BAYESIAN ESTIMATE OF TELECOMMUNICATION SYSTEMS PREPAREDNESS
https://doi.org/10.26467/2079-0619-2021-24-1-16-22
Abstract
The paper assumes a Bayesian estimate of the telecommunication systems availability ratio. Downtime and uptime are described by gamma distributions with positive integer parameters. Estimates of the distribution parameters are obtained using the maximum likelihood method. For the set samples, the values of the desired probability distribution densities are found and an expression for estimating the availability ratio is derived. Numerical estimates for the standard and assumed estimates are given. For a system with two states, a Bayesian estimate of the availability function with consideration of downtime and serviceable condition takes into account the features of backup equipment and the effect of its failure defined by performance reliability and features that ensure the reliability of information signals. The proposed Bayesian approach has the following advantages: it is possible to conduct quantitative estimates with lack of sufficient statistics on functional use indicators; it takes into account all destabilizing factors of various nature; the presence of a lower mean square error compared to traditional methods. To implement the proposed approach that estimates the availability ratio, confidence probabilities are introduced relative to the indicator of failure flows and equipment recovery. The parameters of the a priori information can be determined by different methods or on the basis of sufficient statistical data. To illustrate the discussed calculation algorithm, a digital data transmission system of a standard satellite navigation system consisting of terminal, radio equipment, and a transponder is considered. To estimate the required values, we used data on interruptions in the operation of equipment due to its malfunction during a conditional year. The frequency of downtime caused by signal propagation conditions and equipment failures was evaluated. It was shown that the gamma distribution is suitable for describing the frequency distribution of downtime. The frequency distribution of the cyclicity coefficient with the condition of the selected time interval was also taken into account. Sample mathematical expectations and mean square deviations of the downtime coefficient were found. As a result, the numerical example shows the correctness of using the Bayesian estimate of weighted equipment preparedness.
About the Authors
V. E. Emelyanov
Moscow State Technical University of Civil Aviation
Russian Federation
Russian Federation
Doctor of Technical Sciences, Associate Professor, Professor of the Radio Engineering and Information Security Chair
MoscowS. P. Matyuk
Moscow State Technical University of Civil Aviation
Russian Federation
Russian Federation
Candidate of Technical Sciences, Associate Professor of the Radio Engineering and Information Security Chair
Moscow
References
1. Gorbunov, Yu.N. (2019). Improving the accuracy of measurement time intervals of radio reception in the framework of recursive multi-stage Bayesian estimates. RENSIT, vol. 11, no. 3, pp. 291–298. DOI: 10.17725/rensit.2019.11.291 (in Russian)
2. Bakulin, M.G., Kreyndelin, V.B., Grigoriev, V.A., Aksenov, V.O. and Schesnyak, A.S. (2020). Bayesian estimation with successive rejection and utilization of a priori knowledge. Radiotehnika i Elektronika, vol. 65, no. 3, pp. 257–266. DOI: 10.31857/S0033849420030031 (in Russian)
3. Barlow, R.E. and Proschan, F. (1984). Statisticheskaya teoriya nadezhnosti i ispytaniya na bezotkaznost [Statistical theory of reliability and life testing: probability models]. Translated from English by I.A. Ushakov. Moscow: Nauka, 328 p. (in Russian)
4. Barzilovich, E.Yu., Emelyanov, V.E., Smirnov, V.V. and Topchnev, V.P. (2000). Nekotoryye optimalnyye algoritmy upravleniya v sistemakh razlichnoy prirody [Some optimal control algorithms in systems of different nature]. Nauchnyy Vestnik MGTU GA, no. 32, pp. 5–16. (in Russian)
5. Biryukov, I.D., Buchuchan, P.V. and Timoshenko, P.I. (2020). Information processing algorithms in aviation-based radioelectronic surveillance systems. RENSIT, vol. 12, no. 4, pp. 517–528. DOI: 10.17725/rensit.2020.12.517 (in Russian)
6. Gorshenin, A.K. (2018). Data noising by finite normal and gamma mixtures with application to the problem of rounded observations. Informatics and Applications, vol. 12, no. 3, pp. 28–34. DOI: 10.14357/19922264180304 (in Russian)
7. Emelyanov, V.E. and Logvin, A.N. (2014). Tekhnicheskaya ekspluatatsiya aviatsionnogo radioelektronnogo oborudovaniya [Technical use of aviation radio-electronic equipment]. Moscow: MORKNIGA, 730 p. (in Russian)
8. Korolev, V.Y., Korchagin, A.Y. and Zeifman, A.I. (2015). On the convergence of distributions of statistics constructed from samples of random size to a multivariate generalized variancegamma distributions. Doklady Mathematics, vol. 91, no. 3, pp. 332–335. DOI: 10.1134/S1064562415030205
9. Kochkarov, A.A., Razin'kov, S.N., Timoshenko, A.V. and Shevtsov, V.A. (2020). Comprehensive method of information resources control ensuring the security of telecommunication systems of aviation monitoring complexes. Izvestiya vysshikh uchebnykh zavedenii. Aviatsionnaya tekhnika, pp. 158–166. (in Russian)
10. Kudryavtsev, A.A., Palionnaia, S.I. and Shorgin, V.S. (2018). A priori inverse gamma distribution in Bayesian queuing models. Systems and Means of Informatics, vol. 28, no. 4, pp. 54–60. DOI: 10.14357/08696527180406 (in Russian)
11. Litvinenko, R.S., Jamshhikov, A.S. and Bagaev, A.V. (2016). The practice of applying gamma distribution the theory of reliability of technical systems. Tekhnicheskiye nauki – ot teorii k praktike, no. 56, pp. 153–159. (in Russian)
12. Mazalov, V.V. and Nikitina, N.N. (2018). The maximum likelihood method for detecting communities in communication networks. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, vol. 14, no. 3, pp. 200–214. DOI: 10.21638/11702/spbu10.2018.302 (in Russian)
13. Sidorov, I.G. (2018). Linear minimax filtering of a stationary random process under the condition of the interval fuzziness in the state matrix of the system with a restricted variance. Journal of Communications Technology and Electronics, vol. 63, no. 8, pp. 902–907. DOI: 10.1134/S003384941807015X (in Russian)
14. Alquier, P. and Guedj, B. (2017). An oracle inequality for quasi-Bayesian nonnegative matrix factorization. Mathematical Methods of Statistics, no. 26, pр. 55–67. DOI: 10.3103/S1066530717010045
15. Cuo, W. (1986). Bayes weighted availability for a digital radio transmission system. IEEE. Transactions of Reliability, vol. R-35, pp. 201–207.
16. Hadj-Amar, B., Finkenstädt, R.B., Fiecas, M., Lévi, F. and Huckstepp, R. (2020). Bayesian model search for nonstationary periodic time series. Journal of the American Statistical Association, vol. 115, issue 531, pp. 1320–1335. DOI: 10.1080/01621459.2019.1623043 17. Hamura, Y. and Kubokawa, T. (2019). Bayesian predictive distribution for a negative binomial model. Mathematical Methods of Statistics, vol. 28, pp. 1–17. DOI: 10.3103/S1066530719010010
17. Al-Labadi, L. and Zarepour, M. (2017). Two-sample Kolmogorov-Smirnov test using a Bayesian nonparametric approach. Mathematical Methods of Statistics, vol. 26, pp. 212–225. DOI: 10.3103/S1066530717030048
18. Priem, R., Bartoli, N., Diouane, Y. and Sgueglia, A. (2020). Upper trust bound feasibility criterion for mixed constrained Bayesian optimization with application to aircraft design. Aerospace Science and Technology, vol. 105, ID 105980. DOI: 10.1016/j.ast.2020.105980
19. Wang John, C.H., Shi Kun Tan, Kin Huat Low (2020). Three-dimensional (3D) MonteCarlo modeling for UAS collision risk management in restricted airport airspace. Aerospace Science and Technology, vol. 105, ID 105964. DOI: 10.1016/j.ast.2020.105964
Review
For citations:
Emelyanov V.E., Matyuk S.P. BAYESIAN ESTIMATE OF TELECOMMUNICATION SYSTEMS PREPAREDNESS. Civil Aviation High Technologies. 2021;24(1):16-22. https://doi.org/10.26467/2079-0619-2021-24-1-16-22
Views:
490
Email this article 
