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DETERMINATION OF THE AVAILABILITY FACTOR OF FIBER OPTIC COMMUNICATION LINES DEPENDING ON EXTERNAL ACTIONS AND DIAGNOSIS ERRORS
The article deals with the method for the assessment of the fiber optic communication lines (FOCL) reliability taking into account the effect of the optical fiber tension, the temperature influence and the built-in diagnostic equipment errors of the first kind. In the operation process of FOCL is necessary to monitor their status. Diagnostic and control facilities have integral transducer-converter, providing information on his status and analyzed device structurally isolated from the unit under test. Errors in measurement and control devices, the diagnosis equipment failure, and the human-operator participation lead to the need to take into account the real possibility of errors under testing status. The reliability is determined using the theory of Markov chains and probabilistic mathematical modeling. The reliability is assessed in terms of the availability factor. The external factors include temperature fluctuations and increased strain of fibers. If the strain of the optical fiber exceeds a critical value, the OF will have irreversible changes. It can significantly decrease the lifetime of OF in FOCL in general.For detection OF sections with increased strain and changed temperature the Brillouin optical time-domain reflectometers (BOTDR) are applied. The distribution of Mandelstam - Brillouin backscattering spectrum along the OF is registered and analyzed in BOTDR. The BOTDR application in the monitoring system of OF in FOCL makes it possible to increase the detection efficiency of sections with a modified strain or temperature. To obtain a mathematical model the following steps are performed: the FOCL state is defined and validated; the state graph and system transitions are described; the system transition of states that occur at a certain point are specified; the real and the observed time of system presence in the considered states are identified. According to the permissible value of the availability factor, it is possible to determine the limiting frequency of FOCL maintenance. The work was performed with the financial support of the Ministry of Education and Science of the Russian Federation within the scope of the base part of a State Assignment within the sphere of scientific activity (Project No. 8.9334.2017/8.9).
Information about authors:
Igor V. Bogachkov, Associate professor (docent) of "Communication means and information security" department of Omsk State Technical University (OmSTU), Omsk, Russia
Sergey S. Lutchenko, Associate professor (docent) of "Communication means and information security" department of Omsk State Technical University (OmSTU), Omsk, Russia
Evgeny Y. Kopytov, Associate professor (docent) of "Communication means and information security" department of Omsk State Technical University (OmSTU), Omsk, Russia
Для цитирования:
Богачков И.В., Лутченко С.С., Копытов Е.Ю. Определение коэффициента готовности волс в зависимости от внешних воздействий и ошибок диагностирования // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №6. С. 51-55.
For citation:
Bogachkov I.V., Lutchenko S.S., Kopytov E.Y. (2018). Determination of the availability factor of fiber optic communication lines depending on external actions and diagnosis errors. T-Comm, vol. 12, no.6, pр. 51-55.
Igor V. Bogachkov,
Omsk State Technical University (OmSTU), Omsk, Russia, bogachkov@mail.ru
DOI 10.24411/2072-8735-2018-10108
Sergey S. Lutchenko,
Omsk State Technical University (OmSTU), Omsk, Russia, lutchenko_s@inbox.ru
The study was financially supported by the Ministry of Education and Science of the Russian Federation within the framework of the basic part of the state task in the field of scientific activity (project No. 8.9334.2017/8.9, the Research Advisor is Igor V. Bogachkov).
Evgeny Y. Kopytov,
Omsk State Technical University (OmSTU), Omsk, Russia, jenya87@list.r
Keywords: optical fiber tension, fiber optic communication line, Mandelstam-Brillouin scatter, early diagnostics, temperature influence, diagnostic errors, mathematical model, availability factor.
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in addition, temperature fluctuations in OF can signal the emergence of a "problem" section on the FOCL routing. For instance, the increasing temperature of the OF section can he observed in the burst main on the OC routing. Also there is the decreasing temperature of FOCL section in winter because of the destruction on the OC routing. The 3D-re Hectogram is represented in Fig.l, wherein the distribution of Mandelstam - Brillouin backscattering spectrum along the optical waveguide is composed of different OF: G. 652+G. 657+G. 655, with some sections heated to +70 °C (shown by markers 1-2 (G. 652), 3-4 (G. 657) 5-6 (G, 655)).
These characteristics are attained in a Brillouin optical timedomain re Hectometer (BOTDR) "Ando AO 8603". The suitable distribution of the strain along the fiber length is shown in Fig. 2.
Similar characteristics were obtained for OF, which were under the influence of longitudinal tensile loads |3,4j.
In determining the availability factor the diagnosis errors of first kind of built-in test equipment are taken into account, flic method is based on theory of Markov chains and probabilistic modeling [5-71.
We performed the following steps to obtain a mathematical model.
1. The FOCL state is defined and validated.
2. State graph and system transitions are described.
3. The system transition from state to Sj that occur at a certain point are specified
4. The real and the observ ed time of system presence in the considered states are identified.
The transition probability graph of FOCL is presented in Fig. .3.
Figure 3. The transition probability graph of FOCL
A perfect and up state Sq is initial status of a system. After a random time t a critical failure can happen in the system, it will be detected with a probability of F02(T) and the system will
pass into state Sj and then after recovery time ir it will pass to the perfect state So with probability one.
If the failure is not detected by the integral diagnostic tools, the system will go into a fictitious failure slate S} with a probability of a[ iT) - [l - F01(T)]- After a fault correction time the
system will move to operational condition So with probability one , If during the maintenance period T the system hasn't failures, it will pass into the maintenance state Sjo with a probability of (l -«,(7"))-[l — /-^(7*)]- During the maintenance period
actions of personnel can lead to the failure in the system, so it can go into a slate of critical failure S2. If during the reconstruction work of the system failures are not occurred, the system w ill return to up state S» and its operation will start in a new cycle.
The matrix of transition probability graph of this system is given by:
P=
0 1
0
l-FM
(1 -fi(T)) FJT) fi{T)-FJT) l-FJT)
0 0 0
0 0 1
KMU 0 0
(i)
The further calculation is the same as the definition of dependence a, (T) [6, 7].
Let us write a row matrix for final probabilities:
fr=\n0(T),n2(TU,(TUr„(T)\ (2)
The follow conditions must be satisfied to find final probability of system presence in the St states: '7i0(T) = n2(T) + jr10(T), ^(f) =n,(T) ■ (1- £ (7-)) • (T),
= **(T).[l-Fm{T)]+ *t(T% 5,(7") + x2(T) + 7Tt(T) + nn(T) =1. (3)
Let us solve the combined equation (3) and get an expression for the final probability:
<4>
For convenience, we represent the expression as shown in Eq.(4):
(5)
Thus, we can write the equations for the final probability based on the (4).
^(7') = (l-^1(7')).Jr(i;(7-)-^. (6)
Xjn-fr (7)
ZnAT) = [1 - Fm(T)]~ + A (T) ■ F„2(T) ■ I. (8)
The real lime of system presence in the state Sn is given by:
t t
®0(n= P02 ¡T02dFipM()2)+PM \^dFiH{TM ) +
I
+POTO J1
(9)
'OTO^FOTO\1OTO )
> ( r0TD )■
Lei us write the distribution function for a single step of the process:
KAT)
, npu t <T
I, npur>T
(10)
F„(z)
, npu t <t
Fm(T)
1, npu t>T (11)
|0, npu r <T
[l, npiir>T (12)
We substitute the obtained distribution functions for a single step of process in (9) to obtain the following expression:
(13)
f02(t)
(T) ■ F,, en Jrrf-^g + [ 1 - to]-r-
F"m I ' I
(T)
7TT
Modified equation (13):
r
0
t
+/3x{T)\nlFm{t)+[\-Fm(T)\T.
(14)
con(T)=(\-px(T))-
tfm{t)-\f01(z)dr
T'F02(T)-\F(,2(T)dT
(15)
After simplification the expression o>|](T) becomes:
(on(T)=T-)Fn2{T)dr.
0
The observed time of presence in state S(J is:
t t
Pm
(16)
(17)
+PIITO jToTodF(iTO (rom )■
mction:
i
•, tipu r <T
The distribution functions for a single step of the process are:
Fm(T)
1, up 11 r>T
0, npu r < T
1, npu t > T t 0, npu t <T
(18) (19) (20)
0 '02
(T)-Fi12(T)T + (7-)]-7-. Thus:
7 »
(21)
T-W)-¡F02(T)dT
+A(T)-F„2(T)-T+[\-Fa2(T)}T.
After conversion the equation y„(T) becomes:
n(f)=r - ]f6At)c!t +f^{T)\Fyi(r)dr.
(22)
(23)
(24)
0 0
The observed time of the system presence in a state of critical failure St is determined by components of recovery lime:
(25)
vt{T) = T.
Availability factor for this system is:
x0(T)v0(T) + nt<T)v2(T) + mA(T)v4(T) (27)
0999S
09996
k^ti
09991
om
[1, npu r > T t We now substitute the determined distribution functions for a single step of process in (¡7) to get the following equation:
Fl]2 (r)
The time in a state of dormant failure S4 is equal to an operating lifetime of the system as a built-in diagnostic system is not able to detect failures of this type.
0 600 1.^1^1 SkIO^LO3 3X10s 36=.1 D3Î 1035IO5 &103
Figure 4. The availability factor of FOCL as a function of external actions
For the task solution of detection OF sections with increased strain and changed temperature the Brillouin optical time-domain reflectometers {BOTDR) arc applied. In BOTDR the distribution of Mandelstam - Brillouin backscattering spectrum along the OF is registered and analyzed.
The BOTDR application in the monitoring system of OF in FOCL makes ii possible to increase the detection efficiency of sections with □ modified strain or temperature.
References
1. Bogachkov I. V.. Gorhv N.I. Methods and means of moniioring and early diagnostic of fiber optic communication lines. Omsk: O111STU, 2013, p. 192.
2. Bogachkov 1. V., Gorlov N.I. Detection of sections with a modified temperature of fiber optic communication lines 011 the basis of Brillouin reflectometry method // Journal of SibSUTl. Novosibirsk: SibSUTl, 2015. Vol.4(32). pp. 74-81,
3. Bogachkov I. V. Investigation of influence of essential stretching forces in optical libers 011 brillouin backscattering Spectrum // Systems of Signal Synchronization, Generating and Processing in Telecommunications (SINKHRO1NFO-2016) 2016. Samara, 2017,"pp. 136-139.
4. Bogachkov I. K. Gorlov N.I. Experimental researches of influence of longitudinal stretching loads on brillouin back scattering spectrum ¡11 optical fibers//Journal of SibSUTl. Novosibirsk: SibSUTl, 2015. Vol. 3 (31). pp. 81-88.
5. Lutchenko S.S., Kopytov EY. The methods of definition of the quantitative evaluation of internal safety of communication systems on the basis of the railway transport / 12th International Conference 011 Actual Problems of Electronic Instrument Engineering, APEiE 2014 -Proceedings, 2014, vol.!, pp. 368-371,
6. Maystrenko V.A., Bogachkov I.V., Kopytov EY., Lyuhchenko A.A., Lutchenko S.S.. Castillo P.A. Approach to calculation of integrated reliability index and maintenance intervals of FOCL / Xlll-ih international scientific and technical conference "Actual problems of electronic instrument engineering" IEEE APEP. Novosibirsk, 2016, Vol. 7, pp. 73-78.
7. Lutchenko S.S.. Bogachkov J.V., Kopytov E.Y. The technique of determination of fiber-optical lines availability and maintenance intervals / International Siberian Conference on Control and Communications (SiBCON) 2015. Omsk, 2015, pp. 1-5.
ОПРЕДЕЛЕНИЕ КОЭФФИЦИЕНТА ГОТОВНОСТИ ВОЛС В ЗАВИСИМОСТИ ОТ ВНЕШНИХ ВОЗДЕЙСТВИЙ И ОШИБОК ДИАГНОСТИРОВАНИЯ
Богачков Игорь Викторович, Омский государственный технического университет, Омск, Россия, bogachkov@mail.ru Лутченко Сергей Святославович, Омский государственный технического университет, Омск, Россия Копытов Евгений Юрьевич, Омский государственный технического университет, Омск, Россия
Аннотация
Рассматриваются вопросы надежности, определения коэффициента готовности и периодичности технического обслуживания волоконно-оптических линий связи. В процессе эксплуатации волоконно-оптических линий связи (ВОЛС) возникает необходимость контроля их состояния. Средства диагностики и контроля имеют встроенные в объект датчики-преобразователи, обеспечивающие получение информации о состоянии системы, и анализирующие устройства, конструктивно обособленные от диагностируемого объекта. Погрешности измерительных и контрольных приборов, ряд факторов, обусловливающих отказы аппаратуры диагностирования, наличие человека-оператора - всё это требует учитывать влияние ошибок при тестировании. Теоретические исследования выполнены методами теории цепей Маркова и вероятностного математического моделирования. Особое внимание уделено методу определения коэффициента готовности ВОЛС в зависимости от воздействия внешних факторов и ошибок диагностирования. Внешние факторы включают изменения температуры и напряжения оптических волокон (ОВ), которые могут сигнализировать о появлении "проблемного" участка на трассе прокладки ВОЛС. Если натяжение ОВ превышает критическое значение, в ОВ могут наступить необратимые изменения, которые могут значительно сократить срок службы ОВ и ОК в целом. Для решения задач обнаружения участков ОВ с повышенным натяжением или с изменённой температурой применяются бриллюэновские импульсные рефлектометры (BOTDR), в которых регистрируется и анализируется распределение спектра рассеяния Мандельштама - Бриллюэна вдоль ОВ. Приведены характеристики участков ОВ, полученные с помощью BOTDR. Применение BOTDR в системе мониторинга ОВ ВОЛС позволяет повысить эффективность обнаружения участков с изменённым натяжением или изменённой температурой. Для получения математической модели выполняются следующие этапы: определяются и обосновываются состояния ВОЛС; составляется граф состояний и переходов системы; определяются переходы состояний системы; вычисляются истинное и наблюдаемое время нахождения системы в рассматриваемых состояниях. Моделирование зависимостей функционала готовности от периодичности технического обслуживания ВОЛС позволяет получить достоверную оценку состояния системы.
Работа выполнена при финансовой поддержке Министерства образования и науки Российской Федерации в рамках базовой части государственного задания в сфере научной деятельности (проект № 8.9334.2017/8.9).
Ключевые слова: натяжение, оптоволокно, волоконно-оптическая линия связи, рассеяние Мандельштама - Бриллюэна, ранняя диагностика, температурные влияния, диагностические ошибки, математическая модель, коэффициент готовности.
Литература
1. Богачков И.В., Горлов Н.И. Методы и средства мониторинга и ранней диагностики волоконно-оптических линий передачи. Омск: Изд-во ОмГТУ, 2013. 192 с.
2. Богачков И.В., Горлов Н.И. Обнаружение участков с измененной температурой волоконно-оптических линий связи методом бриллюэновской рефлектометрии // Вестник СибГУТИ. Новосибирск: Изд-во СибГУТИ, 2015. Вып. 4 (32). С. 74-81.
3. Богачков И.В. Исследования влияний существенных растягивающих сил, приложенным к оптическим волокнам, на спектр бриллюэновского рассеяния // Сб. трудов Междунар. науч.-техн. конф. "Синхроинфо-2016", Самара. М.: Медиа Паблишер, 2016. С. 136-139.
4. Богачков И.В., Горлов Н.И. Экспериментальные исследования влияния продольных растягивающих нагрузок на спектр бриллюэновского рассеяния в оптических волокнах // Вестник СибГУТИ. Новосибирск: Изд-во СибГУТИ, 2015. Вып. 3 (31). С. 81-88.
5. Lutchenko S.S., Kopytov E.Y. The methods of definition of the quantitative evaluation of internal safety of communication systems on the basis of the railway transport, 12th International Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2014 / Proceedings, 2014, v.1, рр. 368-371.
6. Майстренко В.А., Богачков И.В., Копытов Е.Ю., Любченко А.А., Лутченко С.С., Castillo P.A. Подход к расчету комплексных показателей надежности и периодичности технического обслуживания ВОЛС / Тр. XIII междунар. науч.-техн. конф. IEEE АПЭП. Новосибирск, 2016. Т. 7. С. 73-78.
7. Lutchenko S.S., Bogachkov I.V., Kopytov E.Y. The technique of determination of fiber-optical lines availability and maintenance intervals, International Siberian Conference on Control and Communications (SIBCON) 2015. Omsk, 2015. pp. 1-5.
Информация об авторах:
Богачков Игорь Викторович, к.т.н., доцент; доцент кафедры "Средства связи и информационная безопасность" Омского государственного технического университета, Омск, Россия
Лутченко Сергей Святославович, к.т.н., доцент; доцент кафедры "Средства связи и информационная безопасность" Омского государственного технического университета, Омск, Россия
Копытов Евгений Юрьевич, к.т.н., доцент; доцент кафедры "Средства связи и информационная безопасность" Омского государственного технического университета, Омск, Россия
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