Markov Process ◽  
Limit Behaviour ◽  
Semi Markov Processes ◽  
Special Case

In this paper the limit behaviour of α-recurrent Markov renewal processes and semi-Markov processes is studied by using the recent results on the concept of α-recurrence for Markov renewal processes. Section 1 contains the preliminary results, which are needed later in the paper. In Section 2 we consider the limit behaviour of the transition probabilities Pij(t) of an α-recurrent semi-Markov process. Section 4 deals with quasi-stationarity. Our results extend the results of Cheong (1968), (1970) and of Flaspohler and Holmes (1972) to the case in which the functions to be considered are directly Riemann integrable. We also try to correct the errors we have found in these papers. As a special case from our results we consider continuous-time Markov processes in Sections 3 and 5.

scholarly journals Mathematical model of the road vibrating roller

2020 ◽  
Vol 1 (1) ◽  
pp. 133-139
Author(s):  
Pavel Aleksandrovich KORCHAGIN ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Road Construction ◽  
Well Being ◽  
Point Of View ◽  
Engineering Industry ◽  
Supporting Surface ◽  
The Road ◽  
Vibration Protection ◽  
The Mathematical Model

Introduction. The process of compaction of the soil foundation by a road vibrating roller is considered as the object of the study. The main purpose of vibrating rollers used in road construction is to reduce the energy consumption of the compaction process and increase the productivity of the operations performed Since the 80s of the last century, the engineering industry has noted a tendency to abstention the production of static rollers. By reducing the amplitude of oscillations or completely disconnecting the vibrator, you can get the same static modes, and accordingly the results of rolling. In addition, the reduction of dynamic impacts positively affects the physical condition of an operator of the road-building machine, stabilizes the well-being and increases productivity. Materials and methods. The mathematical model of the dynamic system “Supporting surface–roller–operator” is presented. The main components of the dynamic system are described in the form of ordered and interacting subsystems. The forces acting on the dynamic system are determined; they are sources of dynamic effects. The calculation schemes of the subsystems “Operator” and “Roller”, which are of the greatest interest from the point of view of vibration protection, are reflected. Results. The result of the work can be considered the compilation of generalized scheme of the dynamic system; calculation scheme of the dynamic system; mathematical model “Supporting surface–operator–roller”; implementation of the mathematical model in MathLab, its additional Simulink extension package. Discussion and conclusion. The presented mathematical model allows carrying out research of the processes occurring in the dynamic system “Supporting surface–roller–operator”. The most rational mathematical model can be used in the development of methods and tools aimed at improving the vibration protection system for operators of road rollers. The mathematical model of a road roller is planned to be used as a basis for creating a robotic complex with an automated control system designed to perform operations to compact coatings and foundations in road construction.

On the entropy for semi-Markov processes

2003 ◽  
Vol 40 (4) ◽  
pp. 1060-1068 ◽  
Author(s):  
Valerie Girardin ◽  
Nikolaos Limnios
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Relative Entropy ◽  
Continuous Time ◽  
Entropy Rate ◽  
Renewal Processes ◽  
Semi Markov Process ◽  
Continuous Time Processes ◽  
Semi Markov Processes ◽  
Jump Markov Processes

The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

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