美賽數(shù)模論文

1、 MCM 2015 Summary Sheet for Team 35565For office use onlyT1 ________________T2 ________________T3 ________________T4 ________________Team Control Number 35565Problem ChosenBFor office use onlyF1 ________________F

2、2 ________________F3 ________________F4 ________________SummaryThe lost MH370 urges us to build a universal search plan to assist searchers to locate the lost plane efficiently and optimize the arrangement of search pla

3、ns.For the location of the search area, we divided it into two stages, respectively, to locate the splash point and the wreckage’s sunk point. In the first stage, we consider the types of crashed aircraft, its motion an

4、d different position out of contact. We also consider the Earth’s rotation, and other factors. Taking all these into account, we establish a model to locate the splash point. Then we apply this model to MH370. we can

5、get the splash point in the open water is 6.813°N 103.49°E and the falling time is 52.4s. In the second stage, considering resistances of the wreckage in different shapes and its distribution affected by ocean

6、 currents, we establish a wreckage sunk point model to calculate the horizontal displacement and the angle deviation affected by the ocean currents. The result is 1517m and 0.11°respectively. Next, we extract a s

7、atellite map of submarine topography and use MATLAB to depict seabed topography map, determining the settlement of the wreckage by using dichotomy algorithm under different terrains. Finally, we build a Bayesian model

8、and calculate the weight of corresponding area, sending aircrafts to obtain new evidence and refresh suspected wreckage area.For the assignment of the search planes, we divide it into two stages, respectively, to determ

9、ine the number of the aircraft and the assignment scheme of the search aircraft. In the first stage, we consider the search ability of each plane and other factors. And then we establish global optimization model. Next

10、 we use Dinkelbach algorithm to select the best n search aircrafts from all search aircrafts. In the second stage, we divide the assignment into two cases whether there are search aircrafts in the target area. If there

11、 is no search aircraft, we take the search area as an arbitrary polygon and establish the subdivision model. Considering the searching ability of each plane, we divide n small polygons into 2n sub-polygons by using No

12、nconvexDivide algorithm, which assigns specific anchor points to these 2n sub-polygons respectively. If there exist search aircrafts, we divide the search area into several polygons with the search aircrafts being at t

13、he boundary of the small polygons. To improve search efficiency, we introduce” maximize the minimum angle strategy” to maximize right-angle subdivision so that we can reduce the turning times of search aircraft. When w

14、e changed the speed of the crashed plane about 36m/s, the latitude of the splash point changes about 1°.When a wreck landing at 5.888m out from the initial zone, it will divorce from suspected searching area, whic

15、h means our models are fairly robust to the changes in parameters. Our model is able to efficiently deal with existing data and modify some parameters basing the practical situation. The model has better versatility and

16、 stability. The weakness of our model is neglect of human factors, the search time and other uncontrollable factors that could lead to deviation compared to practical data. Therefore, we make some in-depth discussions

17、about the model, modifying assumptions establishment above, to optimize our model.Team # 35565 Page 3 of 48Contents1 Introduction...................................

18、..........................................................................................................51.1 Restatement of the Problem ……………………………………….................................….51.2 Literature Review……………………

19、………………………………………………..…...…...62 Assumptions and Justifications...................................................................................................73 Notations………………………………………………………………………………………………….74 Mode

20、l Overview……………...............................................................................................................105 Modeling For Locating the Lost Plane.....................................................

21、.............................105.1 Modeling For Locating the Splash Point………………………………….115.1.1 Types of Planes………………………………………………...…115.1.2 Preparation of the Model—Earth Rotation ………………...….....125.1.3 Modeling……………

22、………………………………………….....135.1.4 Solution of The Model…………………………………………....145.2 Modeling For Locating Wreckage………………………………………...155.2.1 Assumptions of the Model………………………………………..165.2.2 Preparation of the Model……………………………

23、…………….165.2.3 Modeling…………………………………………………………..215.2.4 Solution of the Model……………………………………………..255.3 Verification of the Model……………………………………..……………26 5.3.1 Verification of the Splash Point……………………………….…..265.3.2

24、Verification of the binary search algorithm………………………..276 Modeling For Optimization of Search Plan……………………………...……296.1 The Global Optimization Model…………………………………………...296.1.1 Preparation of the Model…………………………………

25、………..296.1.2 Modeling……………………………………………………….….316.1.3 Solution of the Model……………………………………..……….316.2 The Area Partition Algorithm……………………….…………….…………..……...……336.2.1 Preparation of the Model……………………….………………….336.2.2

26、Modeling………………………………………………………..…346.2.3 Solution of the Model……………………………………….…….356.2.4 Improvement of the Model……………………………..…………367 Sensitivity Analysis……………………………………………………………..388 Further Discussions………………………………………