A four-property and operating cost-oriented civil aircraft system selection decision method

Abstract

The application discloses a kind of four property and operation cost-oriented civil aircraft system selection decision-making method, comprising the following steps: four property index and economy index of civil aircraft system are divided and confirmed;Based on the four property index and economy index confirmed, the interval parameter correlation coefficient of each selection scheme of civil aircraft system is calculated;According to interval parameter correlation coefficient, the attribute parameter weight of civil aircraft system is calculated;According to parameter weight, the comprehensive correlation degree value of scheme is determined.The application reduces the selection cost under the premise of guaranteeing that the four property level of system meets the requirements, eliminates the influence of subjectivity, objectively guarantees the influence of each parameter on correlation degree, reduces the comparability between schemes, can effectively exclude inferior scheme, guide decision maker to pay attention to the different advantages of dominant scheme, and provides complete idea and engineering technical reference for civil aircraft system selection decision-making.

Description

Technical Field

[0001] The present invention belongs to the field of civil aircraft, relates to civil aircraft system selection technology, and specifically relates to a civil aircraft system selection decision method oriented towards four properties and operating costs. Background Art

[0002] In recent years, with the continuous expansion of the global civil aviation market, the number of aircraft system configuration options has increased. Civil aircraft system selection decisions are a complex multi-attribute decision-making problem that integrates multiple factors, including airworthiness, technical performance, and economics. To ensure the safe, stable, and economical operation of complex aircraft systems, the system's reliability, maintainability, testability, and safety should first be evaluated in accordance with relevant airworthiness regulations, and then the optimal system operating costs should be considered. When faced with numerous system configurations with complex component models and varying performance, how to select the configuration that optimizes the four attributes and overall operating costs raises the question of integrated comprehensive evaluation and decision-making.

[0003] In research on system selection decisions based on the four characteristics of civil aircraft and operating costs, domestic and international scholars have applied grey correlation theory and the analytic hierarchy process (AHP) to propose a hierarchical structure and evaluation index system for optimizing top-level aircraft design options, as well as an evaluation model for optimal selection. This allows for comprehensive and objective evaluation and technical selection of candidate civil aircraft systems. Furthermore, they have studied the design of an integrated collaborative work platform framework for the five characteristics of aircraft reliability, maintainability, testability, safety, and security. Overall, there is limited research on integrated decision-making and selection for civil aircraft systems, and most require accurate and detailed analysis of the system structure, clarifying the inherent connections and quantitative relationships between various parameters. This is a laborious task, and errors in the analysis can directly lead to biased evaluation results. In systems science, analyzing the correlations between multiple options and the optimal one is a key research topic. Traditional statistical methods such as regression analysis, principal component analysis, and variance analysis have many limitations, as they are all designed for problems with large data volumes and data distributions that follow a typical probability distribution. In reality, civil aircraft have the characteristics of complex systems, long development cycles, high precision, fierce market competition, and emphasis on operational economy. The four characteristics data of different system configurations are highly complex and volatile, and often have no definite values. Instead, they fluctuate within a certain range. Compared with other parameters, they have greater uncertainty and are difficult to obey a typical probability distribution. In terms of civil aircraft system configuration selection, there is an urgent need for technical solutions that can provide good support for comprehensive decision-making when the data volume is small and the volatility is high. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a civil aircraft system selection decision method based on the four characteristics and operating costs is provided, which provides a complete idea and engineering technology reference for civil aircraft system selection decision.

[0005] Technical Solution: To achieve the above objectives, the present invention provides a civil aircraft system selection decision-making method based on the four characteristics and operating costs, comprising the following steps:

[0006] S1: Confirm the four performance indicators and economic indicators of civil aircraft systems;

[0007] S2: Calculate the correlation coefficient of the interval parameters of the civil aircraft system selection scheme based on the confirmed four performance indicators and economic indicators;

[0008] S3: Calculate the weights of civil aircraft system attribute parameters based on interval parameter correlation coefficients;

[0009] S4: Calculate the comprehensive weighted correlation value of each solution based on the parameter weights.

[0010] Furthermore, the four performance indicators in step S1 include safety, reliability, maintainability and testability indicators, and the economic indicators include operating cost indicators.

[0011] The four characteristics of a civil aircraft system are its ability to perform its specified functions within a specified timeframe, under specified maintenance conditions, within specified reliability requirements, under specified test conditions, and within a specified acceptable safety level. Reliability is essential for ensuring the reliable operation of complex systems and is the ability to guarantee trouble-free operation of the entire system. Safety refers to the ability of the aircraft and its systems to operate without causing casualties, system damage, significant property damage, or endangering human health or the environment. Maintainability refers to the ability to perform repairs on the aircraft as a whole and its components within specified conditions, timeframes, procedures, and methods. Testability refers to the ability of an aircraft system to promptly and accurately determine its operating status and isolate internal faults. The requirements and levels of the four characteristics vary for different systems. Given the interval nature of the parameters, each parameter is required to be highly representative and important. Dispatch reliability, system failure rate, mean planned maintenance interval, and false alarm rate are used as a general indicator system. When making system configuration decisions, economic efficiency is more impacted during the operational phase, with operating costs being used as an economic indicator.

[0012] A single indicator is used for the quantitative evaluation of the four properties. The determination of the indicator needs to be determined by the decision maker based on the specific requirements of different decision-making situations, or based on experience and the importance of the indicator in the industry.

[0013] Furthermore, the method for confirming the four performance indicators and economic performance indicators in step S1 is: based on the four performance characteristics and economic performance characteristics of the civil aircraft system, confirm the quantitative evaluation indicators of system safety, reliability, maintainability, testability and operating cost.

[0014] Furthermore, the calculation method of the correlation coefficient of the interval parameters of the civil aircraft system selection scheme in step S2 is:

[0015] A1: Unify the development trends of the attribute parameters (four performance indicators and economic indicators) of each selection scheme and perform homogenization processing: Since the four performance parameters of the system and the operating cost units are different, the development trends of the parameters are different. By dividing each parameter into benefit-oriented and cost-oriented types, the development trends of the parameters are unified;

[0016] A2: Use the forward interval coverage calculation formula and ranking formula to perform coverage calculation on the target solution and reference configuration parameter interval values ​​to determine the ideal objective reference configuration parameter interval values;

[0017] A3: In order to compare the advantages and disadvantages of the four properties and economic performance of each scheme, the grey system interval correlation coefficient calculation formula is used to calculate the correlation value of the parameter value interval between the target scheme and the reference scheme.

[0018] Furthermore, in step A1, the conversion of the cost-based indicator value interval into the benefit-based indicator value interval is the inverse of the interval number:

[0019]

[0020] Among them, [a ij - ,a ij + ] is Plan A i In the jth evaluation attribute index P j The evaluation interval value, [a ij -* ,a ij +* ] is the interval value after negation normalization.

[0021] Furthermore, the method for obtaining the reference configuration parameter interval value in step A2 is:

[0022] The formula for calculating the positive interval coverage is used to determine the degree to which the j-th attribute parameter interval in the i-th solution positively covers the same attribute parameter intervals in other solutions. The formula is:

[0023]

[0024] Among them, p is the parameter positive coverage value, l aij is the absolute length of the interval, that is

[0025] Then, the forward coverage ranking formula is used to establish the forward coverage sequence p tj =(p 1j ,p 2j ,...,p mj ), and obtain the forward coverage of each parameter in all schemes for comprehensive ranking:

[0026]

[0027] Among them, m is the serial number of the provided solution, p tj is the coverage value of the jth parameter of the tth solution;

[0028] Take the interval value with the highest positive coverage ranking among each parameter to form the reference configuration parameter interval sequence:

[0029] Furthermore, the calculation method of the correlation coefficient value of each parameter value interval between the target solution and the reference solution in step A3 is:

[0030]

[0031] Among them, γ ij is the correlation value, ρ is the adjustment coefficient, which is usually taken as 0.5, where r 0j The values ​​are the upper and lower limits of the reference scheme parameters, taken from the reference configuration parameter interval sequence: For Plan A i In the jth evaluation attribute index P j The lower and upper limits of the evaluation interval.

[0032] Furthermore, the calculation method of the civil aircraft system attribute parameter weight in step S3 is:

[0033] B1: Clarify the calculation method of weighted grey correlation between the target solution and the reference solution;

[0034] B2: When evaluating different configurations of civil aircraft systems, the weights assigned to the four parameters and operating costs are easily influenced by subjective factors, leading to biased decision-making. Therefore, we introduce the gray connotation sequence entropy maximization as a constraint to reduce the uncertainty of the weight coefficients.

[0035] B3: Introduce the Lagrange multiplier extreme value equation, find the optimal solution under the constraints of step B2, and determine the weights of each parameter.

[0036] Furthermore, the weighted grey correlation degree calculation method between the target solution and the reference solution in step B1 is:

[0037]

[0038] Among them, γ(X0 X i ) is the weighted grey relational degree, γ ij For step A3, we obtain the value of the attribute parameter j of solution i, λ j is the weight value of the jth parameter of the target solution;

[0039] Based on formula (5), the density function of the correlation coefficient of each scheme is established:

[0040]

[0041] According to formula (6), we can get

[0042] The constraint conditions for maximizing the entropy of the grey connotation sequence in step B2 are specifically:

[0043] The grey correlation entropy formula of the density value of the correlation coefficient of each scheme is:

[0044]

[0045] where θ j is the correlation coefficient density value in formula (6);

[0046] In step B3, the Lagrange multiplier extreme value equation is used to obtain the density value θ of each attribute under the requirement of maximizing the grey correlation entropy in step B2. j :

[0047] L(θ,β)=H(θ)+β×(g(θ)-1)=0

[0048]

[0049] Where β is a constant;

[0050] Each component of its expansion is in the form of L(θ j ,β)=-θ j lnθ j +βθ j -β, taking partial derivatives of θ for each component of the expansion yields:

[0051]

[0052] From formula (9), we can see that the partial derivative function configurations of each component are consistent, so it can be concluded that when the gray entropy value H is the largest, the gray correlation coefficient density value θ j =θ1=θ2=...=θ j-1 , that is, the density values ​​of each parameter are equal;

[0053] Depend on Combined with equations (6) and (9), we can get:

[0054]

[0055] Furthermore, in step B1, λ1γ is obtained through steps B2 and B3. i1 =λ2γ i2 =...=λ n γ in , that is, the grey correlation coefficients of a certain scheme attribute sequence are equal to each other after weighting. The weighted grey correlation degree between the target scheme and the reference scheme can be calculated by formula (5), and then sorted according to the correlation value to obtain the four properties and economic level of the target scheme.

[0056] Beneficial effects: Compared with the existing technology, the present invention effectively handles the differences between reliability, safety, maintainability, testability, and operating cost parameters in the operation stage of civil aircraft systems, reduces the selection cost while ensuring that the four levels of the system meet the requirements, eliminates subjective influences, objectively ensures the influence of each parameter on the correlation, reduces the comparability between plans, can effectively screen out inferior plans, and guide decision makers to focus on the different advantages of superior plans, providing a complete idea and engineering technology reference for civil aircraft system selection decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A flowchart of the civil aircraft system selection decision-making method based on the four characteristics and operating costs;

[0058] Figure 2 This is a diagram of the four parameters of the aircraft system. DETAILED DESCRIPTION

[0059] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0060] like Figure 1 As shown, the present invention provides a civil aircraft system selection decision method based on the four characteristics and operating costs, comprising the following steps:

[0061] S1: Confirm the four performance indicators and economic indicators of civil aircraft systems:

[0062] The four performance indicators include safety, reliability, maintainability and testability, and the economic indicators include operating cost indicators.

[0063] The method for confirming the four-quality indicators and economic indicators is: based on the four-quality characteristics and economic characteristics of the civil aircraft system, confirm the quantitative evaluation indicators of system safety, reliability, maintainability, testability and operating costs.

[0064] like Figure 2 As shown, in this embodiment, the civil aircraft system reliability assessment parameters include mean time between failures (MTBF), mean time between unplanned departures (MTUs), and dispatch reliability. Dispatch reliability is one of the most core parameters in civil aircraft reliability design. It refers to the percentage of flights departing without technical delays or cancellations. It directly reflects the availability of the aircraft and its systems, directly impacts airline operating costs and revenue, and is a primary objective in commercial aircraft operations. System safety parameters include accident rate, loss rate, and failure probability. Using failure probability as a safety assessment parameter for civil aircraft systems is more comprehensive and representative. Maintainability directly affects airline maintenance costs and also reflects the reliability of aircraft systems and equipment. Therefore, maintainability and reliability form a complementary relationship and are prerequisites for ensuring efficient and economical system operation. Common aircraft system maintainability indicators include mean planned maintenance interval (MTM) and mean time to repair (MTTR). In practice, airline maintenance personnel primarily perform planned maintenance. Establishing maintenance intervals better reflects the safety and reliability of aircraft systems, so mean planned maintenance intervals are used as the maintainability assessment parameter. General indicators of aircraft system testability include fault detection rate and false alarm rate. Timely detection, precise isolation and ultra-low false alarm are powerful means to reduce the occurrence of faults and minimize property losses. The false alarm rate is selected as the system testability evaluation parameter.

[0065] S2: Calculate the correlation coefficient of the interval parameters of the civil aircraft system selection scheme based on the confirmed four performance indicators and economic indicators; including the following steps:

[0066] For the multi-attribute decision-making problem where all the indicators are interval numbers, first assume that there are m options A1, A2, ..., A m , there are n evaluation attribute indicators P1, P2, ..., P n , for each plan A i The various attributes P j The weight vector is Plan A i In the jth evaluation attribute index P j The evaluation interval value is [a ij - ,a ij + ], the decision matrix A composed of interval indicators is:

[0067]

[0068] The attribute parameters in the decision matrix are categorized as "benefit-oriented" and "cost-oriented." For benefit-oriented indicators, larger values ​​are preferred, while for cost-oriented indicators, smaller values ​​are preferred. In this embodiment, benefit-oriented attribute parameters include dispatch reliability and mean planned maintenance interval, while cost-oriented attribute parameters include failure probability, false alarm rate, and operating cost. To ensure consistency in the decision matrix, the attribute parameters are homogenized, converting cost-oriented indicators into benefit-oriented indicators:

[0069]

[0070] Among them, [a ij - ,a ij + ] is Plan A i In the jth evaluation attribute index P j The evaluation interval value, [a ij -* ,a ij +* ] is the interval value after negation normalization.

[0071] Determine the parameter interval of the reference solution. The interval of each attribute of the reference solution is the optimal interval among all alternative solutions. First, use the forward interval coverage formula to process each interval:

[0072]

[0073] Among them, p is the parameter positive coverage value, l aij is the absolute length of the interval, that is

[0074] Use the forward coverage ranking formula to establish the forward coverage sequence p tj =(p 1j ,p 2j ,...,p mj ), and obtain the forward coverage of each parameter in all schemes for comprehensive ranking:

[0075]

[0076] Among them, m is the serial number of the provided solution, p tj is the coverage value of the jth parameter of the tth solution. Take the interval value with the highest positive coverage ranking among all parameters to form the reference solution parameter interval sequence:

[0077]

[0078] After obtaining the reference scheme parameter range, the correlation coefficient of each alternative decision scheme attribute parameter with respect to the reference scheme attribute parameter can be calculated:

[0079]

[0080] where γ ij is the correlation coefficient, ρ is the adjustment coefficient, which is 0.5 in this embodiment, where r 0j The values ​​are the upper and lower limits of the reference scheme parameters, taken from the reference scheme parameter interval sequence: aij- and aij+ are the lower and upper limits of the evaluation interval of the j-th evaluation attribute index Pj of the scheme Ai.

[0081] Formula (5) strengthens the adjustment effect of the adjustment coefficient ρ, and plays a balancing role in the upper and lower limits of the specific attribute parameters; and Taking the maximum value reduces the sensitivity of the correlation coefficient to a certain extent, avoids the situation where the upper or lower limit of a certain interval deviates too far from the extreme value, resulting in a decrease in the comprehensive correlation, and can better support the screening of other alternatives in multi-attribute decision making; using the Euclidean distance between the comparison sequence parameters and the reference sequence parameters As an input item of the correlation coefficient, it can effectively reflect the absolute difference between the interval numbers and control the volatility of the correlation coefficient.

[0082] S3: Calculate the weights of civil aircraft system attribute parameters based on the interval parameter correlation coefficient:

[0083] In grey correlation analysis, the grey correlation coefficient reflects the influence of each point in the comparison sequence on the main behavior sequence. It can be considered that the influence of the comparison sequence within the grey system on the main behavior sequence at different time points should remain stable. Therefore, the weighted correlation coefficients of each point should be kept as balanced as possible to avoid the situation where a single correlation coefficient is high during ranking evaluation, resulting in a high comprehensive correlation degree.

[0084] First, define the weighted grey relational degree between the selection scheme sequence and the reference scheme:

[0085]

[0086] Among them, γ(X0 Xi) is the weighted grey relational degree, γ ij For step A3, we obtain the value of the attribute parameter j of solution i, λ j is the weight value of the j-th parameter of the target solution.

[0087] Based on formula (6), the density function of the correlation coefficient of each scheme parameter is established:

[0088]

[0089] According to formula (7), it is obvious that That is, the sum of the density values ​​of different parameters of the same scheme is 1, which is normalized.

[0090] The grey correlation entropy formula of the density value of the correlation coefficient of each scheme is:

[0091]

[0092] where θ j is the correlation coefficient density value in formula (7);

[0093] When the value of H in equation (8) is the largest, the weight sequence λ=(λ1λ2...λ n ) has the smallest random uncertainty, and the weight of each attribute becomes the problem of optimal solution. Let H take the maximum value as the constraint, construct the Lagrange multiplier extreme value equation about θ, and through the Lagrange multiplier extreme value equation, under the requirement of maximizing the grey correlation entropy, obtain the density value θ of each attribute j :

[0094] L(θ,β)=H(θ)+β×(g(θ)-1)=0

[0095]

[0096] Where β is a constant.

[0097] Each component of its expansion is in the form of L(θ j ,β)=-θ j lnθ j +βθ j -β, taking partial derivatives of θ for each component of the expansion yields:

[0098]

[0099] From formula (10), we can see that the partial derivative function configurations of each component are consistent, so we can know that when the gray entropy value H is the largest, the gray correlation coefficient density value θ j =θ1=θ2=...=θ j-1 , that is, the density values ​​of each parameter are equal.

[0100] Depend on Combined with equations (7) and (10), we can get:

[0101]

[0102] From formula (11), we know that λ1γ i1 =λ2γ i2 =...=λ n γ in, that is, the grey correlation coefficients of a certain scheme attribute sequence are equal to each other after weighting. The weighted grey correlation degree between the target scheme and the reference scheme can be calculated by formula (6), and then sorted according to the size of the correlation value. The higher the value, the better the four properties and economic level of the target scheme.

[0103] Based on the above solution, this embodiment summarizes and analyzes the above solution as follows:

[0104] The present invention provides a system configuration selection decision-making method for the four characteristics and operating costs of civil aircraft, including the confirmation of four characteristic indicators, calculation of correlation coefficients of system selection scheme interval parameters, and calculation of system attribute parameter weights. The four characteristic indicator confirmation analyzes and confirms the civil aircraft system parameter indicators based on the characteristics of the four characteristics of civil aircraft system reliability, safety, maintainability, and testability, as well as the fact that operating costs are interval numbers rather than fixed values. The system selection scheme interval parameter correlation coefficient calculation, based on the research foundation of grey system interval correlation, proposes a formula for calculating the positive coverage of interval numbers and ranking to obtain the optimal reference scheme parameter interval, and then proposes a method for calculating the grey correlation coefficient of interval numbers to calculate the correlation between the four characteristics and operating cost parameters of different selection schemes. The system attribute parameter weight calculation uses the correlation entropy method to perform weighted balancing on the parameter correlation results to ensure the stability of the comprehensive correlation between schemes.

[0105] In summary, based on the characteristics of large volatility, different dimensions, large magnitude differences and interval numbers of the parameters of civil aircraft system reliability, safety, maintainability, testability and operating cost, the present invention proposes an interval number positive coverage formula, combines the sorting formula to extract the optimal parameter sequence, and proposes a model for calculating the grey correlation coefficient of interval numbers on this basis. The grey entropy method weighting is used as a constraint condition, and the Lagrange multiplier extreme value equation is introduced to ensure the stability of the comprehensive correlation between schemes, forming an integrated system selection decision model, effectively dealing with the differences between parameters, eliminating subjectivity, objectively ensuring the influence of each parameter on the correlation, reducing the comparability between schemes, and guiding decision makers to focus on the different advantages of advantageous schemes on the premise of effectively screening out inferior schemes, providing a complete idea and engineering reference for civil aircraft system selection decision-making.

Claims

1. A civil aircraft system selection decision method based on four characteristics and operating costs, characterized by: The steps include: S1: Confirm the four performance indicators and economic indicators of civil aircraft systems; S2: Calculate the correlation coefficient of the interval parameters of the civil aircraft system selection scheme based on the confirmed four performance indicators and economic indicators; S3: Calculate the weights of civil aircraft system attribute parameters based on interval parameter correlation coefficients; S4: Calculate the comprehensive weighted correlation value of each scheme according to the parameter weight; The calculation method of the correlation coefficient of the interval parameters of the civil aircraft system selection scheme in step S2 is: A1: Homogenize the unified development trends of the four quantitative indicators and operating costs of each selected solution. Since the four system parameters and operating cost units are different, they represent different intervals of development trends. By classifying each parameter into benefit-oriented and cost-oriented types, the development trends of the parameters can be unified. A2: Use the forward interval coverage calculation formula and ranking formula to perform coverage calculation on the target solution and the reference configuration parameter interval values ​​to confirm the reference configuration parameter interval values; A3: To compare the four properties and economic performance of each scheme, the grey system interval correlation coefficient calculation formula is used to calculate the correlation value of each parameter value interval between the target scheme and the reference scheme; In step A1, the value interval of the cost-based indicator is converted into the value interval of the benefit-based indicator by taking the inverse interval number: in, For Plan A i In the jth evaluation attribute index P j The evaluation interval value of is the interval value after negation normalization; The method for obtaining the reference configuration parameter interval value in step A2 is: The formula for calculating the positive interval coverage is used to determine the degree to which the j-th attribute parameter interval in the i-th solution positively covers the same attribute parameter intervals in other solutions. The formula is: Among them, p is the parameter positive coverage value, is the absolute length of the interval, that is Then, the forward coverage ranking formula is used to establish the forward coverage sequence p tj =(p 1j ,p 2j ,...,p mj ), and obtain the forward coverage of each parameter in all schemes for comprehensive ranking: Among them, m is the serial number of the provided solution, p tj is the coverage value of the jth parameter of the tth solution; Take the interval value with the highest positive coverage ranking among each parameter to form the reference configuration parameter interval sequence: The calculation method for the correlation coefficient value of each parameter value interval between the target solution and the reference solution in step A3 is: Among them, γ ij is the correlation value, ρ is the adjustment coefficient, where r 0j The values ​​are the upper and lower limits of the reference scheme parameters, taken from the reference configuration parameter interval sequence: a ij - 、a ij + For Plan A i In the jth evaluation attribute index P j The lower and upper limits of the evaluation interval; The calculation method of the civil aircraft system attribute parameter weight in step S3 is: B1: Clarify the calculation method of weighted grey correlation between the target solution and the reference solution; B2: Introduce the maximization of grey connotation sequence entropy as a constraint condition; B3: Introduce the Lagrange multiplier extreme value equation, find the optimal solution under the constraints of step B2, and determine the weights of each parameter; The calculation method of weighted grey relational degree between the target solution and the reference solution in step B1 is: Among them, γ(X0X i ) is the weighted grey relational degree, γ ij is the correlation value of attribute parameter j of scheme i, λ j is the weight value of the jth parameter of the target solution; Based on formula (5), the density function of the correlation coefficient of each scheme is established: According to formula (6), we can get The constraint conditions for maximizing the entropy of the grey connotation sequence in step B2 are specifically: The grey correlation entropy formula of the density value of the correlation coefficient of each scheme is: where θ j is the correlation coefficient density value in formula (6); In step B3, the Lagrange multiplier extreme value equation is used to obtain the density value θ of each attribute under the requirement of maximizing the grey correlation entropy in step B2. j : Where β is a constant; Each component of its expansion is in the form of L(θ j ,β)=-θ j lnθ j +βθ j -β, taking partial derivatives of θ for each component of the expansion yields: From formula (9), we can see that the partial derivative function configurations of each component are consistent, so it can be concluded that when the gray entropy value H is the largest, the gray correlation coefficient density value θ j =θ1=θ2=...=θ j-1 , that is, the density values ​​of each parameter are equal; Depend on Combined with equations (6) and (9), we can get: The comprehensive correlation value in step S4 is determined as follows: λ1γ is obtained in step B1 through steps B2 and B3. i1 =λ2γ i2 =...=λ n γ in , that is, the grey correlation coefficients of a certain scheme attribute sequence are equal to each other after weighting. The weighted grey correlation value between the target scheme and the reference scheme is calculated by formula (5), and then sorted according to the size of the correlation value to obtain the four properties and economic level of the target scheme.

2. The method for civil aircraft system selection decision-making based on four characteristics and operating costs according to claim 1, characterized in that: The four performance indicators in step S1 include safety, reliability, maintainability and testability indicators, and the economic performance indicators include operating cost indicators.

3. The method for civil aircraft system selection decision-making based on four characteristics and operating costs according to claim 2, characterized in that: The method for confirming the four performance indicators and economic indicators in step S1 is as follows: based on the four performance characteristics and economic characteristics of the civil aircraft system and the specific requirements of different decision-making situations, decision makers confirm the quantitative evaluation indicators of system safety, reliability, maintainability, testability and operating costs based on experience and the importance of indicators within the industry.

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