Wu Mengxiang Dong Xue Gao Long

（School of Physics and Electronic-Electrical Engineering， Ningxia University， Yinchuan 750021，China）

Abstract： Space debris is called the image of space junk. In this paper， the definition and classification of space debris are studied. The processing methods of space debris and the earnings of the company are analyzed. In view of the above problems， proposed algorithm based on analytic hierarchy process （AHP） finally， use MATLAB programming to obtain the simulation results， and verify the true results are correct. The innovation of this paper is to propose the method of analytic hierarchy process to solve the problem of space debris.

Key word： AHP ； Space debris； MATLAB

1.Introduction

In a variety of space debris of the previously mentioned， the release， space activities of dispersal property etc. belong to a class of space debris， and explosion on orbit or collision producing organisms and the collision of particles sputtering material， which belongs to the second level of space debris. Thus， paint peeling block and the protective layer some space launch directly produce a fragment， and some other space particle impact generated by the spacecraft surface of the secondary debris[1-3].

2 Analytic hierarchy process

2.1 Build hierarchy model

According to the factors of influence of space debris， the problem is divided into three levels， the top is the target layer， namely space debris processing results； the middle layer is the rule layer， distribution of space debris shape and quality， space debris， remove the four factors， the operation speed of the space debris in the existing technology， space debris； the bottom is the indicator layer， namely， cost， revenue， technical difficulty and risk.

Construction of the following indicators system of the results of space debris processing：

Fig .1 the results of space debris processing

2.2 Processing model of space debris

Assuming that the above layer of elements is the rule， the relationship of the next layer are ，，，. Our aim is to give ，，， corresponding weights according to their relative importance to the criteria. So we use the comparative method， the specific method is：

is a matrix composed of ， and is called the comparative judgment matrix.

According to the above properties， matrix are symmetric， so when filling， usually to fill in the part of ， then just judge and fill in the triangle or below the triangle n（n-1）/2 element on.

In exceptional cases， matrix can have transitivity， which satisfy equation：

aij*ajk=ajk

When all elements of the judgment matrix are established， the judgment matrix is called the consistency matrix.

According to the analytic hierarchy process， we have to establish a test principle， namely the consistency of the test of the formula for the average random consistency criterion is：

The average consistency index is shown in the following table data.

Because of the 1& 2-order positive reciprocal matrices is always consistent. When ， it is pair wise comparison matrix， CI is Consistency index， RI is Random index， CR is Random Coincidence Rate of the same order （Refers to the same n）.

The above can be considered that the degree of inconsistency in the paired comparison matrix within the allowable range， can be used as the weight vector of the feature vector， or to re pair comparison， to adjust the paired comparison matrix.

The effect of the three elements of the criterion layer on the target layer is first compared with the comparison method， and the paired comparison matrix is obtained. And then， the influence of the 4 factors on the criterion layer is compared by using the paired comparison method， and the paired comparison matrix is obtained.

2.3 Model integrated computing results

Use of MATLAB software program calculate the Maximum Eigenvalue of matrix

The normalized eigenvectors

CI

CR

is the 3rd floor of the paired comparison matrices. Then， can get following：wk（1） is weight vector， is Maximum Eigenvalue. is consistency index.

<1， and all through a one-time inspection

In order to see more clearly the weight of each index， use Excelon rationality index of agricultural insurance as a bar chart.

Obtained by the calculation：

Similarly available：

Then：

This result can be interpreted as costs， income， technical barrier， the hazard of occupying space debris in weighting process were： 47.4%，28.8%，7.6%，16.2%. After a comprehensive analysis of the risks and calculate the total space debris processing obtained as follows： 16.2%. Therefore， we must increase investment in research and technology in order to avoid risks.

3 Conclusion

Using analytic hierarchy process （AHP） to calculate the income， cost， technical barrier，hazard ， in the final costs of the required weight， so as to make a quantitative analysis of the formula. Finally， the results of the model， we get is probably， there is a certain error， this is where we need to improve.

reference

[1] Dudziak R， Tuttle S， Barraclough S. Harpoon technology development for the active removal of space debris[J]. Advances in Space Research， 2015， 16（3）：509-527.

[2] Xu X， Wang L. Weather analysis and processing verification for space debris photometric observations[J]. Optoelectronic Imaging & Multimedia Technology II， 2012， 8558（1）：

[3] Murtazov A. Comparison of space-debris and asteroid photometric properties[J]. Asteroids， 2014.