A reliable allocation method for ion electric propulsion based on PFHWA operator

Abstract

The application relates to the field of space electric propulsion power technology, in particular to a backup ion electric propulsion reliability distribution method based on a PFHWA operator, which comprises the following steps: 1, based on the reliability of the whole satellite task, the reliability of each single machine of the ion electric propulsion is preliminarily distributed; 2, based on a backup strategy, a backup correction factor of the ion electric propulsion is solved; 3, based on the backup correction factor, the reliability of the whole machine of the ion electric propulsion is corrected; 4, based on the PFHWA operator, the reliability of the whole machine of the ion electric propulsion is redistributed; 5, the reliability distribution result of the ion electric propulsion component is reversely checked, if the reliability target is not met, the steps 2-4 are executed again; 6, if the reliability target is met, the ion electric propulsion distribution result is listed. The application comprehensively considers the influence of quantitative spare parts, reduces the influence of expert subjectivity and hesitation, and provides a theoretical basis for ion electric propulsion reliability distribution.

Description

TECHNICAL FIELD

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

[0002] Ion electric propulsion is a complex single machine product composed of components in series, such as cathodes, discharge chambers, grids, neutralizers, cathode gas path insulators, anode gas path insulators, and neutralizer gas path insulators. As the core single machine of the propulsion system, ion electric propulsion is currently widely used in position maintenance and orbit transfer tasks of communication and remote sensing satellites. Due to its high specific impulse technical characteristics, ion electric propulsion has higher application benefits than chemical propulsion. However, in the application field of long-term tasks such as earth-moon and deep space exploration, the application reliability of ion electric propulsion needs to be improved.

[0003] Reliability allocation is a basic research work for improving the reliability of ion electric propulsion. Using a reliability allocation method that adapts to the physical characteristics and engineering actual conditions of the product can effectively avoid resource waste and maximize the reliability of the whole machine and even the whole satellite under the constraints of many influencing factors. The propulsion system of the whole satellite has different task forms, and usually uses cold backup to ensure the successful implementation of the task. However, the existing research has not fully considered the influence of spare parts on the reliability of the propulsion system, resulting in deviation in the determination of the top-level reliability.

[0004] The 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 of ion electric propulsion new research products at the initial design stage and the incomplete transparency of user data, ion electric propulsion has the characteristics of poor information and asymmetric data. In addition, as a complex single machine, there is still cognitive uncertainty in the modeling of the physical mechanism and evolution of ion electric propulsion based on plasma at the present stage, and the applicability of the traditional reliability allocation method relying on expert experience is greatly reduced. SUMMARY

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

[0006] In order to achieve the above object, the application provides a backup ion electric propulsion reliability distribution method based on PFHWA operator, comprising the following steps: step 1: based on the reliability of the whole satellite task, the reliability of each single machine of the ion electric propulsion is preliminarily distributed; 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 whole machine of the ion electric propulsion is corrected; step 4: based on the PFHWA operator, the reliability of the whole machine of the ion electric propulsion is redistributed; step 5: the reliability distribution result of the ion electric propulsion component is reversely calculated, if the reliability target is not met, the steps 2-4 are returned to execute; step 6: if the reliability target is met, the ion electric propulsion distribution result is listed, and the ion electric propulsion reliability distribution is completed.

[0007] Further, in step 1, the position keeping task, the attitude control task and the orbit transfer task are divided into three parallel subsystems according to the task target by using the ion electric propulsion, and the reliabilities of the subsystems are R s1 (t), R s2 (t) and R s3 (t) respectively.

[0008] Further, in step 2, the backup correction factor of the ion electric propulsion is solved in the following process:

[0009] Step 2.1: the replacement sequence of the component is determined, which is expressed by the following formula:

[0010]

[0011] Wherein, δ is the lower threshold value of the reliability of the whole satellite propulsion system, T0 is the task cycle, is the cost benefit importance degree, f c is the mapping function at the j c th replacement time;

[0012] Step 2.2: the backup correction factor is determined, after the replacement sequence of the component is determined, the failure number N in the task cycle is counted, and the backup rate is obtained by combining the number of ion electric propulsion components u i .

[0013] τ=g(u i , N);

[0014] Then the backup correction factor is:

[0015]

[0016] Wherein, g(·) is the ion electric propulsion backup strategy function, R ij(t) is the reliability of the jth component of the ith subsystem ion electric propulsion, k is the failure count.

[0017] Further, in step 3, after the correction by the backup correction factor, the reliability of the ion electric propulsion system of each subsystem is respectively:

[0018]

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

[0020] Step 4.1: Construct the reliability cost function, based on the basic principles of cost-reliability function model construction, the reliability cost function is represented by the following formula:

[0021]

[0022] where f j represents the quantitative index of improving the feasibility of the jth component, represents the importance of the jth component, R jmin and R jmax represent the existing reliability and the reliability limit value under the existing technology, respectively, R j is the reliability value to be allocated;

[0023] Step 4.2: Construct the allocation model, the nonlinear optimization model for reliability allocation is:

[0024]

[0025] where C represents the total cost of implementing the reliability of the ion electric propulsion system, is the system reliability calculated according to the component reliability allocation result, is the target value of the ion electric propulsion system reliability;

[0026] Step 4.3: Quantify model parameters; in the cost objective function, two constants f j and are involved, where f j is adjusted according to actual engineering applications; PFHWA operator is used to calculate;

[0027] Step 4.4: Solve the optimization allocation model; genetic algorithm is used to solve, and the allocation result of the reliability of each component of the ion electric propulsion system of each subsystem after the correction by the backup correction factor is obtained.

[0028] Further, in step 4.3, the process of calculating f by PFHWA operator is as follows:

[0029] Step 4.3.1: Constructing hesitant fuzzy set;

[0030] Constructing expert set E = {E1, E2, …, En} with n experts, and component set U = {U1, U2, …, Um} with m components; p n q m

[0031] For ion electric propulsion, the evaluation elements of component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, component quantity, failure damage, work independence, and work duration;

[0032] Then the upper and lower limits of the pthexpert's score on the importance of the qthcomponent are The score result constitutes a hesitant fuzzy element, where The expert score set is a hesitant fuzzy set h e (n).

[0033] Let the score matrix of each expert on the importance of each component be:

[0034]

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

[0036] The hesitation degree ζ pq is the expert score interval value, i.e.

[0037] The hesitant fuzzy entropy ΔS of expert score is: pq

[0038]

[0039] Then the membership degree of the Pythagorean fuzzy function of the pthexpert's score on the importance of the qthcomponent is The non-membership degree is

[0040] Let the membership degree and non-membership degree matrices be:

[0041]

[0042] Step 4.3.3: Calculate the influence degree of each component. From step 4.3.2, the Pythagorean fuzzy number of the pthexpert's score on the importance of the qthcomponent is Then introduce the PFHWA operator, and the score of each component is:

[0043] ​​​​​

[0044] Wherein, γ is a variable parameter, a increasing function Ω(γ) about γ is constructed to carry out Monte Carlo random sampling, γ satisfying is selected to determine the value of the variable coefficient, then the importance of each component is obtained:

[0045]

[0046] Further, in step 5, each component constituting the ion electric propulsion is divided into two types, wherein the main cathode and the neutralizer are the first type, and the discharge chamber, the grid, the cathode gas path insulator, the anode gas path insulator, and the neutralizer gas path insulator are the second type, then

[0047]

[0048] The distribution result is calculated using the above formula to determine whether it meets the target reliability.

[0049] The PFHWA operator-based backup ion electric propulsion reliability distribution method provided by the application has the following beneficial effects:

[0050] The top reliability index of the whole spacecraft propulsion system is distributed from top to bottom to each component of the ion electric propulsion, the backup ion electric propulsion reliability spare part correction factor is determined according to the cost-benefit importance principle, the preliminary decomposition result of the propulsion system reliability target to the subsystem is corrected, on this basis, the parameters in the reliability distribution target function are quantified more accurately through the PFHWA operator, that is, the Pythagorean fuzzy Hamacher weighted average operator, and the distribution accuracy is further improved; the subjective hesitation of the importance scoring of each component under the poor information, asymmetric and uncertain fuzzy information and the dynamic deficiency of the weight are overcome, and the influence of the propulsion system main backup switching on the reliability distribution is comprehensively considered, the model accuracy and engineering practicability of the ion electric propulsion reliability distribution are improved. BRIEF DESCRIPTION OF DRAWINGS

[0051] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The drawings illustrate embodiments of the present application and, together with the description, serve to explain the principles of the present application. In the drawings:

[0052] Figure 1 is a flowchart of the PFHWA operator-based backup ion electric propulsion reliability distribution method provided by the embodiment of the application; DETAILED DESCRIPTION

[0053] In the following, the technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort should belong to the scope of protection of the present application.

[0054] It should be noted that the terms "first", "second", and the like in the description and claims of the present application and the above drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or a chronological sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented. In addition, the terms "comprise" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units does not necessarily limit to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to the process, method, product or device.

[0055] In the present application, the terms "upper", "lower", "left", "right", "front", "back", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. These terms are mainly used to better describe the present application and its embodiments, and are not intended to limit the indicated devices, elements or components to have a specific orientation, or to be constructed and operated in a specific orientation.

[0056] In addition, in addition to indicating the orientation or positional relationship, the above-mentioned part of the terms can also be used to indicate other meanings, for example, the term "upper" can also be used to indicate a certain dependent relationship or connection relationship in some cases. For a person of ordinary skill in the art, the specific meaning of these terms in the present application can be understood according to the specific circumstances.

[0057] In addition, the meaning of the term "a plurality of" should be two and more than two.

[0058] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0059] As shown in Figure 1 The present application provides a reliable distribution method for a backup ion electric propulsion based on a PFHWA operator, which comprises the following steps:

[0060] Step 1: Based on the reliability of the whole satellite task, the reliability of each ion electric propulsion unit is preliminarily allocated; taking a satellite propulsion system as an example, the position keeping task, the attitude control task and the orbit transfer task are divided into three parallel subsystems by ion electric propulsion according to the task target, and the reliability of the whole satellite propulsion system can be expressed as:

[0061]

[0062] wherein r is the number of subsystems, u i is the number of ion electric propulsion contained components of each subsystem, R ij (t) is the reliability of the jth component of the ith subsystem ion electric propulsion; the initial allocation is performed according to the principle of independent and equal weight of subsystems, and the initial allocation values of the whole machine reliability of each subsystem ion electric propulsion are R s1 (t) = 0.9725, R s2 (t) = 0.9725, R s3 (t) = 0.9725.

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

[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 preferentially executes the task, when the reliability of the whole satellite propulsion system decreases to the lower threshold value δ, the component replacement or the whole machine backup is performed, the main cathode can adopt the cathode array mode for component replacement, and the components such as grid which cannot be replaced are replaced by the method of whole machine backup to realize the equivalent effect of component replacement; according to the principle of cost benefit importance, that is, the principle of maximizing the system reliability of unit cost at any replacement time, the component replacement sequence is expressed as:

[0065]

[0066] wherein δ is the lower threshold value of the reliability of the whole satellite propulsion system, T0 is the task cycle, is the cost benefit importance, f c is the mapping function at the j c th replacement time;

[0067] The satellite in-orbit mission duration is 17500 hours, i.e. T0=17500, and the lower limit threshold of the satellite propulsion system reliability is 0.94, i.e. δ=0.94. When the propulsion system reliability decreases to the lower limit threshold, the cost-effectiveness importance of each component is calculated, and the component with the largest cost-effectiveness importance is replaced. The main cathode can be replaced by a cathode array, and the components such as the grid that cannot be replaced are replaced by the equivalent effect of the whole machine backup.

[0068] Step 2.2: Determine the backup correction factor. After determining the replacement sequence of the components according to the cost-effectiveness importance principle, the number of failures N in the mission period is counted, and the number of ion electric propulsion components u is combined i , and the spare parts support 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 ith subsystem ion electric propulsion, and k is the failure count.

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

[0074] After correction by the backup correction factor, the reliability of the whole ion electric propulsion of each subsystem is respectively:

[0075]

[0076] Combined with the telemetry data of the satellite, the spare parts correction factor α=0.9814 is determined, and the corrected reliability of the whole ion electric propulsion of each subsystem is

[0077] Step 4: Based on the PFHWA operator, the reliability of the whole ion electric propulsion is redistributed;

[0078] Step 4.1: Construct the reliability cost function. Based on the basic principle of constructing the cost-reliability function model, the reliability cost function is represented by the following formula:

[0079]

[0080] Where f j represents the quantitative index of improving the feasibility of the jth component, Rj represents the importance of the jth component assembly jmin and R jmax represent the existing reliability and the reliability limit value under the existing technology, respectively, R j is the reliability value to be allocated;

[0081] Step 4.2: Constructing an allocation model, for ion electric propulsion, the whole machine is composed of a main cathode, a discharge chamber, a grid, a neutralizer, a cathode gas path insulator, an anode gas path insulator and a neutralizer gas path insulator 7 component assemblies in series, and a nonlinear optimization model for reliability allocation is constructed to minimize the cost paid for the reliability of the whole machine, as follows:

[0082]

[0083] wherein C represents the total cost of the reliability implementation of the ion electric propulsion whole machine, is the whole machine reliability calculated according to the component reliability allocation result, is the subsystem ion electric propulsion whole machine reliability target value;

[0084] Step 4.3: Quantifying model parameters; f j and two constants are involved in the cost objective function, wherein f j is adjusted according to actual engineering application, and is a relative quantity depending on the simplicity of the improvement of the component reliability; and is determined depending on the ion electric propulsion expert knowledge, and is calculated using a PFHWA operator to reduce the error influence of the subjectivity and hesitation of the expert scoring on the component importance evaluation, and the specific process is as follows:

[0085] Step 4.3.1: Constructing a hesitant fuzzy set;

[0086] Constructing an expert set E = {E1, E2, …, E p ,…E n} with n experts, and a component set U = {U1, U2, …, U q ,…,U m} with m components;

[0087] For ion electric propulsion, the evaluation elements of the component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, component quantity, failure damage, work independence and work duration;

[0088] Then the upper and lower limits of the score of the pth expert on the qth component importance constitute the hesitant fuzzy element of the scoring result, wherein The expert scoring set is the hesitant fuzzy set h e n).

[0089] The scoring matrix of each expert on the importance of each component is:

[0090]

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

[0092] Hesitation degree ζ pq The scoring interval value for the expert is, that is,

[0093] The hesitation fuzzy entropy ΔS of the expert scoring is pq :

[0094]

[0095] Then the membership degree of the Pythagorean fuzzy function scoring of the pth expert on the importance of the qth component is The non-membership degree is

[0096] Denote the membership degree and non-membership degree matrices as:

[0097]

[0098] Step 4.3.3: Calculate the influence degree of each component. From step 4.3.2, the Pythagorean fuzzy number of the pth expert scoring on the importance of the qth component is Then introduce the PFHWA operator, and the score of each component is:

[0099]

[0100] Where γ is a variable parameter, and the increasing function Ω(γ) about γ is constructed to perform Monte Carlo random sampling. Select γ that satisfies to determine the value of the variable coefficient. Then the importance of each component is obtained as:

[0101]

[0102] For ion electric propulsion, six experts including designers, testers, etc. scored the importance of each component according to the design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, component quantity, fault damage, work independence and work duration, and the scoring matrix was constructed. The membership degree matrix and non-membership degree matrix are as follows:

[0103]

[0104] By constructing the increasing function Ω(γ) about γ, Monte Carlo random sampling is performed, and γ that satisfies The value of the variable coefficient is determined by γ = 1.3, and the importance of each component is calculated by combining the above formulas:

[0105]

[0106] The importance of each component obtained by introducing the PFHWA operator is substituted into the reliability allocation nonlinear optimization, and the final component reliability allocation result is obtained by solving;

[0107] Step 4.4: Solve the optimization allocation model; since the optimization model has more optimization variables, the genetic algorithm is used to solve the nonlinear model, and the reliability allocation result of each component of the ion electric propulsion system after the backup correction factor correction is obtained:

[0108]

[0109] Step 5: The reliability allocation result of the ion electric propulsion component is checked in reverse, according to the current understanding of the physical mechanism and operation law of different components of the ion electric propulsion and the richness of historical test data, each component of the ion electric propulsion is divided into two types, the main cathode and the neutralizer are the first type, and the discharge chamber, the grid, the cathode gas path insulator, the anode gas path insulator, and the neutralizer gas path insulator are the second type, then:

[0110]

[0111] The allocation result is checked to see if it meets the target reliability, if not, steps 2 to 4 are re-executed, if it does, the final allocation result is listed, and the ion electric propulsion reliability allocation is completed.

[0112] The above allocation result is substituted into the ion electric propulsion reliability calculation formula to obtain

[0113]

[0114] Step 6: Through the calculation, it is found that the reliability of the ion electric propulsion whole machine meets the reliability target requirement, the above allocation result is reasonable, and the ion electric propulsion reliability allocation is completed.

[0115] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Those skilled in the art can make various changes and modifications to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A PFHWA operator based reliability allocation method for a redundant ion electric propulsion, characterized by, The method comprises the following steps: Step 1: based on the reliability of the whole satellite task, the reliability of each single machine of the ion electric propulsion 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 whole machine of the ion electric propulsion is corrected; Step 4: based on the PFHWA operator, the reliability of the whole machine of the ion electric propulsion is re-allocated; Step 4.1: a reliability cost function is constructed, based on the basic principle of constructing the cost-reliability function model, the reliability cost function is expressed as follows: ； wherein f j represents a quantification index of improving the feasibility of the jth component assembly, represents the importance of the jth component assembly, R jmin and R jmax respectively represent the existing reliability and the reliability limit value under the existing technology, R j is the reliability value to be assigned; Step 4.2: a distribution model is constructed, the nonlinear optimization model for reliability distribution is constructed as follows: ； Wherein, C represents the total cost of ion electric propulsion system reliability implementation, The total reliability of the ion electric propulsion system is calculated according to the reliability distribution of the subassemblies, The total reliability of the ion electric propulsion system is calculated according to the reliability distribution of the subassemblies, Step 4.3: Quantize model parameters; involve f in the cost objective function j and Two constants, where f j Adjust according to actual engineering application; Use PFHWA operator to calculate; Step 4.4: the optimization distribution model is solved; genetic algorithm is adopted to solve, and the allocation result of the reliability of each component of the ion electric propulsion after the correction of the backup correction factor is obtained; Step 5: the reliability distribution result of the ion electric propulsion component is checked reversely, if the reliability target is not met, the step 2-4 is returned to execute; Step 6: if the reliability target is met, the ion electric propulsion distribution result is listed, and the reliability distribution of the ion electric propulsion is completed.

2. The PFHWA algorithm based reliability allocation method for a redundant ion electric propulsion system according to claim 1, characterized in that, In step 1, the position keeping task, the attitude control task and the orbit transfer task are divided into three parallel subsystems according to the mission objectives using ion electric propulsion, and the reliabilities of the subsystems are R s1 (t), R s2 (t), R s3 (t).

3. The PFHWA algorithm based reliability allocation method for a redundant ion electric propulsion system according to claim 2, characterized in that, In step 2, when the backup correction factor of the ion electric propulsion is solved, the process is as follows: Step 2.1: the replacement sequence of the component is determined, which is expressed as follows: ； Wherein, δ is the lower threshold of the whole satellite propulsion system reliability, T0 is the mission cycle, For cost-effectiveness importance, f c The mapping function of the j c th replacement time. Step 2.2: Determine the backup correction factor, after determining the replacement sequence of the component group, the number of failures N in the task cycle is obtained by statistics, combined with the number of ion electric propulsion components u i The spare parts support rate is obtained as: ； 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 ith subsystem ion electric propulsion, k is the failure count.

4. The PFHWA algorithm based reliability allocation method for a redundant ion electric propulsion system according to claim 3, characterized in that, In step 3, after correction by the backup correction factor, the reliability of the ion electric propulsion system of each subsystem Respectively: 。 5. The PFHWA algorithm based reliability allocation method for a redundant ion electric propulsion system as claimed in claim 4, wherein, In step 4.3, the PFHWA operator is used to calculate The process is as follows: Step 4.3.1: a hesitant fuzzy set is constructed; set of experts n experts, set of components m components; For the ion electric propulsion, the evaluation elements of the component importance include design difficulty, manufacturing difficulty, maintenance difficulty, assembly difficulty, component weight, component quantity, failure damage, work independence and work time length; So the upper and lower limits of the pth expert scoring the qth component importance The hesitant fuzzy element constituting the scoring result, wherein, The expert scoring set is a hesitant fuzzy set ; Let the scoring matrix of each expert on the importance of each component be: ； Step 4.3.2: the membership degree of the Pythagorean fuzzy number is calculated; Hesitancy Interval values for expert scoring, i.e. ; Expert scoring hesitancy fuzzy entropy Is: ； Then the membership of the Pythagorean fuzzy function of the pth expert scoring the qth component importance , and the non-membership is ; Let the membership degree matrix and the non-membership degree matrix be: ， ； Step 4.3.3: Calculate the influence degree of each component, the Pythagorean fuzzy number of the pth expert's scoring of the importance of the qth component can be obtained from step 4.3.2 Then, the PFHWA operator is introduced, and the score of each component is as follows: ； where, is a variable parameter, the construction of the increase function Monte Carlo random sampling, selected to meet to determine the value of the variable coefficient, then the various components of the importance of the degree is:​​ 。 6. The PFHWA algorithm based reliability allocation method for a redundant ion electric propulsion system as claimed in claim 5, wherein, In step 5, each component constituting the ion electric propulsion is divided into two types, wherein the main cathode and the neutralizer are the first type, and the discharge chamber, the grid, the cathode gas path insulator, the anode gas path insulator, the neutralizer gas path insulator are the second type, so that: ； The above formula is used to check whether the allocation result meets the target reliability.

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