Safety analysis for stochastic systems arising in air traffic management application
This thesis studies the stochastic safety analysis and resolution for the Air Traffic Management (ATM) systems. Based on a simplified stochastic differential equation model of aircraft dynamics, three approaches to estimating the aircraft safety are introduced: a Multi- level Markov Chain (MMC) approximation method for probabilistic prediction of the aircraft conflict, an Adaptive Multi-level Markov Chain (AMMC) approximation method, and an Air Traffic Density Estimation (ATDE) approach, which is a simulation-based method for predicting congestions in the airspace within a period of time. The MMC and AMMC approximation approaches achieve a better compromise between accuracy and computational time compared with the one-level Markov chain approximation. Since, both MMC and AMMC can only handle few number of aircraft and for multi-aircraft encounters, the computation time would become prohibitive. Therefore, the ATDE is developed to evaluate traffic density for encounters involving many aircraft also it is considered as a high-level view of traffic map. Thus, it estimates the traffic of a certain region of the airspace regardless of the number of aircrafts travel in that region. The generated air traffic density indicates the congestion zone to be avoided or less congestion zone to be alert. Using the estimated aircraft safety, we then formulate an optimal trajectory planning problem and develop an efficient solution algorithm for resolving the conflicts. Numerical examples arising in ATM systems are presented to evaluate and compare the two conflict detection approaches along with the developed conflict resolution algorithm.
Hu, Purdue University.
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