Searching for a Lost Plane-2015美赛原版-L文.pdfVIP

Searching for a Lost Plane February 10, 2015 1 Summary The year 2014 witnessed a series of air disasters that resulted in huge loss of life, among them is the mysterious disappearance of Malaysia Airlines Flight 370 (MH370) in the Indian Ocean. Although the related countries spent great efforts on the crucial task of finding the plane, considering the vast space to search and the paucity of information, the plane is still not found. In past experiences, mathematical models played a leading role in helping find lost planes in open water. In this paper, we discuss mathematical models that can assist to find aircrafts lost in sea. In order to build a mathematical model to assist the planning of a search for a lost plane considered to have crashed in open water, we first analyze the possi- ble scenarios and propose our assumptions and hypothesis. Then we establish a collision model to predict the number of drifters resulting from the crash accord- ing to the type of the plane we are searching for. For the main part, we set up a search model based on Bayes’ theorem, considering the behavior of the drifters resulted from the crash, the outcome of water surface search and underwater search sequentially to instruct further searching process. Moreover, the alloca- tion of search areas to diverse search planes use branch and bound algorithm to optimize the possible result of the search process, both on the water surface and underwater. A simulation module is built to test our model using both fictional and real situations and to carry out the calculations. Then we apply our model in the actual cases of Air France Flight 447 (AF447) and MH370, applying the real world data. Our recommended searching area for the AF447 case matches the location of the wreckage underwater, while for MH370 we predict its possible wreckage position based on accessible info