美赛数模论文英文版

Searching For a Lost Plane

Control#35565

February 10, 2014

Contents

1 Introduction.............................................................................................................................................5

1.1 Restatement of the Problem ……………………………………….................................….5

1.2 Literature Review……………………………………………………………………..…...…...6

2 Assumptions and Justifications...................................................................................................7

3 Notations………………………………………………………………………………………………….7

4 Model Overview……………...............................................................................................................10

5 Modeling For Locating the Lost Plane..................................................................................10

5.1 Modeling For Locating the Splash Point………………………………….11

5.1.1 Types of Planes………………………………………………...…11

5.1.2 Preparation of the Model—Earth Rotation ………………...….....12

5.1.3 Modeling……………………………………………………….....13

5.1.4 Solution of The Model…………………………………………....14

5.2 Modeling For Locating Wreckage………………………………………...15

5.2.1 Assumptions of the Model………………………………………..16

5.2.2 Preparation of the Model………………………………………….16

5.2.3 Modeling…………………………………………………………..21

5.2.4 Solution of the Model……………………………………………..25

5.3 Verification of the Model……………………………………..……………26

5.3.1 Verification of the Splash Point……………………………….…..26

5.3.2 Verification of the binary search algorithm………………………..27

6 Modeling For Optimization of Search Plan……………………………...……29

6.1 The Global Optimization Model…………………………………………...29

6.1.1 Preparation of the Model…………………………………………..29

6.1.2 Modeling……………………………………………………….….31

6.1.3 Solution of the Model……………………………………..……….31

6.2 The Area Partition Algorithm……………………….…………….…………..……...……33

6.2.1 Preparation of the Model……………………….………………….33

6.2.2 Modeling………………………………………………………..…34

6.2.3 Solution of the Model……………………………………….…….35

6.2.4 Improvement of the Model……………………………..…………36

7 Sensitivity Analysis……………………………………………………………..38

8 Further Discussions……………………………………………………………..39

9 Strengths and Weaknesses………………………………………………..…….41

9.1 Strengths ……………………………………………………..…….………41

9.2 Weaknesses…………………………………………………………….…..42

10 Non-technical Paper……………………………………………………………..42

1 Introduction

An airplane (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller. Its main feature is fast and safe. Typically, air travel is approximately 10 times safer than travel by car, rail or bus. However, when using the deaths per journey statistic, air travel is significantly more dangerous than car, rail, or bus travel. In an aircraft crash, almost no one could survive [1]. Furthermore, the wreckage of the lost plane is difficult to find due to the crash site may be in the open ocean or other rough terrain.

Thus, it will be exhilarating if we can design a model that can find the lost plane quickly. In this paper, we establish several models to find the lost plane in seawater and develop an optimal scheme to assign search planes to model to locate the wreckage of the lost plane.

1.1 Restatement of the Problem

We are required to build a mathematical model to find the lost plane crashed in open water. We decompose the problem into three sub-problems:

● Work out the position and distributions of the plane’s wreckage

● Arrange a mathematical scheme to schedule searching planes

In the first step, we seek to build a model with the inputs of altitude and other factors to locate the splash point on the sea-level. Most importantly, the model should reflect the process of the given plane. Then we can change the inputs to do some simulations. Also we can change the mechanism to apply other plane crash to our model. Finally, we can obtain the outputs of our model.

In the second step, we seek to extend our model to simulate distribution of the plane wreckage and position the final point of the lost plane in the sea. We will consider more realistic factors such as ocean currents, characteristics of plane.

We will design some rules to dispatch search planes to confirm the wreckage and decide which rule is the best.

Then we attempt to adjust our model and apply it to lost planes like MH370. We also consider some further discussion of our model.

1.2 Literature Review

A model for searching the lost plane is inevitable to study the crashed point of the plane and develop a best scheme to assign search planes.

According to Newton's second law, the simple types of projectile motion model can

work out the splash point on the seafloor. We will analyze the motion state of 

the plane when it arrives at the seafloor considering the effect of the earth's rotation,

After the types of projectile motion model was established, several scientists were devoted to finding a method to simulate the movement of wreckage. The main difficulty was to combine natural factors with the movement. Juan Santos-Echeandía introduced a differential equation model to simplify the difficulty [2]. Moreover, A. Boultif and D. Louër introduced a dichotomy iteration algorithm to circular computing which can be borrowed to combine the motion of wreckage with underwater terrain [3]. Several conditions have to be fulfilled before simulating the movement: (1) Seawater density keeps unchanged despite the seawater depth. (2) The velocity of the wreck stay the same compared with velocity of the plane before it crashes into pieces. (3) Marine life will not affect our simulation. (4) Acting force

of seawater is a function of the speed of ocean currents.

However the conclusion above cannot describe the wreckage zone accurately. This inaccuracy results from simplified conditions and ignoring the probability distribution of wreckage. In 1989, Stone et.al introduced a Bayesian search approach for searching problems and found the efficient search plans that maximize the probability of finding the target given a fixed time limit by maintaining an accurate target location probability density function, and by explicitly modeling the target’s process model [4].

To come up with a concrete dispatch plan. Xing Shenwei first simulated the model with different kinds of algorithm. [5] In his model, different searching planes are assessed by several key factors. Then based on the model established before, he use the global optimization model and an area partition algorithm to propose the number of aircrafts. He also arranged quantitative searching recourses according to the maximum speed and other factors. The result shows that search operations can be ensured and effective.

Further studies are carried out based on the comparison between model and

reality. Some article illustrate the random error caused by assumptions.

2 Assumptions and Justifications

To simplify the problem, we make the following basic assumptions, each of

which is properly justified.

● Utilized data is accuracy. A common modeling assumption.

● We ignore the change of the gravitational acceleration. The altitude of an aircraft is less than 30 km [6]. The average radius of the earth is 6731.004km, which is much more than the altitude of an aircraft. The gravitational acceleration changes weakly.

● We assume that aeroengine do not work when a plane is out of contact. Most air crash resulted from engine failure caused by aircraft fault, bad weather, etc.

● In our model, the angle of attack do not change in an air crash and the fuselage don’t wag from side to side. We neglect the impact of natural and human factors

● We treat plane as a material point the moment it hit the sea-level. The crashing plane moves fast with a short time-frame to get into the water. The shape and volume will be negligible.

● We assume that coefficient of air friction is a constant. This impact is negligible compared with that of the gravity.

● Planes will crash into wreckage instantly when falling to sea surface. Typically planes travel at highly speed and may happen explosion accident with water. So we ignore the short time.

3 Notations

All the variables and constants used in this paper are listed in Table 1 and Table 2.

Table 1 Symbol Table–Constants

Table 2 Symbol Table-Variables

4 Model Overview

Most research for searching the lost plane can be classified as academic and practical.

As practical methods are difficult to apply to our problem, we approach the

problem with academic techniques. Our study into the searching of the lost plane takes several approaches.

Our basic model allows us to obtain the splash point of the lost plane. We focus on the force analysis of the plane. Then we We turn to simple types of projectile motion model. This model gives us critical data about the movement and serves as a stepping stone to our later study.

The extended model views the problem based on the conclusion above. We run differential equation method and Bayesian search model to simulate the movement of wreckage. The essence of the model is the way to combine the effect of natural factors with distribution of the wreckage. Moreover, using distributing conditions, we treat size of the lost plane as “initial wreckage zone” so as to approximately describe the distribution. Thus, after considering the natural factors, we name the distribution of wreckage a “wreck zone” to minimize searching zone. While we name all the space needed to search “searching zone”.

Our conclusive model containing several kinds of algorithm attempts to tackle a more realistic and more challenging problem. We add the global optimization model and

an area partition algorithm to improve the efficiency of search aircrafts according to the area of search zone. An assessment of search planes consisting of search capabilities and other factors are also added. The Dinkelbach and NonConvexDivide algorithm for the solutions of the results are also added.

We use the extended and conclusive model as a standard model to analyze the

problem and all results have this two model at their cores.

5 Modeling For Locating the Lost Plane

We will start with the idea of the basic model. Then we present the Bayesian search

model to get the position of the sinking point.

5.1 Modeling For Locating the Splash Point

The basic model is a academic approach. A typical types of projectile behavior consists of horizontal and vertical motion. We also add another dimension considering the effect of the earth's rotation. Among these actions, the force analysis is the most crucial part during descent from the point out of contact to the sea-level. Types of plane might impact trajectory of the crashing plane.

5.1.1 Types of Planes

We classify the planes into six groups [7]:

● Helicopters: A helicopter is one of the most timesaving ways to transfer between the city and airport, alternatively an easy way to reach remote destinations.

● Twins Pistons: An economical aircraft range suitable for short distance flights. Aircraft seating capacity ranging from 3 to 8 passengers.

● Turboprops: A wide range of aircraft suitable for short and medium distance flights with a duration of up to 2-4 hours. Aircraft seating capacity ranging from 4 to 70 passengers.

● Executive Jets: An Executive Jet is suitable for medium or long distance flights. Aircraft seating capacity ranging from 4 to 16 passengers

● Airliners: Large jet aircraft suitable for all kinds of flights. Aircraft seating capacity ranging from 50 to 400 passengers.

● Cargo Aircrafts: Any type of cargo. Ranging from short notice flights carrying vital spare parts up to large cargo aircraft that can transport any voluminous goods.

The lost plane may be one of these group. Then we extract the characteristics of planes into three essential factors: mass, maximum flying speed, volume. We use these three factors to abstract a variety of planes:

● Mass: Planes of different product models have their own mass.

● Maximum flying speed: Different planes are provided with kinds of mechanical configuration, which will decide their properties such as flying speed.

● Volume: Planes of distinct product models have different sizes and configuration, so the volume is definitive .

5.1.2 Preparation of the Model—Earth Rotation

When considering the earth rotation, we should know that earth is a non-inertial running system. Thus, mobile on the earth suffers two other non-inertial forces except air friction Fr. They are inertial centrifugal force Fg and Coriolis force Fk. According to Newton’s second law of motion, the law of object relative motion to the earth is:

Rotational angular velocity of the earth is very small, about

.

For a big mobile vr, it suffers far less inertial centrifugal force than Coriolis force, so we can ignore it. Thus, the equation can be approximated as follows:

Now we establish a coordinate system: x axis z axis pointing to the east and south respectively, y axis vertical upward, then vr, ω and Fr in the projection coordinate system are as follows:

φis the latitude of the lost contact point of the lost plane. Put equation 1-3 and equation 1-2 together, then the component of projectile movement in differential equation is:

5.1.3 Modeling

Considering the effect caused by earth rotation and air draught to plane when crashing to sea level, we analyze the force on the X axis by using Newton’s second law, the differential equation on x y and axis, we can conclude:

In conclusion, we establish the earth rotation and types of projectile second order differential model:

According to Coriolis theorem, we analyze the force of the plane on different directions. By using the Newton’s laws of motion, we can work out the resultant acceleration on all directions:

CD is the angle of attack of a plane flew in the best state, w is the angular speed of a moving object, vector j and k are the unit vector on y and z direction respectively,μis the coefficient of viscosity of the object.

5.1.4 Solution of the Model

When air flows through an object, only the air close to layer on the surface of the object in the laminar airflow is larger, whose air viscosity performance is more noticeable while the outer region has negligible viscous force [8]. Typically, to simplify calculation, we ignore the viscous force produced by plane surface caused by air resistance.

Step 1: the examination of dimension in model

To verify the validity of the model based on Newton’s second theorem, first, we standardize them respectively, turn them into the standardization of dimensionless data to diminish the influence of dimensional data.

The standard equation is:

Step 2: the confirmation of initial conditions

In a space coordinate origin based on plane, we assume the earth's rotation direction for the x axis, the plane's flight heading as y axis, the vertical downward direction for z axis. Space coordinate system are as follows:

Figure 1 Space coordinate system

Step 3: the simplification and solution

After twice integrations of the model, ignoring some of the dimensionless in the integral process, we can simplify the model and get the following:

We can calculate the corresponding xyz by putting in specific data to get the information about the point of losing contact.

Step 4: the solution of the coordinate

The distance of every latitude on the same longitude is 111km and the distance of every longitude on the same latitude is 111*cos (the latitude of this point) (km). Moreover, the latitude distance of two points on the same longitude is r×cos(a×pi/180) and the longitude distance of two points on the same latitude is: r×sin(a×pi/180)[9].

We assume a as the clockwise angle starting with the due north direction and r as the distance between two points; X、Y are the latitude and longitude coordinates of the known point P respectively; Lon, Lat are the latitude and longitude coordinates of the unknown point B respectively.

Therefore, the longitude and latitude coordinates of the unknown point Q is:

Thus, we can get coordinates of the point of splash by putting in specific data.

5.2 Modeling For Locating Wreckage

In order to understand how the wreckage distributes in the sea, we have to understand the whole process beginning from the plane crashing into water to reaching the seafloor. One intuition for modeling the problem is to think of the ocean currents as a stochastic process decided by water velocity. Therefore, we use a differential equation method to simulate the impact on wreckage from ocean currents.

A Bayesian Searching model is a continuous model that computing a probability distribution on the location of the wreckage (search object) in the presence of uncertainties and conflicting information that require the use of subjective probabilities. The model requires an initial searching zone and a set of the posterior distribution given failure of the search to plan the next increment of search. As the search proceeds, the subjective estimates of the detection will be more reliable.

5.2.1 Assumptions of the Model

The following general assumptions are made based on common sense and we

use them throughout our model.

● Seawater density keeps unchanged despite the seawater depth.

Seawater density is determined by water temperature, pressure, salinity etc.

These factors are decided by or affected by the seawater density. Considering the falling height, the density changes slightly. To simplify the calculation, we consider it as a constant.

● The velocity of the wreck stay the same compared with velocity of the plane before it crashes into pieces. The whole process will end quickly with a little loss of energy. Thus, we simplify the calculation.

● Marine life will not affect our simulation. Most open coast habitats are found in the deep ocean beyond the edge of the continental shelf, while the falling height of the plane cannot hit.

● Acting force of seawater is a function of the speed and direction of ocean currents. Ocean currents is a complicated element affected by temperature, wide direction, weather pattern etc. we focus on a short term of open sea. Acting force of seawater will not take this factors into consideration.

5.2.2 Preparation of the Model

● The resistance of objects of different shapes is different. Due to the continuity of the movement of the water, when faced with the surface of different shapes, the water will be diverted, resulting in the loss of partial energy. Thus the pressure of the surface of objects is changed. Based on this, we first consider the general object, and then revise the corresponding coefficients.

● 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 increases as the flow rate increases. This kind of stream regimen is called transition 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.

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 uncertain, and the density of the fluid density changes, resulting in uneven flow distribution. This indirectly causes the change of drag coefficient, and the resistance of the fluid is calculated as follows:

● GLCM texture of submarine topography

In order to describe the impact of submarine topography, we choose a rectangular 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 certain gray relation between two pixels which are separated by a certain distance, which is space correlation character of gray in images. GLCM is a common way to describe the texture by studying the space correlation character 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

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. Therefore, 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 produces accelerated speed in opposite direction, so the objects decelerate in the horizontal direction.

The disturbance under the condition of currents could form a complex function 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:

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

● Analysis of Bayesian approach

Bayesian analysis is ideally suited to planning complicated and difficult searches involving uncertainties that are quantified by a combination of objective and subjective probabilities.

We are not able to recreate the conditions of the crash 1000 times and record the distribution of locations where the aircraft hits the water. As a result, definitions of probability distributions in terms of relative frequencies of events do not apply. Instead, we are faced with computing a probability distribution on the location of the wreckage (search object) in the presence of uncertainties and conflicting information that require the use of subjective probabilities. In an ideal situation, search effort is applied in an optimal fashion to maximize the probability of detecting the search object within the effort available. The optimal search problem is a Bayesian decision problem often based on a subjective probability distribution.

As the search proceeds and the search object is not found, the posterior distribution given failure of the search is computed and used as the basis for planning the next increment of search. Even at this stage, subjective estimates of the detection capability of the sensors must often be used because of the lack of previous testing against the search object. Bayesian statistics and decision theory are ideally suited to the task.

5.2.3 Modeling

Step 1: Analysis of motion underwater

The resulting force of object when dropping underwater is :

The equation of buoyancy is:

The acceleration caused by resulting force is:

Acceleration and velocity can be expressed as

Sz is the displacement vector in Z axis. The initial state can be showed as

According to the Newton’s second law, we can get the differential equation on Y axis:

Sy is the displacement vector in Y axis. The initial state can be showed as

The initial state on X axis can be showed as

We can also get the differential equation on X axis:

The differential equation model can be listed as

Step 2: Solution of the motion trail

We can compute the equation by double integral, we can get the list of results:

We can also find that fluid and ocean currents have little impact on the motion of the

object. To simplify the calculation, we omit these two factors to get the equation of

motion trail.

Step 3: Solution of the splash point

When given a Marine depth, the equation can get Sx and Sy. The schematic diagram

can be showed as

Figure 6 Turbulence of ocean currents

Step 4: Solution of the coordinates to final position

The improved binary search algorithm is based on the binary search algorithm. Considering the different heights of the mountains and the long horizontal distance, it is difficult to get the precise value. Thus, the improved binary search algorithm is used to find the range of the object position. The steps of our algorithm steps are as follows.

● First find the time t, the horizontal displacement of the object s, the falling height h of the object and the corresponding depth of the sea H when the horizontal velocity v0=0.

● Compare H to h. If H > h, then find out the sinking point, break out of the loop and finish the program. Else go to the next step.

● Find out the point where H is the maximum on the left. Calculate the falling time at this point, the horizontal displacement s of the object and the horizontal distance between falling point and this point.

● Compare S to s. If S > s, then go to last procedure. If S = s, then find the final sinking point, break out of the loop and finish the program. If S = s, then go to the next step.

● Find out the point where H is the maximum on the right of the point. Calculate the falling time at this point, the horizontal displacement s of the object and the horizontal distance between falling point and this point.

● Compare S with s.If S > s, then go to step3. If S = s, then find the sinking point, break out of the loop and finish the program. If S = s,then go to step4.

● If S = s, H > h , then break out of the loop and finish the program, outputting the coordinate of the final point (s, h).

When the horizontal velocity is zero, due to

The correction factor K is -138.3285. Supposing the initial velocity at the splash point is v0, the figures which show the falling track of the object in the sea made by MATLAB as follows.

Figure 7 track of the object(H > h) Figure 8 track of the object(H > h)

Step 5: Area of wreckage zone

Based on the algorithm above, the initial wreckage zone and wreckage zone affected

by ocean currents can be generated as:

Figure 9 The wreckage distribution

We build a coordinate system that treat A as the origin of the system. S remarks the

final distribution of the wreckage. The area is:

5.2.4 Solution method for the model

The area of searching zone can be divided into several distinct with an area of. In the model, we suppose the probability of the object happening to be found in a particular distinct is p.

The probability of completion is q, then the searching process is completed. In case the searching cannot find the object, according to the Bayesian approach, the probability can be refreshed to：

In the rest of the zone, the probability of finding the lost object also will be refreshed. (The initial probability is r and new probability is)

After searching of n times, the probability of an censored distinct is

When, the probability of other distinct becomes larger.

5.3 Verification of the Model

We adjust our model and apply it to the lost plane MH370. Although it hasn’t be found, we are eager to compare our algorithm with the prediction of experts to testify its applicability and fault tolerance.

5.3.1 Verification of the Splash Point

We can get the data of motion state and the latitude and longitude coordinates of MH370 when it lost contact with the satellite some related information as follows:

Then we substitute it into model:

With

We get

The calculated level distance of two points from P to Q by means of the latitude and longitude coordinates is LPQ = 9824.15m [11], which is in the range of fault tolerance. Therefore we consider the model is correct.

5.3.2 Verification of the binary search algorithm

We analyze the process of the lost plane from the splash point to the final point in the sea. Here are some information about ocean currents

Table 2 information about ocean currents

Considering the velocity of surface currents flow gradually slow down with depth, we take average velocity of different ocean currents flow as initial velocity of surface currents in the subsequent calculation.

can be acquired from falling process established in the basic model:

Substituting it into formula, we can get:

Thus, we can verify that the accuracy of our model will not matter with the simplification of ocean currents.

6 Modeling For Optimization of Search Plan

We need to know key parameters of kinds of planes to determine the most optimized scheduling solution of the searching zone. Whatever the shape of searching zone, we all use the probability calculated by the Bayesian model to act as weight coefficient. Then we multiply the coefficient with the corresponding area to get the equivalent area. The scheduling scheme should meet two condition: (1) Searching planes must cover the searching area. (2) We should select proper kind and quantity of searching plane. Thus, we obtain the key factors to solution – function expression and parameters. By using the Dinkelbach and NonConvexDivide algorithm we can work out the most optimized solution with high efficiency.

6.1 The Global Optimization Model

6.1.1 Preparation of the Model

● Considering maximum speed, search ability, maximum battery life and initial distance from searching area of professional search and rescue plane differs from each other, we establish a mathematical model as follows:

The time of plane i to make a round-trip at full speed is

The time of plane i to implement operations in the sea to be searching zone is

The whole mobilized number of plane i is

The equivalent area of the searching zone can be expressed as

● The goals of the model is to confirm the best of search and rescue plane to make a complete search for the entire zone with the least amount of time T. Given this ,we introduce the following decision variables:

1, plane ai take part in the searching action

0, plane ai will not take part in the action

To implement search coverage rapidly and efficiently in the searching zone , we need to analyze air forces in the composition of the time used in the search operation.

We assume the whole operation begins at ts, ends at te, so the time of the whole action is T = te - ts. Only planes that arrive at searching zone before the end of the operation can participate in action. Every plane ai has the opportunity to take part in the search. Yet it needs to perform repeatedly search due to the limited battery life .

● The time of every sortie equals to its maximum battery life, which contains 3 parts:

The time of plane ai reaching searching area from bases

The time of plane ai implement search operation

The time of plane ai fly from searching area to bases

For convenience, we assume the time of each plane reaching searching zone equals to the time flying back to base and do not consider the time of plane in the base used to replenish fuel. Thus the time of plane ai used to implement search operation in the whole action during the whole time T equals to the total time for all sorties executive search assignments, namely.

6.1.2 Modeling

From the analysis above, it needs to make complete coverage of the searching zone

Thus, the model can be expressed as follows:

6.1.3 Solution of the Model

The model establishes a three-dimensional search for global optimization model with

special objective function (Fractional objective function，and the control variable of

numerator and denominator is either 0 or 1) and linear constraint, we take them equal

to “fractional knapsack problem”. We can calculate the value by using Dinkelbach

arithmetic in polynomial time to meet the practical need.

Step 1 The equivalent transformation of the model

To clarify the character of model 3-1 and interpret the solution of it better, we make a equivalent transformation to the objective function:

Assume that （）

Then the equivalent transformation is

We can know by the classification of optimizing model mentioned before that model II belongs to 0-1 programming in the integer programming. Due to its objective function is a nonlinear function and it belongs to nonlinear programming model also with only one special linear equation constraints. Its particularity lies in the control variables () and the coefficient ahead is 1, so it is called “gross constraint”.

The following will analyze the value of and control variable: according to the expression

We know that the value of is related to the three positive parameters as follow:

(1): the search ability of plane, and

(2): the time plane needed to fly to and back from the target search sea area, and

(3): the maximum battery life of plane, and

In addition, for any plane, only when it meets this condition:, that can it take part in the search movement. In other words, it should have the ability to fly to and back from the target search sea area within its maximum battery life. Therefore, we call 3-1 the precondition. For any plane meeting this precondition, there is. Assume that, then. Besides, we can always meet the following relations by changing the order:

（is the number of planes meeting the precondition）

Step 2 Dinkelbach arithmetic

Equations can be worked out by using Dinkelbach arithmetic: first constructs an auxiliary problem with parameters which have the same optimal solution of the model, and then through the iterative search method. The specific algorithm is as follow:

Assume that:

Constructs an auxiliary problem with parameters which have the same optimal solution of model:

Then we can get the optimal solution:

,

Dinkelbach algorithm has been proved to be needing iteration times in the worst case in solving model, so the algorithm can meet the needs of the actual according to calculate.

6.2 The Area Partition Algorithm

6.2.1 Preparation of the Model

● The area partition algorithm aims to scientifically assign searching resources and enhance interloper ability. In practical searching process, scientists usually adopt polygon to establish search area. By using the global optimization model, we can select some kind high quality searching plane and calculate the overarea of each plane.

● For arbitrary polygon, there exists kinds of polynomial time algorithm to divide the polygon into non-overlaping convex polygon. We name it as “CP” to for convenience.

For any two of the CP, CIk, CIj , if k < j, CIk is the forerunner of CIj, CIj is the successor of CIk. If CIk, CIj has a side in common, they are neighbor to each other. For CI, all the neighbor CP can be named as NextNeighbor(CI).

The set of vertex and anchor W(CI) number the point according to counter-clockwise order. And the line segment (wn,w1) is the common between CI and its NextNeighbor(CI).

The polygon made up by CI and NextNeighbor(CI) is originated from CI. We name it as Poly(CI).

L = (Ls, Le) means the lie with two endpoint on the polygon. Ls is the start point of L, while Le is the end point. When both points begins to move, the moving range will be restricted by the anchor point of CI.

and are the feasible moving range of Ls and Le.

6.2.2 Modeling

Conditions of the model:

Polygon I stands for the area to be searched, whose area is.

There will be N planes assigned to conduct the search and rescue work.

The search ability of plane I is, and it satisfys.

All the search planes set off form initial point at full speed, and enter into the search

area from a particular point, we name it as CSP.

To perform the task quickly, the search planes carry out search work instantly when

arriving at CSP.

Considering overarea of searching plane and the position CSP, we can transform the problem into the following two cases:

Case 1: No search planes is in the search area the search begins.

Case 2: Some searching planes happen to be in the area the search begins.

6.2.3 Solution of the Model

Case 1: No search planes is in the search area at the beginning.

We can combine NonconvexDivide and DetachAndAssign algorithm to work out the

best dispatch of coverage of the search area.

The cutting algorithm of arbitrary polygon I is on the basis of the scan lines. First, we

cut I into

Then dealing with these parts to form a new and complete polygon Ii, Because CIj

usually is not self-contained. So when Area(CIj) < AreaRequired

(S(CIj)), CIj needs to get some parts of area from its neighbor to increase itself.

When Area(CIj) < AreaRequired(S(CIj)), CIj needs to give some parts to his neighbor

to decrease itself. In both cases, the unhandled parts in I should be connected.

The Nonconvex Divde algorithm is used to build scanning lines and cut the PredPoly() into two parts. The DetachAndAssign algorithm is used to distribute the two parts to the anchor or cut them when necessary [10]. We alternate the two algorithms to deal with each CP.

Case 2 Some planes happen to be in the area at the beginning.

When the search begins, the planes in the searching area can carry out search in time.

The CSP of the planes are the initial position of them. We also need to assign searcing

task to them according to the searching ability.

First, we should subdivide the search zone into CPs. And the CSP is in the edge of CP.

We can see this from figure 10. This zone is a non-convex polygon that has 4 anchor

point. are in the edge while are inside.

Figure 10 sample of searching zone I

We subdivide I into four CPs (CI1 - CI4) to guarantee and is in the boundary

line of respectively. Thus we can use the method above to realize the subdivision of

anchor area.

Figure 11 The subdivision of searching zone

6.2.4 Improvement of the Model

By alternating the two algorithms, we can make a reasonable allocation according to searching ability of each plane in order to cover the whole searching zone. Because subdividing arbitrary polygon is not necessarily a convex polygon. The new polygon is depending on the shape of the CPs and the position of the scanning lines.

When the shape of the zone keep unchanged, we can maximize the minimum angle. That is to adjust the interior angles on the same side by moving the scanning line. 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

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 clockwise can reach a nearer anchor point.

● If the polygon satisfy:

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. 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:

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.

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 longitude 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:, it means when the range of speed of the crashed plane changes, the location of the splash point changes. 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

When the distance between wreckage and the center of the wreckage circle is and it meets, the wreckage is out of the effective range of the wreckage circle due to ocean current.

It means that the wreckage is in the effective range of the wreckage zone when, and out of the range of the wreckage circle if.

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 being 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 hydrophone 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 than the artificial diving depth, it requires the use of special search equipment. 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 accuracy, 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 current-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 current 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 model:

After the suspicious wreckage sea area is determined, search and rescue air craft find two pieces of wreckage far distance. For example, the sea area appears surface circulation from the west to the east, and two pieces of wreckage are in the northernmost and southernmost respectively. Then we should consider the existence of eddy.

In order to find the drift efficiently, not only should we refresh suspicious area constantly according to the Bayesian methods, but also we should refer the circulation field data with higher accuracy and numerical simulation method. Accurate numerical simulations results depend on the accurate simulation of eddy current. For the final confirmation of the wreckage distribution area, we should consider the sea surface of the wind speed, wind direction, solar radiation, the net surface heat flux, precipitation and evaporation, tide and so on. We can improve our established model through a higher precision and advanced analysis model.

9 Strengths and Weaknesses

9.1 Strengths

● Our basic model allows us to have a close look at the crashing behavior. This model gives us critical data and serves as a stepping stone to our later study, hence improve the efficiency.

● We establish the differential equation model combined with the earth rotation, which is based on practical situation. This model can also extend to other projects.

● Ocean currents are complicated and mixed due to many factors and independent on inertia. In the extended model, we extract the typical turbulence to representative ocean currents to enhance the applicability of model.

● The conclusive model are capable of utilizing data and results. We consider the equivalent area to adjust searching recourses, which contributes to the optimization of the searching rule.

● Our models are fairly robust to the changes in parameters based on sensitivity analysis. It means a slight change in parameters will not cause a

significant change in the result.

9.2 Weaknesses

● Factors of human judgments and natural factors may be over-simplified. We simply overlooked the influencing ingredients in the crashing process respectively. Actual situation

may be more complicated.

● We assumed that the velocity of the wreck stay the same compared with velocity of the plane. Actually, part of the energy was consumed to compensate for kinds of thermal energy to cause some change in velocity vectors.

● Some of the parameters were revised to simplify the simulation such as sea water density, speed of sea water etc. We didn’t take these factors into consideration entirely.

● Some uncontrollable external factors may cause irreversible interference on important evidence. Thus the evidence may not occur in a continuous mode. The Bayesian approach can play a smaller role.

10 Non-technical paper

The airlines held a press conference and announced that they already have a system could best determine the location of the lost plane which is crashed in the open water and the most optimized plan to arrange search planes for future searches.

In an aircraft crash, almost no one could survive. Furthermore, the wreckage of the lost plane is difficult to find due to the crash site in the open water. There is a clear request to locate the crashed plane，and to do so in a much efficient way.

In their search scheme，searchers should consider the impact of different types of lost aircraft on the splash position, the different effects of the search device equipped with aircraft and other factors in the search process. In fact, there are many factors that may affect the location of the plane crash. In order to improve the predicting efficiency to determine the distribution of the aircraft wreckage and the implementation of optimal search scheme, the scheme divides the process that is from the point out of contact of the aircraft with satellite to the specific location of the wreck into four stages: the plane falling into the seafloor from point out of contact, the final distribution of the plane wreckage in open water, determining the number of search aircraft and arranging the search plan.

As is known to all, the search of the lost plane is an extremely rigorous scientific scheme. The uncertainty of the cash point, restrictions of the search equipment and other factors make the search of work cannot be carried out smoothly. This scheme makes full use of the variously objective information of the lost aircraft at the point out of contact, including a predetermined speed, latitude and longitude at this point, and delimit fall within the scope of the position of the aircraft route.

For the final position of the crashed wreckage in the open water , the scheme incorporates influence and restrictions of ocean currents, water fluid and seabed terrain conditions , by comparing the practical height decreasing with the depth of the ocean, with the practical horizontal displacement of plane as the final distribution of regional debris together. What even more surprising is that according to the data of current velocity that airlines provide as the impact of this variable factors on the results is tiny, it increases the robustness of the model.

When arranging the search planes to salvage, we innovate the scheme by searching twice of the area. First searching part of the search area to get an intuitive understanding of search zone. As to the equivalent area, we calculate the probability distribution density to act as coefficient of the weight to multiple corresponding area.

Then according to maximum speed，initial distance to search zone, the search ability, the maximum battery life of search aircraft to carry out selecting of aircraft, to make the search region can be completely covered and the highest efficiency.

However, in practical situation, some conditions of the scheme ignored or over simplified may affect the results, the airlines also need to do further revisions to the scheme.

In brief, the four stages can apply to any kind of aircraft's search and determine which of search the plane arrangement scheme. Make full use of the existing information, you will find scientific ways to search for the lost plane.

References

[1] Wikipedia. Airplane. http://en.wikipedia.org/wiki/Airplane#Characteristics

[2] Juan Santos-Echeandía, Ricardo Prego& Antonio Cobelo-García. Influence of the heavy

fuel spill from the Prestige tanker wreckage in the overlying seawater column levels of copper, nickel and vanadium. Marine Research Institute. 2006

[3] A. Boultif & D. Louër. Powder pattern indexing with the dichotomy method. J. Appl. Cryst. 2004

[4] L.D. Stone, Theory of Optimal Search, Operations Research Society of America, ORSA Books, Arlington, VA, 1989

[5] Xing Shenwei. Research On Global Optimization Model and Simulation of Joint Aeronautical and Maritime Search. Dalian Maritime University Traffic Engineering and Control. 2012

[6] Wikipedia. Lockheed SR-71 Blackbird.

http://en.wikipedia.org/wiki/Lockheed_SR-71_Blackbird#Overview.

[7] Aircraft types for charter. http://www.aircraft-charter-world.com/aircraft_types.htm.

[8] Parthapratim Biswas, P. Sa´nchez, Michael R. Swift, and P. J. King. Numerical

simulations of air-driven granular separation. School of Physics and Astronomy, University of

Nottingham, Nottingham，2003

[9] Wikipedia. Latitude. http://en.wikipedia.org/wiki/Latitude

[10] Hert Susan, Lumelsky Valdimir. Polygon Area Decomposition for Multi-robot

Workspace Division[J]. International Journal of Computational Geometry & Applications

(S0218-1959), 1998,8(4):437-466.

[11] Tang Bohu, Where has the MH370 crashed

http://i.ifeng.com/news/sharenews.f?aid=79537811

[12] The Beijing News.

http://news.ifeng.com/world/special/malaixiyakejishilian/content-4/detail_2014_04/08/35542237_0.shtml. 2014

[13] Li Guo, The difficult locating wreckage: Satellite Monitoring of Chinese Academy of Sciences. The 21st century business herald. 2014

Appendix

• Matlab Source Code for Submarine Topography

clc,clear

I=imread('map.jpg');

imshow(I);

[x,y]=size(I);

[x,y]=ginput(36);

xlswrite('book.xls',[x,y])



clc, clear

a=xlsread('book.xls');

x=a(:,1)';

y=a(:,2)';

z=-a(:,3)';

xmm=minmax(x);  

ymm=minmax(y);  

xi=xmm(1):xmm(2);

yi=ymm(1):ymm(2);

zi1=griddata(x,y,z,xi,yi','cubic'); 

zi2=griddata(x,y,z,xi,yi','nearest'); 

zi=zi1;  

zi(isnan(zi1))=zi2(isnan(zi1));  

figure(1), plot(x,y,'*')

figure(2), mesh(xi,yi,zi)

• Track of the Object In The Water

clc,clear

m=242000;

g=9.8;

p=1030;

k=-138.32815;

v=200*0.28;

g_h=(m*g-p*g*v)/m;

a=0.04;

h=3400;

v0=200*0.28;

t_end=sqrt(2*h/g_h);

t=0:0.1:t_end;

h=-1/2.*g_h.*t.*t;

x=v0.*t-1/2.*a.*t.*t;

plot(x,h);

hold on;

x_end=v0*t_end-1/2*a*t_end*t_end

h_end=-3400;

v0_end=v0-a*t_end

a_down=1-0.308/2420*(v0_end/2)^2

t2_end=v0_end/a_down;

t2=0:0.1:t2_end;

l=v0_end.*t2-1/2.*a_down.*t2.*t2+x_end;

[k len]=size(t2);

h2=zeros(1,len)-3400;

plot(l,h2);

figure(2)

plot(x,h);

• Algorithm Flow of NonconvexDivide

anddo

if then

if then

if then

Else if

毕业设计（论文）原创性声明和使用授权说明

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基本要求：写毕业论文主要目的是培养学生综合运用所学知识和技能，理论联系实际，独立分析，解决实际问题的能力，使学生得到从事本专业工作和进行相关的基本训练。毕业论文应反映出作者能够准确地掌握所学的专业基础知识，基本学会综合运用所学知识进行科学研究的方法，对所研究的题目有一定的心得体会，论文题目的范围不宜过宽，一般选择本学科某一重要问题的一个侧面。

毕业论文的基本教学要求是：

1、培养学生综合运用、巩固与扩展所学的基础理论和专业知识，培养学生独立分析、解决实际问题能力、培养学生处理数据和信息的能力。2、培养学生正确的理论联系实际的工作作风，严肃认真的科学态度。3、培养学生进行社会调查研究；文献资料收集、阅读和整理、使用；提出论点、综合论证、总结写作等基本技能。

毕业论文是毕业生总结性的独立作业，是学生运用在校学习的基本知识和基础理论，去分析、解决一两个实际问题的实践锻炼过程，也是学生在校学习期间学习成果的综合性总结，是整个教学活动中不可缺少的重要环节。撰写毕业论文对于培养学生初步的科学研究能力，提高其综合运用所学知识分析问题、解决问题能力有着重要意义。

毕业论文在进行编写的过程中，需要经过开题报告、论文编写、论文上交评定、论文答辩以及论文评分五个过程，其中开题报告是论文进行的最重要的一个过程，也是论文能否进行的一个重要指标。

撰写意义：1.撰写毕业论文是检验学生在校学习成果的重要措施，也是提高教学质量的重要环节。大学生在毕业前都必须完成毕业论文的撰写任务。申请学位必须提交相应的学位论文，经答辩通过后，方可取得学位。可以这么说，毕业论文是结束大学学习生活走向社会的一个中介和桥梁。毕业论文是大学生才华的第一次显露，是向祖国和人民所交的一份有份量的答卷，是投身社会主义现代化建设事业的报到书。一篇毕业论文虽然不能全面地反映出一个人的才华，也不一定能对社会直接带来巨大的效益，对专业产生开拓性的影响。但是，实践证明，撰写毕业论文是提高教学质量的重要环节，是保证出好人才的重要措施。

2.通过撰写毕业论文，提高写作水平是干部队伍“四化”建设的需要。党中央要求，为了适应现代化建设的需要，领导班子成员应当逐步实现“革命化、年轻化、知识化、专业化”。这个“四化”的要求，也包含了对干部写作能力和写作水平的要求。

3.提高大学生的写作水平是社会主义物质文明和精神文明建设的需要。在新的历史时期，无论是提高全族的科学文化水平，掌握现代科技知识和科学管理方法，还是培养社会主义新人，都要求我们的干部具有较高的写作能力。在经济建设中，作为领导人员和机关的办事人员，要写指示、通知、总结、调查报告等应用文；要写说明书、广告、解说词等说明文；还要写科学论文、经济评论等议论文。在当今信息社会中，信息对于加快经济发展速度，取得良好的经济效益发挥着愈来愈大的作用。写作是以语言文字为信号，是传达信息的方式。信息的来源、信息的收集、信息的储存、整理、传播等等都离不开写作。

论文种类：毕业论文是学术论文的一种形式，为了进一步探讨和掌握毕业论文的写作规律和特点，需要对毕业论文进行分类。由于毕业论文本身的内容和性质不同，研究领域、对象、方法、表现方式不同，因此，毕业论文就有不同的分类方法。

按内容性质和研究方法的不同可以把毕业论文分为理论性论文、实验性论文、描述性论文和设计性论文。后三种论文主要是理工科大学生可以选择的论文形式，这里不作介绍。文科大学生一般写的是理论性论文。理论性论文具体又可分成两种：一种是以纯粹的抽象理论为研究对象，研究方法是严密的理论推导和数学运算，有的也涉及实验与观测，用以验证论点的正确性。另一种是以对客观事物和现象的调查、考察所得观测资料以及有关文献资料数据为研究对象，研究方法是对有关资料进行分析、综合、概括、抽象，通过归纳、演绎、类比，提出某种新的理论和新的见解。

按议论的性质不同可以把毕业论文分为立论文和驳论文。立论性的毕业论文是指从正面阐述论证自己的观点和主张。一篇论文侧重于以立论为主，就属于立论性论文。立论文要求论点鲜明，论据充分，论证严密，以理和事实服人。驳论性毕业论文是指通过反驳别人的论点来树立自己的论点和主张。如果毕业论文侧重于以驳论为主，批驳某些错误的观点、见解、理论，就属于驳论性毕业论文。驳论文除按立论文对论点、论据、论证的要求以外，还要求针锋相对，据理力争。

按研究问题的大小不同可以把毕业论文分为宏观论文和微观论文。凡届国家全局性、带有普遍性并对局部工作有一定指导意义的论文，称为宏观论文。它研究的面比较宽广，具有较大范围的影响。反之，研究局部性、具体问题的论文，是微观论文。它对具体工作有指导意义，影响的面窄一些。

另外还有一种综合型的分类方法，即把毕业论文分为专题型、论辩型、综述型和综合型四大类：

1．专题型论文。这是分析前人研究成果的基础上，以直接论述的形式发表见解，从正面提出某学科中某一学术问题的一种论文。如本书第十二章例文中的《浅析领导者突出工作重点的方法与艺术》一文，从正面论述了突出重点的工作方法的意义、方法和原则，它表明了作者对突出工作重点方法的肯定和理解。2．论辩型论文。这是针对他人在某学科中某一学术问题的见解，凭借充分的论据，着重揭露其不足或错误之处，通过论辩形式来发表见解的一种论文。3．综述型论文。这是在归纳、总结前人或今人对某学科中某一学术问题已有研究成果的基础上，加以介绍或评论，从而发表自己见解的一种论文。4．综合型论文。这是一种将综述型和论辩型两种形式有机结合起来写成的一种论文。如《关于中国民族关系史上的几个问题》一文既介绍了研究民族关系史的现状，又提出了几个值得研究的问题。因此，它是一篇综合型的论文。

写作步骤：毕业论文是高等教育自学考试本科专业应考者完成本科阶段学业的最后一个环节，它是应考者的 总结 性独立作业，目的在于总结学习专业的成果，培养综合运用所学知识解决实际 问题 的能力。从文体而言，它也是对某一专业领域的现实问题或 理论 问题进行 科学 研究 探索的具有一定意义的论说文。完成毕业论文的撰写可以分两个步骤，即选择课题和研究课题。

首先是选择课题。选题是论文撰写成败的关键。因为，选题是毕业论文撰写的第一步，它实际上就是确定“写什么”的问题，亦即确定科学研究的方向。如果“写什么”不明确，“怎么写”就无从谈起。

教育部自学考试办公室有关对毕业论文选题的途径和要求是“为鼓励理论与工作实践结合，应考者可结合本单位或本人从事的工作提出论文题目，报主考学校审查同意后确立。也可由主考学校公布论文题目，由应考者选择。毕业论文的总体要求应与普通全日制高等学校相一致，做到通过论文写作和答辩考核，检验应考者综合运用专业知识的能力”。但不管考生是自己任意选择课题，还是在主考院校公布的指定课题中选择课题，都要坚持选择有科学价值和现实意义的、切实可行的课题。选好课题是毕业论文成功的一半。

第一、要坚持选择有科学价值和现实意义的课题。科学研究的目的是为了更好地认识世界、改造世界，以推动社会的不断进步和发展 。因此，毕业论文的选题，必须紧密结合社会主义物质文明和精神文明建设的需要，以促进科学事业发展和解决现实存在问题作为出发点和落脚点。选题要符合科学研究的正确方向，要具有新颖性，有创新、有理论价值和现实的指导意义或推动作用，一项毫无意义的研究，即使花很大的精力，表达再完善，也将没有丝毫价值。具体地说，考生可从以下三个方面来选题。首先，要从现实的弊端中选题，学习了专业知识，不能仅停留在书本上和理论上，还要下一番功夫，理论联系实际，用已掌握的专业知识，去寻找和解决工作实践中急待解决的问题。其次，要从寻找科学研究的空白处和边缘领域中选题，科学研究。还有许多没有被开垦的处女地，还有许多缺陷和空白，这些都需要填补。应考者应有独特的眼光和超前的意识去思索，去发现，去研究。最后，要从寻找前人研究的不足处和错误处选题，在前人已提出来的研究课题中，许多虽已有初步的研究成果，但随着社会的不断发展，还有待于丰富、完整和发展，这种补充性或纠正性的研究课题，也是有科学价值和现实指导意义的。

第二、要根据自己的能力选择切实可行的课题。毕业论文的写作是一种创造性劳动，不但要有考生个人的见解和主张，同时还需要具备一定的客观条件。由于考生个人的主观、客观条件都是各不相同的，因此在选题时，还应结合自己的特长、兴趣及所具备的客观条件来选题。具体地说，考生可从以下三个方面来综合考虑。首先，要有充足的资料来源。“巧妇难为无米之炊”，在缺少资料的情况下，是很难写出高质量的论文的。选择一个具有丰富资料来源的课题，对课题深入研究与开展很有帮助。其次，要有浓厚的研究兴趣，选择自己感兴趣的课题，可以激发自己研究的热情，调动自己的主动性和积极性，能够以专心、细心、恒心和耐心的积极心态去完成。最后，要能结合发挥自己的业务专长，每个考生无论能力水平高低，工作岗位如何，都有自己的业务专长，选择那些能结合自己工作、发挥自己业务专长的课题，对顺利完成课题的研究大有益处。

致 谢

这次论文的完成，不止是我自己的努力，同时也有老师的指导，同学的帮助，以及那些无私奉献的前辈，正所谓你知道的越多的时候你才发现你知道的越少，通过这次论文，我想我成长了很多，不只是磨练了我的知识厚度，也使我更加确定了我今后的目标：为今后的计算机事业奋斗。在此我要感谢我的指导老师——***老师，感谢您的指导，才让我有了今天这篇论文，您不仅是我的论文导师，也是我人生的导师，谢谢您！我还要感谢我的同学，四年的相处，虽然我未必记得住每分每秒，但是我记得每一个有你们的精彩瞬间，我相信通过大学的历练，我们都已经长大，变成一个有担当，有能力的新时代青年，感谢你们的陪伴，感谢有你们，这篇论文也有你们的功劳，我想毕业不是我们的相处的结束，它是我们更好相处的开头，祝福你们！我也要感谢父母，这是他们给我的，所有的一切；感谢母校，尽管您不以我为荣，但我一直会以我是一名农大人为荣。

通过这次毕业设计，我学习了很多新知识，也对很多以前的东西有了更深的记忆与理解。漫漫求学路，过程很快乐。我要感谢信息与管理科学学院的老师，我从他们那里学到了许多珍贵的知识和做人处事的道理，以及科学严谨的学术态度，令我受益良多。同时还要感谢学院给了我一个可以认真学习，天天向上的学习环境和机会。

即将结束*大学习生活，我感谢****大学提供了一次在**大接受教育的机会，感谢院校老师的无私教导。感谢各位老师审阅我的论文。

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