发布时间 : 星期五 文章美赛数模论文 - 图文更新完毕开始阅读6a82508558fafab068dc028d
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Thus we can optimize the subdividing result. The difference is that, its endpoint?s range of movement calculate as follows:
? Ls moving at the direction of anti-clockwise from current position t3 can reach
a nearer anchor point while moving at the direction of clockwise can reach wm when
Area(CIj?T)?AreaRequired(S(CIj))rr
If PredPoly(CI, (t1, t2)) =φ, Le moving at the direction of anti-clockwise from current position t3 can reach a nearer anchor point while moving at the direction of clockwise can reach wm extremely. If PredPoly(CI, (t1, t2))≠φ, Le moving at the direction of anti-clockwise from current position t3 can t2 while moving at the direction of clock-wise can reach a nearer anchor point.
? If the polygon satisfy:
Area(CIj?T)?AreaRequired(S(CIj))Area(CIj?PredPoly(CI,(t1,t2)))?AreaRequired(S(CIj))
rrrr
Ls moving at the direction of anti-clockwise from current position t3 can reach a near-er anchor point while moving at the direction of clockwise can reach wm. Le moving at the direction of anti-clockwise from current position t3 can reach a nearer anchor point while moving at the direction of clockwise can reach t1.
? If the polygon satisfy:
Area(CIj?T)?AreaRequired(S(CIj))Area(CIj?PredPoly(CI,(t1,t2)))?AreaRequired(S(CIj))rrrr
Ls can only move at the direction of anti-clockwise from current position t3 to reach wm. Le can only move at the direction of clockwise from current position to t2.
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7 Sensitivity Analysis
7.1 Sensitivity Analysis of the Basic Model
It leads to changes of latitude and longitude coordinates of drowning point by reason of different type and motion state in the air and flight height of the hunted plane. We conduct sensitivity analysis of the basic model through altering the latitude and lon-gitude coordinates of drowning point to get the changes of motion state in the air of crash plane.
For the basic model, fed into the data about MH370 and calculate, we can get this:???1?,?v?36m/s, it means when the range of speed of the crashed plane changes ?v?36m/s, the location of the splash point changes ???1?. Thus, We can think that the sensitivity of the basic is good.
7.2 Sensitivity Analysis of the Basic Model
We equivalent the radius of the initial search zone of the crashed plane as R. Due to some irresistible factors (such as wind-force), the wreckage may out of the range of initial wreckage circle. We calculate the distance between the wreckage and the center of the wreckage circle when the wreckage is just out of the wreckage circle due to ocean current , and according to this, we analysis the sensitivity of model 2. As figure 12 shows：
Figure 12 Random Error of the Radius
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When the distance between wreckage and the center of the wreckage circle is R??R and it meets ?R?2SX, the wreckage is out of the effective range of the wreckage circle due to ocean current.
R?63.6m??t?6.423s???SX?2.944m ?SY?1517m????R?2SX?5.888m
It means that the wreckage is in the effective range of the wreckage zone when
?R?5.888, and out of the range of the wreckage circle if ?R?5.888.
8 Further Discussions
? Considering the signal from Black Box when searching the lost plane
The location of the Black Box mainly depends on ULB under water .When the Black Box comes across water, the ULB is activated, which generates
underwater acoustic pulse signal with the frequency of 37.5KHZ per second. The built –in battery can work 30 days at least in a row. With the power be-ing depleted, the ultrasonic signal will be weaker until it stops working 30 days later. Because the detectable range of the beacon signal is extremely limited in contrast with the sea, we use the following ways to find the Black Box quickly [12].
According to the model above, we locate the zone where we search the wreckage.
We narrow the scope of location by dispatching search and rescue aircraft and using the towed sonar. Finally, we use the source direction of the hy-drophone positioning signal and position the Black Box.
The signal can be detected by detector in the range of 1800~3600 meters in
the distance to the beacon. When the ULB emits signal, this can be located through special sonar detectors. If the Black Box sinks into shallow sea, the divers can salvage it out of water. If it sinks into deep sea, which is more
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than the artificial diving depth, it requires the use of special search equip-ment. The operator positions the Black Box to salvage mechanically through integrated display console, which is performed by control of the submarine sonar scanning device, beacon direction locator and deep-sea camera.
? Considering the strategy of the pilot when locating the wreckage zone
When the aircraft fails engine power, experienced pilots often choose the appropriate landing field, and control the plane as much as possible. In the basic model, the aircraft is equivalent as a particle. There does not exist
swinging around in the process of falling. The flight path can be regarded as a parabola from the point of losing contact to diving into water. It is not possible to deviate from the original channel. In order to improve the accu-racy, we need to enlarge the possible zone of the initial wreckage.
If lost contact point has a continental plate nearby, considering the pilots will regard the neighboring continent as big-weighted landing, describing new geographic outline can improve the search efficiency.
We estimate the new initial wreckage zone in the extended model, finding the wreckage zone which is affected by ocean current ring. This will ensure that we will not ignore suspicious wreckage area.
? Considering the variety of ocean currents, especially eddies
The variability of the ocean currents is the most important interference to the uncertainty of the position of wreckage, which will make the multiple current models and the algorithm of the satellite buoy drift trajectory play an ineffective role. For example, India Ocean has stable Antarctic Circumpolar Current from west to east, which exist a lot of eddy. When the bending of the current within a certain range is exceedingly big, part of the current will be separate with the maternal current, which form an independent eddy cur-rent-it is a local current revolving, in the meantime, moving forward. The range of the influence is between 100-200 km, which will be a few days or a few years [13]. When it meets special terrain, mobile track of the eddy cur-rent will change. So it is difficult to locate the wreckage direction accurately. We can use the following steps to improve the prediction ability of the mod-el: