15年美赛B题一等奖论文

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T1________________ T2________________ T3________________ T4________________ Team Control Number

32642

Problem Chosen

B

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F2________________

F3________________

F4________________ 2015

Mathematical Contest in Modeling (MCM/ICM) Summary Sheet

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Searching a crashed plane in the sea is a hard job, while searching a lost plane presumed crashed in the open sea is much harder. To help find a lost plane, we restore the whole process, divide it into three periods and construct models respectively.

The first model is a Stochastic Particle Simulation Model(SPSM), which describes the process that the plane loses contact with the ground and falls into the sea. Then we treat debris of the plane as separate particles and build a Drift Model based on Stochastic Particle Migration Model, which helps us to describe the motion of the debris of the plane and find the possible area containing the lost plane. Finally, we use BP-Artificial Neural Network Algorithm to choose the most suitable type of search planes and try to plan the optimal routine based on Time Homogeneous Markov Chain Model.

In the first period, we break it down into two models: Fly Model and Fall Model. In the Fly Model, considering the great uncertainty on the plane crash, we use SPSM to find the distributions of the position where the plane lost power. Also, we get the distributions of flight speed, fight course and flight duration in that position. Then we divided the crashed plane into two types: with gliding function and without gliding function. Each type of the plane falls down in different way.

In the second period, our goal is to simulate the motion of the debris in the water. We assume that the debris of the plane float on the surface, and it is small enough to ignore the affection of wave force. Based on the Leeway Model, we analyze its acceleration while considering the disturbance of environment at the same time. Then we check the model with data from National Oceanographic Data Center (NOAA) and get a good result.

In the third period, we should choose the most suitable type of search plane and plan the optimal search routine. Using BP-ANNs Model, we determine the input layer as some factors on sea states and the output layer as several factors on the performance of a search plane. The outputs we get are the criterion by which we choose the most suitable plane. Then we try to find the optimal routine based on Time Homogeneous Markov Chain Model.

We conduct Sensitive Analysis on the BP-ANNs and find that the model is robust. We also analyze our strengths and weaknesses and give a brief conclusion.