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154 Scientific Journals 24(96)

Scientific Journals

Zeszyty Naukowe

Maritime University of Szczecin

Akademia Morska w Szczecinie

2010, 24(96) pp. 154–157 2010, 24(96) s. 154–157

The method for selection of technical objects to be used

in an operation system

Metoda doboru obiektów technicznych do użytkowania

w systemie eksploatacji

Maciej Woropay, Daniel Perczyński

University of Technology and Life Sciences, Machine Maintenance Department Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy, Zakład Eksploatacji Maszyn 85-791 Bydgoszcz, ul. Prof. S. Kaliskiego 7, e-mail: perkol@utp.edu.pl

Key words: method for selection, urban transport system, Markov process, operation and maintenance

process

Abstract

The article presents a method for choosing technical objects to be used for execution of tasks by a control subsystem. The research object used to illustrate the discussion presented in the paper is a municipal bus transport network, in a given agglomeration. In order to solve the discussed problem the homogenous Markov's process has been accepted to be a mathematical model of the bus operation process. The ratio of the object's mean probability of being in its serviceability state to a time unit ,has been accepted as a criterion for choice (purchase) of a given make of the bus.

Słowa kluczowe: metoda doboru, transport miejski, jednorodny process Markowa, proces eksploatacji Abstrakt

W artykule przedstawiono metodę doboru obiektów technicznych do realizacji zadań przyjętych przez pod-system sterujący. Obiektem badań, na którym zilustrowano rozważania przedstawione w niniejszej pracy, jest system eksploatacji autobusów komunikacji miejskiej w wybranej aglomeracji. W celu rozwiązania omawia-nego problemu przyjęto założenie, że matematycznym modelem procesu eksploatacji autobusów jest jedno-rodny proces Markowa. Jako kryterium wyboru (zakupu) określonej marki autobusu do eksploatacji przyjęto wskaźnik prawdopodobieństwa przebywania obiektu technicznego w stanie zdatności na jednostkę czasu.

Introduction

The paper presents a method for selection of technical objects which are to be used for execution of tasks by a control subsystem. The research object is an operation system of municipal bus transport (ZKA), in a given urban agglomeration. Effects resulting from the operation of the analyzed system are closely related to its management rationality, understood as an ability to control resources, processes and information in order to optimize their use. A method for an optimal choice of a transport means, in a municipal bus transport network, has been demonstrated in the paper.

The research object

The research object used for illustration of the discussion presented in the paper is a municipal bus transport network in a given agglomeration. The main goal of the considered network is accom-plishment of effective and safe passenger transports with the use of bus transport means, within the assigned quantity and territory.

For the purposes of this research, there have been distinguished two basic subsystems of the analyzed municipal bus transport network operation (Fig. 1):

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Method for selection of technical objects to be used in an operation system

Zeszyty Naukowe 24(96) 155

 executive subsystem, made up of elementary subsystems (driver-bus), which perform the network main tasks (passenger transports);  subsystem providing serviceability, made up of

its particular subsystems performing diagnostics, and repairs, providing services, and supplying elementary subsystems of the executive system.

Fig. 1 A scheme of simplified structure of the analyzed municipal bus transport network

Rys. 1. Schemat uproszczonej struktury analizowanego system miejskiej komunikacji autobusowej

A direct execution of the system tasks is the responsibility of the executive subsystem contain-ing elementary subsystems of the type H – TO (driver-bus), where the man is coupled with the technical object by a structure of series type. Relia-bility of the operated technical objects is main-tained at a proper level thanks to performance of servicing within the subsystem of serviceability ensuring. The subsystem providing the object with serviceability contains two subsystems:

 a subsystem of providing serviceability in a ser-vice station (SS) situated within the Bus Trans-port Company (BTC), consisting of its particular subsystems, where diagnostics, servicing and repairs are performed,

 a subsystem of providing serviceability by tech-nical service units (TS).

The analyzed system consists of two depots in which there are service stations for vehicles: • depot no. 1 with a service station no. 1 – (SS1), • depot no. 2 with a service station no. 2 – (SS2). The service stations perform all the actions which aim at ensuring serviceability and they carry out diagnostic processes, including:

 daily servicing,  overhauls,  current repairs,  technical state checks.

Within the subsystem ensuring serviceability there is also a subsystem, the so called local servicing units, a set of technical service units. The main tasks of the units are: providing buses which are outside the depot with serviceability, in the

shortest period of time, or towing damaged buses to service stations (in case there is no possibility to repair them in the place they are).

After having completed all the services the roadworthy vehicle is referred to the executive subsystem (stand-by and operating – if the number of vehicles in the operating system is too small for the tasks to be performed). The duration time of the vehicle servicing (the vehicle being in the system ensuring its serviceability) is of random character. For further considerations there has been accepted that in the system, there are used homogenous objects.

Selected results of preliminary operation tests Within the initial tests, performed in a real municipal bus transport network, an analysis of times during which the buses were in the specified states of their operation was made. The tests were carried out in natural conditions with the use of a passive experiment method.

The tests results discussed further, are concerned with buses of Mann make (16 vehicles) and Volvo (90 vehicles) used in the analyzed system and they cover the time period from 01.01.2008 to 30.06.2008. In tables 1 and 2 there are results of initial tests concerning selected time statistics of:  appropriate operation of buses (T1),

 renovation of the bus by a technical service (T2),

 renovation of the bus by the service station (T3),

 whereas in figure 2 there is presented a time distribution for proper operation of the Mann make buses in the form of a frequency histo-gram.

The analysis of service times performed by technical service, accounted only for services due to which there occurred a delay of a transport task accomplishment. However, data on the times of services provided in service stations included only

Executive subsystem

Serviceability ensuring system

TS SS

System of municipal bus transport operation

Table 1. Values of selected statistics of the examined features for Volvo buses

Tabela 1. Wartości wybranych statystyk badanych cech dla autobusów marki Volvo

Volvo Statistics T1 T2 T3 Number of observations 823 474 407 Mean value 242.5 1.13 1.67 Standard deflection 289.9 0.72 0.85 Minimum 0.34 0.03 0.47 Maximum 2237.67 4.88 7.23 Gap 2237.33 4.85 6.76 Difference 84092.40 0.51 0.73 Mediana 143.65 143.65 1.40 Mode 24 1.00 1.07

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Maciej Woropay, Daniel Perczyński

156 Scientific Journals 24(96)

those which were the effect of the technical object damage occurred during the task accomplishment (resulting in a loss of a ride).

0 400 800 1200 1600 2000 2400 T1 [hours] 0 10 20 30 40 50 60 fre qu en cy

Fig. 2. Histogram of Mann buses appropriate operation time Rys. 2. Histogram czasu poprawnej pracy autobusów marki Mann

Model of the operation process carried out in the research object

In result of the research object identification, there have been distinguished three, significant in terms of the paper goal, operation states, that is [1]:

S1 – operation state, accomplishment of transport

tasks,

S2 – renovation state executed by the technical

service units,

S3 – renovation state executed in the service

station.

An assumption has been accepted that the initial mathematical model of the bus operation process is a stochastic process {X(t), t  0}. The analyzed stochastic process {X(t), t  0} has a finite phase space S, S = {S1, S2, S3}. Markov’s theory of

homogenous processes has been assumed to be used for the description of the analyzed technical objects operation process analysis.

Fig. 3. A directed graph of the operation process Rys. 3. Graf skierowany procesu eksploatacji

The intensity the analyzed process transitions is rendered in the form of the so called transition intensity matrixes                   2 2 3 3 1 1 2 1 2 1 0 ) ( ) (           (1)

Mathematical model of the operation process

The choice of a mathematical tool for a descrip-tion of the examined operadescrip-tion process (carried out in the research object) was made on the basis of the following premises:

 the research goal;

 the model accuracy to reflect the real process;  complexity degree of the applied mathematical

tool;

 possibility of obtaining data on the operation process, executed in the research object.

In result of the carried out analysis of assump-tions and constraints, the Markov’s process and the theory concerning the process analysis, are consi-dered as being the best tool – in terms of the research goal – for mathematical modeling of a real operation process, executed within the research object. Stochastic process X(t) being a homogenous Markov’s process with a finite set of states S, can be fully defined by means of [2, 3]:

 the initial process distribution X(t),

 matrix A of the Markov’s process states change intensity.

Using the homogenous Markov’s process for mathematical modeling of the operation process for the research purposes, a basic assumption has been accepted that this process is good enough, in terms of the research goal, to reflect the real operation process. S1 S2 S3 1 2 1 2 3

Table 2. Values of the examined features selected statistics for Mann buses

Tabela 2. Wartości wybranych statystyk badanych cech dla autobusów marki Mann

Mann Statistics T1 T2 T3 Number of observations 174 89 87 Mean value 295.06 1.15 1.71 Standard deflection 353.74 0.54 1.15 Minimum 7.22 0.05 0.23 Maximum 1824 2.75 6.17 Gap 1816.78 2.70 5.94 Difference 125131.0 0.29 1.32 Mediana 165.81 1.15 1.30 Mode 48 1.67 0.92

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Method for selection of technical objects to be used in an operation system

Zeszyty Naukowe 24(96) 157

Matrix algorithm of a differential equation system solution for Markov’s process

Using the theory of Markov’s processes it is possible to determine probabilities Pi(t), i = 1, 2, 3

of the technical object’s being in the distinguished operation states S, for the operation process model. For this purpose, it is necessary to solve a N Kołmogorow’s system of differential equations, in the form:

P'(t) = P(t)  (2)

where: P'(t) – column vector consisting of derivatives Pi'(t), P(t) – vector of unconditional

probability Pi (t),  – matrix of the process states

change intensity.

In order to determine value Pi (t), i = 1, 2, 3

a calculation algorithm has been developed and a computer program has been written in Turbo Pascal v 6.0 [4] language.

Method of selection technical objects for use in an operation system

In the system of a public bus transport operation, there are used different technical objects. If there is a necessity of buying a bus, the system decision makers are faced with the problem of choosing a proper make. A ratio of the bus probability of being in the serviceability state in a time unit, has been accepted as a criterion deciding on a purchase of a given technical object, which is given with the use of the following dependence:

 

 

a t a u t t t P t W a

 0 1 d (3) where: t – the time of analysis, P1(t) – probability

of the bus being in the state of operation.

As the ratio value depends on the value of parameters defining the model (of the operation process for a bus of given make) can be diagnostic signal on the usefulness of the given type of object for operation in the system existing operation conditions.

In order to illustrate the discussion, values of ratio Wu (ta) were determined for two buses

of selected makes. Data concerning the expected value E(T) of the time of the analyzed objects appropriate operation, is presented in table 3.

Table 3. Expected values of appropriate operation for buses of analyzed makes

Tabela 3. Wartości oczekiwane czasu poprawnej pracy autobu-sów analizowanych marek

The bus make Volvo Mann

Value E(T1) [h] 242.50 295.06

The remaining basic data defining the operation process model for buses of selected makes has been given in tables 4 and 5. In table 6, there have been presented the obtained values of W ratio for accepted calculation variants and the analysis time

t = 100 hours.

Table 4. Initial data for a Mann bus calculations

Tabela 4. Dane wejściowe do obliczeń autobusu marki Mann

1 2 1 2 3

0.0017 0.0016 0.6216 0.5848 0.27 Table 5. Initial data for a Volvo bus calculations

Tabela 5. Dane wejściowe do obliczeń autobusu marki Volvo

1 2 1 2 3

0.0015 0.0026 0.5575 0.5988 0.3274 Table 6. Values of Wu index for particular calculation variants

Tabela 6. Wartości wskaźnika Wu dla poszczególnych

warian-tów obliczeń

variant mann Volvo

Wu 0.9912 0.9961

From the analysis of the examined value index it results that a purchase of a Volvo bus would be a better solution for the accepted criterion.

Conclusions

The goal of the paper was to develop a method for choice of technical objects to accomplish tasks accepted by the control subsystem, with the use of the Markov model of the operation process, after a change of the model initial parameters values. The change of initial parameters values simulates the influence of internal and external factors on the system behavior.

References

1. LANDOWSKI B., WOROPAY M., PERCZYŃSKI D.: Method

of supporting the decision makers in the control process of a transport system operation. Systems Research Institute of the Polish Academy of Sciences, Warsaw 2004. 2. BUSLENKO N., KAŁASZNIKOW W., KOWALENKO I.: Theory

of complex systems. PWN, Warszawa 1979.

3. SOŁOWIEW A.D.: Analytic methods in reliability theory.

WNT, Warszawa 1983.

4. KNOPIK L.,LANDOWSKI B.,PERCZYŃSKI D.: Prognozowanie

stanu systemu eksploatacji transformatorów rozdzielczych na podstawie badań modelowych. Zagadnienia eksploatacji maszyn, PAN, Radom 2002, 4(132), 37, 2002, 163–175.

Recenzent: prof. dr hab. inż. Oleh Klyus Akademia Morska w Szczecinie

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