美国大学生数学建模竞赛美赛--论文-

1、 Team # 40906 Page 19 of 22 4.2 Error Analysis of the Model During the crash,the plane will shift with the force of the monsoon and the current.But in practice, the monsoon and the current is different from time to time.However, we assume that the directs of the monsoon and the current are constant

2、in the model.Besides, we ignore the inuence of the attitude of the plane. So there must be errors in the trajectory of the plane calculating. The model bases on the assumption that the plane crashes immediately the last signal sent.But the plane sends signals every ve minutes.So the point where the

3、plane crashes is possibly not the point the last signal sent.This will also leads errors in the model. 5 Conclusion We take the MH370 for example for different crash without any signal in this paper, and build a dynamic model of the plane. Follow the above parts, we calculate the trajectory of the p

4、lane and the ideal fall area. Then in the fall area, we calculate plane position probability density function based on central limit theory and independence principle. We use Bayesian search in the whole probable area, and in each small area we use spiral search. Making use of all kinds of electroni

5、c devices and sensors to search the plane, it improves the search efciency. 6 Strengths and Weaknesses Like any model,the one present above has its strengths and weaknesses. Some of the major points are presented below. 6.1 Strengths Full consideration to the plane movement inuence on monsoon and oc

6、ean current, we analyze the plane force to be more perfect, and improve the accuracy of the model greatly. Before the crash, the study of ight condition determined the search scope area, and avoided blindsearching. It can also improve the search efciency. We ignore thepossibility of plane disintegra

7、tion and the inuence of the plane crashedgesture, ignoring secondary factors in order to simplied mathematical model. We establish themodel and give full consideration to the different models of the plane andsearching process, it has wide range of application. Team # 40906 Page 20 of 22 6.2 Weakness

8、es Because we assumethat plane lost power in the moment, in actually, it may be lost power after yingfor a long time. And it will have a certain error in trajectory calculating. Model does nottake human factors into consideration, such as the possibility of a hijacking. Thesearch method has several

9、limitations. References 1 JJ Bertin, ML Smith - 1989 - Prentice Hall Englewood Cliffs 2 Prosser M J. The hydraulic design of pump sumps and intakesM. BHRA, 1977. 3 Furukawa T, Bourgault F, Lavis B, et al. Recursive Bayesian search-andtracking using coordinated UAVs for lost targetsC/Robotics and Aut

10、omation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on. IEEE, 2006: 2521-2526. 4 Woolsey C. Vehicle dynamics in currentsJ. 2011. Team # 40906 Page 21 of 22 Appendices Plan for Future Searches The loss of the plane has brought the great sorrow to the relations and friends of the

11、passengers, and our heart are very heavy. Please accept my deepest sympathies. We will do everything to search passengers and the plane, and then let me explain our plan for future searches. Because the plane lost in the open ocean, the area is too vast to search. And the lost plane can not send out

12、 any signals, so it is very difcult to search the plane. To nd the lost plane in the shortest time and to improve efciency of search, we decide to search by the following method. Firstly, we need to nd the location where the plane fell into the sea in theory. From the signal that satellites received

13、 for the last time, we can judge the approximate location, speed and direction of the plane when it lost. Then according to the monsoon and weather of the area where the plane lost, judging the trajectory of the plane in the air. And calculate the approximate location in the theory. Secondly, nd the

14、 location where the plane fell into the bottom of the sea in theory. Measure the speed and the direction of the ocean current where the plane fall into the sea using the light buoy sensor. Then probing the topographical condition with radar. The planes move in the sea will be inuenced by ocean curre

15、nt. Giving the speed of the ocean current and the parameter of the plane, we can get the moving trajectory in the theory by analyzing the force analysis. The intersection aof the trajectory and the ocean oor relief map is the location where the plane exist in the theory. Thirdly, we have determine t

16、he theoretical position above two steps. However in the process of crashing, the plan will be affected by various of factors. So the real position of the plane lands in the sea is somtimes different with the theoretical position. Because the plane remains its speed during the process of crashing,add

17、itionally the role of the sea currents tend to be certain in a sea area. So the probability of the plan can be found around the theoretical posi- Team # 40906 Page 22 of 22 tion is unequal. Calculate the probability density distribution of the plan possiblly falling off by mathematical method. In order to improve the efciency of the rescue,we determine to devide the wild area to small areas. And then search the plan in the region with the highest probability preferentially. Then search for the areas where