Research on Reliability Model Evaluation of Satellite Communication System

Traditional model evaluation methods such as analytic hierarchy process (AHP) cannot provide specific theoretical basis for the later optimization of satellite communication system. To solve this problem, this paper presents an evaluation algorithm based on the reliability modelling process of satellite communication system. The algorithm combines the subjective analysis and objective data in the process of modelling to obtain the fuzzy quantitative evaluation value of the three links of system definition, mathematical model determination and reliability calculation in the process of modelling, and the final Evaluation result is calculated by using Bayesian theory. The validity and feasibility of the algorithm are verified by an example, and some references are provided for the further optimization of the model.


Introduction
The performance and business requirements of the satellite communication system are gradually improved, making the composition and design of the satellite communication system more and more complicated [1], which brings many uncertain factors to the reliability of the satellite communication system, and also contributes to the reliability of the satellite communication system. The design brought severe tests [2,3]. The key to reliability research is to establish a reliability model. At present, there have been a lot of researches on the reliability model of satellite communication systems [4,5], for example, reliability models based on jump plane nodes, reliability models based on structural differences, and reliability models based on natural connectivity. With the continuous deepening of reliability model research, there are two problems that need to be solved urgently [6]: (1) Optimal choice of reliability model of satellite communication system. That is, how to choose the best model from different reliability models in a specific scenario.
(2) Optimization of reliability model of satellite communication system. That is to improve the incomplete model, improve the accuracy and then put it into use.
At present, the evaluation methods used in the field of evaluation systems and transportation systems such as analytic hierarchy process and fuzzy evaluation method have been developed and mature [7,8] V for the comment sentence set, showing each evaluation index evaluation levels, where n is the total assessment of the number of levels (typically divided into 3~5 levels).
Defined 1 Factors and evaluation set V similarity metric is the degree of membership. Defined 2 The evaluation is conducted from A single factor i u to determine the membership degree of the evaluation object l Pt to the evaluation set V., referred to as single factor fuzzy evaluation.
The fuzzy relation matrix ij m n r       R between U and V can be obtained by single factor fuzzy evaluation of each evaluation factor in the evaluation factor set U. Where ij r ( , i m j n   ) represents the membership degree of the evaluation factor i u of the object to be evaluated to the evaluation comment j v ( j n  ). Finally Suitable Fuzzy Composite Operators "  " fuzzy weight vector A and the fuzzy relation matrix R intake line complex computation [10], The fuzzy comprehensive evaluation vector b of the evaluated object is obtained. Where j b ( j n  ) represents the similarity between the assessed object l Pt and the comment j v on the whole.
However, the traditional fuzzy comprehensive evaluation method cannot solve the problems caused by the correlation between various links in the reliability model modelling process. Therefore, based on the modelling process of satellite communication network reliability model, this paper improves the traditional fuzzy evaluation method and designs a fuzzy quantitative evaluation method.

Fuzzy quantitative evaluation method
The second chapter shows that the object set by the x th element of the composition   UC , which is obtained by entropy weight coefficient method [11].Finally, the fuzzy set is obtained by compound operation transformation: Among them, sj b represents the degree to which s ud of the evaluated data factor has the evaluation j v , namely the membership degree of j v to the fuzzy set s B .
The probability    (1) is determined. Neither the prior probability nor the subjective experience can be fully believed in the evaluation of the model, so the Bayesian theory can be used to combine the two information organically. Considering the independence of each index factor, the posterior probability of s ud can be obtained by using the total probability formula and Bayes' theorem: Where,   s p ud is the prior probability of data factor s ud . The result combines the prior probability of data factor and subjective experience, that is, both objective data and subjective factors are taken into account. Therefore, the quantitative evaluation value of s ud is: Among them, l k represents the weight of object l k in this evaluation, which can be determined according to the actual application of the model.

Fuzzy quantitative evaluation based on reliability modeling process
The current common evaluation methods are all simple evaluations of the model as a whole, but these evaluation methods cannot accurately find the parts of the model that need to be optimized [12]. Therefore, this paper proposes an evaluation method based on the reliability model establishment process to evaluate each link in the reliability model modeling process, so that the final result can reflect the weak links of reliability modeling and provide directions for further optimization of the model.

satellite communication system reliability model modeling process
Reliability models are divided into basic reliability models and mission reliability models [13]. Satellite communication systems are extremely complex, so mission reliability models are usually established. Figure 1 is the process from establishment to use and optimization of the reliability model of the satellite communication system [14].

Fuzzy quantitative evaluation of reliability models for satellite communication networks
This chapter mainly evaluates the three links in the process shown in Figure 1, namely, Specifying System Definitions (SD), Determining Mathematical Models (DM), and Reliability Calculations (RC). The evaluation result reflects the accuracy of the reliability model of the satellite communication system to be evaluated. When the evaluation result is not ideal, it can provide a basis for further optimization of the model [15] . It can be seen from Chapter 3 that the evaluation reliability model needs to set three sets, which are object set, factor set and evaluation set. The object set Part is composed of three processes SD, DM and RC established by the reliability model, namely The data factor set UD is determined based on the actual situation of each process established by the reliability model of the satellite communication system and is objective. The SD data factor investigation model can complete tasks and the number of functions, the number of performance parameters when the model failure is defined, the performance parameter range (confidence interval) when the system fails, the failure criterion, etc., and then the data can be characterized by different units to obtain Data set , where md SD represents the amount of data.
The data factor of DM examines the sensitivity and robustness of the model. Sensitivity is the relative change of the model when a certain parameter changes slightly, that is, the ratio of the change to the original value; if the model does not depend on the assumptions relative to the actual situation Accuracy, the model is robust, and the data set   The index factor set UC is to evaluate whether each element in the data factor conforms to the rules, which is determined by the evaluation expert and is subjective. The evaluation criteria mainly include completeness, consistency, accuracy and real-time [16].
(1) Completeness (CM): Refers to whether the data is missing, it may be that the entire data record is missing, or it may be that some field information is missing.
(2) Consistency (CN): refers to whether the data is standardized and whether the data collection format is uniform. Since each index factor has a different dimension, it is necessary to standardize the values of x models under the same index factor s ud t uc [17], as shown in formula (8) Fuzzy quantitative evaluation of the above data can get the final quantitative evaluation value EVA of the model .

evaluation simulation example verification
Herein is selected from the viewpoint model invulnerability reliability analysis of a satellite communication system, a satellite communication system provided with a N number nodes, respectively, based on the jump plane node, and natural structural differences of the three methods of establishing the communication system Reliability evaluation model. Now use the fuzzy quantitative evaluation method of this article to evaluate and compare these three models.
(1) Determine three sets The index factor set of the object set, evaluation set and factor set has been given in Chapter 4 , namely, the object set (2) Get the data factor set Analyse the three models, firstly analyse the model to obtain the data factor set of SD link and RC link, which is the result in Table 1. Table 1 Data factor values of SD and RC in the modelling process The data factor value of the DM link requires the model sensitivity, and the local sensitivity analysis method is used [18]. Only one of the parameters is set as a variable, and the other parameters take the center value. The sensitivity of the reliability model with respect to this parameter is the amount of change each time the parameter changes.
In the reliability model based on jump plane nodes, the reliability   with the path length of 2 between any two nodes, and the total number of paths 3 2 DM ud with the path length of 3 between any two nodes. In the reliability model based on natural connectivity, the reliability of satellite communication system    Table 2.  Table 3 to Table 5  uc is 0.6. To ensure that the experiment is rigorous and accurate, the following results are based on the average value of the evaluation data of 50 evaluation experts: Table 3 The quantitative evaluation value of the modelling process SD  Table 4 The quantitative evaluation value of the modelling process DM  (3) Obtain the fuzzy quantitative evaluation value After normalizing the data standards in Table 3 to Table 5 , the fuzzy quantitative evaluation value of each link can be obtained by using the algorithm in this paper, and then the evaluation results of each link of the model are merged twice to obtain the reliability of each satellite communication system. The fuzzy quantitative evaluation value EVA of the model is shown in Table 6  According to EVA, the three models are ranked as follows: Based on the jump plane node < Based on the structural difference < Based on the natural connectivity The above results are consistent with the results obtained by analysing the reliability models of three satellite communication systems in literature [19], which confirms the accuracy of the algorithm in this paper

Model optimization analysis
Considering the complexity of the satellite communication system, the reliability model is usually not directly put into use, that is, the reliability model needs to be optimized, and the algorithm proposed in this paper can provide direction for further optimization of the model. Take the optimization of the reliability model of a satellite communication system based on structural differences as an example: first observe the evaluation results of each link in Table 6. The evaluation value of RC is 0.662 , which is the lowest evaluation value of the three links, so the RC link is improved first ; (6) and, the RC assessment depends links in Table 1 in each of the data elements ud complex evaluation, according to the formula (5) can be seen ud integrated in the evaluation value by its corresponding factor evaluation index uc decision on the evaluation value the evaluation results are shown in table 5 the last analysis table; Table 5  In summary, when optimizing the reliability model of a satellite communication system based on structural differences, first consider reducing the time complexity of this algorithm.

Conclusion
Reliability model is the key of reliability analysis of satellite communication system. Reliability model evaluation is one of the key points of reliability model development and reliability analysis research.
This paper presents a fuzzy quantitative evaluation method based on the reliability modelling process, which combines objective data and subjective analysis to evaluate the reliability model, and the results are complete. The evaluation results provide the basis for the optimal selection of the satellite communication system reliability model under specific scenarios, and provide a reference for the further optimization of the reliability model.