2015年美国大学生数学建模竞赛论文之Exactly Search Crashed rashed Airplane

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Team Control Number

34364

Problem Chosen

B

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2015 Mathematical Contest in Modeling (MCM) Summary Sheet

Exactly Search Crashed Airplane

Summary

When investigating the cause of a plane crash, people mainly analyze on the black box of the plane, including the mysterious disappearance of Malaysia Airlines MH370. There have been dozens of aircraft disappeared in the ocean . It is a tough problem to search the downed plane in the sea. In this paper, we search the crashed plane according to following methods .

First, we use K- means clustering analysis method to divide most of airplanes into three categories(large commercial plane, small plane and medium-sized passenger aircraft mix). The number of first category planes falled into sea is more than the other two , so large airplanes are our object of study. Considering the sailing speed, sailing height, pressure drag of the plane and the initial crashing location, and so on, we analyze force of crashed aircraft .We establish mathematical model to simulate the crashed planes’crashed track ,which help us to determine the different probability of three regions and obtain the horizontal distance between falling point and initial position .These three areas will be divided into a number of grid .For each grid , based on the speed and direction of ocean currents, seabed topography and Monte Carlo simulation methods ,we obtain the probability of each grid respectively. Then, according to the probability of priority ,we use Bayesian model and center of the spiral to search above area exactly.

In the search process, the search plane use two different search routes - rules and random to search the falling area. Taking into account the expensive cost of search, we adopt the use of unconstrained optimization for search program planning to make the search cost minimum, Through simulation results, if the search area is 10 km * 10 km of the sea ,we should dispatched two flying routes with one plane respectively.all three planes,and the probability we searched for downed plane is 0.1325.

Finally, we simulate 447 Air France which verificates that our model is feasible.