Backup ion electric propulsion reliability distribution method based on PFHWA operator

Abstract

The invention relates to the technical field of space electric propulsion power, in particular to a backup ion electric propulsion reliability distribution method based on a PFHWA operator, and the method comprises the steps: 1, carrying out the preliminary distribution of the reliability of each single machine of ion electric propulsion based on the reliability of a whole-satellite task; 2, based on a backup strategy, solving a backup correction factor of ion electric propulsion; 3, on the basis of the backup correction factor, correcting the whole machine reliability of ion electric propulsion; 4, based on a PFHWA operator, redistributing the reliability of the whole ion electric propulsion machine; 5, reverse checking calculation is conducted on the reliability distribution result of the ion electric propulsion part assembly, and if the reliability distribution result does not meet the reliability target, the steps 2-4 are executed again; and 6, if the reliability target is met, listing an ion electric propulsion distribution result. According to the method, the influence of quantitative spare parts is integrated, the subjectivity and hesitance influence of experts is reduced, and a theoretical basis is provided for ion electric propulsion reliability distribution.

Description

Technical Field

[0001] The present application relates to the field of space electric propulsion technology, and in particular to a backup ion electric propulsion reliability allocation method based on the PFHWA operator. Background Art

[0002] Ion propulsion is a complex, single-unit product consisting of a cathode, discharge chamber, grid, neutralizer, cathode gas path insulator, anode gas path insulator, and neutralizer gas path insulator, all connected in series. As the core unit of the propulsion system, ion propulsion is currently widely used in satellite station maintenance and orbit transfer missions for communications and remote sensing. Its high specific impulse technology offers greater application benefits than chemical propulsion. For applications such as Earth-Moon and deep space exploration, where mission durations are significantly increasing, improving the reliability of ion propulsion has become a key focus.

[0003] Reliability allocation is a fundamental research topic for improving the reliability of ion electric propulsion. Using a reliability allocation method tailored to the physical characteristics of the product and engineering realities can effectively avoid resource waste and maximize the reliability of the entire system and even the entire satellite, within the constraints of numerous influencing factors and constraints. Satellite propulsion systems have different mission types and typically utilize cold backups to ensure successful mission execution. However, existing research has not fully considered the impact of spare part type on propulsion system reliability, resulting in biased top-level reliability determination.

[0004] Existing traditional reliability allocation methods include equal allocation method, scoring allocation method, fault tree allocation method, etc. Due to the lack of sufficient reliability data in the early design stage of newly developed ion electric propulsion products and the incomplete transparency of user data, ion electric propulsion has information-poor and asymmetric data characteristics; in addition, as a complex single machine, ion electric propulsion currently has cognitive uncertainty in its plasma-based physical mechanism and evolution modeling, which greatly reduces the applicability of traditional reliability allocation methods that rely on expert experience. Summary of the Invention

[0005] This application provides a backup ion electric propulsion reliability allocation method based on the PFHWA operator, which integrates the impact of quantified spare parts, reduces the influence of expert subjectivity and hesitation, and provides a theoretical basis for the reliability allocation of ion electric propulsion in the field of deep space exploration.

[0006] In order to achieve the above-mentioned purpose, the present application provides a backup ion electric propulsion reliability allocation method based on the PFHWA operator, comprising the following steps: Step 1: Based on the reliability of the entire satellite mission, the reliability of each ion electric propulsion unit is preliminarily allocated; Step 2: Based on the backup strategy, the backup correction factor of the ion electric propulsion is solved; Step 3: Based on the backup correction factor, the reliability of the entire ion electric propulsion unit is corrected; Step 4: Based on the PFHWA operator, the reliability of the entire ion electric propulsion unit is redistributed; Step 5: Reversely verify the reliability allocation results of the ion electric propulsion components. If the reliability target is not met, return to execute steps 2-4; Step 6: If the reliability target is met, the ion electric propulsion allocation results are listed to complete the ion electric propulsion reliability allocation.

[0007] Furthermore, in step 1, the position keeping task, attitude control task, and orbit transfer task are divided into three parallel subsystems by ion electric propulsion according to the task objectives, and the reliability of each subsystem is obtained as R s1 (t), R s2 (t), R s3 (t).

[0008] Furthermore, in step 2, the process of solving the backup correction factor of ion electric propulsion is as follows:

[0009] Step 2.1: Determine the replacement sequence of the components, expressed as follows:

[0010]

[0011] Among them, δ is the lower limit threshold of the reliability of the entire satellite propulsion system, T0 is the mission period, is the cost-effectiveness importance, f c For the jth c The mapping function of the replacement moment;

[0012] Step 2.2: Determine the backup correction factor. After determining the replacement sequence of the components, calculate the number of failures N within the mission cycle and combine it with the number of ion electric propulsion components u. i , and the spare parts guarantee rate is:

[0013] τ=g(u i , N);

[0014] Then the backup correction factor is:

[0015]

[0016] Where g(·) is the ion electric propulsion backup strategy function, R ij(t) is the reliability of the jth component of the ion electric propulsion subsystem i, and k is the number of failures.

[0017] Furthermore, in step 3, after the backup correction factor is corrected, the reliability of the ion electric propulsion system of each subsystem is They are:

[0018]

[0019] Furthermore, in step 4, the process of redistributing the reliability of the entire ion electric propulsion system is as follows:

[0020] Step 4.1: Construct a reliability cost function. Based on the basic principles of cost-reliability function model construction, the reliability cost function is expressed as follows:

[0021]

[0022] Among them, f j represents the quantitative index for improving the feasibility of the j-th component, represents the importance of the jth component, R jmin and R jmax Represent the existing reliability and the reliability limit under the existing technology, R j is the reliability value to be assigned;

[0023] Step 4.2: Construct the allocation model. The nonlinear optimization model of reliability allocation is constructed as follows:

[0024]

[0025] Where C represents the total cost of achieving the reliability of the ion electric propulsion system. is the reliability of the whole machine calculated based on the reliability distribution results of the components. The reliability target value of the ion electric propulsion subsystem is:

[0026] Step 4.3: Quantify model parameters; involve f in the cost objective function j and Two constants, among which f j Adjust according to actual engineering application; The PFHWA operator is used for calculation;

[0027] Step 4.4: Solve the optimization allocation model; use the genetic algorithm to solve and obtain the distribution results of the reliability of each component of the subsystem ion electric propulsion after correction by the backup correction factor.

[0028] Furthermore, in step 4.3, the PFHWA operator is used to calculate The process is as follows:

[0029] Step 4.3.1: Construct hesitant fuzzy sets;

[0030] Construct expert set E={E1,E2,…,E p ,…E n} There are n experts in total, and the component set U={U1,U2,…,U q ,…,U m} A total of m components;

[0031] For ion electric propulsion, the evaluation factors of component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, number of components, failure damage, working independence and working time;

[0032] Then the upper and lower limits of the importance score of the qth component by the pth expert are The hesitant fuzzy element that constitutes the scoring result, where The expert scoring set is the hesitant fuzzy set h e (n);

[0033] The scoring matrix of each expert's importance of each component is recorded as:

[0034]

[0035] Step 4.3.2: Calculate the Pythagorean fuzzy number membership degree;

[0036] Hesitation pq is the expert scoring interval value, that is

[0037] Hesitant fuzzy entropy ΔS of expert scoring pq for:

[0038]

[0039] Then the Pythagorean fuzzy function membership of the p-th expert's score on the q-th component importance is The non-membership degree is

[0040] The membership and non-membership matrices are respectively:

[0041]

[0042] Step 4.3.3: Calculate the influence of each component. From step 4.3.2, we can get the Pythagorean fuzzy number of the p-th expert's score on the q-th component's importance: Then the PFHWA operator is introduced, and the scores of each component are:

[0043]

[0044] Among them, γ is a variable parameter, and the increasing function Ω(γ) about γ is constructed for Monte Carlo random sampling, and the parameters that satisfy γ is used to determine the value of the variable coefficient, and the importance of each component is obtained as follows:

[0045]

[0046] Furthermore, in step 5, the components constituting ion electric propulsion are divided into two major types, wherein the main cathode and neutralizer are of the first type, and the discharge chamber, grid, cathode gas path insulator, anode gas path insulator, and neutralizer gas path insulator are of the second type. Then, there are:

[0047]

[0048] Use the above formula to verify whether the allocation result meets the reliability of the target.

[0049] The present application provides a backup ion electric propulsion reliability allocation method based on the PFHWA operator, which has the following beneficial effects:

[0050] This application distributes the top-level reliability indicators of the entire spacecraft propulsion system to the various ion electric propulsion components from top to bottom, and determines the backup ion electric propulsion reliability spare parts correction factor based on the cost-effectiveness importance principle to correct the preliminary decomposition result of the propulsion system reliability target into the subsystem. On this basis, the parameters in the reliability allocation objective function are more accurately quantified through the Pythagorean fuzzy Hamacher weighted average operator, namely PFHWA operator, to further improve the allocation accuracy; overcome the subjective hesitation and lack of weight dynamics in the importance scoring of each component under poor information, asymmetric and uncertain fuzzy information, and comprehensively consider the impact of the actual engineering practice of the main and backup switching of the propulsion system on the reliability allocation, thereby improving the model accuracy and engineering practicality of the ion electric propulsion reliability allocation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings that constitute part of this application are used to provide a further understanding of this application and make other features, objects and advantages of this application more apparent. The illustrative embodiment drawings of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0052] Figure 1 This is a flow chart of a backup ion electric propulsion reliability allocation method based on the PFHWA operator provided in an embodiment of the present application; DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0054] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present application described here. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0055] In this application, terms such as "upper," "lower," "left," "right," "front," "back," "top," "bottom," "inner," "outer," "center," "vertical," "horizontal," "transverse," and "longitudinal" indicate positions or locations based on the positions or locations shown in the accompanying drawings. These terms are primarily intended to better describe this application and its embodiments and are not intended to limit the devices, elements, or components indicated to having a specific orientation, or to being constructed or operated in a specific orientation.

[0056] Furthermore, some of the above terms may be used to express other meanings besides indicating a position or location. For example, the term "on" may also be used to indicate a dependency or connection in certain circumstances. Those skilled in the art will understand the specific meanings of these terms in this application based on the specific circumstances.

[0057] Additionally, the term "plurality" shall mean two or more.

[0058] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0059] like Figure 1 As shown, the present application provides a backup ion electric propulsion reliability allocation method based on the PFHWA operator, comprising the following steps:

[0060] Step 1: Based on the reliability of the entire satellite mission, the reliability of each ion electric propulsion unit is preliminarily allocated. Taking a satellite propulsion system as an example, the ion electric propulsion for the station keeping mission, attitude control mission, and orbit transfer mission is divided into three parallel subsystems according to the mission objectives. The reliability of the entire satellite propulsion system can be expressed as:

[0061]

[0062] Where r is the number of subsystems, u i The number of ion electric propulsion components for each subsystem, R ij (t) is the reliability of the jth component of the ion electric propulsion of the i-th subsystem; the initial allocation is based on the principle of mutual independence and equality of subsystems, so that the initial allocation values ​​of the reliability of the ion electric propulsion of each subsystem are R s1 (t)=0.9725,R s2 (t)=0.9725,R s3 (t)=0.9725.

[0063] Step 2: Based on the backup strategy, solve the backup correction factor of ion electric propulsion;

[0064] Step 2.1: Determine the replacement sequence of components. Each subsystem adopts the working mode of main ion electric propulsion + backup ion electric propulsion. The main electric propulsion takes priority in executing its corresponding tasks. When the reliability of the entire satellite propulsion system drops to the lower limit threshold δ, the components are replaced or the whole system is switched to backup. The main cathode can be replaced by the cathode array method, while the grid and other components that cannot be replaced are replaced by the whole system switching to backup to achieve the equivalent effect of component replacement. According to the principle of cost-effectiveness, that is, the replacement of components at any replacement time maximizes the system reliability of the unit cost increase, the component replacement sequence is expressed as follows:

[0065]

[0066] Among them, δ is the lower limit threshold of the reliability of the entire satellite propulsion system, T0 is the mission period, is the cost-effectiveness importance, f c For the jth c The mapping function of the replacement moment;

[0067] The satellite's on-orbit mission duration is 17,500 hours, or T0 = 17,500. The lower limit threshold for the propulsion system's reliability is 0.94, or δ = 0.94. When the propulsion system's reliability drops to the lower limit, the cost-effectiveness of each component is calculated, and the most cost-effective component is replaced. The main cathode can be replaced using a cathode array, while components that cannot be replaced, such as the grid, are replaced using a complete system replacement method.

[0068] Step 2.2: Determine the backup correction factor. After determining the replacement sequence of components based on the principle of cost-effectiveness and importance, calculate the number of failures N within the mission cycle and combine it with the number of ion electric propulsion components u. i , and the spare parts guarantee rate is:

[0069] τ=g(u i , N);

[0070] Then the backup correction factor is:

[0071]

[0072] Where g(·) is the ion electric propulsion backup strategy function, R ij (t) is the reliability of the jth component of the ion electric propulsion subsystem i, and k is the number of failures.

[0073] Step 3: Based on the backup correction factor, the reliability of the ion electric propulsion system is corrected;

[0074] After the backup correction factor is corrected, the reliability of the ion electric propulsion system of each subsystem is They are:

[0075]

[0076] Combined with the satellite telemetry data, the spare parts correction factor α is determined to be 0.9814, and the reliability of the ion electric propulsion subsystem after correction is:

[0077] Step 4: Based on the PFHWA operator, redistribute the overall reliability of the ion electric propulsion system;

[0078] Step 4.1: Construct a reliability cost function. Based on the basic principles of cost-reliability function model construction, the reliability cost function is expressed as follows:

[0079]

[0080] Among them, f j represents the quantitative index for improving the feasibility of the j-th component, represents the importance of the jth component, R jmin and R jmax Represent the existing reliability and the reliability limit under the existing technology, R j is the reliability value to be assigned;

[0081] Step 4.2: Construct a distribution model. For ion electric propulsion, the entire system consists of seven components connected in series: the main cathode, discharge chamber, grid, neutralizer, cathode gas path insulator, anode gas path insulator, and neutralizer gas path insulator. To minimize the cost of achieving the reliability of the entire system, a nonlinear optimization model for reliability distribution is constructed as follows:

[0082]

[0083] Where C represents the total cost of achieving the reliability of the ion electric propulsion system. is the reliability of the whole machine calculated based on the reliability distribution results of the components. The reliability target value of the ion electric propulsion subsystem is:

[0084] Step 4.3: Quantify model parameters; involve f in the cost objective function j and Two constants, among which f j Adjustment based on actual engineering applications is a relative amount determined by the ease with which component reliability can be improved; The determination of relies on the knowledge of ion electric propulsion experts and is calculated using the PFHWA operator to reduce the influence of the subjectivity and hesitation of experts in scoring on the error in the evaluation of component importance. The specific process is as follows:

[0085] Step 4.3.1: Construct hesitant fuzzy sets;

[0086] Construct expert set E={E1,E2,…,E p ,…E n} There are n experts in total, and the component set U={U1,U2,…,U q ,…,U m} A total of m components;

[0087] For ion electric propulsion, the evaluation factors of component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, number of components, failure damage, working independence and working time;

[0088] Then the upper and lower limits of the importance score of the qth component by the pth expert are The hesitant fuzzy element that constitutes the scoring result, where The expert scoring set is the hesitant fuzzy set h e )n);

[0089] The scoring matrix of each expert's importance of each component is recorded as:

[0090]

[0091] Step 4.3.2: Calculate the Pythagorean fuzzy number membership degree;

[0092] Hesitation pq is the expert scoring interval value, that is

[0093] Hesitant fuzzy entropy ΔS of expert scoring pq for:

[0094]

[0095] Then the Pythagorean fuzzy function membership of the p-th expert's score on the q-th component importance is The non-membership degree is

[0096] The membership and non-membership matrices are respectively:

[0097]

[0098] Step 4.3.3: Calculate the influence of each component. From step 4.3.2, we can get the Pythagorean fuzzy number of the p-th expert's score on the q-th component's importance: Then the PFHWA operator is introduced, and the scores of each component are:

[0099]

[0100] Among them, γ is a variable parameter, and the increasing function Ω(γ) about γ is constructed for Monte Carlo random sampling, and the parameters that satisfy γ is used to determine the value of the variable coefficient, and the importance of each component is obtained as follows:

[0101]

[0102] For ion electric propulsion, six experts, including designers and testers, scored the importance of each component based on nine evaluation factors: design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, number of components, failure damage, working independence, and working time. The results formed a scoring matrix, and the membership matrix and non-membership matrix were solved as follows:

[0103]

[0104] By constructing an increasing function Ω(γ) about γ and performing Monte Carlo random sampling, we select γ is used to determine the value of the variable coefficient, and γ = 1.3 is obtained. Combining the above formulas, the importance of each component is calculated as follows:

[0105]

[0106] Substituting the importance parameters of each component obtained by introducing the PFHWA operator into the nonlinear optimization of reliability allocation, the final component reliability allocation result can be obtained;

[0107] Step 4.4: Solve the optimization allocation model. Since the optimization model has many optimization variables, a genetic algorithm is used to solve the nonlinear model. The reliability allocation results of each component of the ion electric propulsion subsystem after the backup correction factor are obtained as follows:

[0108]

[0109] Step 5: Reverse-check the reliability distribution results of the ion propulsion components. Based on the current understanding of the physical mechanisms and operating laws of different ion propulsion components and the richness of historical test data, the components that make up the ion propulsion are divided into two major types. Among them, the main cathode and neutralizer are the first type, and the discharge chamber, grid, cathode gas path insulator, anode gas path insulator, and neutralizer gas path insulator are the second type. Then, we have:

[0110]

[0111] This is used to verify whether the allocation result meets the target reliability. If not, re-execute steps 2 to 4. If so, list the final allocation result to complete the ion electric propulsion reliability allocation.

[0112] Substituting the above distribution results into the ion electric propulsion reliability calculation formula, we can get

[0113]

[0114] Step 6: Through verification, it is found that the reliability of the ion electric propulsion system meets the reliability target requirements. The above allocation results are reasonable, and the ion electric propulsion reliability allocation is completed.

[0115] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

Claims

1. A backup ion electric propulsion reliability allocation method based on PFHWA operator, characterized in that: The steps include: Step 1: Based on the reliability of the entire satellite mission, make a preliminary allocation of the reliability of each ion electric propulsion unit; Step 2: Based on the backup strategy, solve the backup correction factor of ion electric propulsion; Step 3: Based on the backup correction factor, the reliability of the ion electric propulsion system is corrected; Step 4: Based on the PFHWA operator, redistribute the overall reliability of the ion electric propulsion system; Step 5: Perform reverse calculation on the reliability distribution results of the ion electric propulsion unit components. If the reliability target is not met, return to steps 2-4. Step 6: If the reliability target is met, the ion electric propulsion allocation results are listed to complete the ion electric propulsion reliability allocation.

2. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 1 is characterized in that: In step 1, the position keeping mission, attitude control mission, and orbit transfer mission are divided into three parallel subsystems by ion electric propulsion according to the mission objectives, and the reliability of each subsystem is obtained as R s1 (t), R s2 (t), R s3 (t).

3. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 2 is characterized in that: In step 2, the process of solving the backup correction factor for ion electric propulsion is as follows: Step 2.1: Determine the replacement sequence of the components, expressed as follows: Among them, δ is the lower limit threshold of the reliability of the entire satellite propulsion system, T0 is the mission period, is the cost-effectiveness importance, f c For the jth c The mapping function of the replacement moment; Step 2.2: Determine the backup correction factor. After determining the replacement sequence of the components, calculate the number of failures N within the mission cycle and combine it with the number of ion electric propulsion components u. i , and the spare parts guarantee rate is: τ=g(u i ,N); Then the backup correction factor is: Where g(·) is the ion electric propulsion backup strategy function, R ij (t) is the reliability of the jth component of the ion electric propulsion subsystem i, and k is the number of failures.

4. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 3 is characterized in that: In step 3, after the backup correction factor is corrected, the reliability of the ion electric propulsion system of each subsystem is They are:

5. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 4 is characterized in that: In step 4, the process of redistributing the reliability of the ion electric propulsion system is as follows: Step 4.1: Construct a reliability cost function. Based on the basic principles of cost-reliability function model construction, the reliability cost function is expressed as follows: Among them, f j represents the quantitative index for improving the feasibility of the j-th component, represents the importance of the jth component, R jmin and R jmax Represent the existing reliability and the reliability limit under the existing technology, R j is the reliability value to be assigned; Step 4.2: Construct the allocation model. The nonlinear optimization model of reliability allocation is constructed as follows: Where C represents the total cost of achieving the reliability of the ion electric propulsion system. is the reliability of the whole machine calculated based on the reliability distribution results of the components. The reliability target value of the ion electric propulsion subsystem is: Step 4.3: Quantify model parameters; involve f in the cost objective function j and Two constants, among which f j Adjust according to actual engineering application; The PFHWA operator is used for calculation; Step 4.4: Solve the optimization allocation model; use the genetic algorithm to solve and obtain the distribution results of the reliability of each component of the subsystem ion electric propulsion after correction by the backup correction factor.

6. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 5 is characterized in that: In step 4.3, the PFHWA operator is used to calculate The process is as follows: Step 4.3.1: Construct hesitant fuzzy sets; Construct expert set E={E1,E2,…,E p ,…E n } There are n experts in total, and the component set U={U1,U2,…,U q ,…,U m } A total of m components; For ion electric propulsion, the evaluation factors of component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, number of components, failure damage, working independence and working time; Then the upper and lower limits of the importance score of the qth component by the pth expert are The hesitant fuzzy element that constitutes the scoring result, where The expert scoring set is the hesitant fuzzy set h e (n); The scoring matrix of each expert's importance of each component is recorded as: Step 4.3.2: Calculate the Pythagorean fuzzy number membership degree; Hesitation pq is the expert scoring interval value, that is Hesitant fuzzy entropy ΔS of expert scoring pq for: Then the Pythagorean fuzzy function membership of the p-th expert's score on the q-th component importance is The non-membership degree is The membership and non-membership matrices are respectively: Step 4.3.3: Calculate the influence of each component. From step 4.3.2, we can get the Pythagorean fuzzy number of the p-th expert's score on the q-th component's importance: Then the PFHWA operator is introduced, and the scores of each component are: Among them, γ is a variable parameter, and the increasing function Ω(γ) about γ is constructed for Monte Carlo random sampling, and the parameters that satisfy γ is used to determine the value of the variable coefficient, and the importance of each component is obtained as follows:

7. The backup ion electric propulsion reliability allocation method based on the PFHWA operator according to claim 6 is characterized in that: In step 5, the components that make up the ion electric propulsion are divided into two categories. Among them, the main cathode and neutralizer are the first type, and the discharge chamber, grid, cathode gas path insulator, anode gas path insulator, and neutralizer gas path insulator are the second type. Then, there are: Use the above formula to verify whether the allocation result meets the reliability of the target.

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