Reliability and maintainability cooperative distribution method for high-speed train bogie

Abstract

The invention relates to a high-speed train bogie reliability and maintainability cooperative distribution method. The method comprises the following steps: S1, constructing a high-speed train bogie state model; s2, constructing a reliability and maintainability distribution model; and S3, joint distribution model construction and global optimization solution are carried out. Through the reliability and maintainability joint distribution model constructed by the method, collaborative distribution of reliability and maintainability indexes is realized, and the globally optimal reliability and maintainability indexes can be obtained as constraints in the design process of the high-speed train bogie.

Description

TECHNICAL FIELD

[0001] The present application relates to a high-speed train bogie design method, in particular to a high-speed train bogie reliability and maintainability collaborative allocation method. BACKGROUND

[0002] With the continuous breakthrough of high-speed train research and development technology, the development of the new generation of high-speed train must meet the comprehensive index composed of reliability, availability, maintainability and safety. From the technical point of view, the availability and safety targets of the system can be achieved by reliability and maintainability technology control. As a key component of high-speed train, the bogie undertakes multiple important functions such as traction, braking and load bearing, and the reliability and maintainability design of the bogie is of great significance to the long-term stable and safe operation of the train. At present, the design process of high-speed train bogie pays less attention to the collaborative design of reliability and maintainability, and it is difficult to effectively identify potential risks in the design stage and also to take into account the maintenance requirements. The existing research on the collaborative design of reliability and maintainability is mostly based on the assumption of "normal work" and "complete failure", ignoring the process of gradual degradation of performance during actual service.

[0003] Therefore, with the increasing demand for reliability and maintainability indicators in the design process of high-speed train bogie, how to effectively allocate the reliability and maintainability of high-speed train bogie while representing the service performance state transfer of high-speed train bogie in the service process as much as possible is a key technical problem in the design process of high-speed train bogie. SUMMARY

[0004] A high-speed train bogie reliability and maintainability collaborative allocation method, comprising the following steps:

[0005] Step S1: high-speed train bogie state model construction;

[0006] Step S2: reliability and maintainability allocation model construction;

[0007] Step S3: joint allocation model construction and global optimization solution;

[0008] Among them, step S1 includes steps S11-S13:

[0009] Step S11: high-speed train bogie service performance state analysis; Step S12: high-speed train bogie Markov chain quantitative analysis; Step S13: high-speed train bogie service performance state transfer model construction;

[0010] Among them, step S2 includes steps S21-S22:

[0011] Step S21: maintenance allocation model construction; step S22: maintenance allocation model construction;

[0012] Wherein, step S3 includes step S31-step S32:

[0013] Step S31: joint allocation model construction based on cost optimization; step S32: global optimization solution.

[0014] Preferably, in step S1, according to the service performance of high-speed train bogie in actual operation, it is divided into three typical states:

[0015] Stable degradation state e0: high-speed train bogie system and internal physical module are in the state of new and normal service wear and tear, and do not reach the threshold of maintenance intervention;

[0016] Minor fault state e1: high-speed train bogie system and internal physical module decline to need light maintenance, but do not reach the degree of overhaul;

[0017] Complete failure state e2: high-speed train bogie system and internal physical module service performance completely invalid, can not normal operation.

[0018] Preferably, in step S12, the service performance state space is defined as E={e0, e1, e2}; the service performance change process of high-speed train bogie is discretized, and the service performance state x(t n ) at time t is only affected by the state x(t n-1 ) at time t-1; the service performance state transition process of high-speed train bogie is represented by discrete Markov chain; the service performance state transition probability P ij is represented as formula (1);

[0019] P ij =P{x(t n )=e j |x(t n-1 )=e i} (1)

[0020] In the formula, P ij represents the probability of bogie transition from state e i to state e j ; x(t n ) and x(t n-1 ) respectively represent the state of bogie at t n and t n-1 time;

[0021] e i and e j represent the state of bogie;

[0022] The service performance state transition probability P of the high-speed train bogie ij is expressed as formula (2) by matrix Q.

[0023]

[0024] In the formula, P ij represents the probability that the high-speed train bogie is transferred from state e i to state e j .

[0025] Q represents the service performance state transition probability matrix of the high-speed train bogie.

[0026] Let the initial service performance state vector of the high-speed train bogie be x0, then the service performance state probability distribution x k of the high-speed train bogie after k time steps is expressed as formula (3).

[0027] x k = x0Q k (3)

[0028] In the formula, x k represents the service performance state probability distribution of the high-speed train bogie after k time steps.

[0029] x0 represents the initial service performance state of the high-speed train bogie.

[0030] k represents the time step.

[0031] Preferably, step S13 includes steps S131-S133.

[0032] Step S131: State degradation model construction; the state degradation model is used to represent the probability of service performance degradation of the physical module; historical record data of the same type of product is collected and arranged to determine the state degradation frequency of the physical module The state degradation probability of the physical module is calculated by formula (4).

[0033]

[0034] In the formula, f represents the frequency that the physical module is degraded from state e i to state e j .

[0035] represents the probability that the physical module is degraded from state e i to state e j .

[0036] The state degradation model is represented by a state degradation matrix, as shown in formula (5).

[0037]

[0038] wherein: denotes the probability that the physical module is degraded from state e i to state e j ;

[0039] STP d denotes the state degradation matrix;

[0040] Step S132: State recovery model construction; the state recovery model is used to represent the probability of the service performance state recovery of each physical module after taking maintenance measures; the maintenance measures obey normal distribution, and the recovery probability p r of the physical module is represented as formula (6), and the probability density function is represented as formula (7);

[0041] p r ~N(μ,σ) (6)

[0042]

[0043] μ=sp n +(1-sp n )×c ml (10)

[0044] wherein: p r denotes the recovery probability of the physical module;

[0045] N(μ,σ) denotes the normal distribution function of the state recovery probability; μ and σ in the formula respectively denote the mean and variance, which are obtained by statistical analysis of the previous maintenance data;

[0046] t denotes the average maintenance time of the physical module;

[0047] c ml denotes the state recovery coefficient of different maintenance measures, which is obtained by statistical analysis of the previous maintenance data;

[0048] sp n denotes the current state coefficient of the physical module;

[0049] Based on formula (6)-(10), the state recovery probability of the physical module is calculated by formula (11) The state recovery model is represented by a state recovery matrix, as shown in formula (12):

[0050]

[0051] wherein: sp i and sp j denote the state e iand e j the state coefficient of e

[0052] the probability of the physical module transferring from state e i to state e j ;

[0053]

[0054] wherein: the probability of the physical module transferring from state e i to state e j ;

[0055] STP r represents the state transition matrix;

[0056] Step S133: State transition model construction; the bogie of the high-speed train has multiple state degradation and recovery processes in the entire service cycle, and the state transition model is used to represent the state change process; based on the state degradation model and the state recovery model established in steps S131 and S132, the state transition model of the high-speed train bogie is represented by a state transition matrix STP t , as shown in formula (13):

[0057]

[0058] wherein: s represents the degradation step number of the physical module state;

[0059] q represents the recovery step number of the physical module state;

[0060] the probability of the physical module transferring from state e i to state e j ;

[0061] STP t represents the state transition matrix;

[0062] Let the initial service performance state vector of the physical module be x0, then the state probability distribution after completing k state degradation-repair cycles is represented by formula (14);

[0063] x0STP t k =(π0,π1,π2) (14)

[0064] wherein: x0 represents the initial service performance state vector of the physical module;

[0065] k represents the cycle number;

[0066] STP t represents the state transition matrix;

[0067] Pio, pi1, pi2 represent the probability of the physical module being in state e0, e1, e2.

[0068] Preferably, the step S21 comprises steps S211-S212.

[0069] Step S211: quantitative weight calculation.

[0070] Step S212: qualitative weight calculation.

[0071] Preferably, in the step S211:

[0072] The quantitative weight is calculated according to the comprehensive importance of the physical module; the comprehensive importance refers to the probability change size of the bogie system of the high-speed train from the normal state to state v (v e {e0, e1, e2}) when the physical module degrades from the normal state to state u (u e {e0, e1, e2}); the comprehensive importance of the physical module is expressed as formula (15).

[0073]

[0074] In the formula: The comprehensive importance of the physical module, i.e. the probability change size of the bogie system of the high-speed train from the normal state to state v when the physical module degrades from the normal state to state u;

[0075] C i represents the state of the physical module;

[0076] S k represents the state of the bogie system;

[0077] P(S k =v|C i =u) represents the probability of the bogie system of the high-speed train being in state v when the physical module degrades to state u;

[0078] P(S k =v|C i =0) represents the probability of the bogie system of the high-speed train being in state v when the physical module is in the normal state;

[0079] P(C i =u) represents the probability of the physical module being in state u;

[0080] The state probabilities of the bogie system and the internal physical module of the high-speed train are calculated by using the diagnostic reasoning function of the Bayesian network to determine the comprehensive importance of each physical module, comprising the following steps:

[0081] Step S2111: Bayesian network construction; the Bayesian network represents three states {e0, e1, e2} of the bogie and internal physical modules; the physical modules are taken as bottom nodes, the subsystems are taken as upper nodes, and the bogie system is taken as a top node to complete the construction of the Bayesian network structure;

[0082] Step S2112: quantitative weight calculation; formula (16) is used to calculate the probability of the bogie system being in state v (v∈{e1, e2}) when the physical module is transferred from the normal state to state u (u∈{e1, e2}); formula (17) is used to calculate the quantitative weight

[0083]

[0084] In the formula, which represents the sum of the probability distribution changes of all failure states of the high-speed train bogie system when the physical module is degraded from the normal state to all states;

[0085] which represents the sum of the probability distribution changes of all failure states of the high-speed train bogie system when the physical module is degraded from the normal state to state u;

[0086] which represents the comprehensive importance of the physical module, that is, the probability change size of the high-speed train bogie system being degraded from the normal state to state v when the physical module is degraded from the normal state to state u;

[0087] n represents the total number of physical modules;

[0088] which represents the quantitative weight.

[0089] Preferably, step S212 includes steps S2121-S2123;

[0090] Step S2121: construction of a hierarchical structure model; a hierarchical structure model is constructed according to a decision target, according to a target layer, a criterion layer, a sub-criterion layer, and a scheme layer; the bogie failure rate is taken as the target layer; the criterion layer includes complexity, technical level, and failure severity; the sub-criterion layer includes standardization degree, maintenance accessibility, design level, manufacturing level, system impact, and environmental impact; among them, the standardization degree and the maintenance accessibility in the sub-criterion layer correspond to the complexity in the criterion layer; the design level and the manufacturing level in the sub-criterion layer correspond to the technical level in the criterion layer; the system impact and the environmental impact in the sub-criterion layer correspond to the failure severity in the criterion layer; the scheme layer includes each module in the bogie;

[0091] Step S2122: construction of a comparison matrix; a comparison matrix A=(a ij ) n×n, a ij represents the importance of the ith element compared to the jth element, and 1-9 represents the importance of the former compared to the latter;

[0092] Step S2123: qualitative weight calculation; the qualitative weight is calculated by using formula (18)-(20); formula (18) is used to normalize the comparison matrix column constructed in step S2122; formula (19) is used to sum the comparison matrix constructed in step S2122 by row; formula (20) is used to normalize the comparison matrix constructed in step S2122 to calculate the qualitative weight Finally, consistency test is performed, and if CR<0.1, it is considered to have consistency.

[0093]

[0094] Preferably, in step S213, the weight calculation results in step S211 and step S212 are introduced into a cost-based optimization allocation method, a reliability improvement cost is taken as the target, system failure rate and physical module failure rate meet the design conditions as constraints, formula (21)-(24) are established as a high-speed train bogie reliability allocation model; wherein formula (21) represents the comprehensive weight of the physical module; formula (22) represents that the reliability improvement cost is taken as the target; formula (23) represents that the failure rate of the physical module meets the design requirements; formula (24) represents that the failure rate of the system needs to meet the overall system failure rate requirement by using the failure rate of the physical module allocation;

[0095]

[0096] s.t.ω i λ s ≤λ i ≤λ i,max (23)

[0097] G(λ1,λ2,...,λ n )≤λ S (24)

[0098] In the formula, α is a weighted coefficient, and its value is determined by a person skilled in the art according to data statistics;

[0099] C R represents the reliability improvement cost;

[0100] C i represents the preventive cost of the physical module i for daily maintenance each time;

[0101] T represents the bogie running time;

[0102] λ represents the failure rate of the physical module;

[0103] λ i,max represents the highest failure rate of physical module i;

[0104] G(λ1,λ2,…,λ n ) represents the failure rate of the whole system predicted by the failure rate of the physical module distribution;

[0105] In step S22, the failure rate of each physical module obtained in the reliability distribution model is taken as the input of the maintainability distribution model, and the maintainability distribution model of the bogie of the high-speed train is established by taking the minimum maintenance cost as the target, the system availability and the average maintenance time as the constraints, and equations (25)-(28) are taken as the maintainability distribution model of the bogie of the high-speed train; equation (25) represents the minimum maintenance cost; equation (27) represents that the availability of the bogie system calculated by using the availability of the physical module meets the availability requirement of the bogie system; and equation (28) represents that the maintenance time meets the requirement;

[0106]

[0107]

[0108] s.t.G(x 01 ,x 02 ,…,x 0n )≥A s (27)

[0109]

[0110] In the equations, C M represents the maintenance measure cost;

[0111] k i,1 and k i,2 respectively represent the cost of taking different maintenance measures when the physical module is in states e1 and e2;

[0112] β i represents the probability that the physical module i is degraded from state e0 to state e1, and is the proportion of the sum of all degradation process probabilities;

[0113] λ i represents the failure rate result obtained by the distribution of the physical module i;

[0114] T represents the running time of the bogie;

[0115] and represent the average repair time of the physical module i in states e1 and e2;

[0116] x 0i represents the probability that the physical module i is in state e0 for a long time;

[0117] G(x 01 ,x 02 ,…,x 0n ) represents the availability of the bogie system calculated by the availability of the physical modules;

[0118] A s represents the target availability of the bogie system;

[0119] represents the target mean repair time of the system.

[0120] Preferably, step S3 comprises the following steps:

[0121] Step S31: joint allocation model construction based on cost optimization; based on the reliability and maintainability allocation model constructed in step S2, a joint objective function is established, represented as formula (29), and the constraints are represented as formula (23)-(24), formula (26)-(28):

[0122]

[0123] Step S32: global optimization solution; genetic algorithm is used as the global optimization solution method, including the following steps:

[0124] Step S321: population initialization and chromosome coding; a set of initial candidate solutions that satisfy the constraint conditions are randomly generated to form an initial population; the chromosome represents the combination scheme of the physical module decision variables, the gene locus represents the physical module, and the gene value of the allele represents the decision variable;

[0125] Step 322: fitness evaluation; the joint objective function is used as the fitness function, and all constraints are embedded into the penalty function, and the fitness value is the reciprocal of the sum of the reliability improvement cost, the maintenance cost and the penalty function;

[0126] Step S323: selection, crossover and mutation; the tournament selection mechanism is used to select individuals with higher fitness to enter the breeding process of the next generation; single-point crossover is used to exchange parent chromosome genes to produce multiple offspring; random mutation of individual genes is used to maintain population diversity and avoid local optimum;

[0127] Step S324: population update and termination; combine the new individuals obtained by crossover and mutation with the original population to form a new population; repeat until the predetermined number of iterations is reached or the fitness value is below the threshold;

[0128] Step S325: output the optimal solution; output the joint optimal solution λ i * is the optimal failure rate of reliability allocation, and To assign the optimal average repair time for maintainability.

[0129] Compared with the prior art, the present application has the beneficial effects of:

[0130] (1) The inventor found in practice that the high-speed train bogie design process pays less attention to the coordinated allocation of reliability and maintainability indicators, making it difficult to identify potential risks in the design stage and unable to take into account maintenance needs. The present application builds a reliability and maintainability joint allocation model, realizes the coordinated allocation of reliability and maintainability indicators, and can obtain globally optimal reliability and maintainability indicators as constraints in the design process of high-speed train bogies.

[0131] (2) The inventor found in research that existing research on reliability and maintainability analysis of high-speed train bogies is mostly based on the assumption of "normal operation" and "complete failure" of two states, ignoring the process of gradual degradation of service performance during actual service. The present application discretizes the service performance state into three states: stable degradation state, slight failure state and complete failure state. A state transition model is constructed using Markov chain quantitative analysis to represent the state change process as the basis for reliability and maintainability allocation.

[0132] (3) The inventor found in research that existing research on reliability indicator allocation mainly falls into three categories: quantitative allocation method, qualitative allocation method and cost optimization allocation method. The quantitative allocation method may result in key functional modules obtaining excessively high reliability targets, thereby increasing overall maintenance costs; the qualitative allocation method is greatly influenced by expert judgment, and the calculation complexity increases with the increase of system size; the cost optimization allocation method does not fully consider the relative importance of each functional module, which may result in insufficient reliability allocation of key functional modules. The present application proposes a cost optimization joint allocation model, which combines the objectivity of the quantitative allocation method, the judgment ability of the qualitative allocation method under multi-factor consideration, and the economy of the cost optimization allocation method, to improve the scientificity and practicality of the allocation scheme.

[0133] (4) The inventor found in practice that the reliability and maintainability joint allocation model of high-speed train bogies presents nonlinear characteristics. The present application uses genetic algorithm for global optimization solution to obtain globally optimal reliability and maintainability indicator allocation results of high-speed train bogies.

[0134] (5) The inventor found in practice that for high-speed train bogies, which are composed of multiple complex systems with complex structure and function, the design is limited by physics and technology, and while meeting the demand of a certain top-level design indicator, other indicators will be sacrificed accordingly. Therefore, the present application constructs a comprehensive competitiveness calculation model of the bogie, which comprehensively considers various top-level design indicators to realize the reasonable calculation of the comprehensive performance of the bogie.

[0135] (6) The inventor found in practice that the importance of the top-level design indicators under different evaluation criteria to the comprehensive competitiveness of high-speed trains is different. To this end, the application establishes a hierarchical structure between the evaluation criteria and the comprehensive competitiveness, providing a basis for more reasonable comprehensive competitiveness calculation.

[0136] (7) The inventor found in practice that there are problems such as long design cycle, strong subjectivity of definition results, and poor interpretability in the definition process of traditional high-speed train bogie design indicators. The application constructs a high-speed train bogie top-level design indicator comprehensive competitiveness optimization model based on historical product and competitive product data and solves it through a genetic algorithm to determine the optimal top-level design indicator combination scheme. BRIEF DESCRIPTION OF DRAWINGS

[0137] Figure 1 A schematic diagram of a high-speed train bogie reliability and maintainability collaborative allocation method;

[0138] Figure 2 A schematic diagram of the hierarchical structure in step S2121. DETAILED DESCRIPTION

[0139] To make the purpose, technical solutions and advantages of the embodiments of the application clearer, the technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the application, not all.

[0140] A high-speed train bogie reliability and maintainability collaborative allocation method, comprising the following steps:

[0141] Step S1: High-speed train bogie state model construction.

[0142] Step S2: Reliability and maintainability allocation model construction.

[0143] Step S3: Joint allocation model construction and global optimization solution.

[0144] Preferably, step S1 constructs a state degradation model and a state recovery model based on the service performance state of the high-speed train bogie, and then constructs a high-speed train bogie state transition model, comprising the following steps S11-S13:

[0145] Step S11: High-speed train bogie service performance state analysis. According to the service performance of the high-speed train bogie in actual operation, it is divided into three typical states:

[0146] Stable degradation state e0: The high-speed train bogie system and internal physical modules are in a brand-new and normal service wear degradation state, and have not reached the threshold of maintenance intervention.

[0147] Minor fault state e1: the bogie system and internal physical modules of the high-speed train degrade to the extent that minor maintenance is required, but not to the extent that major maintenance is required.

[0148] Complete fault state e2: the bogie system and internal physical modules of the high-speed train completely fail in service performance and cannot operate normally.

[0149] It is worth noting that the present application is applicable to the bogie of a high-speed train that meets the following conditions:

[0150] 1. If no maintenance intervention is performed, the functional failure of the bogie system and internal physical modules of the high-speed train will become more and more serious, and after the maintenance intervention, the service performance of the bogie system and internal physical modules will be restored;

[0151] 2. The wear and degradation processes of the internal physical modules of the bogie of the high-speed train are independent of each other;

[0152] 3. The maintenance measures for the internal physical modules of the bogie of the high-speed train are various, and the costs, times and restoration degrees of different maintenance measures are different.

[0153] Step S12: Markov chain quantification analysis of the bogie of the high-speed train. Define the service performance state space as e = {e0, e1, e2}. Discretize the service performance change process of the bogie of the high-speed train, and the service performance state x(t n ) of the bogie of the high-speed train at time t is only affected by the state x(t n-1 ) at time t-1. Use a discrete Markov chain to represent the service performance state transition process of the bogie of the high-speed train. The service performance state transition probability P ij of the bogie of the high-speed train is represented by formula (1).

[0154] P ij = P{x(t n ) = e j | x(t n-1 ) = e i} (6)

[0155] In the formula, P ij represents the probability of the bogie being transferred from state e i to state e j ; x(t n ) and x(t n-1 ) represent the states of the bogie at times t n and t n-1 , respectively;

[0156] e i and e j represent the states of the bogie.

[0157] The service performance state transition probability P of the high-speed train bogie ij is expressed as formula (2) by matrix Q.

[0158]

[0159] In the formula, P ij represents the probability of the high-speed train bogie transitioning from state e i to state e j ;

[0160] Q represents the service performance state transition probability matrix of the high-speed train bogie.

[0161] Let the initial service performance state vector of the high-speed train bogie be x0, then the service performance state probability distribution x k of the high-speed train bogie after k time steps is expressed as formula (3).

[0162] x k = x0Q k (8)

[0163] In the formula, x k represents the service performance state probability distribution of the high-speed train bogie after k time steps;

[0164] x0 represents the initial service performance state of the high-speed train bogie;

[0165] k represents the time step.

[0166] Step S13: Construction of the service performance state transition model of the high-speed train bogie. The state transition model is used to represent the evolution of the service performance state of the system, and is composed of a state degradation model and a state recovery model.

[0167] Step S131: Construction of the state degradation model. The state degradation model is used to represent the probability of service performance degradation of the physical module. Historical record data of the same type of product is collected to determine the state degradation frequency of the physical module The state degradation probability of the physical module is calculated by formula (4).

[0168]

[0169] In the formula, f represents the frequency of the physical module degrading from state e i to state e j ;

[0170] represents the probability of the physical module degrading from state e i to state e j ;

[0171] The state degradation model is represented by a state degradation matrix, as shown in equation (5).

[0172]

[0173] wherein: represents the probability that the physical module degrades from state e i to state e j ;

[0174] STP d represents the state degradation matrix.

[0175] Step S132: State recovery model construction. The state recovery model is used to represent the probability of the service performance state recovery of each physical module after taking maintenance measures. The maintenance measures are subject to normal distribution, and the recovery probability p r of the physical module can be represented by equation (6), and the probability density function is represented by equation (7).

[0176] p r ~ N(μ,σ) (6)

[0177]

[0178] μ = sp n +(1-sp n )×c ml (10)

[0179] wherein: p r represents the recovery probability of the physical module;

[0180] N(μ,σ) represents the normal distribution function of the state recovery probability; μ and σ in it represent the mean and variance, respectively, which are obtained by statistical analysis of the previous maintenance data;

[0181] t represents the average maintenance time of the physical module, which is preferably obtained from the maintenance records of similar products;

[0182] c ml represents the state recovery coefficient of different maintenance measures, which is obtained by statistical analysis of the previous maintenance data;

[0183] sp n represents the current state coefficient of the physical module.

[0184] Based on equations (6)-(10), the state recovery probability p of the physical module is calculated by equation (11):

[0185]

[0186] where sp i and sp j denotes the probability that the physical module is in state e i and e j state coefficient;

[0187] denotes the probability that the physical module is in state e i from state e j .

[0188]

[0189] where: denotes the probability that the physical module is in state e i from state e j .

[0190] STP r denotes the state recovery matrix.

[0191] Step S133: State transition model construction. The high-speed train bogie has multiple state degradation and recovery processes during the entire service cycle, and the state transition model is used to represent the state change process. Based on the state degradation model and the state recovery model established in steps S131 and S132, the state transition model of the high-speed train bogie can be represented by the state transition matrix STP t denotes, as shown in equation (13):

[0192]

[0193] where s denotes the number of state degradation steps of the physical module;

[0194] q denotes the number of state recovery steps of the physical module;

[0195] denotes the probability that the physical module is in state e i from state e j .

[0196] STP t denotes the state transition matrix.

[0197] Let the initial service performance state vector of the physical module be x0, then the state probability distribution after completing k state degradation-repair cycles can be represented as equation (14).

[0198] x0STP t k = (π0, π1, π2) (14)

[0199] where x0denotes the initial service performance state vector of the physical module;

[0200] k represents the number of cycles;

[0201] STP t denotes the state transition matrix;

[0202] π0, π1, π2 represent the probabilities of the physical module being in states e0, e1, e2.

[0203] Preferably, in step S2, the failure rate and the average repair time are respectively used to represent the reliability and maintainability of the physical module of the high-speed train bogie, and the reliability allocation model and the maintainability allocation model of the physical module of the high-speed train bogie are constructed. The following steps are included:

[0204] Step S21: Reliability allocation model construction. In the reliability model construction, the quantitative weight and the qualitative weight are introduced into the reliability index allocation method based on cost by comprehensively considering the objectivity of the quantitative allocation method, the multi-factor judgment ability of the qualitative allocation method, and the cost optimization and other factors. The specific steps are as follows:

[0205] Step S211: Quantitative weight calculation. The quantitative weight is calculated based on the comprehensive importance of the physical module. The comprehensive importance refers to the probability change size of the high-speed train bogie system from the normal state to state v (v ∈ {e0, e1, e2}) when the physical module degrades from the normal state to state u (u ∈ {e0, e1, e2}). The comprehensive importance of the physical module is represented by formula (15).

[0206]

[0207] In the formula: denotes the comprehensive importance of the physical module, i.e. the probability change size of the high-speed train bogie system from the normal state to state v when the physical module degrades from the normal state to state u;

[0208] C i denotes the state of the physical module;

[0209] S k denotes the state of the bogie system;

[0210] P(S k = v | C i = u) denotes the probability of the high-speed train bogie system being in state v when the physical module degrades to state u;

[0211] P(S k = v | C i = 0) denotes the probability of the high-speed train bogie system being in state v when the physical module is in the normal state;

[0212] P(C i = u) denotes the probability of the physical module being in state u.

[0213] The diagnostic inference function of the Bayesian network is used to calculate the state probability of the high-speed train bogie system and internal physical modules to determine the comprehensive importance of each physical module, including the following steps:

[0214] Step S2111: Bayesian network construction. The Bayesian network represents the three states {e0, e1, e2} of the bogie and internal physical modules. The physical modules are taken as the bottom nodes, the subsystems are taken as the upper nodes, and the bogie system is taken as the top node to complete the structure construction of the Bayesian network, wherein: the bogie system includes 6 subsystems of driving device, primary suspension device, secondary suspension device, wheelset and axlebox device, foundation brake device, and frame and positioning device. The driving device subsystem includes 4 bottom nodes of traction rod, traction motor, gear box, and coupling; the primary suspension device subsystem includes 2 bottom nodes of axlebox spring and vertical damper; the secondary suspension device subsystem includes 4 bottom nodes of anti-snaking damper, lateral damper, anti-roll torsion bar, and air spring; the wheelset and axlebox device subsystem includes 3 bottom nodes of axlebox, wheel, and axle; the foundation brake device subsystem includes 2 bottom nodes of brake disc and brake caliper; and the frame and positioning device subsystem includes 2 bottom nodes of crossbeam and side beam.

[0215] Preferably, the prior probability of the bottom node is determined by the state degradation matrix constructed from the historical failure information of similar products and combined with expert experience. The conditional probability between nodes is obtained by inferring the failure information using the EM algorithm. The method involved in this paragraph is prior art and will not be expanded.

[0216] Step S2112: quantitative weight calculation. Formula (16) is used to calculate the probability of the bogie system being in state v (v ∈ {e1, e2}) when the physical module is transferred from the normal state to state u (u ∈ {e1, e2}). Formula (17) is used to calculate the quantitative weight

[0217]

[0218] In the formula: represents the sum of the probability distribution changes of all failure states of the high-speed train bogie system when the physical module degrades from the normal state to all states;

[0219] represents the sum of the probability distribution changes of all failure states of the high-speed train bogie system when the physical module degrades from the normal state to state u;

[0220] represents the comprehensive importance of the physical module, i.e. the probability change size of the bogie system of the high-speed train from the normal state to state v when the physical module degrades from the normal state to state u;

[0221] n represents the total number of physical modules;

[0222] represents the quantitative weight.

[0223] Step S212: qualitative weight calculation. The qualitative weight of the physical model is determined by using the analytic hierarchy process. The following steps are included:

[0224] Step S2121: construction of a hierarchical structure model. According to the decision target, a hierarchical structure model is constructed according to the target layer, the criterion layer, the sub-criterion layer, and the scheme layer. The bogie failure rate is taken as the target layer; the criterion layer includes complexity, technical level, and fault severity; the sub-criterion layer includes standardization degree, maintenance accessibility, design level, manufacturing level, influence on the system, and influence on the environment. Among them, the standardization degree and the maintenance accessibility in the sub-criterion layer correspond to the complexity in the criterion layer; the design level and the manufacturing level in the sub-criterion layer correspond to the technical level in the criterion layer; the influence on the system and the influence on the environment in the sub-criterion layer correspond to the fault severity in the criterion layer; the scheme layer includes each module in the bogie.

[0225] Step S2122: construction of a comparison matrix. A comparison matrix A=(a ij ) n×n a ij represents the importance of the i-th element compared with the j-th element, which is represented by 1-9. For example: 1 represents that the two factors have the same importance; 3 represents that the former is slightly more important than the latter; 5 represents that the former is obviously more important than the latter; 7 represents that the former is strongly more important than the latter; 9 represents that the former is extremely more important than the latter; 2, 4, 6, and 8 represent intermediate states of the adjacent judgments; the importance of the latter compared with the former is represented by the reciprocal of 1-9, for example: 1 / 3 represents that the latter is slightly more important than the former; 1 / 5 represents that the latter is obviously more important than the former; 1 / 7 represents that the latter is strongly more important than the former; 1 / 9 represents that the latter is extremely more important than the former; 1 / 2, 1 / 4, 1 / 6, and 1 / 8 represent intermediate states of the adjacent judgments.

[0226] Table 1 evaluation scale

[0227]

[0228]

[0229] Step S2123: qualitative weight calculation. The sum-product method is used to calculate the qualitative weight by using formula (18)-(20). Formula (18) is used to normalize the comparison matrix constructed in step S2122; formula (19) is used to sum the comparison matrix constructed in step S2122 by row; and formula (20) is used to normalize the comparison matrix constructed in step S2122 to calculate the qualitative weight Finally, a consistency test is performed, and if CR<0.1, it is considered to have consistency.

[0230]

[0231] Step S213: reliability distribution model construction considering cost factors. The weight calculation results in steps S211 and S212 are introduced into the cost-based optimization distribution method, a reliability improvement cost minimum is taken as an objective, system failure rate and physical module failure rate meet design conditions are taken as constraints, formula (21)-(24) are established as a reliability distribution model of the bogie of the high-speed train. Formula (21) represents calculation of the comprehensive weight of the physical module; formula (22) represents taking the reliability improvement cost minimum as the objective; formula (23) represents that the failure rate of the physical module needs to meet the design requirement; and formula (24) represents that the failure rate of the system needs to meet the overall system failure rate requirement by using the failure rate of the physical module distribution.

[0232]

[0233] s.t.ω i λ s ≤λ i ≤λ i,max (23)

[0234] G(λ1,λ2,…,λ n )≤λ S (24)

[0235] In the formula, α is a weighting coefficient, and a person skilled in the art determines its value according to data statistics;

[0236] C R represents reliability improvement cost;

[0237] C i represents preventive cost of each time of daily maintenance of the physical module i;

[0238] T represents bogie operation time;

[0239] λ represents failure rate of the physical module;

[0240] λ i,max represents the highest failure rate of the physical module i;

[0241] G(λ1, λ2,..., λn) represents the failure rate of the whole system predicted by the failure rate of the physical modules. Preferably, to simplify the calculation, the bogie of the high-speed train is regarded as a series system, and in the case of constant failure rate of the physical modules, the failure rate of the system is obtained by adding the failure rates of the physical modules. n ) represents the failure rate of the whole system predicted by the failure rate of the physical modules. Preferably, to simplify the calculation, the bogie of the high-speed train is regarded as a series system, and in the case of constant failure rate of the physical modules, the failure rate of the system is obtained by adding the failure rates of the physical modules.

[0242] Step S22: Maintenance distribution model construction. The failure rates of the physical modules obtained in the reliability distribution model are taken as the input of the maintenance distribution model, and the minimum maintenance cost is taken as the target, and the system availability and the average maintenance time are taken as the constraints, to establish equations (25)-(28) as the maintenance distribution model of the bogie of the high-speed train. Equation (25) represents the minimum maintenance cost; equation (27) represents that the availability of the bogie system calculated by the availability of the physical modules meets the availability requirement of the bogie system; and equation (28) represents that the maintenance time meets the requirement.

[0243]

[0244] s.t.G(x 01 ,x 02 ,...,x 0n )≥A s (27)

[0245]

[0246] In the equations, C M represents the maintenance measure cost;

[0247] k i,1 and k i,2 respectively represent the costs of taking different maintenance measures when the physical module is in states e1 and e2;

[0248] β i represents the probability that the physical module i degrades from state e0 to state e1, and is the proportion of the sum of all degradation process probabilities, which can be calculated by equation (5);

[0249] λ i represents the failure rate result of the physical module i obtained by the distribution in step S213;

[0250] T represents the running time of the bogie;

[0251] and represent the average repair time of the physical module i in states e1 and e2;

[0252] x 0iThe probability of long-term staying in state e0 of physical module i can be regarded as the availability of the physical module, which can be calculated by the transition probability after a series of state transitions, i.e.

[0253] G(x 01 ,x 02 ,…,x 0n ) represents the availability of the bogie system calculated by the availability of the physical module. Preferably, the high-speed train bogie is regarded as a series system, and the availability of the system can be obtained by multiplying the availability of each physical module.

[0254] A s represents the target availability of the bogie system;

[0255] represents the target mean repair time of the system.

[0256] Preferably, step S3 constructs a joint allocation model based on cost optimization based on the reliability and maintainability allocation model of the high-speed train bogie, including joint allocation objective function and constraint construction, and solves it to complete the index allocation of reliability and maintainability, including the following steps:

[0257] Step S31: joint allocation model construction based on cost optimization. To simplify the calculation and avoid the problems of hierarchical nesting, complexity and the like in the solving process, based on the reliability and maintainability allocation model constructed in step S2, a joint objective function is established, represented by formula (29), and its constraints are represented by formula (23)-(24), formula (26)-(28):

[0258]

[0259] Step S32: global optimization solution. Genetic algorithm is used as a global optimization solution method, including the following steps:

[0260] Step S321: population initialization and chromosome coding. A group of initial candidate solutions satisfying the constraint conditions are randomly generated to form an initial population. The chromosome represents the combination scheme of the physical module decision variables, and the gene locus represents the physical module. The gene value of the allele represents the decision variable.

[0261] Step 322: fitness evaluation. The joint objective function is used as the fitness function, and all constraints are embedded into the penalty function. The fitness value is the reciprocal of the sum of the reliability improvement cost, the maintenance cost and the penalty function, so that the combination scheme with lower reliability improvement cost and maintenance cost corresponds to higher fitness value.

[0262] Step S323: selection, crossover, mutation. Using the tournament selection mechanism, select the individual with higher fitness into the next generation of breeding process; using single-point crossover method to exchange the parent chromosome gene, produce multiple individuals; using random variation of individual gene instance selection to maintain population diversity, avoid local optimum.

[0263] Step S324: population update and termination. Combine the new individuals obtained by crossover and mutation with the original population to form a new generation population. Repeat until the predetermined number of iterations is reached or the fitness value is lower than the threshold.

[0264] Step S325: output optimal solution. Output the joint optimal solution λ i * assign the optimal failure rate to reliability, and assign the optimal mean repair time to maintainability.

[0265] Therefore, the following detailed description of the embodiments of the present application is not intended to limit the scope of the claimed application, but merely represents some embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative labor fall within the scope of protection of the present application.

[0266] The above embodiments are only used to illustrate the technical solutions described in the present application and are not intended to limit the present application. Although the present application has been described in detail with reference to the above embodiments, the present application is not limited to the above specific embodiments. Therefore, any modification or equivalent replacement of the present application; all technical solutions and improvements that do not deviate from the spirit and scope of the application are covered by the scope of the claims of the present application.

Claims

1. A method for coordinating the allocation of reliability and maintainability of high-speed train bogies, characterized in that: Includes the following steps: Step S1: Construction of the state model of the high-speed train bogie; Step S2: Construction of reliability and maintainability allocation model; Step S3: Construction of the joint allocation model and global optimization solution; Step S1 includes steps S11-S13: Step S11: Service performance status analysis of high-speed train bogies; Step S12: Markov chain quantification analysis of high-speed train bogies; Step S13: Construction of service performance status transition model for high-speed train bogies; Step S2 includes steps S21-S22: Step S21: Construction of the maintainability allocation model; Step S22: Construction of the maintainability allocation model; Step S3 includes steps S31-S32: Step S31: Construct a joint allocation model based on cost optimization; Step S32: Solve the global optimization problem.

2. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 1, characterized in that: In step S1, based on the service performance of the high-speed train bogie in actual operation, it is divided into three typical states: Stable degradation state e0: The high-speed train bogie system and internal physical modules are in a brand new and normal service wear and degradation state, and have not reached the threshold for maintenance intervention; Minor Fault Status e1: The bogie system and internal physical modules of the high-speed train have deteriorated to the point where minor maintenance is required, but not to the point where major overhaul is required; Complete Failure Status e2: The high-speed train bogie system and internal physical modules have completely failed in service and cannot operate normally.

3. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 2, characterized in that: In step S12, the service performance state space is defined as E = {e0, e1, e2}; the service performance change process of the high-speed train bogie is discretized, and the service performance state x(t) at time t is... n ) is only affected by the state x(t) at time t-1 n-1 The influence of ), using discrete Markov chains to characterize the service performance state transition process of high-speed train bogies; the service performance state transition probability P of high-speed train bogies. ij Represented as Equation (1); P ij =P{x(t n )=e j |x(t n-1 )=e i } (1) In the formula: P ij This indicates that the bogie is in state e. i Transition to state e j The probability of x(t); n ) and x(t n-1 ) represent the bogie at t n and t n-1 The state at any given moment; e i and e j This indicates the state of the bogie; The service performance state transition probability P of high-speed train bogies ij The matrix Q is represented by equation (2); In the formula: P ij This indicates that the high-speed train bogie is in state e. i Transition to state e j The probability of; Q represents the state transition probability matrix of the service performance of the high-speed train bogie; Let x0 be the initial service performance state vector of the high-speed train bogie. Then, the probability distribution of the service performance state of the high-speed train bogie after k time steps is x0. k Represented as equation (3); x k =x0Q k (3) In the formula: x k This represents the probability distribution of the service performance status of a high-speed train bogie after k time steps. x0 represents the initial service performance status of the high-speed train bogie; k represents the time step.

4. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 3, characterized in that: Step S13 includes steps S131-S133; Step S131: Construction of the state degradation model; the state degradation model is used to characterize the probability of service performance degradation of the physical module; collect and organize historical data of similar products to determine the state degradation frequency of the physical module. Physical module state degradation probability Calculated using equation (4); In the formula: The physical module is represented by state e i Degenerate to state e j The frequency; The physical module is represented by state e i Degenerate to state e j The probability of; The state degradation model is represented by a state degradation matrix, as shown in equation (5); In the formula: The physical module is represented by state e i Degenerate to state e j The probability of; STP d Represents the state degradation matrix; Step S132: Construction of the state recovery model; the state recovery model is used to characterize the probability of the service performance state of each physical module being restored after maintenance measures are taken; the maintenance measures follow a normal distribution, and the recovery probability p of the physical module is... r It is expressed as equation (6), and the probability density function is expressed as (7); p r ~N(μ,σ) (6) μ=sp n +(1-sp n )×c ml (10) Where: p r Indicates the probability of recovery of the physical module; N(μ,σ) represents the normal distribution function of the probability of condition recovery; where μ and σ represent the mean and variance, respectively, and are obtained by statistical analysis of past maintenance data. t represents the average repair time of the physical module; c ml The state recovery coefficient, representing different maintenance measures, is obtained through statistical analysis of past maintenance data. sp n Represents the current state coefficient of the physical module; Based on equations (6)-(10), the state recovery probability of the physical module is calculated using equation (11). The state recovery model is represented by a state recovery matrix, as shown in equation (12): In the formula: sp i and sp j This indicates that the physical module is in state e. i and e j State coefficients; The physical module is represented by state e i Restore to state e j The probability of; In the formula: The physical module is represented by state e i Restore to state e j The probability of; STP r Represents the state recovery matrix; Step S133: State transition model construction; High-speed train bogies undergo multiple state degradation and recovery processes throughout their service life. The state transition model is used to characterize these state change processes. Based on the state degradation and recovery models established in steps S131 and S132, the high-speed train bogie state transition model uses the state transition matrix STP. t This is represented as shown in equation (13): In the formula: s represents the number of degradation steps of the physical module state; q represents the number of steps to restore the physical module state; The physical module is represented by state e. i Transition to state e j The probability of; STP t Represents the state transition matrix; Let the initial service performance state vector of the physical module be x0, then the state probability distribution after completing k state degradation-repair cycles is expressed as Equation (14); In the formula: x0 represents the initial service performance state vector of the physical module; k represents the number of loops; STP t Represents the state transition matrix; π0, π1, π2 represent the probabilities that the physical module is in state e0, e1, e2.

5. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 4, characterized in that: Step S21 includes steps S211-S212; Step S211: Calculate the quantitative weights; Step S212: Qualitative weight calculation.

6. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 5, characterized in that: In step S211: The quantitative weight is calculated based on the overall importance of the physical module; the overall importance refers to the probability change of the high-speed train bogie system from the normal state to the state v (v∈{e0,e1,e2}) when the physical module degenerates from the normal state to the state u (u∈{e0,e1,e2}); the overall importance of the physical module is expressed as Equation (15); In the formula: The overall importance of the physical module is represented by the probability change of the high-speed train bogie system from the normal state to the state v when the physical module degenerates from the normal state to the state u. C i Indicates the status of the physical module; S k Indicates the status of the bogie system; P(S k =V|C i =u) represents the probability that the high-speed train bogie system is in state v when the physical module degenerates to state u; P(S k =v|C i =0) represents the probability that the high-speed train bogie system is in state v when the physical module is in normal state; P(C i =u) represents the probability that the physical module is in state u; The diagnostic reasoning function of Bayesian networks is used to calculate the state probabilities of the high-speed train bogie system and its internal physical modules to determine the overall importance of each physical module. This involves the following steps: Step S2111: Bayesian network construction; The Bayesian network represents the three states {e0, e1, e2} of the bogie and internal physical modules; The physical modules are used as the bottom-level nodes, the subsystems are used as the upper-level nodes, and the bogie system is used as the top-level node to complete the construction of the Bayesian network structure. Step S2112: Calculate the quantitative weights; use Equation (16) to calculate the probability that the bogie system is in state v (v∈{e1,e2}) when the physical module transitions from the normal state to state u (u∈{e1,e2}); use Equation (17) to calculate the quantitative weights. In the formula: This represents the sum of the changes in the probability distribution of all failure states of the high-speed train bogie system when the physical module degenerates from the normal state to all states; This represents the sum of the changes in the probability distribution of all failure states of the high-speed train bogie system when the physical module degenerates from the normal state to state u. The overall importance of the physical module is represented by the probability change of the high-speed train bogie system from the normal state to the state v when the physical module degenerates from the normal state to the state u. n represents the total number of physical modules; This indicates the quantitative weight.

7. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 6, characterized in that: Step S212 includes steps S2121-S2123; Step S2121: Construct a hierarchical model; based on the decision-making objectives, construct a hierarchical model according to the objective layer, criterion layer, sub-criterion layer, and solution layer; use the bogie failure rate as the objective layer; the criterion layer includes complexity, technical level, and failure severity; the sub-criterion layer includes standardization degree, maintenance accessibility, design level, manufacturing level, impact on the system, and impact on the environment; among them, the standardization degree and maintenance accessibility in the sub-criterion layer correspond to the complexity in the criterion layer; the design level and manufacturing level in the sub-criterion layer correspond to the technical level in the criterion layer; the impact on the system and the environmental impact in the sub-criterion layer correspond to the failure severity in the criterion layer; the solution layer includes the various modules in the bogie; Step S2122: Construct the comparison matrix; Construct the comparison matrix A = (a ij ) n×n a ij This indicates the importance of the i-th element relative to the j-th element, with 1-9 representing the importance of the former relative to the latter; Step S2123: Qualitative weight calculation; Qualitative weights are calculated using equations (18)-(20); Equation (18) is used to normalize the columns of the comparison matrix constructed in step S2122; Equation (19) is used to sum the rows of the comparison matrix constructed in step S2122; Equation (20) is used to normalize the comparison matrix constructed in step S2122 and calculate the qualitative weights. Finally, a consistency test is performed. If CR < 0.1, then the system is considered to be consistent.

8. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 7, characterized in that: In step S213, the weight calculation results from steps S211 and S212 are introduced into a cost-based optimization allocation method. With the goal of minimizing the cost of reliability improvement and the constraint that the system failure rate and physical module failure rate meet the design conditions, equations (21)-(24) are established as a reliability allocation model for high-speed train bogies. Equation (21) represents the calculation of the comprehensive weight of the physical module; Equation (22) represents the goal of minimizing the cost of reliability improvement; Equation (23) represents that the failure rate of the physical module must meet the design requirements; Equation (24) represents that the failure rate of the system predicted by the failure rate allocated by the physical module must meet the overall system failure rate requirements. stω i l s ≤λ i ≤λ i,max (23) G(λ1,λ2,...,λ n )≤λ S (24) In the formula: α is a weighting coefficient, the value of which is determined by those skilled in the art based on statistical data; C R Indicates the cost of reliability improvements; C i This represents the preventative cost of each routine maintenance of physical module i. T represents the bogie running time; λ represents the failure rate of the physical module; λ i,max This represents the highest failure rate of physical module i; G(λ1,λ2,…,λ n This indicates that the failure rate of the overall system is predicted using the failure rate allocated to the physical modules.

9. The method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 8, characterized in that: In step S22, the failure rates of each physical module obtained from the reliability allocation model are used as inputs to the maintainability allocation model. With the minimum maintenance cost as the objective and system availability and average maintenance time as constraints, equations (25)-(28) are established as the maintainability allocation model for high-speed train bogies. Equation (25) indicates the minimum maintenance cost; Equation (27) indicates that the availability of the bogie system calculated using the availability of physical modules must meet the availability requirements of the bogie system; Equation (28) indicates that the maintenance time must meet the requirements. s.t.G(x 01 ,x 02 ,...,x 0n )≥A s (27) In the formula: C M Indicates the cost of maintenance measures; k i,1 and k i,2 These represent the costs of taking different maintenance measures when the physical module is in states e1 and e2, respectively. β i This represents the probability that physical module i degenerates from state e0 to state e1, as a proportion of the sum of all degeneration probabilities. λ i This represents the failure rate result obtained by assigning physical module i; T represents the bogie running time; and This represents the average repair time of physical module i in states e1 and e2; x 0i This represents the probability that physical module i remains in state e0 for an extended period of time. G(x 01 ,x 02 ,…,x 0n This indicates that the availability of the bogie system is calculated using the availability of physical modules; A s Indicates the target availability of the bogie system; This represents the system's target mean time to repair.

10. A method for coordinated allocation of reliability and maintainability of high-speed train bogies as described in claim 9, characterized in that: Step S3 includes the following steps: Step S31: Construct a joint allocation model based on cost optimization; Based on the reliability and maintainability allocation model constructed in step S2, establish a joint objective function, expressed as equation (29), with constraints expressed as equations (23)-(24), (26)-(28): Step S32: Global optimization solution; A genetic algorithm is used as the global optimization solution method, including the following steps: Step S321: Population initialization and chromosome encoding; a set of initial candidate solutions that satisfy the constraints are randomly generated to form the initial population; chromosomes represent the combination scheme of physical module decision variables, loci represent physical modules, and allele gene values ​​represent decision variables; Step 322: Fitness evaluation; The joint objective function is used as the fitness function, and all constraints are embedded into the penalty function. The fitness value is the reciprocal of the sum of the reliability improvement cost, maintenance cost and the penalty function. Step S323: Selection, crossover, and mutation; using the tournament selection mechanism, individuals with higher fitness are selected to enter the next generation's breeding process; using single-point crossover, the genes of the parent chromosomes are exchanged to produce multiple generations; using random mutation of individual gene instances to select and maintain population diversity, avoiding local optima; Step S324: Population update and termination; Combine the new individuals obtained from crossover and mutation with the original population to form a new generation of population; repeat until the predetermined number of iterations is reached or the fitness value is lower than the threshold. Step S325: Output the optimal solution; Output the joint optimal solution λ i * Assign the optimal failure rate to ensure reliability. and Allocate the optimal average repair time for maintainability.

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