CN111881575A - Wind turbine generator reliability distribution method considering subsystem multi-state and fault correlation - Google Patents

Wind turbine generator reliability distribution method considering subsystem multi-state and fault correlation Download PDF

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CN111881575A
CN111881575A CN202010729429.XA CN202010729429A CN111881575A CN 111881575 A CN111881575 A CN 111881575A CN 202010729429 A CN202010729429 A CN 202010729429A CN 111881575 A CN111881575 A CN 111881575A
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CN111881575B (en
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汪臻
屠劲林
梁思超
王森
冯笑丹
邓巍
赵勇
张晓朝
张建军
牛凤国
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Xian Thermal Power Research Institute Co Ltd
Huaneng Group Technology Innovation Center Co Ltd
Huaneng Renewables Corp Ltd
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Huaneng Group Technology Innovation Center Co Ltd
Huaneng Renewables Corp Ltd
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Abstract

The invention discloses a wind turbine generator reliability distribution method considering the multi-state and fault correlation of a subsystem, which comprises the steps of reasonably distributing reliability indexes distributed by the subsystem to each part, calculating the reliability distribution initial weight of each part, establishing a three-state transfer model of the subsystem, and correcting the reliability distribution initial weight of each part in the subsystem by comprehensively considering the propagation influence of faults according to the steady-state availability of the subsystem under the influence of each part; based on the reliability index of the subsystem, the reliability index of each part is distributed to each part, and the reliability distribution index of each part is obtained. The improved subsystem reliability distribution method, namely the correction coefficient distribution method, overcomes the defects of the traditional fuzzy distribution method, comprehensively considers the multi-state and fault propagation characteristics of the subsystem, and improves the objectivity and the accuracy in the reliability distribution process.

Description

Wind turbine generator reliability distribution method considering subsystem multi-state and fault correlation
Technical Field
The invention belongs to the field of reliability distribution, relates to a method for configuring the reliability of a wind turbine subsystem, and particularly relates to a method for distributing the reliability of a wind turbine by considering the multi-state and fault correlation of the subsystem.
Background
The reliability distribution is to divide the system reliability index specified in the product development stage from top to bottom step by step according to a certain distribution principle and method, and reasonably distribute the system reliability index to each subsystem, equipment, unit and part, thereby determining the quantitative reliability requirement of each component unit of the system. The reliability assignment includes an unconstrained assignment and a constrained assignment. The unconstrained reliability distribution aims at the designed product to meet the specified reliability index, and no constraint condition exists except the reliability index. The traditional unconstrained reliability allocation methods include equal allocation methods, scoring allocation methods, similar product methods and the like, and the methods are widely used in the initial development stage of reliability engineering.
The equal distribution method considers that the reliability of each component unit of the system is the same, and the method is simple but not reasonable, because in actual products, the situation that the reliability level of each unit is equal is generally impossible. The scoring distribution method is a distribution method in which under the condition that reliability data is very lack, a plurality of factors influencing the reliability are scored by experienced designers or experts, the scoring values are comprehensively analyzed to obtain relative reliability values among the component units of the product, and each unit is distributed with a reliability index according to the relative reliability values. The scoring distribution method generally considers factors such as unit complexity, technical development level, unit working time, environmental conditions and the like, the method depends heavily on experience of scoring experts and self level, and distribution results are high in subjectivity. The similar product method is generally applied to the condition that newly designed products are very similar to old products, and fault interest rates are distributed to all units of new products according to the fault rates of all units in the old products and the reliability requirements of the new products. Similar product law thinks that the original product basically reflects the reliability level that the product can realize in a certain period, and individual units of a new product do not have any major technical breakthrough, so according to the actual level, the new reliability index can be proportionally adjusted according to the original capability. The method is only suitable for the conditions that the structures, materials, processes, use environments and the like of new and old products are similar, and the use conditions are harsh under the condition that the statistical data of the old products or the distribution is carried out on the basis of the predicted data of the existing component units.
In the reliability allocation, due to the lack of reliability data in the initial design stage, experts with experience in related fields are often asked to score each reliability evaluation index, and the expert scoring method excessively depends on the own experience of the experts, so that the subjectivity of an evaluation result is too high. In order to solve the problem of strong subjectivity of expert scoring, some scholars introduce a fuzzy theory into a reliability allocation method and widely apply the fuzzy theory in theoretical research and actual engineering. Chang et al consider that the allocation factor in traditional reliability allocation is a single linguistic variable, so that a fuzzy linguistic set and a minimum variance weight are combined in reliability allocation, and the allocation result is reduced by subjectivity; chen et al propose a numerical control machine tool rest reliability allocation method based on fuzzy comprehensive evaluation, which comprehensively considers various factors influencing the reliability of the numerical control machine tool rest. Ebrahimipour and the like adopt a learning fuzzy reasoning system based on emotion, so that the accuracy and the universality of the reliability evaluation of the system on the redundancy allocation problem are improved; sriramdas and the like represent the distribution factors as trapezoidal fuzzy numbers, evaluate the trapezoidal fuzzy numbers by using fuzzy linguistic variables in the reliability distribution process, and distribute system reliability indexes to subsystems by using fuzzy scale factors; gianpaolo et al combines an analytic hierarchy process with an IFM process, and assigns different weights to different factors and different components according to the magnitude of reliability of the assignment process.
In summary, in the initial stage of design, the reliability statistical data is lacking, and the incorporation of fuzzy mathematical methods into the reliability allocation can reduce the influence of inaccurate subjective data and the like. However, reliability allocation based on fuzzy theory still has the disadvantages of low precision and large influence of human factors, and even the reliability of a certain subsystem is more than 1 in allocation. In addition, at present, most of the distribution results of reliability distribution research only stay at the subsystem layer, and the research of implementing reliability distribution of parts by using the reliability of the subsystem as an index is relatively less. Meanwhile, the current reliability allocation research does not take into account the multi-state and fault propagation characteristics of the subsystems.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a wind turbine generator reliability distribution method considering the multi-state and fault correlation of a subsystem, and provides an improved subsystem reliability distribution method, namely a correction coefficient distribution method, on the basis of a fuzzy distribution method, wherein the reliability indexes of the subsystem are distributed to all parts, so that the defects of the traditional fuzzy distribution method are overcome, the multi-state and fault propagation characteristics of the subsystem are comprehensively considered, and the objectivity and the accuracy in the reliability distribution process are improved.
In order to achieve the above purpose, the invention adopts the technical proposal that,
a wind turbine generator reliability distribution method considering subsystem multi-state and fault correlation comprises the following steps:
1) collecting historical operation fault data of each subsystem of the wind turbine generator, and calculating fault correlation among parts in the subsystem by adopting a decision laboratory analysis method, namely a DEMATEL method;
2) establishing a repairable three-state transition model of each subsystem according to the Markov state transition model;
3) constructing a state transition probability matrix of the subsystem according to the three-state-transition-capable subsystem model established in the step 2):
Figure BDA0002602624860000031
wherein: k is a radical of11＝λ1+λ3，k22＝μ1+λ2，k33＝μ2+μ3；λ1Failure rate for the subsystem from state 0 to state 1; lambda [ alpha ]2Failure rate for the subsystem from state 1 to state 2; lambda [ alpha ]3Failure rate for the subsystem from state 0 to state 2; mu.s1Maintenance rate for subsystem from state 1 to state 0; mu.s2Maintenance rate for subsystem from state 2 to state 1; mu.s3Maintenance rate for subsystem from state 2 to state 0;
4) according to the subsystem state transition probability matrix constructed in the step 3), comprehensively considering the fault correlation of each part in the subsystem, and calculating the steady-state availability of the subsystem under the influence of each part;
5) analyzing factors influencing the reliability distribution of the subsystem, and calculating the reliability distribution initial weight of each part in the subsystem by adopting a good-bad solution distance method, namely a TOPSIS method;
6) adopting the reliability distribution initial weight of each part obtained in the step 4) of correcting the steady-state availability degree influenced by each part in the step 5) of correcting the subsystem to obtain the reliability distribution correction weight of each part:
Figure BDA0002602624860000041
wherein: w is apiDistributing a correction weight for the reliability of the ith part of the subsystem;
7) distributing correction weight according to the reliability of each part in the subsystem, and distributing the reliability of the subsystem to each part:
Figure BDA0002602624860000042
wherein:
Figure BDA0002602624860000043
assigning a value to the reliability of the ith part of the subsystem;
Figure BDA0002602624860000044
reliability of the components under equal distribution; r*Reliability of the subsystem;idistributing a correction coefficient for the reliability of the ith part; beta is a regulating factor which ensures that the reliability after distribution meets the reliability requirement of the subsystem, and beta belongs to [0.5,1 ]]。
The step 1) comprises the following steps:
1.1) establishing a fault mode influence relation matrix according to the propagation influence relation among the fault modes:
Figure BDA0002602624860000045
wherein: pFA fault mode impact relationship matrix for the subsystem; f. ofijCorrelation of ith failure mode to jth failure mode for a subsystem; n isFThe number of subsystem failure modes;
1.2) defining a standardized matrix according to the fault mode influence relation matrix:
Figure BDA0002602624860000051
Figure BDA0002602624860000052
wherein:
Figure BDA0002602624860000053
a standardized matrix for subsystem fault propagation effects;
1.3) calculating a comprehensive influence relation matrix according to the standardized matrix:
Figure BDA0002602624860000054
wherein: i is an identity matrix; t is tijThe method comprises the steps of obtaining an original of the ith row and the jth column in a comprehensive influence relation matrix;
1.4) calculating the influence degree and the influenced degree among all parts in the subsystem according to the comprehensive influence relation matrix:
Figure BDA0002602624860000055
Figure BDA0002602624860000056
wherein: r (p)t,pk) The influence degree of the t-th part to the k-th part of the subsystem; d (p)t,pk) The influence degree of the kth part on the t-th part for the subsystem; p is a radical oftIs the t-th part of the subsystem; p is a radical ofkIs the kth part of the subsystem; n istThe number of failure modes in the t-th part; n iskThe number of the fault modes is the kth part;
1.5) calculating the fault correlation coefficient among the parts in the subsystem according to the influence degree and the influenced degree among the parts:
Figure BDA0002602624860000057
wherein:
Figure BDA0002602624860000058
a fault correlation coefficient between the t-th part and the k-th part of the subsystem is obtained;
the step 2) comprises the following steps:
2.1) the three states in the modifiable three-state transition model are defined as: the system comprises a normal state, a state to be maintained and a maintenance state, wherein the normal state is defined as that the subsystem has no potential safety hazard, the state to be maintained is defined as that the subsystem has the potential safety hazard but can still normally run, and the maintenance state is defined as that the system is shut down and starts to be maintained;
2.2) respectively representing the normal state, the state to be maintained and the maintenance state of the subsystem by using a 0 state, a 1 state and a 2 state in the repairable three-state transition model; the transition direction between the states is represented by an arrow, and the value on the arrow represents the transition probability of the subsystem from the current state to another state; by λi、μiAnd i is 1,2 and 3 respectively represent the fault rate and the repair rate of the subsystem in various states, the fault rate is defined as the ratio of the fault frequency of the subsystem to the total fault frequency in a statistical period, and the repair rate is defined as the ratio of the time spent on repairing the fault to the total time in the same statistical period.
The step 4) comprises the following steps:
4.1) calculating the steady-state availability of the subsystem under the influence of each fault mode:
Figure BDA0002602624860000061
wherein:
Figure BDA0002602624860000062
for subsystems in fault mode fj(ii) steady state availability under influence; f. ofjIs the jth failure mode of the subsystem;
4.2) calculating the steady-state availability of the subsystem under the influence of each part:
Figure BDA0002602624860000063
wherein:
Figure BDA0002602624860000064
for sub-system in part pi(ii) steady state availability under influence; p is a radical ofiIs the ith part of the subsystem; n isiFor the i-th part p of the subsystemiThe number of failure modes of (2);
4.3) generally, the failure of one part can cause the failure of other parts, so that a certain failure correlation is presented among parts of.
The step 5) comprises the following steps:
5.1) factors influencing the reliability allocation of the subsystem mainly comprise the importance of parts, the fault hazard of the parts, the complexity vector of the parts, the current technical level of the parts, the working time of the parts and the working environment of the parts;
5.2) grading the factors influencing the reliability distribution of the subsystems by adopting an expert grading mode according to the experience and historical data of grading experts to obtain a reliability distribution comprehensive influencing factor matrix:
Figure BDA0002602624860000071
wherein: gamma rayijAssigning a score value of an influencing factor to the jth reliability of the ith part; n is the number of the parts of the subsystem;
and 5.3) analyzing the reliability distribution comprehensive influence factor matrix in the step 5.2) by adopting a good-bad solution distance method to obtain the reliability distribution initial weight of each part in the subsystem.
Further, the step 4.3) comprises the following steps:
4.3.1) calculating the steady state availability of the subsystem under the influence of the ith part when considering the first order fault propagation influence:
Figure BDA0002602624860000072
wherein:
Figure BDA0002602624860000073
in order to consider the first-order fault propagation influence, the steady-state availability of the subsystem under the influence of the ith part;
Figure BDA0002602624860000074
fault correlation coefficients for the ith and kth parts of the subsystem;
Figure BDA0002602624860000075
the steady-state availability of the subsystem under the influence of the kth part;
4.3.2) calculating the steady-state availability of the subsystem under the influence of the ith part when considering the second-order fault propagation influence:
Figure BDA0002602624860000076
wherein:
Figure BDA0002602624860000081
in order to consider the influence of second-order fault propagation, the steady-state availability of the subsystem under the influence of the ith part;
Figure BDA0002602624860000082
fault correlation coefficients for the kth and the tth parts of the subsystem;
Figure BDA0002602624860000083
is the steady state availability 'of the subsystem under the influence of the tth part'
Since higher order fault propagation after the second order has less impact on the subsystem steady state availability, only the fault propagation impact of the previous second order is considered.
Further, the step 5.3) comprises the following steps:
5.3.1) carrying out standardization processing on the reliability distribution comprehensive influence factor matrix:
Figure BDA0002602624860000084
Figure BDA0002602624860000085
wherein:
Figure BDA0002602624860000086
distributing a comprehensive influence factor matrix for the standardized reliability;
Figure BDA0002602624860000087
assigning a value of an influencing factor to the jth reliability of the normalized ith part;
5.3.2) according to the standardized reliability distribution comprehensive influence factor matrix obtained in the step 5.3.1), calculating a weighting decision matrix:
Figure BDA0002602624860000088
Figure BDA0002602624860000089
wherein: v is a weighting decision matrix;
Figure BDA00026026248600000810
assigning a weight of an influencing factor to the jth reliability; v. ofijAssigning a value of an influencing factor for the jth reliability of the ith component after normalization and taking the weight into account;
5.3.3) calculating the optimal value and the worst value of each reliability distribution influence factor according to the weighting decision matrix obtained in the step 5.3.2):
Figure BDA0002602624860000091
Figure BDA0002602624860000092
wherein:
Figure BDA0002602624860000093
allocating an optimal value of an influence factor for the jth reliability;
Figure BDA0002602624860000094
distributing the worst value of the influencing factors for the jth reliability;
5.3.4) calculating the distance from the reliability distribution influence factor set of each part to the optimal value set and the worst value set:
Figure BDA0002602624860000095
Figure BDA0002602624860000096
wherein:
Figure BDA0002602624860000097
distributing the distance from the influence factor set to the optimal value set for the reliability of the ith part;
Figure BDA0002602624860000098
distributing the distance from the influence factor set to the worst value set for the reliability of the ith part;
5.3.5) calculating the closeness of the reliability allocation influence factor set of each part to the optimal value set:
Figure BDA0002602624860000099
wherein: ciThe closeness of the reliability assignment impact factor set of the ith part to the optimal value set;
5.3.6) calculating the reliability assignment initial weight of each part in the subsystem:
Figure BDA00026026248600000910
wherein:
Figure BDA00026026248600000911
an initial weight is assigned to the reliability of the ith part.
Compared with the existing reliability distribution method, the invention provides the wind turbine generator reliability distribution method considering the multi-state and fault correlation of the subsystem, the reliability index distributed by the subsystem is reasonably distributed to each part, the reliability distribution initial weight of each part is calculated, the three-state transfer model of the subsystem is established, and the reliability distribution initial weight of each part of the subsystem is corrected by comprehensively considering the propagation influence of the fault according to the steady-state availability of the subsystem under the influence of each part. Based on the reliability index of the subsystem, the reliability index of each part is distributed to each part, and the reliability distribution index of each part is obtained. The improved subsystem reliability distribution method, namely the correction coefficient distribution method, overcomes the defects of the traditional fuzzy distribution method, comprehensively considers the multi-state and fault propagation characteristics of the subsystem, and improves the objectivity and the accuracy in the reliability distribution process.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a modifiable state transition model.
Detailed Description
The invention is further explained below with reference to specific embodiments and the drawing of the description.
As shown in fig. 1, the present invention is a wind turbine generator reliability allocation method considering multi-state and fault correlation of subsystems, which specifically includes the following steps:
1) taking a variable pitch system of a certain type of wind turbine generator as an analysis object, collecting historical fault data of the wind turbine generator of the type, as shown in the following table: calculating the fault correlation among all parts in the variable pitch system by adopting a decision laboratory analysis method;
Figure BDA0002602624860000101
Figure BDA0002602624860000111
2) establishing a repairable three-state transition model of the variable pitch system according to the Markov state transition model, wherein the established repairable three-state transition model is shown in figure 2;
3) according to a repairable three-state transition model of the variable pitch system, a state transition probability matrix of the variable pitch system is constructed, and the transition probability of the states of the variable pitch system caused by each part can be represented by the frequency of faults and the reciprocal of repair time of the variable pitch system under the influence of each part:
Figure BDA0002602624860000112
Figure BDA0002602624860000121
4) according to the state transition probability matrix of the variable pitch system constructed in the step 3), comprehensively considering the fault correlation of each part in the variable pitch system, and calculating the steady-state availability of the variable pitch system under the influence of each part;
Figure BDA0002602624860000122
5) analyzing factors influencing the reliability distribution of the variable pitch system, and calculating the reliability distribution initial weight of each part in the variable pitch system by adopting a good-bad solution distance method;
Figure BDA0002602624860000123
6) distributing initial weight to the reliability of each part obtained in the step 5) by adopting the steady-state availability degree of each part affected by the variable pitch system obtained in the step 4), and obtaining the reliability distribution correction weight of each part:
Figure BDA0002602624860000131
7) distributing correction weight according to the reliability of each part in the variable pitch system, and distributing the reliability of the variable pitch system to each part, wherein the reliability distribution index of the variable pitch system is 0.9874:
Figure BDA0002602624860000132

Claims (1)

1. a wind turbine generator reliability distribution method considering subsystem multi-state and fault correlation is characterized by comprising the following steps:
1) the method comprises the following steps of collecting historical operation fault data of each subsystem of the wind turbine generator, and calculating fault correlation among parts in each subsystem by adopting a decision laboratory analysis method, wherein the method specifically comprises the following steps:
1.1) establishing a fault mode influence relation matrix according to the propagation influence relation among the fault modes in the subsystem:
Figure FDA0002602624850000011
wherein: pFA fault mode impact relationship matrix for the subsystem; f. ofijCorrelation of ith failure mode to jth failure mode for a subsystem; n isFThe number of subsystem failure modes;
1.2) defining a standardized matrix according to the fault mode influence relation matrix:
Figure FDA0002602624850000012
Figure FDA0002602624850000013
wherein:
Figure FDA0002602624850000014
a standardized matrix for subsystem fault propagation effects;
1.3) calculating a comprehensive influence relation matrix according to the standardized matrix:
Figure FDA0002602624850000015
wherein: i is an identity matrix; t is tijThe method comprises the steps of obtaining an original of the ith row and the jth column in a comprehensive influence relation matrix;
1.4) calculating the influence degree and the influenced degree among all parts in the subsystem according to the comprehensive influence relation matrix:
Figure FDA0002602624850000021
Figure FDA0002602624850000022
wherein: r (p)t,pk) The influence degree of the t-th part to the k-th part of the subsystem; d (p)t,pk) The influence degree of the kth part on the t-th part for the subsystem; p is a radical oftIs the t-th part of the subsystem; p is a radical ofkIs the kth part of the subsystem; n istThe number of failure modes in the t-th part; n iskThe number of the fault modes is the kth part;
1.5) calculating the fault correlation coefficient among the parts in the subsystem according to the influence degree and the influenced degree among the parts:
Figure FDA0002602624850000023
wherein:
Figure FDA0002602624850000024
a fault correlation coefficient between the t-th part and the k-th part of the subsystem is obtained;
2) establishing a repairable three-state transition model of each subsystem according to the Markov state transition model, which specifically comprises the following steps:
2.1) the three states in the modifiable three-state transition model are defined as: the system comprises a normal state, a state to be maintained and a maintenance state, wherein the normal state is defined as that the subsystem has no potential safety hazard, the state to be maintained is defined as that the subsystem has the potential safety hazard but can still normally run, and the maintenance state is defined as that the system is shut down and starts to be maintained;
2.2) respectively representing the normal state, the state to be maintained and the maintenance state of the subsystem by using a 0 state, a 1 state and a 2 state in the repairable three-state transition model; the transition direction between the states is represented by an arrow, and the value on the arrow represents the transition probability of the subsystem from the current state to another state; by λi、μiI is 1,2 and 3 respectively represent the fault rate and the repair rate of the subsystem converted among various states, the fault rate is defined as the ratio of the fault times of the subsystem to the total fault times in a statistical period, and the repair rate is defined as the ratio of the time spent on repairing the fault to the total time in the same statistical period;
3) constructing a state transition probability matrix of the subsystem according to the three-state-transition-capable subsystem model established in the step 2):
Figure FDA0002602624850000031
wherein: k is a radical of11＝λ1+λ3，k22＝μ1+λ2，k33＝μ2+μ3；λ1Failure rate for the subsystem from state 0 to state 1; lambda [ alpha ]2Failure rate for the subsystem from state 1 to state 2; lambda [ alpha ]3Failure rate for the subsystem from state 0 to state 2; mu.s1Maintenance rate for subsystem from state 1 to state 0; mu.s2Maintenance rate for subsystem from state 2 to state 1; mu.s3Maintenance rate for subsystem from state 2 to state 0;
4) calculating the steady-state availability of the subsystem under the influence of each part according to the subsystem state transition probability matrix constructed in the step 3), and specifically comprises the following steps:
4.1) calculating the steady-state availability of the subsystem under the influence of each fault mode:
Figure FDA0002602624850000032
wherein:
Figure FDA0002602624850000033
for subsystems in fault mode fj(ii) steady state availability under influence; f. ofjIs the jth failure mode of the subsystem;
4.2) calculating the steady-state availability of the subsystem under the influence of each part:
Figure FDA0002602624850000034
wherein:
Figure FDA0002602624850000035
for sub-system in part pi(ii) steady state availability under influence; p is a radical ofiIs the ith part of the subsystem; n isiFor the i-th part p of the subsystemiThe number of failure modes of (2);
4.3) when a component fails, some other components also fail, so that some components present a certain fault correlation, and therefore when analyzing the influence of each component on the steady-state availability of the subsystem, the additional influence caused by the fault correlation should be considered, which specifically includes the following steps:
4.3.1) calculating the steady state availability of the subsystem under the influence of the ith part when considering the first order fault propagation influence:
Figure FDA0002602624850000041
wherein:
Figure FDA0002602624850000042
in order to consider the first-order fault propagation influence, the steady-state availability of the subsystem under the influence of the ith part;
Figure FDA0002602624850000043
fault correlation coefficients for the ith and kth parts of the subsystem;
Figure FDA0002602624850000044
the steady-state availability of the subsystem under the influence of the kth part;
4.3.2) calculating the steady-state availability of the subsystem under the influence of the ith part when considering the second-order fault propagation influence:
Figure FDA0002602624850000045
wherein:
Figure FDA0002602624850000046
in order to consider the influence of second-order fault propagation, the steady-state availability of the subsystem under the influence of the ith part;
Figure FDA0002602624850000047
fault correlation coefficients for the kth and the tth parts of the subsystem;
Figure FDA0002602624850000048
is aThe steady-state availability of the system under the influence of the tth part;
because the influence of the high-order fault propagation after the second order on the steady-state availability of the subsystem is small, only the fault propagation influence of the first second order is considered;
5) analyzing factors influencing the reliability distribution of the subsystem, and calculating the reliability distribution initial weight of each part in the subsystem by adopting a good-bad solution distance method, namely a TOPSIS method, and specifically comprising the following steps:
5.1) factors influencing the reliability allocation of the subsystem mainly comprise the importance of parts, the fault hazard of the parts, the complexity vector of the parts, the current technical level of the parts, the working time of the parts and the working environment of the parts;
5.2) grading the factors influencing the reliability distribution of the subsystems by adopting an expert grading mode according to the experience and historical data of grading experts to obtain a reliability distribution comprehensive influencing factor matrix:
Figure FDA0002602624850000051
wherein: gamma rayijAssigning a score value of an influencing factor to the jth reliability of the ith part; n is the number of the parts of the subsystem;
5.3) analyzing the reliability distribution comprehensive influence factor matrix in the step 5.2) by adopting a good-bad solution distance method to obtain the reliability distribution initial weight of each part in the subsystem, and specifically comprising the following steps:
5.3.1) carrying out standardization processing on the reliability distribution comprehensive influence factor matrix:
Figure FDA0002602624850000052
Figure FDA0002602624850000053
wherein:
Figure FDA0002602624850000054
distributing a comprehensive influence factor matrix for the standardized reliability;
Figure FDA0002602624850000055
assigning a value of an influencing factor to the jth reliability of the normalized ith part;
5.3.2) according to the standardized reliability distribution comprehensive influence factor matrix obtained in the step 5.3.1), calculating a weighting decision matrix:
Figure FDA0002602624850000056
Figure FDA0002602624850000057
wherein: v is a weighting decision matrix;
Figure FDA0002602624850000058
assigning a weight of an influencing factor to the jth reliability; v. ofijAssigning a value of an influencing factor for the jth reliability of the ith component after normalization and taking the weight into account;
5.3.3) calculating the optimal value and the worst value of each reliability distribution influence factor according to the weighting decision matrix obtained in the step 5.3.2):
Figure FDA0002602624850000061
Figure FDA0002602624850000062
wherein:
Figure FDA0002602624850000063
allocating an optimal value of an influence factor for the jth reliability;
Figure FDA0002602624850000064
distributing the worst value of the influencing factors for the jth reliability;
5.3.4) calculating the distance from the reliability distribution influence factor set of each part to the optimal value set and the worst value set:
Figure FDA0002602624850000065
Figure FDA0002602624850000066
wherein:
Figure FDA0002602624850000067
distributing the distance from the influence factor set to the optimal value set for the reliability of the ith part;
Figure FDA0002602624850000068
distributing the distance from the influence factor set to the worst value set for the reliability of the ith part;
5.3.5) calculating the closeness of the reliability allocation influence factor set of each part to the optimal value set:
Figure FDA0002602624850000069
wherein: ciThe closeness of the reliability assignment impact factor set of the ith part to the optimal value set;
5.3.6) calculating the reliability assignment initial weight of each part in the subsystem:
Figure FDA00026026248500000610
wherein:
Figure FDA00026026248500000611
is the ith partAssigning an initial weight to the reliability of (1);
6) and correcting the reliability distribution initial weight of each part by adopting the steady-state availability of the subsystem under the influence of each part to obtain the reliability distribution correction weight of each part:
Figure FDA0002602624850000071
wherein:
Figure FDA0002602624850000072
distributing a correction weight for the reliability of the ith part of the subsystem;
7) distributing correction weight according to the reliability of each part in the subsystem, and distributing the reliability of the subsystem to each part:
Figure FDA0002602624850000073
wherein:
Figure FDA0002602624850000074
assigning a value to the reliability of the ith part of the subsystem;
Figure FDA0002602624850000075
reliability of the components under equal distribution; r*Reliability of the subsystem;
Figure FDA0002602624850000076
distributing a correction coefficient for the reliability of the ith part; n is the number of parts; beta is a regulating factor which ensures that the reliability after distribution meets the reliability requirement of the subsystem, and beta belongs to [0.5,1 ]]。
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