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August & September  2019, 12(4&5): 957-968. doi: 10.3934/dcdss.2019064

## Applications of mathematics to maritime search

 1 School of Computer and Computing, Zhejiang University City College, Hangzhou 310015, China 2 Department of investigation, Zhejiang Police College, Hangzhou 310053, China 3 School of Business, Zhejiang University City College, Hangzhou 310015, China 4 School of Business and Economics, Australian National University, Acton ACT 2061, Australia

* Corresponding author: Jinming Zhang

Received  October 2017 Revised  January 2018 Published  November 2018

The issue of searching missing aircraft is valuable after the event of MH370. This paper provides a global optimal model to foster the efficiency of maritime search. Firstly, the limited scope, a circle whose center is the last known position of the aircraft, should be estimated based on the historical data recorded before the disappearance of the aircraft. And Bayes' theorem is applied to calculate the probability that the plane falling in the region can be found. Secondly, the drift of aircraft debris under the influence of wind and current is considered via Finite Volume Community Ocean Model(FVCOM) and Monte Carlo Method(MC), which make the theory more reasonable. Finally, a global optimal model about vessel and aircraft quantitative constraints is established, which fully considers factors including the area of sea region to be searched, the maximum speed, search capabilities, initial distance of the vessels by introducing 0-1 decision variables.

Citation: Jinling Wei, Jinming Zhang, Meishuang Dong, Fan Zhang, Yunmo Chen, Sha Jin, Zhike Han. Applications of mathematics to maritime search. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 957-968. doi: 10.3934/dcdss.2019064
##### References:

show all references

##### References:
The bounding limit of aircraft in distress
Wind-induced drift component diagram
Ocean Surface Zonal Currents-Ocean Surface Meridional Currents(meter/sec)
Sketch of calculation process
Time taken by exhaustive method for optimal solution with quantitative constraint
 Problem size $n$ Number of package $S$ Number of package $t$ 30 $2^{30}$=1073741824 About 1s 50 $2^{50}$=1125899906842624 About 13 days 100 $2^{100}$ About $4\times{}10^{13}$ days
 Problem size $n$ Number of package $S$ Number of package $t$ 30 $2^{30}$=1073741824 About 1s 50 $2^{50}$=1125899906842624 About 13 days 100 $2^{100}$ About $4\times{}10^{13}$ days
Time taken by exhaustive method for optimal solution with quantitative constraint
 Problem size $n$ Number of package $S$ Computation time $t$ 30(20 ships, 10 planes) $\binom{20}{10}\cdot\binom{10}{5}=46558512$ About 0.05 s 50(40 ships, 10 planes) $\binom{40}{10}\cdot\binom{10}{5}=213610453056$ About 4 s 100(90 ships, 10 planes) $\binom{100}{10}\cdot\binom{10}{5}=1441602661439556$ About 400 hours
 Problem size $n$ Number of package $S$ Computation time $t$ 30(20 ships, 10 planes) $\binom{20}{10}\cdot\binom{10}{5}=46558512$ About 0.05 s 50(40 ships, 10 planes) $\binom{40}{10}\cdot\binom{10}{5}=213610453056$ About 4 s 100(90 ships, 10 planes) $\binom{100}{10}\cdot\binom{10}{5}=1441602661439556$ About 400 hours
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