Searching for a lost airplane generic model and examples-2015美国数学建模竞赛-一等奖.docxVIP

Team # 33842?????? ???????????????? Page PAGE \* MERGEFORMAT29 of 25 For office use onlyT1________________T2________________T3________________T4________________Team Control Number33842?Problem ChosenBFor office use onlyF1________________F2________________F3________________F4________________ 2015 Mathematical Contest in Modeling (MCM) Summary Sheet Searching for a lost airplane: generic model and examples Abstract Although airplanes can be regarded as the safest transport, passengers have little chance to survive if accidents occur. Once crashed, it is difficult to find the accurate location, especially on open water. And an effective search strategy is necessary to save search time and expense. In this paper, we develop a generic model to search for a lost airplane, which consists of three phases: the global search area decision, search area division, local area search. In the global search area decision phase, the falling trajectory is divided into two stages: the falling trajectory in the air and falling trajectory in the water. For falling trajectory in the air, gravity, air friction and lift are taken into account in the force diagram and thus the falling trajectory in the air can be decided. For the falling trajectory in the water, the buoyancy, gravity and water friction are considered which determines the falling trajectory in the water. What’s more, the accurate time of the accident, the possible changes in flight direction and other uncertainties are also considered so as to get a search area. In the second phase, the Bayesian statistic is applied which has been used to search for lost boats and airplanes successfully. Based on the Bayesian statistic, Bayesian search theory is put forward. We first decide the prior distribution according to the known information, then construct the search order in which the area with higher probability is searched at first, and finally