Aircraft safety analysis based on differential manifold theory and bifurcation method

Chi ZHOU; Ying-hui LI; Wu-ji ZHENG; Peng-wei WU

doi:10.1631/FITEE.1700435

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Aircraft safety analysis based on differential manifold theory and bifurcation method

Regular Papers | Updated：2022-05-19

- Aircraft safety analysis based on differential manifold theory and bifurcation method
- 基于微分流形理论和分岔理论的飞机安全性分析
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 2, Pages: 292-299(2019)
- Affiliations：
  
  School of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xioan 710038, China
- Author bio：
  
  Chi ZHOU, E-mail: 15279122641@163.com
- Funds：
- DOI：10.1631/FITEE.1700435
  CLC： V328
- Received：01 July 2017，
  
  Revised：2019-;1-22，
  
  Published：2019-02
- Accepted：
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Chi ZHOU, Ying-hui LI, Wu-ji ZHENG, et al. Aircraft safety analysis based on differential manifold theory and bifurcation method[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(2): 292-299.
DOI：

Chi ZHOU, Ying-hui LI, Wu-ji ZHENG, et al. Aircraft safety analysis based on differential manifold theory and bifurcation method[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(2): 292-299. DOI： 10.1631/FITEE.1700435.

摘要

失控（LOC）被认为是导致世界范围内致命飞机事故的主要原因之一。减少飞机失控对于提高飞行安全意义重大。虽然目前航空界对失控的定义还比较模糊，但研究表明失控通常与飞行状态超出安全包线、飞机动力学的非线性影响以及飞行机组人员不当操纵有关。本文主要针对飞机动力学的非线性影响和驾驶员不当操纵导致的失控展开研究，利用分岔分析方法确定飞行状态的失速点和分岔点。研究结果表明，驾驶员操纵过度将直接导致飞机失速。此外，飞行状态接近飞行包线边界时，驾驶员的操纵会变得特别敏感，稍微改变操纵指令就可能导致飞行状态超出安全包线。即使在某个操纵指令下存在稳定平衡状态，飞行状态仍可能处于安全包线之外。为提升飞行安全，引入微分流形理论确定安全包线。以NASA的通用模型作为案例展开研究。

Abstract

Loss of control (LOC) is considered one of the leading causes of fatal aircraft accidents worldwide. Reducing LOC is critical to improve flight safety. Although it is still vaguely defined

LOC is generally associated with a flight state that is outside the safety envelope

with nonlinear influences of aircraft dynamics and incorrect handling by the flight crew. We have studied how nonlinear factors and pilot operations contribute to LOC. In this study

the stall point and bifurcation point are confirmed using the bifurcation analysis

and the results show that the aircraft will stall when excessive elevator movement is commanded. Moreover

even though there may be an equilibrium state in one of the elevator deflections

the flight state may still be outside the flight safety envelope. When the flight state is near the edge of the flight safety envelope

the strategy to regulate the elevator deflection is super-sensitive

and a slight change in the elevator deflection may contribute to a flight state outside the safety envelope. To solve this issue

the differential manifold theory is introduced to determine the safety envelope. Examples are provided using NASAos generic transport model.

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references

AM Bayen , , , IM Mitchell , , , MK Oishi , , , 等 . . Aircraft autolander safety analysis through optimal control-based reach set computation . . J Guid Contr Dynam , , 2007 . . 30 ( ( 1 ): ): 68 - - 77 . . DOI: 10.2514/1.21562 http://doi.org/10.2514/1.21562 . .

M Chaichi , , , E Garc a-R o , , , ME V zquez-Abal . . Three-dimensional Lorentz manifolds admitting a parallel null vector field . . J Phys A Math Gener , , 2005 . . 38 ( ( 4 ): ): 841 - - 850 . . DOI: 10.1088/0305-4470/38/4/005 http://doi.org/10.1088/0305-4470/38/4/005 . .

HD Chiang , , , MW Hirsch , , , FF Wu . . Stability regions of nonlinear autonomous dynamical systems . . IEEE Trans Autom Contr , , 1988 . . 33 ( ( 1 ): ): 16 - - 27 . . DOI: 10.1109/9.357 http://doi.org/10.1109/9.357 . .

JAA Engelbrecht , , , SJ Pauck , , , IK Peddle . . Bifurcation analysis and simulation of stall and spin recovery for large transport aircraft . . AIAA Atmospheric Flight Mechanics Conf , , 2012 . . p.1 - - 12 . . DOI: 10.2514/6.2012-4801 http://doi.org/10.2514/6.2012-4801 . .

E Goncharova , , , A Ovseevich . . Small-time reachable sets of linear systems with integral control constraints: birth of the shape of a reachable set . . J Optim Theory Appl , , 2016 . . 168 ( ( 2 ): ): 615 - - 624 . . DOI: 10.1007/s10957-015-0754-4 http://doi.org/10.1007/s10957-015-0754-4 . .

S Haghighatnia , , , RK Moghaddam . . Enlarging the guaranteed region of attraction in nonlinear systems with bounded parametric uncertainty . . J Zhejiang Univ-Sci C (Comput & Electron) , , 2013 . . 14 ( ( 3 ): ): 214 - - 221 . . DOI: 10.1631/jzus.C1200213 http://doi.org/10.1631/jzus.C1200213 . .

C Jahnke , , , FEC Culick . . Application of bifurcation theory to the high-angle-of-attack dynamics of the F-14 . . J Aircraft , , 1994 . . 31 ( ( 1 ): ): 26 - - 34 . . DOI: 10.2514/3.46451 http://doi.org/10.2514/3.46451 . .

AK Khatri , , , NK Sinha . . Aircraft maneuver design using bifurcation analysis and nonlinear control techniques . . 49 th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition , , 2011 . . p.1 - - 12 . . DOI: 10.2514/6.2011-924 http://doi.org/10.2514/6.2011-924 . .

L Khodadadi , , , B Samadi , , , H Khaloozadeh . . Estimation of region of attraction for polynomial nonlinear systems: a numerical method . . ISA Trans J Autom , , 2014 . . 53 ( ( 1 ): ): 25 - - 32 . . DOI: 10.1016/j.isatra.2013.08.005 http://doi.org/10.1016/j.isatra.2013.08.005 . .

DH Klyde , , , D McRuer . . Smart-cue and smart-gain concepts to alleviate loss of control . . J Guid Contr Dynam , , 2009 . . 32 ( ( 5 ): ): 1409 - - 1417 . . DOI: 10.2514/1.43156 http://doi.org/10.2514/1.43156 . .

B Krauskopf , , , HM Osinga . . Two-dimensional global manifolds of vector fields . . Chaos Interdiscip J Nonl Sci , , 1999 . . 9 ( ( 3 ): ): 768 - - 774 . . DOI: 10.1063/1.166450 http://doi.org/10.1063/1.166450 . .

B Krauskopf , , , HM Osinga , , , EJ Doedel , , , 等 . . A survey of methods for computing (un)stable manifolds of vector fields . . Int J Bifurc Chaos , , 2005 . . 15 ( ( 3 ): ): 763 - - 791 . . DOI: 10.1142/S0218127405012533 http://doi.org/10.1142/S0218127405012533 . .

HG Kwatny , , , JET Dongmo , , , BC Chang , , , 等 . . Nonlinear analysis of aircraft loss of control . . J Guid Contr Dynam , , 2013 . . 36 ( ( 1 ): ): 149 - - 162 . . DOI: 10.2514/1.56948 http://doi.org/10.2514/1.56948 . .

J Lygeros , , , C Tomlin , , , S Sastry . . Controllers for reachability specifications for hybrid systems . . Automatica , , 1999 . . 35 ( ( 3 ): ): 349 - - 370 . . DOI: 10.1016/S0005-1098(98)00193-9 http://doi.org/10.1016/S0005-1098(98)00193-9 . .

JM Merret , , , KN Hossain , , , MB Bragg . . Envelope protection and atmospheric disturbances in icing encounters . . 40 th AIAA Aerospace Sciences Meeting & Exhibit , , 2002 . . p.1 - - 18 . . DOI: 10.2514/6.2002-814 http://doi.org/10.2514/6.2002-814 . .

HM Osinga . . Two-dimensional invariant manifolds in four-dimensional dynamical systems . . Comput Graph , , 2005 . . 29 ( ( 2 ): ): 289 - - 297 . . DOI: 10.1016/j.cag.2004.12.016 http://doi.org/10.1016/j.cag.2004.12.016 . .

R Pandita , , , A Chakraborty , , , P Seiler , , , 等 . . Reachability and region of attraction analysis applied to GTM dynamic flight envelope assessment . . AIAA Guidance, Navigation, and Control Conf , , 2009 . . p.1 - - 21 . . DOI: 10.2514/6.2009-6258 http://doi.org/10.2514/6.2009-6258 . .

R Qi , , , D Cook , , , W Kliemann , , , 等 . . Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics . . J Nonl Sci , , 2000 . . 10 ( ( 2 ): ): 175 - - 195 . . DOI: 10.1007/s003329910008 http://doi.org/10.1007/s003329910008 DOI: 10.1007/s003329910008 http://doi.org/10.1007/s003329910008 . .

H Ranter . . Airliner Accident Statistics 2006 . . Available from , , 2007 . . [Accessed on Dec. 17, 2018] https://aviation-safety.net/pubs/asn/ASN_Airliner_Accident_Statistics_2006.pdf https://aviation-safety.net/pubs/asn/ASN_Airliner_Accident_Statistics_2006.pdf , , . .

V Sharma , , , PG Voulgaris , , , E Frazzoli . . Aircraft autopilot analysis and envelope protection for operation under icing conditions . . J Guid Contr Dynam , , 2004 . . 27 ( ( 3 ): ): 454 - - 465 . . DOI: 10.2514/1.1214 http://doi.org/10.2514/1.1214 . .

J Sieber , , , B Krauskopf . . Control based bifurcation analysis for experiments . . Nonl Dynam , , 2008 . . 51 ( ( 3 ): ): 365 - - 377 . . DOI: 10.1007/s11071-007-9217-2 http://doi.org/10.1007/s11071-007-9217-2 . .

K Weekly , , , A Tinka , , , L Anderson , , , 等 . . Autonomous river navigation using the Hamilton-Jacobi framework for underactuated vehicles . . IEEE Trans Robot , , 2014 . . 30 ( ( 5 ): ): 1250 - - 1255 . . DOI: 10.1109/TRO.2014.2327288 http://doi.org/10.1109/TRO.2014.2327288 . .

Q Xin , , , ZK Shi . . Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack . . Chin J Aeronaut , , 2015 . . 28 ( ( 1 ): ): 250 - - 259 . . DOI: 10.1016/j.cja.2014.12.022 http://doi.org/10.1016/j.cja.2014.12.022 . .

Y Zhang , , , CC de Vissery , , , QP Chu . . Online safe flight envelope prediction for damaged aircraft: a database-driven approach . . AIAA Modeling and Simulation Technologies Conf , , 2016 . . p.1 - - 14 . . DOI: 10.2514/6.2016-1189 http://doi.org/10.2514/6.2016-1189 . .

ZQ Zuo , , , YH Fu , , , YP Chen , , , 等 . . A new method of reachable set estimation for time delay systems with polytopic uncertainties . . Appl Math Comput , , 2013 . . 221 639 - - 647 . . DOI: 10.1016/j.amc.2013.06.099 http://doi.org/10.1016/j.amc.2013.06.099 . .

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