美赛数模论文 - 图文

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? Ocean currents and influencing factors

Ocean currents, also called sea currents, are large-scale seawater movements which have relatively stable speed and direction. Only in the land along the coast, due to tides, terrain, the injection of river water, and other factors, the speed and direction of ocean currents changes.

Figure 2 Distribution of world ocean currents

It can be known from Figure 2 that warm and cold currents exist in the area where aircraft incidences happened. Considering the fact that the speed of ocean currents slows down as the increase of the depth of ocean, the velocity with depth sea surface currents gradually slowed down, vx is set as the initial speed of ocean currents in subsequent calculations.

? Turbulent layer

Turbulent flow is one kind of state of the fluid. When the flow rate is very

low, the fluid is separated into different layers, called laminar flow, which do not mix with each other. As the flow speed increases, the flow line of the fluid begins to appear wavy swing. And the swing frequency and amplitude in-creases as the flow rate increases. This kind of stream regimen is called tran-sition flow. When the flow rate becomes great, the flow line is no longer clear and many small whirlpools, called turbulence, appeared in the flow field.

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Under the influence of ocean currents, the flow speed of the fluid changes as the water depth changes gradually, the speed and direction of the fluid is un-certain, and the density of the fluid density changes, resulting in uneven flow distribution. This indirectly causes the change of drag coefficient, and the re-sistance of the fluid is calculated as follows:

f?kv2

? GLCM texture of submarine topography

In order to describe the impact of submarine topography, we choose a rectan-gular region from 33°33?W, 5°01?N to 31°42?W , 3°37?N. As texture is formed by repetitive distribution of gray in the spatial position, there is a cer-tain gray relation between two pixels which are separated by a certain dis-tance, which is space correlation character of gray in images. GLCM is a common way to describe the texture by studying the space correlation cha-racter of gray. We use correlation function of GLCM texture in MATLAB:

I=imread ('map.jpg'); imshow(I);

We arbitrarily select a seabed images and import seabed images to get the coordinate of highlights as follows：

Table 1 Coordinate of highlights NO. 1 2 3 4 5 6 7 8 9 10 11 12 x/km 154.59 151.25 174.6 172.38 165.71 215.75 262.46 331.42 320.29 272.47 107.88 25.579 y/km 1.365 8.19 14.02 19.23 24.82 26.31 22.96 22.34 27.55 27.55 28.79 27.05 NO. 13 14 15 16 17 18 19 20 21 22 23 24 x/km 91.2 40.04 117.89 74.51 45.6 103.43 48.934 212.42 272.47 325.85 230.21 280.26 y/km 22.71 18.12 14.89 12.29 8.56 5.58 3.51 2.85 2.48 6.45 7.32 9.93 NO. 25 26 27 28 29 30 31 32 33 34 35 36 x/km 331.42 235.77 240.22 331.42 102.32 229.1 176.83 123.45 32.252 31.14 226.88 291.38 y/km 16.63 13.9 17.75 24.45 19.48 18.24 9.18 3.23 11.79 27.8 16.01 5.46

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Then we use HDVM algorithm to get the 3D image of submarine topography, which can be simulated by MATLAB.

Figure 3 3D image of submarine topography

? Objects force analysis under the condition of currents

f is the resistance, fi is the disturbance resistance, Ff is the buoyancy, G is

gravity of object.

Figure 4 Force analysis of object under the conditions of currents

Considering the impact of currents on the sinking process of objects, when interfered with currents, objects will sheer because of uneven force. There-

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fore, taking the object as a reference point, the sinking direction as X, movement direction as Y, the axis which is perpendicular to Z and Y as X, the force of spatial coordinate system can be drawn as follows:

Figure 5 Force analysis of objects under the coordinate system

We analyze the force on objects. According to the hypothesis 1 (assuming that the movement condition of aircraft did not change in the moment of the crash), there is some initial velocity when objects fall into the water. When the initial velocity is decomposed in a coordinate system, we can get velocity

component vx in the horizontal direction and vy in the vertical direction. As the force on the upper and lower surfaces is equal, so the joint force is zero. Only resistance is existed in the horizontal direction and the resistance pro-duces accelerated speed in opposite direction, so the objects decelerate in the horizontal direction.

The disturbance under the condition of currents could form a complex func-tion which varies with the time. Here we assume that the disturbance force is a function which varies with the speed of currents as follows: The disturbance resistance of objects:

fi

K is the fluid drag coefficient, K = 0.6, Sz is the displacement of an object un-der the disturbance force.

? Analysis of Bayesian approach

?k?(sZ)???k?vZ22