A Mixed Safety and Reliability Evaluation Method for the Spacecraft Power Supply System

A spacecraft power distribution system is a multi-parameter, strongly coupled complex system, and the safety of a spacecraft power distribution system directly affects the working status of the spacecraft. In order to achieve better research results in the safety analysis system of spacecraft energy systems, it is very necessary to establish an assessment method for the safety of spacecraft power distribution systems. Previous research mainly focuses on the safety assessment of power systems or aircraft power systems and has not formed a relatively complete assessment method for the safety of spacecraft power distribution systems. This paper proposes a comprehensive evaluation method for the safety of spacecraft power distribution systems. It combines objective and subjective evaluation methods to comprehensively evaluate the safety of spacecraft power distribution systems. The objective parameters of the spacecraft power distribution system are processed and objectively evaluated; Subjective evaluations are obtained using analytic hierarchy. The proposed method can reasonably evaluate the safety of spacecraft power distribution systems and assist in the selection of different spacecraft power distribution systems.


Introduction
As the core part of the spacecraft system, the spacecraft power distribution system is responsible for providing a stable and reliable power supply.As space technology continues to devolve and spacecraft missions become more and more complex, safety assessments of spacecraft power distribution systems become increasingly important.By evaluating the safety of the spacecraft power distribution system, potential problems can be detected early, and corresponding measures can be taken to optimize the reliability and safety of the spacecraft power distribution system, so as to ensure the normal operation of the spacecraft in various environments and missions.Although the safety assessment of spacecraft power supply and distribution systems has received a certain degree of attention and research, there are still some gaps.This paper aims to propose a comprehensive and systematic evaluation method to better evaluate the safety of spacecraft power distribution systems.
Many studies on safety evaluation of the aircraft power supply system have been conducted and certain achievement has been achieved.Kong et al. [1] analyzed the reliability of the aircraft power system using a Bayesian network and common cause failure.However, the accuracy and reliability of this method will be affected when there is not sufficient data [2].Moreover, this method requires a large amount of computation and strong algorithm support.Liang et al. [3] used the Bayesian fusion method to comprehensively evaluate the aircraft power supply.The parameters selected by this method were only applicable to specific aircraft, and a general model applicable to all aircraft was not established.Meng [4] evaluated the quality of aircraft DC energy through gray correlation degree and ideal solution.However, the determination of weight is too reliant on subjective factors, and the ideal solution may lead to ideal results, affecting the accuracy of the evaluation.Meng [4] used rough set theory to evaluate the AC power quality of aircraft.However, rough set theory is more sensitive to data quality and attributes, and improper data selection may cause inaccurate or distorted results [5].
For the safety evaluation of power systems, many investigations also have been conducted.Zhang [6] conducted a security assessment of urban power supply based on the analytic hierarchy process (AHP) and entropy weight method.This method requires a large amount of data, which brings difficulties to data collection and processing.Li [7] used an accident tree and combined weight method to identify risk sources of the power grid and then carried out a safety assessment of the power grid based on the fuzzy analytic hierarchy process and CRITIC method.Yin et al. [8] conducted a security assessment of the power grid through an evaluation method based on multi-factor analysis.There are too many evaluation indexes in this method, and the evaluation indexes have strong uncertainty when the environmental parameters change [9].Xiao et al. [10] used a multi-level fuzzy comprehensive evaluation method to evaluate the power grid, fully considering the influence of certain and uncertain factors on power grid security.However, this method requires a large amount of data, and the model construction process is relatively inefficient.
The spacecraft power distribution system is a complex system with multi-parameter and multicoupling.It is necessary to consider both the expert experience and the actual operating parameters when evaluating its safety.In this paper, a method aimed to evaluate the safety of spacecraft power distribution systems was built and its feasibility was validated.This method evaluates the safety of spacecraft power supply and distribution systems from both subjective and objective aspects.
This paper has been organized as follows: The comprehensive evaluation method combining both subjective and objective evaluation processes is discussed in Section 2. A brief case study is presented in Section 3. Section 4 concludes the paper.

Combined Weight Assessment Method
Taking into account the characteristics of the spacecraft power distribution system, it is necessary to consider selecting an appropriate performance evaluation method and establishing a model.In this section, the basic principles of the combination weight assessment method in the evaluation of spacecraft power distribution systems are analyzed.This method initially utilizes the analytic hierarchy process to calculate subjective weights and the information entropy method to calculate objective weights.Then, using the game theory synthesis method, it reasonably combines the subjective and objective weight values to analyze the quantitative data of risk factors in the performance indicator model of the spacecraft power distribution system.Finally, the fuzzy comprehensive evaluation method is applied to assess the performance of the spacecraft power distribution system and provide an evaluation based on the assessment values.The complementary advantages of the combined calculation method improve the accuracy of the assessment by capitalizing on strengths and minimizing weaknesses.

Analytic Hierarchy Process
Building a judgment matrix is a fundamental step in establishing the mathematical model of the Analytic Hierarchy Process (AHP).Experts use integers from 1 to 9 based on their experience to represent the relative importance of each indicator to the performance of the spacecraft power distribution system.They compare the importance levels of each indicator to the spacecraft power distribution system in pairs, obtaining the ratios of importance between indicators.
The importance ranking index r is calculated by improving the method to calculate the weights.The judgment matrix P is constructed by summing the elements in the comparison matrix A. The elements pij in the matrix P are: , where r is the maximum value of ri, and r is the minimum value of ri.
Then we construct the transfer matrix H and the optimal transfer matrix G and construct the proposed optimal consistent transfer matrix B according to the above equation.
, lg , , 1,2,3,..., For the nearly optimal consistent transfer matrix B, a new and simpler solution method is applied, which is easier to use compared to the multiplication method.Moreover, it has been verified that this method yields the same weight values as the multiplication method.Therefore, this particular method is adopted to calculate the subjective weights u = (u1, u2, ... , un), and Finally, the eigenvalues and eigenvectors of the judgment matrix are calculated, and a consistency test is performed.If the consistency condition is satisfied, the eigenvector corresponding to the largest eigenvalue is normalized to obtain the weight coefficients.

Entropy Method
Using the entropy weight method, we calculate the values of the safety system indicators for aerospace power distribution systems and determine the objective weights.The specific calculation process is as follows: x We establish an evaluation indicator matrix for an evaluation subject Y. Assuming there are n criteria at the scheme level and m evaluation samples, the initial evaluation matrix is ij m n Y y u , where yij represents the evaluation value of the j th indicator for the i th sample.x Since the dimensions and scales of different indicators vary, it is necessary to standardize them for comparison and assessment.The dimension-normalized evaluation indicator matrix is x We calculate the weight 1 ) ( ¦ of the th i indicator for the th j evaluation sample.
x We calculate the entropy ln x We calculate the weight By performing the calculations mentioned above, the objective weight values w are obtained.

Game theory
In the evaluation of energy system performance, there are various comprehensive weighting methods, such as the product method, weight summation method, and so on.However, these methods simply involve multiplying or subjectively assigning different weights and then multiplying and adding them together.This can lead to issues with inaccurate calculations and strong subjectivity.By using the comprehensive weighting method of game theory, these problems can be effectively addressed.Therefore, the application of game theory is used to couple the subjective and objective weights of performance indicators in the spacecraft power distribution system, aiming to enhance the scientific validity of the comprehensive weights.First, a set of basic weights , where S represents a comprehensive weight vector derived from the L sets of weights.
To derive the most reasonable weight values from them, it is necessary to optimize the L weight vectors k a to minimize the difference between S and Sk.The best comprehensive weighting solution is selected from the L alternative options to obtain the integrated weights combining subjective and objective factors.Then the conversion formula is as follows.
We calculate the values of vector > @ , , ,..., L a a a a , normalize them to obtain vector ¦ , and obtain the comprehensive weights * * 1

Fuzzy integrated evaluation model
The spacecraft power distribution system needs to be evaluated as a whole using the method of fuzzy comprehensive evaluation.The evaluation is conducted on the indicator level, the overall system evaluation score is obtained through the fuzzy comprehensive matrix and the calculated values of the known weights of the spacecraft power distribution system performance indicators.First, it is necessary to construct an indicator model.If there are n schemes and m evaluation levels, the indicator set is denoted as { , ,..., } m S s s s of the scheme layer are obtained through game theory.By establishing the evaluation set using individual elements from the scheme layer, the fuzzy comprehensive evaluation matrix is ultimately created.The fuzzy weight data E can be represented by the evaluation matrix D and the combination weight S, as shown in Equation (6).
By performing calculations, weight data , the overall performance score of the spacecraft power distribution system is determined.

Application to Safety Assessment for Spacecraft Power Supply and Distribution
In this section, a spacecraft power distribution system was chosen as a case study to validate the effectiveness and practicality of the proposed combined weight assessment method.

Indicator System
The construction of the indicator system is a prerequisite and foundation for the entire evaluation work.Building an indicator system for the safety assessment of spacecraft power distribution systems requires reflecting the impact of system risks on the entire system in a reasonable and objective manner.Therefore, establishing an effective safety assessment system for spacecraft power distribution systems is highly necessary.The spacecraft power distribution system exhibits distinct characteristics of a multi-level structure and multiple interconnected indicators, requiring the application of a rational and scientific approach to constructing the indicator system.For such a system with this structure, it is advisable to use a hierarchical structure to establish the framework of the evaluation system and subsequently assess the spacecraft power distribution system.The hierarchical structure is illustrated in Fig. 1. In

Integrated Weight Calculation
In the safety assessment of aerospace power distribution systems, subjective evaluations mainly manifest in expert weighting.Firstly, an expert meeting is organized to invite relevant experts to conduct sampling surveys and scoring of safety assessment events for the designated system.The expert group should consist of technical personnel from various sub-fields, and based on the scores given by the expert group, an analytic hierarchy process judgment matrix can be constructed.After conducting consistency checks on the judgment matrix, subjective weights can be obtained.Then, based on the frequency of occurrence and the extent of losses caused by various risk indicators in the past five years, objective weights can be calculated.Finally, by applying Equation ( 5), the combination weights of various indicators of the aerospace power distribution system can be calculated.
Combining the aforementioned evaluation methods, an assessment is conducted on a batch of aerospace power distribution systems, referred to as Product A and Product B. The combined weights of each indicator in Product A are calculated as shown in Equation ( 7), while the calculated results of combined weights for Product B are shown in Equation (8) where the risk scores for each indicator are indicated within the brackets.The overall scores for Product A and Product B can be calculated using Equation (6).The overall score for Product A is MA=75.69,while the overall score for Product B is MB=81.29.Based on the comparison of scores, Product B is ultimately chosen as the aerospace power distribution system.

Conclusions
This study puts forward a method to evaluate the safety of spacecraft power distribution systems based on the objective operation of spacecraft systems and expert experience, which fills the gap in the research field.The feasibility of this method is proved by a concrete example.This method can effectively evaluate the safety of different types of spacecraft power distribution systems, which is helpful in the selection and design of spacecraft power distribution systems.Future studies could introduce more data to further refine and expand the applicability of this method.

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of the j th indicator.

Figure 1 .
Figure 1.Spacecraft power supply and distribution system hierarchy diagram the figure, B1 to B3 represent the weightings of criteria indicators in the criterion layer, and C11 to C34 represent the weightings of indicators in the indicator layer. .