creexpCrede Experto: транспорт, общество, образование, языкCrede Experto: transport, society, education, language2312-1327Иркутский филиал ФГБОУ ВО «МГТУ ГА»10.51955/2312-1327_2025_3_35creexp-32Research ArticleБЕЗОПАСНОСТЬ НА ВОЗДУШНОМ ТРАНСПОРТЕСпособ определения маршрута обхода воздушным судном грозы методом нахождения кратчайшего пути на графеMethod for determining an aircraft route to avoid a thunderstorm using the shortest path on a graphhttps://orcid.org/0000-0002-4849-8878КоваленкоГ. В.KovalenkoG. V.

Геннадий Владимирович Коваленко, доктор технических наук, профессор

ул. Пилотов, 38, Санкт-Петербург, 196210

Gennadiy V. Kovalenko, Doctor of technical sciences, professor

38, Pilotov Saint-Petersburg, 196210

kgvf@inbox.ruhttps://orcid.org/0009-0007-3978-6345ЯдровИ. А.YadrovI. A.

Илья Александрович Ядров, аспирант

ул. Пилотов, 38, Санкт-Петербург, 196210

Ilya A. Yadrov, graduate student

38, Pilotov Saint-Petersburg, 196210

yadrov.ilya@gmail.comСанкт-Петербургский государственный университет гражданской авиации имени Главного маршала авиации А.А. НовиковаРоссияSt. Petersburg State University of Civil Aviation named after Air Chief Marshal A.A. NovikovRussian Federation202527112025033555Copyright © Коваленко Г.В., Ядров И.А., 20252025Коваленко Г.В., Ядров И.А.Kovalenko G.V., Yadrov I.A.This work is licensed under a Creative Commons Attribution 4.0 License.https://ce.if-mstuca.ru/jour/article/view/32

В статье представлены результаты разработки метода определения оптимального маршрута обхода воздушным судном (ВС) постоянной во времени (неподвижной) зоны грозовой деятельности и сильных ливневых осадков, основанного на нахождении кратчайшего пути на графе, при построении которого учитываются геометрии опасных метеоявлений и минимальные безопасные расстояния до них. Приведено сравнение стратегий, основанных на использовании при формировании зон обхода грозы выпуклых и вогнутых оболочек. Установлено наличие статистически значимого различия в центральных тенденциях соответствующих длин маршрутов, а также показано, что маршруты, при построении которых используются вогнутые оболочки, в среднем на 2% короче, при возможных абсолютных различиях длин до нескольких сотен километров. Основной практический результат работы заключается в том, что предлагаемый метод определения оптимального маршрута обхода грозы может быть использован как инструмент повышения ситуационной осведомлённости пилотов ВС и оптимизации работы экипажа при выполнении полётов в условиях неблагоприятной метеорологической обстановки, может позволить осуществлять обход грозы в автоматическом режиме с использованием автопилота, а также может способствовать повышению экономической эффективности полётов в неблагоприятных метеорологических условиях за счёт сокращения расхода топлива благодаря выбору оптимального маршрута их обхода.

The article presents the results of developing a method for determining the optimal route for bypassing an aircraft (AC) of a temporally constant (stationary) zone of thunderstorm activity and heavy rainfall. The method is based on finding the shortest path on a graph. It takes into account the geometries of hazardous meteorological phenomena and the minimum safe distances to them. The authors compare strategies based on the use of convex and concave hulls in the formation of thunderstorm bypass zones. The analysis reveals a statistically significant difference in the central tendencies of the corresponding route lengths. It demonstrates that routes using concave hulls are on average 2% shorter, with possible absolute differences in lengths of up to several hundred kilometers. The main practical result of the work is that the proposed method for determining the optimal route to avoid a thunderstorm can be used as a tool to increase the situational awareness of aircraft pilots and optimize crew operations when flying in adverse weather conditions. It allows automatic thunderstorm avoidance using an autopilot and contribute to improved economic efficiency of flights by reducing fuel consumption through the selection of the optimal bypass routes.

авиациябезопасность полётовоптимизацияобход грозыкратчайший путь на графеалгоритм Дейкстрыминимальная оболочкаaviationflight safetyoptimizationthunderstorm avoidanceshortest path on a graphDijkstra's algorithmminimum envelopeReferencesКоваленко Г. В. Методология построения методики обучения пилотов по управлению высокоавтоматизированным воздушным судном с использованием когнитивно-информационных преобразователей алгоритмов деятельности / Г. В. Коваленко, И. С. Муравьев, К. А. Куц // Известия высших учебных заведений. Авиационная техника. 2023. № 1. С. 35-41. EDN: TMSQFRAgarwal D., Bharti P. S. (2018). A review on comparative analysis of path planning and collision avoidance algorithms. Algorithms. 30: 31.Коваленко Г. В. Применение Seq2seq-моделей для прогнозирования развития грозовой деятельности с целью повышения уровня ситуационной осведомленности пилота в полете / Г. В. Коваленко, И. А. Ядров // Научный вестник МГТУ ГА. 2025. №1 (28). С. 20-38. DOI: 10.26467/2079-0619-2025-28-1-20-38. EDN: QMTDXAAsaeedi S., Didehvar F., Mohades A. (2017). α-Concave hull, a generalization of convex hull. Theoretical Computer Science. 702: 48-59.Муравьев И. С. Экспериментальная проверка метода оценки функционирования автоматизированных систем на воздушных судах последнего поколения / И. С. Муравьев // Crede Experto: транспорт, общество, образование, язык. 2022. № 3. С. 20-33. DOI: 10.51955/23121327_2022_3_20. EDN: FVZDIYBahreinian M., Aasi E., Tron R. (2021). Robust path planning and control for polygonal environments via linear programming. 2021 American Control Conference (ACC), IEEE. 5035-5042.A concave hull algorithm for scattered data and its applications / J. Xu, Z. Zheng, Y. Feng, X. Qing // 2010 3rd International Congress on Image and Signal Processing. IEEE, 2010. № 5. P. 2430-2433. DOI: http://dx.doi.org/10.1109/CISP.2010.5648277Bezabih T. D., Glaety M. G., Wako D. A., Worku S. G. (2024). Geospatial Data Analysis: A Comprehensive Overview of Python Libraries and Implications. Ethics, Machine Learning, and Python in Geospatial Analysis. 72-93.A survey of shortest-path algorithms / A. Madkour, W. G. Aref, F. U. Rehman, M. A. Rahman, S. Basalamah // arXiv preprint arXiv:1705.02044. 2017. 26 p.Boyd D. D. (2017). In-flight decision-making by general aviation pilots operating in areas of extreme thunderstorms. Aerospace Medicine and Human Performance. 88(12): 1066-1072.Agarwal D. A review on comparative analysis of path planning and collision avoidance algorithms / D. Agarwal, P. S. Bharti // Algorithms. 2018. № 30. P 31.Chaerani D., Rusyaman E., Muslihin K. R. (2021). A comprehensive survey on convex analysis in robust optimization. Journal of Physics: Conference Series. 1722(1): 012075.Asaeedi S. α-Concave hull, a generalization of convex hull / S. Asaeedi, F. Didehvar, A. Mohades // Theoretical Computer Science. 2017. № 702. P. 48-59. DOI: http://dx.doi.org/10.1016/j.tcs.2017.08.014Chen C., Reniers G., Khakzad N., Yang M. (2021). Operational safety economics: Foundations, current approaches and paths for future research. Safety Science. 141: 105326.Bahreinian M. Robust path planning and control for polygonal environments via linear programming / M. Bahreinian, E. Aasi, R. Tron // 2021 American Control Conference (ACC). IEEE, 2021. P. 5035-5042. DOI: http://dx.doi.org/10.23919/ACC50511.2021.9483196Das K. R., Imon A. (2016). A brief review of tests for normality. American Journal of Theoretical and Applied Statistics. 5(1): 5-12.Boyd D. D. In-flight decision-making by general aviation pilots operating in areas of extreme thunderstorms // Aerospace Medicine and Human Performance. 2017. № 12 (88). P. 1066-1072. DOI: http://dx.doi.org/10.3357/AMHP.4932.2017Dinas S., Bañón J. M. (2015). A literature review of bounding volumes hierarchy focused on collision detection. Ingeniería y Competitividad. 17(1): 49-62.Chaerani D. A comprehensive survey on convex analysis in robust optimization / D. Chaerani, E. Rusyaman, K. R. A. Muslihin // Journal of Physics: Conference Series. 2021. № 1 (1722). P. 012075.Eele A., Richards A. (2009). Path-planning with avoidance using nonlinear branch-and-bound optimization. Journal of Guidance, Control, and Dynamics. 32(2): 384-394.Comparative analysis of nonlinear programming solvers: performance evaluation, Benchmarking, and Multi-UAV optimal path planning / G. Lavezzi, K. Guye, V. Cichella, M. Ciarcià // Drones. 2023. № 8 (7). P. 487. DOI: http://dx.doi.org/10.3390/drones7080487Evans J. K. (2013). An Examination of Aviation Accidents Associated with Turbulence, Wind Shear and Thunderstorm. 42 p.Das K. R. A brief review of tests for normality / K. R. Das, A. Imon // American Journal of Theoretical and Applied Statistics. 2016. № 1 (5). P. 5-12.Fardnia P., Kaspereit T., Walker T., Xu S. (2021). Financial performance and safety in the aviation industry. International Journal of Managerial Finance. 17(1): 138-165.Dinas S. A literature review of bounding volumes hierarchy focused on collision detection / S. Dinas, J. M. Bañón // Ingeniería y Competitividad. 2015. № 1 (17). P. 49-62.Fultz A. J., Ashley W. S. (2016). Fatal weather-related general aviation accidents in the United States. Physical Geography. 37(5): 291-312.Eele A. Path-planning with avoidance using nonlinear branch-and-bound optimization / A. Eele, A. Richards // Journal of Guidance, Control, and Dynamics. 2009. № 2 (32). P. 384-394. DOI: http://dx.doi.org/10.2514/1.40034Gasparetto A., Boscariol P., Lanzutti A., Vidoni R. (2015). Path planning and trajectory planning algorithms: A general overview. Motion and Operation Planning of Robotic Systems: Background and Practical Approaches. 3-27.Evans J. K. An Examination of Aviation Accidents Associated with Turbulence, Wind Shear and Thunderstorm. 2013. 42 p.Gerald B., Patson T. F. (2021). Parametric and nonparametric tests: A brief review. International Journal of Statistical Distributions and Applications. 7(3): 78-82.Financial performance and safety in the aviation industry / P. Fardnia, T. Kaspereit, T. Walker, S. Xu // International Journal of Managerial Finance. 2021. Vol. 17. № 1. P. 138-165. DOI: http://dx.doi.org/10.1108/IJMF-03-2019-0095Gultepe I. (2023). A review on weather impact on aviation operations: Visibility, wind, precipitation, icing. Journal of Airline Operations and Aviation Management. 2(1): 1-44.Fultz A. J. Fatal weather-related general aviation accidents in the United States / A. J. Fultz, W. S. Ashley // Physical Geography. 2016. № 5 (37). P. 291-312. DOI: http://dx.doi.org/10.1080/02723646.2016.1211854Hoole P. R. P., Fisher J., Hoole S. R. H. (2022). Thunderstorms and Pre-lightning Electrostatics. Lightning Engineering: Physics, Computer-based Test-bed, Protection of Ground and Airborne Systems. 51-83.Geospatial Data Analysis: A Comprehensive Overview of Python Libraries and Implications / T. D. Bezabih, M. G. Glaety, D. A. Wako, S. G. Worku // Ethics, Machine Learning, and Python in Geospatial Analysis. 2024. P. 72-93. DOI http://dx.doi.org/10.4018/979-8-3693-6381-2.ch004ICAO Safety Report. (2024). International Civil Aviation Organization. 29 p.Gerald B. Parametric and nonparametric tests: A brief review / B. Gerald, T. F. Patson // International Journal of Statistical Distributions and Applications. 2021. № 3 (7). P. 78-82. DOI: http://dx.doi.org/10.11648/j.ijsd.20210703.12Jayaram M. A., Fleyeh H. (2016). Convex hulls in image processing: a scoping review. American Journal of Intelligent Systems. 6(2): 48-58.Gultepe I. A review on weather impact on aviation operations: Visibility, wind, precipitation, icing // Journal of Airline Operations and Aviation Management. 2023. № 1 (2). P. 1-44. DOI: http://dx.doi.org/10.56801/jaoam.v2i1.1Khattak A., Zhang J., Chan P. W., Chen F., Hussain A., Almujibah H. (2024). Wind shear and aircraft aborted landings: A deep learning perspective for prediction and analysis. Atmosphere. 15(5): 545.Hoole P. R. P. Thunderstorms and Pre-lightning Electrostatics / P. R. P. Hoole, J. Fisher, S. R. H. Hoole // Lightning Engineering: Physics, Computer-based Test-bed, Protection of Ground and Airborne Systems. 2022. P. 51-83. DOI: http://dx.doi.org/10.1007/978-3-030-94728-6_2Kovalenko G. V., Muravev I. S., Kuts K. A. (2023). Methodology for training pilots to control a highly automated aircraft using cognitive-information converters of activity algorithms [Metodologiya postroeniya metodiki obucheniya pilotov po upravleniyu vysokoavtomatizirovannym vozdushnym sudnom s ispol'zovaniem kognitivno-informacionnyh preobrazovatelej algoritmov deyatel'nosti]. Proceedings of Higher Educational Institutions. Aeronautical engineering [Izvestiya vysshih uchebnyh zavedenij. Aviacionnaya tekhnika]. 1: 35-41. (In Russian)ICAO Safety Report. International Civil Aviation Organization. 2024. 29 p.Kovalenko G. V., Yadrov I. A. (2025). Application of Seq2seq models for predicting the development of thunderstorm activity to enhance pilot situational awareness in flight [Primenenie Seq2seq-modelej dlya prognozirovaniya razvitiya grozovoj deyatel'nosti s cel'yu povysheniya urovnya situacionnoj osvedomlennosti pilota v polete]. Scientific Bulletin of MSTU GA [Nauchnyj vestnik MGTU GA]. 28(1): 20-38. (In Russian)In-Flight Measurements of Lightning Locations Using an Aircraft-Mounted Lightning Mapper / Z. Milani, L. Nichman, E. Matida, L. Fleury, M. Wolde, E. Bruning, G. M. McFarquhar, P. Kollias // Aerospace Science and Technology. 2025. P. 110038. DOI: http://dx.doi.org/10.1016/j.ast.2025.110038Kovalenko G. V., Yadrov I. A., Kuts K. A. (2023). Intelligent Adaptive Flight Crew Decision Support System for Thunderstorm Avoidance. Russian Aeronautics. 66(3): 552-559.Jayaram M. A. Convex hulls in image processing: a scoping review / M. A. Jayaram, H. Fleyeh // American Journal of Intelligent Systems. 2016. №. 2 (6). P. 48-58.Lavezzi G., Guye K., Cichella V., Ciarcià M. (2023). Comparative analysis of nonlinear programming solvers: performance evaluation, Benchmarking, and Multi-UAV optimal path planning. Drones. 7(8): 487.Kovalenko G. V. Intelligent Adaptive Flight Crew Decision Support System for Thunderstorm Avoidance / G. V. Kovalenko, I. A. Yadrov, K. A. Kuts // Russian Aeronautics. 2023. № 3 (66). P. 552-559. DOI: http://dx.doi.org/10.3103/S1068799823030170Li B., Chen B. (2021). An adaptive rapidly-exploring random tree. IEEE/CAA Journal of Automatica Sinica. 9(2): 283-294.Li B. An adaptive rapidly-exploring random tree / B. Li, B. Chen // IEEE/CAA Journal of Automatica Sinica. 2021. №. 2 (9). P. 283-294. DOI: http://dx.doi.org/10.1109/JAS.2021.1004252Madkour A., Aref W. G., Rehman F. U., Rahman M. A., Basalamah S. (2017). A survey of shortest- path algorithms. arXiv preprint arXiv:1705.02044. 26 p.Nita I. A. Aviation accidents related to atmospheric instability in the United States (2000–2020) / I. A. Nita, C. Radu, S. Cheval // Theoretical and Applied Climatology. 2024. № 6 (155). P. 5483–5497.Milani Z., Nichman L., Matida E., Fleury L., Wolde M., Bruning E., McFarquhar G. M., Kollias P. (2025). In-Flight Measurements of Lightning Locations Using an Aircraft-Mounted Lightning Mapper. Aerospace Science and Technology. 110038.Operational safety economics: Foundations, current approaches and paths for future research / C. Chen, G. Reniers, N. Khakzad, M. Yang // Safety Science. 2021. Vol. 141. P. 105326. DOI: http://dx.doi.org/10.1088/1742-6596/1722/1/012075Muravyev I. S. (2022). Experimental test of the method for evaluating the functioning of automated systems on latest-generation aircraft [Eksperimental'naya proverka metoda ocenki funkcionirovaniya avtomatizirovannyh sistem na vozdushnyh sudah poslednego pokoleniya]. Crede Experto: transport, society, education, language [Crede Experto: транспорт, общество, образование, язык]. 3: 20-33. (In Russian)Park J. S. A new concave hull algorithm and concaveness measure for n-dimensional datasets / J. S. Park, S. J. Oh // Journal of Information Science and Engineering. 2012. № 3 (28). P. 587-600.Nita I. A., Radu C., Cheval S. (2024). Aviation accidents related to atmospheric instability in the United States (2000–2020). Theoretical and Applied Climatology. 155(6): 5483–5497.Path planning and trajectory planning algorithms: A general overview / A. Gasparetto, P. Boscariol, A. Lanzutti, R. Vidoni // Motion and Operation Planning of Robotic Systems: Background and Practical Approaches. 2015. P. 3-27. DOI: http://dx.doi.org/10.1007/978-3-319-14705-5_1Park J. S., Oh S. J. (2012). A new concave hull algorithm and concaveness measure for n-dimensional datasets. Journal of Information Science and Engineering. 28(3): 587-600.Rachmawati D. Analysis of Dijkstra’s algorithm and A* algorithm in shortest path problem / D. Rachmawati, L. Gustin // Journal of Physics: Conference Series. IOP Publishing, 2020. № 1 (1566). 7 p. DOI: http://dx.doi.org/10.1088/1742-6596/1566/1/012061Rachmawati D., Gustin L. (2020). Analysis of Dijkstra’s algorithm and A* algorithm in shortest path problem. Journal of Physics: Conference Series, IOP Publishing. 1566(1): 7.Ravankar A. A. HPPRM: hybrid potential based probabilistic roadmap algorithm for improved dynamic path planning of mobile robots / A. A. Ravankar, A. Ravankar, T. Emaru, Y. Kobayashi // IEEE Access. 2020. Vol. 8. P. 221743-221766. DOI: http://dx.doi.org/10.1109/ACCESS.2020.3043333Ravankar A. A., Ravankar A., Emaru T., Kobayashi Y. (2020). HPPRM: hybrid potential based probabilistic roadmap algorithm for improved dynamic path planning of mobile robots. IEEE Access. 8: 221743-221766.Saalfeld A. Topologically consistent line simplification with the Douglas-Peucker algorithm // Cartography and Geographic Information Science. 1999. № 1 (26). P. 7-18. DOI: http://dx.doi.org/10.1559/152304099782424901Saalfeld A. (1999). Topologically consistent line simplification with the Douglas-Peucker algorithm. Cartography and Geographic Information Science. 26(1): 7-18.Tan C. S. A comprehensive review of coverage path planning in robotics using classical and heuristic algorithms / C. S. Tan, R. Mohd-Mokhtar, M. R. Arshad // IEEE Access. 2021. Vol. 9. P. 119310-119342. DOI: http://dx.doi.org/10.1109/ACCESS.2021.3108177Tan C. S., Mohd-Mokhtar R., Arshad M. R. (2021). A comprehensive review of coverage path planning in robotics using classical and heuristic algorithms. IEEE Access. 9: 119310-119342.Turbulence characteristics of thunderstorms before the first flash in comparison to non-thunderstorms / C. Zhao, D. Zheng, Y. Zhang, X. Liu, Y. Zhang, W. Yao, W. Zhang // Geophysical Research Letters. 2021. Vol. 48. № 18. 10 p. DOI: http://dx.doi.org/10.1029/2021GL094821Xu J., Zheng Z., Feng Y., Qing X. (2010). A concave hull algorithm for scattered data and its applications. 3rd International Congress on Image and Signal Processing, IEEE. 5: 2430-2433.Wind shear and aircraft aborted landings: A deep learning perspective for prediction and analysis / A. Khattak, J. Zhang, P. W. Chan, F. Chen, A. Hussain, H. Almujibah // Atmosphere. 2024. Vol. 15. № 5. P. 545. DOI: http://dx.doi.org/10.3390/atmos15050545Yilmaz N. K. (2008). Path planning of autonomous underwater vehicles for adaptive sampling using mixed integer linear programming. IEEE Journal of Oceanic Engineering. 33(4): 522-537.Yilmaz N. K. Path planning of autonomous underwater vehicles for adaptive sampling using mixed integer linear programming // IEEE Journal of Oceanic Engineering. 2008. № 4 (33). P. 522-537. DOI: http://dx.doi.org/10.1109/JOE.2008.2002105Zhao C., Zheng D., Zhang Y., Liu X., Zhang Y., Yao W., Zhang W. (2021). Turbulence characteristics of thunderstorms before the first flash in comparison to non‐thunderstorms. Geophysical Research Letters. 48(18): 10.

The authors declare that there are no conflicts of interest present.