Icing is one of the leading causes of fatal aircraft accidents worldwide. Encountering icing conditions, dynamic characteristics of the aircraft will be damaged, thereby greatly affecting flight safety. Research on real-time estimations of the safety envelope under icing conditions is critical to improve flight safety. In order to determine the safety envelope, the reachability analysis based on the level set method is presented. The reachable set is obtained via computing the Hamilton-Jacobi partial differential equation (HJPDE), which is based on optimal control and is used in the landing phase of an aircraft. The results show that icing will shrink the safety envelope. Particularly under severe icing conditions, the stall speed of the aircraft will increase, and dynamic behavior will be more sensitive. A slight change of command by the pilot may contribute to the flight state moving outside the safety envelope. Furthermore, the effect of flap deflection was considered, which positively impacts the expanding safety envelope during the landing phase. Finally, a maneuvering coping strategy based on safety envelope is proposed. Examples are provided using the NASA’s generic transport model (GTM), and the results can be applied to flight safety risk assessment, providing theoretical guidance for the design of envelope protection systems.
<p>Rising El Ni&#241;o&#8211;Southern Oscillation (ENSO) variability is expected to influence Earth&#8217;s forest ecosystems, through changes in how coordinated annual tree growth is across large spatiotemporal scales. However, the mechanisms by which changes in ENSO variability affect tree growth remains poorly understood, especially in understudied subtropical forests. We use a newly built tree ring network collected from 4,028 trees at 144 forest locations across East Asian subtropical forests (EASF) at subcontinental scales (&#8764;2,000 km), to assess long-term influences of ENSO on the spatiotemporal variability in tree radial growth across China. Our results demonstrate a west-east dipole pattern of synchronized tree growth in EASF moisture-limited tree populations, with positive growth responses to El Nino in southeastern China, and negative growth responses in the southwestern China. Specifically, trees grew more in El Ni&#241;o years in eastern populations, but less in western populations. This pattern likely results from the contrasting effects of ENSO on drought limitation along a longitudinal gradient. Our results also show that increasingly severe El Ni&#241;o/La Ni&#241;a years have caused a sharp rise in tree growth coherence over past 150 years in these moisture-limited populations. A further increase in climate variability, as is expected with climate change, could destabilize subtropical forest ecosystems by synchronizing tree growth to an unprecedented level. In all, our results highlight the need for further research on the ecological implications of rising synchrony, given its increasing relevance to global forest ecosystems in a time of rising climate variability.</p>
The exact region of attraction plays an important role in autonomous nonlinear system, while the results based on the conventional method, such as Lyapunov function approach, are always conservative. However, results via the manifold method, which is the main approach studied, are exact. This method optimizes the distribution of points on the circle through modifying the end point of the former trajectory and inserting/deleting point on the circle on the basis of trajectory arc length method to improve the accuracy and efficiency. First, the basic theory of manifold method is introduced. Secondly, a methodology for determining stable manifold are proposed, which is the core of the manifold method in stability boundary determining. Finally, on this basis, three examples about academic model, power system and aviation system are taken to illustrate the advantages of the method. The results show that the method can improve the accuracy and significantly reduce the calculation time, and can be widely used in engineering systems.
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