结冰会导致飞机飞行包线萎缩，在驾驶员没有正确处理的情况下极易发生飞行事故。为定量计算结冰条件下飞机飞行风险进而制定合理的结冰风险规避策略，以飞机纵向动力学系统为分析对象，基于吸引域方法计算得到飞机结冰后的二维吸引域及稳定边界，并以飞行状态超出稳定边界作为飞行事故判定条件。建立了典型的人-机-环系统模型，通过蒙特卡罗仿真提取了飞行安全关键参数极值样本；根据极值理论，建立二元极值Copula模型；通过遗传算法辨识模型参数，依据多种拟合优度检验方法确定最优分布模型，进而计算不同结冰影响程度下的飞行风险概率，并由此来指导驾驶员操纵，从而保证飞行安全。文中所述方法，为定量计算结冰条件下飞行风险概率提供了新的思路，具有较好的工程应用前景。
Icing will cause the flight envelope of the aircraft to shrink, and flight accidents are prone to occur if the pilot does not handle it properly. To quantitatively calculate the aircraft flight risk under icing conditions and formulate a reasonable icing risk avoidance strategy, the aircraft longitudinal dynamics system is analyzed. The two-dimensional region of attraction of the aircraft after icing is calculated based on the region of attraction method, and the flight state beyond the region of attraction is used as the judging criterion for flight accident. A typical man-machine-loop system model is established. The extreme value samples of key flight safety parameters are extracted through Monte Carlo simulation. According to the extreme value theory, a binary extreme value Copula model is established. The model parameters are identified by the genetic algorithm. A goodness-of-fit test method is used to determine the optimal distribution model, and then the flight risk probability under the conditions of different icing influence levels is calculated, which can provide guidance for the pilot to maneuver to ensure flight safety. The method proposed provides a new idea for quantitatively calculating the flight risk probability under icing conditions, and has good application prospects.
[1] Boeing Commercial Airplanes. Statistical summary of commercial jet airplane accidents[R]. Seattle:Boeing Commercial Airplanes, 2015.
[2] MOHAGHEGH Z, KAZEMI R, MOSLEH A. Incorporating organizational factors into Probabilistic Risk Assessment (PRA) of complex socio-technical systems:A hybrid technique formalization[J]. Reliability Engineering & System Safety, 2009, 94(5):1000-1018.
[3] BROOKER P. Experts, Bayesian belief networks, rare events and aviation risk estimates[J]. Safety Science, 2011, 49(8-9):1142-1155.
[4] DE MENDONÇA C B, DA SILVA E T, CURVO M, et al. Model-based flight testing[J]. Journal of Aircraft, 2013, 50(1):176-186.
[5] BLUM D, THIPPHAVONG D, RENTAS T, et al. Safety analysis of the advanced airspace concept using Monte Carlo simulation[C]//AIAA Guidance, Navigation, and Control Conference. Reston:AIAA, 2010.
[6] 雷桂媛. 关于蒙特卡罗及拟蒙特卡罗方法的若干研究[D]. 杭州:浙江大学, 2003. LEI G Y. Several researches on Monte Carlo and quasi-Monte Carlo methods[D]. Hangzhou:Zhejiang University, 2003(in Chinese).
[7] 郭媛媛, 孙有朝, 李龙彪. 基于蒙特卡罗方法的民用飞机故障风险评估方法[J]. 航空学报, 2017, 38(10):221126. GUO Y Y, SUN Y C, LI L B. Failure risk assessment method of civil aircraft based on Monte Carlo method[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(10):221126(in Chinese).
[8] 武朋玮, 李颖晖, 郑无计, 等. 基于可达集方法的结冰飞机着陆阶段安全风险评估[J]. 航空学报, 2018, 39(12):122139. WU P W, LI Y H, ZHENG W J, et al. Flight risk evaluation based on reachable set method at the phase of icing aircraft landing[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(12):122139(in Chinese).
[9] LI Z, XU H J, XUE Y, et al. Flight risk quantitative assessment based on extreme values of flight parameters[C]//The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018), 2019.
[10] LI Z, XU H J, XUE Y, et al. On flight risk quantitative evaluation under icing conditions[J]. Mathematical Problems in Engineering, 2019, 2019:1-14.
[11] WEI Y, XU H J, XUE Y, et al. Quantitative assessment and visualization of flight risk induced by coupled multi-factor under icing conditions[J]. Chinese Journal of Aeronautics, 2020, 33(8):2146-2161.
[12] HUI K, WOLDE M, BROWN A, et al. Flight dynamics model of turboprop transport aircraft icing effects based on preliminary flight data[C]//43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 2005.
[13] LAMPTON A, VALASEK J. Prediction of icing effects on the dynamic response of light airplanes[J]. Journal of Guidance, Control, and Dynamics, 2007, 30(3):722-732.
[14] LAMPTON A, VALASEK J. Prediction of icing effects on the lateral/directional stability and control of light airplanes[J]. Aerospace Science and Technology, 2012, 23(1):305-311.
[15] BRAGG M, HUTCHISON T, MERRET J. Effect of ice accretion on aircraft flight dynamics[C]//38th Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 2000.
[16] DOGAN A, KAEWCHAY K. Probabilistic human pilot approach:application to microburst escape maneuver[J]. Journal of Guidance, Control, and Dynamics, 2007, 30(2):357-369.
[17] KHODADADI L, SAMADI B, KHALOOZADEH H. Estimation of region of attraction for polynomial nonlinear systems:a numerical method[J]. ISA Transactions, 2014, 53(1):25-32.
[18] CHAKRABORTY A, SEILER P, BALAS G J. Nonlinear region of attraction analysis for flight control verification and validation[J]. Control Engineering Practice, 2011, 19(4):335-345.
[19] JARVIS-WLOSZEK Z. Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization[J]. Optimization, 2003, 23(5):1-49.
[20] TAN W. Nonlinear control analysis and synthesis using sum-of-squares programming[D]. Berkeley:University of California, 2006.
[21] 李宁. 基于矩量理论和Sum-of-Squares最优化理论的吸引域估计[D]. 沈阳:东北大学, 2008. LI N. Estimating domains of attraction based on moment and sum-of-squares optimization[D]. Shenyang:Northeastern University, 2008(in Chinese).
[22] HUESCHEN R M. Development of the Transport Class Model (TCM) aircraft simulation from a sub-scale Generic Transport Model (GTM) simulation:NASA/TM-2011-217169[R]. Washington, D.C.:NASA, 2011.
[23] PANDITA R, CHAKRABORTY A, SEILER P, et al. Reachability and region of attraction analysis applied to GTM dynamic flight envelope assessment[C]//AIAA Guidance, Navigation, and Control Conference. Reston:AIAA, 2009.
[24] FRENCH J, KOKOSZKA P, STOEV S, et al. Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional data[J]. Computational Statistics & Data Analysis, 2019, 131:176-193.
[25] LI Z, XU H J, XUE Y, et al. On flight risk quantitative evaluation under icing conditions[J]. Mathematical Problems in Engineering, 2019(10):1-14.
[26] NELSEN R B. Introduction[M]//An introduction to copulas. New York:Springer, 1999.
[27] CHAKRABORTY A, SEILER P, BALAS G J. Susceptibility of F/A-18 flight controllers to the falling-leaf mode:linear analysis[J]. Journal of Guidance, Control, and Dynamics, 2011, 34(1):57-72.
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