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2015年美赛O奖论文B题Problem_B_32879

2015年美赛O奖论文B题Problem_B_32879

2015Mathematical Contest in Modeling(MCM)Summary Sheet

Into the Void:A Probabalistic Approach to the Search for Missing Aircraft

In recent years,the disappearance of major commercial aircraft over open ocean has led to expensive international search efforts.These searches require the efficient allocation of resources and time in order tofind survivors of the crash and the airplane itself.

We develop a generic probabilistic model to not only predict the location of the downed aircraft,but to also aid in optimizing the search in a time effective manner.This model assumes that at the moment of lost signal,the plane experiences a failure and is no longer powered.Specifically,we accomplish the following:

•Initial Probability Distribution:We create a prior probability density function to model the potential locations of the missing plane.This distribution is based solely on the knowledge that we have about the plane at the time of lost contact:its location, bearing,cruise altitude,and lift-to-drag ratio.

•Search Patterns:We implement four independent search patterns and develop a method to measure their effectiveness based on the total probability offinding the aircraft.We construct an optimization algorithm to determine the most effective means of conducting each search.

•Dynamic Probability Model:We employ Bayesian Inference to continuously adjust the probabilities of our distribution as information from the search is collected and processed.This allows us to create a posterior probability distribution which refines the data utilized in subsequent searches.

•Versatility:We explore variations of crash and search scenarios that realistically simulate actual incidents.This adaptability is achieved through the incorporation of adjustable input parameters that reflect unique circumstances.

Ultimately,our model demonstrates that an easily-packed and spacially-efficient pattern, such as the rectangular parallel-sweep,most efficiently maximizes the probability offinding a lost aircraft over time.

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