# Increasing the Safety of Flights with the Use of Mathematical Model Based on Status Functions

• Irina Veshneva
• Aleksander Bolshakov
• Aleksei Kulik
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)

## Abstract

The article deals with application of complex-valued status functions for development of the method of mathematical modeling of flights to ensure their safety based on the prevention of flight accidents. The application of the proposed method on the basis of status functions is shown using a precedent matrix of flight accidents. The method contains the steps corresponding to the Mamdani algorithm for the following purposes: the formation of the rules base, fuzzification, aggregation, activation, accumulation. Notable is the use of orthonormal basis of complex-valued status functions instead of membership functions, which changes the implementation at each stage. The configuration of flight operations safety management system is used on the input of which the information is received about the condition of the crew, instruments for measuring external factors and airborne equipment. The main parameters of the aircraft flight safety assessment are identified by formalization of expert information and the values of linguistic variables are formulated with their use. Orthonormal status functions were formed for which interpretation rules are presented. For activation we used status functions, which makes it possible to create a rule for the double evaluation of object and phenomenon when creating rules database. Analogues of minimax operations are used for accumulation with a demonstration of the form of these functions for different values of factors. Comparison of the proposed method with analogues is given (algorithms of Mamdani, Tsukamoto, Larsen and Sugeno).

## Keywords

Status functions Membership functions Mamdani algorithm Flight safety Mathematical model

## References

1. 1.
Popov, Ju.V.: Safety indicators of aviation flights. Internet-zhurnal «Tehnologii tehnosfernoj bezopasnosti» , №6(58) (2014). http://agps-2006.narod.ru/ttb/2014-6/10-06-14.ttb.pdf. Accessed 12 Apr 2017. (in Russian)
2. 2.
Kluev, V.V., Rezchikov, A.F., Kushnikov, V.A., Tverdokhlebov, V.A., Ivashenko, V.A., Bogomolov, A.S., Filimonyuk, L.Yu.: An analysis of critical situations caused by unfavorable concurrence of circumstances. Kontrol’ Diagn. − Test. Diagn. 7, 12–14 (2014). (in Russian)Google Scholar
3. 3.
Sapogov, V.A., Anisimov, K.S., Novozhilov, A.V.: Fail-safe computing system for integrated flight control systems. Electronyi J. «Trudy MAI»—Electron. J. «Trudy MAI» № 45, 42 (2008). www.mai.ru/science/trudy. (in Russian)
4. 4.
Harris, J.: An Introduction to Fuzzy Logic Applications. Springer, Dordrecht (2000)
5. 5.
Bol’shakov, A.A., Kulik, A.A., Sergushov, I.V. Development the control system algorithms functioning of flight safety for the aircraft of helicopter type. Izvestija Samarskogo nauchnogo centra RAN Scientific Journal of “Proceedings of the Samara Scientific Center of the Russian Academy of Sciences”, 18, №1 (2), 358–362 (2016). (in Russian)Google Scholar
6. 6.
Luo, J., Lan, E.: Fuzzy logic controllers for aircraft flight control. In: Fuzzy Logic and Intelligent Systems. International Series in Intelligent Technologies, vol. 3. Springer, Dordrecht (1995)Google Scholar
7. 7.
Nonami, K., Kendoul, F., Suzuki, S., Wang, W., Nakazawa, D.: Autonomous Flying Robots, Unmanned Aerial Vehicles and Micro Aerial Vehicles. Springer, Japan (2010). ISBN 978-4-431-53855-4
8. 8.
Ionita, S., Sofron, E.: The fuzzy model for aircraft landing control. In: Pal, N.R., Sugeno, M. (eds.) Advances in Soft Computing—AFSS 2002. AFSS 2002. LNCS, vol. 2275. Springer, Heidelberg (2002)
9. 9.
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. SMC-3(1), 28–44 (1973)
10. 10.
Fedunov, B.E., Prohorov, M.D.: Conclusion on the precedent in knowledge bases of onboard intellectual systems. Artif. Intell. Decis. Mak. №3, 63–72 (2010). (in Russian)Google Scholar
11. 11.
Kontogiannis, T., Malakis, S.: Proactive approach to detecting and identifying human errors in aviation and air traffic control. Sci. Saf. 47, 693–706 (2009)
12. 12.
Vishnjakova, L.V., Degtjarev, O.V., Slatin, A.V.: Simulating operational modeling of processes of functioning of difficult aviation systems and management complexes. In: SPb.: SPIIRAN—Conference Proceedings «Simulation Modeling: Theory and Practice». SPIIRAS, vol. 1, pp. 30–41 (2011). (in Russian)Google Scholar
13. 13.
Veshneva, I.V., Chistjakova, T.B., Bol’shakov, A.A.: The status functions method for processing and interpretation of the measurement data of interactions in the educational environment. SPIIRAS Proc. 49, 144–166 (2016). (in Russian)
14. 14.
Veshneva, I.V., Chistjakova, T.B., Bol’shakov, A.A., Singatulin, R.A.: Model of formation of the feedback channel within ergatic systems for monitoring of quality of processes of formation of personnel competences. Int. J. Qual. Res. 9(3), 495–512 (2015)Google Scholar
15. 15.
Ossovskij, S.: Neural networks for information processing. M.: Finansy i statistika (2002). (in Russian)Google Scholar
16. 16.
Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controller. Int. J. Man-Mach. Stud. 8, 669–678 (1976)
17. 17.
Sinicyn, I.N.: Canonical representations of random functions and their application in problems of computer support of scientific research. M.: TORUS-PRESS (2009). (in Russian)Google Scholar
18. 18.
Batenkov, K.A.: Continuous channel modeling in shape of some space transformation operators. SPIIRAS Proc. 32, 171–198 (2014). (in Russian)
19. 19.
Matthew, S., Sunitha, M.S.: Links in graphs and fuzzy graphs. Achiev. Fuzzy Sets Syst. 6, 107–119 (2010)
20. 20.
Shevchenko, A.M., Nachinkina, G.N., Solonnikov, Ju.I.: Modeling of means of information support of the pilot during the take-off phase of the aircraft. In: Proceedings of the Moscow Institute of Electromechanics and Automatics (MIEA), vol. 5, pp. 54–64 (2012). (in Russian)Google Scholar
21. 21.
Bol’shakov, A.A., Veshneva, I.V., Mel’nikov, L.A., Perova, L.G.: New methods of mathematical modeling of the dynamics of the formation and management of competences in the learning process at the university. Hot Line—Telekom, Moscow (2014). (in Russian)Google Scholar