Optimization Method for Component Exchange When Two Complex Equipment are Repaired Simultaneously

Abstract

The present invention relates to the technical field of complex equipment maintenance. Specifically, it is an optimization method for component exchange when two complex equipments are sent for repair simultaneously, which can effectively reduce the total maintenance cost on the premise of ensuring the stable and reliable operation of complex equipments. It is characterized in that, first, an opportunistic maintenance model for a single complex equipment is established; second, an algorithm for quickly solving the opportunistic maintenance problem of a single complex equipment is constructed; and finally, the opportunistic maintenance problems of two complex equipments are solved respectively, and an evaluation criterion is formulated. The algorithm proposed by the present invention can obtain the exchange scheme of the unit bodies and life components of complex equipments within a short time, and the obtained exchange scheme of the unit bodies and life components can reduce the life losses of the unit bodies and life components generated by the maintenance of two complex equipments. At the same time, the proposed algorithm can also be applied to the exchange problems of unit bodies and life components of two complex equipments on a larger scale.

Description

Technical Field:

[0001] The present invention relates to the technical field of complex equipment maintenance, and specifically to an optimization method for component exchange when two complex equipments are sent for repair, which can effectively reduce the total maintenance cost on the premise of ensuring the stable and reliable operation of the complex equipment. Background Art:

[0002] Long-life complex equipment consists of a large number of components. During its subsequent use, multiple repairs and maintenance are required. Taking a civil aviation engine as an example, it needs to be repaired multiple times during its whole life cycle. Each time the engine is sent for repair, a fixed in-plant repair cost will be generated due to the disassembly, transportation, etc. of the engine.

[0003] Currently, in the structural design of aero-engines, the design concept of unit bodies is mostly adopted. An engine generally consists of multiple detachable unit bodies and life parts. Driven by the design concept of modular and standardized unit bodies, the maintenance of the engine is carried out centered around the unit body. Each time the engine is sent for repair, first the engine is removed from the aircraft and transported to the repair factory, and then the engine is disassembled into unit bodies. Taking the unit body as the maintenance unit, the life parts that have reached or are about to reach their service life within the unit body are replaced, and at the same time, a certain level of maintenance is carried out on the unit body. Taking the CFM56-5B model engine widely used in China as an example, its whole machine consists of 4 main units, 17 sub-unit bodies and 20 life parts, and its structure is as Figure 1 shown. Engine life parts are components that are strictly controlled by service life. When their service time reaches the life limit, they must be replaced. An engine generally has multiple life parts. Due to the differences in the working environment, structure, etc. of each life part, the life limits of each life part vary greatly. For example, the life limit of the supercharger rotor of the CFM56-5B model engine is 30,000 flight cycles, while the life limit of the high-pressure turbine rotor disk is 20,000 flight cycles. In actual engineering applications, airlines generally adopt the idea of opportunistic replacement to replace multiple life parts in the engine at one time. The advantage of doing this is that the number of engine repairs is greatly reduced, but it will cause waste of some life parts.

[0004] The unit body and the life part are an integrated whole that affects each other. When the engine is sent for repair, the unit body is often also repaired. For the engine unit body, airlines generally divide different maintenance levels. Taking the CFM56-5B series engine as an example, the maintenance levels of the unit body can be divided into: visual inspection, minimum repair, performance restoration and overhaul. Among them, overhaul means completely disassembling the unit body and performing the most comprehensive restoration. It has the highest level, is the most important, and also has the highest maintenance cost. Taking the fan casing unit body of the CFM56-5B engine as an example, the overhaul cost for a single repair is about 100,000 US dollars.

[0005] For the major overhaul of engine unit, the engineering generally gives its corresponding soft time limit and hard time limit for major overhaul. The hard time limit for major overhaul refers to the limit of the service time after the unit is overhauled, which is similar to the life limit of life parts. The unit is repaired during the soft time limit for major overhaul, and the repair effect is the best and the repair cost is relatively the lowest. If the unit is overhauled outside the soft time limit for major overhaul, it may lead to over-maintenance or under-maintenance of the engine, indirectly increasing the repair cost. When the service time of the engine reaches the full life limit, the engine can no longer be used. However, some life parts and units in the engine have not reached the end of their life, so they still have a certain residual value. It mainly includes the residual value of life parts and the residual value of units. Therefore, the problem of the full-life maintenance decision of the engine is that for a given civil aviation engine, it is necessary to formulate the optimal maintenance plan within its full life cycle according to the current state of the engine. That is, to determine the maintenance timing of each time in the engine's full life, the maintenance strategy of the unit, and the replacement strategy of life parts, so that the replacement cost of life parts within the full life cycle of the engine is minimized, the maintenance cost of the unit is minimized, and the residual value when the engine reaches the life limit is maximized.

[0006] The remaining life of each component of the engine affects the timing of the engine's current repair, and the current repair timing of the engine affects the repair strategy of this repair, and the current repair strategy affects the remaining life of each component. Therefore, it can be said that the relationship among the remaining life of each component, the repair timing, and the repair strategy of the engine is mutually influential. When two engines are sent for repair at the same time, the units and life parts can be exchanged according to the actual situation, thus affecting the remaining life of the two engines, affecting the repair timing, and further affecting the repair strategy, thereby affecting the repair cost. The relationship is as Figure 2 shown. For two engines sent for repair at the same time, the remaining life of the units and life parts can be changed by exchanging their units and life parts, changing the repair strategies of the units of the two engines and the replacement strategies of life parts, and further achieving the purpose of reducing the total repair cost. Summary of the Invention:

[0007] In view of the problems existing in the prior art, the present invention proposes an optimization method for component exchange when two complex equipments are sent for repair at the same time, which can obtain a reasonable exchange plan for units and life parts in complex equipments, and further effectively reduce the repair cost.

[0008] The present invention is achieved by the following measures:

[0009] An optimization method for component exchange when two complex equipments are sent for repair simultaneously, characterized in that, first, an opportunistic maintenance model for a single complex equipment is established; second, an algorithm for quickly solving the opportunistic maintenance problem of a single complex equipment is constructed; finally, the opportunistic maintenance problems of two complex equipments are solved respectively, and an evaluation criterion is formulated; the opportunistic maintenance model of the single complex equipment is specifically as follows: The complex equipment includes p (p≥1) unit bodies and q (q≥1) life components, and the disassembly and assembly cost required for maintaining the unit body and replacing the life component is C b , which is independent of the number of replaced life components, and each unit body is denoted as M i (i = 1, 2, …, p), and the hard time limit for overhaul is denoted as The soft time limit for overhaul is denoted as The overhaul cost is denoted as Each life component is denoted as L j (j = 1, 2, …, q), the limited life is denoted as The replacement cost is denoted as The equipment usage time is denoted as T, and the usage time of M i is denoted as The remaining life is denoted as L j The usage time is denoted as The remaining life is denoted as As T increases, and increase correspondingly, and decrease correspondingly; when is reached, M i must be overhauled, and the cost incurred is When is reached, L j must be replaced, and the cost incurred is The unit body can be repaired with a delay, and the hourly loss and waste caused by delaying the repair of the unit body M i is

[0010] If M i is repaired at T k , it is repaired in advance, and its loss cost is C i ,

[0011]

[0012] If M i is repaired at T k , it is repaired with a delay, and its loss cost is C i ,

[0013]

[0014] If L j at T k is replaced, the loss cost is C j ,

[0015]

[0016] The goal of the opportunistic maintenance problem for a single complex equipment is to determine the opportunistic maintenance strategies for the unit bodies and life components, that is, to determine m, T k , the unit bodies and life components to be overhauled each time when sent for repair, so that the total loss cost C is minimized, which can be expressed as Equation (4)

[0017]

[0018]

[0019] In the formula: s——s = (m, T1, T2, …, T m , e 1,1 , e 1,2 , …, e p,m , f 1,1 , f 1,2 , …, f q,n ), the solution vector composed of decision variables;

[0020] m——the number of full-life maintenance times;

[0021] C b ——the fixed maintenance cost for the complex equipment when sent to the factory for repair;

[0022] N——natural number;

[0023] e i,k ——whether to overhaul at the k-th repair, the overhaul value is 1, otherwise 0; i j,k

[0024] f j,k ——whether to replace L at the k-th repair, the replacement value is 1, otherwise 0; j lim

[0025] Ω——Ω = {s|m ∈ N ∩ [0, T lim , T k ∈ N ∩ [0, T lim , e i,k ∈ {0, 1}, f j,k ∈ {0, 1}}

[0026] where i = 1, 2, …, p, j = 1, 2, …, q, k = 1, 2, …, m

[0027] The solution space of the opportunistic maintenance problem for a single complex equipment is shown in Equation (5):

[0028]

[0029] The algorithm for constructing a fast solution to the opportunistic maintenance problem of a single complex equipment specifically includes the following steps:

[0030] Step 1-1: According to reduction rule 1 and reduction rule 2, on the premise of knowing the remaining life of all components, determine the potential next maintenance time after simplification, where the reduction rule 1 is that if A = {T1, T2, …, T k}, then The reduction rule 2 is:

[0031] Let The number of its elements is s. Considering that there may be unit bodies and life components with the same remaining life, s ≤ p + q. Arrange the elements of S res in a column in ascending order, and denote them as r1, r2, …, r s . Let the minimum remaining life of the life component be r m , and the minimum remaining life of the unit body be r n . If r1 = r m , since the life component must be maintained when its life expires, the next maintenance time T pot = r1. If r1 = r n , since the unit body allows delayed maintenance, r2 can also be used as the next potential maintenance time. Also, since the life component must be maintained when its life expires, T pot = {r|r = r1, r2, …, r m} is the potential maintenance time for the next maintenance, but the potential maintenance time can be further reduced according to cost analysis, and r l can be found to satisfy and r l is the maximum maintenance time that satisfies the total penalty cost of the unit body's delayed maintenance not exceeding the disassembly and assembly cost C b . Let r k = min{r l , r m}, then the next potential maintenance time T pot = {r|r1, r2, …, r k};

[0032] Step 1-2: According to reduction rule 3, determine the optimal maintenance strategy under each potential next maintenance time, and calculate the average loss cost K s corresponding to each optimal maintenance strategy, where the reduction rule 3 is: Define the average loss cost K n as follows:

[0033]

[0034] Where: l—the number of non-delay maintenance unit bodies for this maintenance;

[0035] m—the number of life component replacements for this maintenance;

[0036] n—the number of delay maintenance unit bodies for this maintenance;

[0037] T—the timing of this maintenance;

[0038] s—the total number of unit bodies and replaced life components for this maintenance; s = l + m + n

[0039] Step 1-3: According to the average loss cost K corresponding to all optimal maintenance strategies s , find the minimum average loss cost, and determine the corresponding maintenance timing and the most optimal maintenance strategy as the maintenance timing and maintenance strategy for this maintenance;

[0040] Step 1-4: Set the overhaul soft time limit for the unit bodies maintained in the maintenance strategy, set the remaining life of the life components replaced in the maintenance strategy as their limit life, and subtract the maintenance timing from the remaining life of all unit bodies and life components not in this maintenance strategy to complete the update of the remaining life of all unit bodies and life components;

[0041] Step 1-5: Add up the maintenance timings to obtain the maintenance timing and compare K with the total life R of the complex equipment. If K < R, repeat Steps 1-1 to 1-4. If K > R, output all the obtained maintenance timings and maintenance strategies.

[0042] In the present invention, the above algorithm is used for both two complex equipments to find their minimum total loss cost C tem1 and C tem2 , and the minimum total loss cost sum C tem,sum = C tem1 + C tem2 can characterize the life loss degree of the unit bodies and life components of the opportunity maintenance of the two complex equipments.

[0043] In the present invention, to calculate and obtain the optimal solution of the component exchange scheme for two complex equipments, according to the genetic algorithm principle, the following steps are included:

[0044] Step 2-1: Encoding step, represent the exchange situation of the unit bodies and life components of the two complex equipments with binary codes. If the complex equipment under study has p (p≥1) unit bodies and q (q≥1) life components, the number of exchange schemes is 2 p+q-1 , so the exchange scheme of the unit bodies and life components can be represented by p + q - 1 bit binary codes;

[0045] Step 2-2: Exchange link. In the genetic algorithm, the setting of the fitness function is closely related to the selection link. For the selection link, the roulette wheel algorithm makes it more likely for individuals with larger fitness values to be selected as parents to generate new individuals, and there is a greater chance of obtaining better offspring. Therefore, the roulette wheel algorithm is selected for the selection link. Since the roulette wheel algorithm selects individuals with larger fitness values as parents, and in this problem, the goal is to solve the exchange method with the minimum total loss cost of two complex equipment, the reciprocal of the sum of the total loss costs of the two complex equipment can be used as the fitness function F for this problem, that is

[0046]

[0047] Step 2-3: Crossover link. Set a pc greater than 0 and less than 1 as the mating probability. If the random number generated from 0 to 1 is less than pc, the adjacent two groups of solution vectors will be crossed. The crossover nodes are also randomly generated;

[0048] Step 2-4: Mutation link. Set a pm greater than 0 and less than 1 as the mutation probability. If the random number generated from 0 to 1 is less than pm, a certain bit of the solution vector will change, from 0 to 1 or from 1 to 0.

[0049] The algorithm proposed by the present invention can obtain the exchange scheme of the unit body and the life component of the complex equipment in a relatively short time, and the obtained exchange scheme of the unit body and the life component can reduce the life loss of the unit body and the life component generated by the maintenance of the two complex equipment; at the same time, the proposed algorithm can also be applied to the exchange problem of the unit body and the life component of two complex equipment on a relatively large scale. Description of the drawings:

[0050] Att Figure 1 is a schematic structural diagram of a CFM56-5B type engine.

[0051] Att Figure 2 is a schematic diagram of the relationship between the remaining life of the engine, the maintenance time, the maintenance strategy, and the component exchange scheme.

[0052] Att Figure 3 is the full life cycle flowchart of a single machine in the present invention. Specific implementation manner:

[0053] Example 1:

[0054] Taking the complex equipment - aeroengine as an example, the present invention is further described below.

[0055] Considering that the studied aeroengine includes p (p≥1) unit bodies and q (q≥1) life components. The disassembly and assembly cost required for maintaining the unit body and replacing the life component is C b, which is independent of the number of replaceable life components. Each unit is denoted as M i (i = 1, 2, …, p), the hard time limit for major overhaul is denoted as The soft time limit for major overhaul is denoted as The cost of major overhaul is denoted as Each life component is denoted as L j (j = 1, 2, …, q), the limited life is denoted as The replacement cost is denoted as The equipment usage time is denoted as T, M i The usage time is denoted as The remaining life is denoted as L j The usage time is denoted as The remaining life is denoted as Obviously, As T increases, and increase correspondingly, and decrease correspondingly. When occurs, M i must undergo a major overhaul, and the cost incurred is When occurs, L j must be replaced, and the cost incurred is The unit can be repaired with a delay. The hourly loss and waste caused by delaying the repair of unit M i is

[0056] If M i is repaired at T k , it is a premature repair, and the loss cost is C i .

[0057]

[0058] If M i is repaired at T k , it is a delayed repair, and the loss cost is C i .

[0059]

[0060] If L j is replaced at T k , the loss cost is C j .

[0061]

[0062] The goal of the opportunistic maintenance problem for a single engine is to determine the opportunistic maintenance strategies for the unit and life components, that is, to determine m, Tk , each time when sending for repair, the unit bodies and life components to be overhauled are such that the total loss cost C is minimized, which can be expressed as Equation (4).

[0063]

[0064]

[0065] In the formula: s——s = (m, T1, T2, …, T m , e 1,1 , e 1,2 , …, e p,m , f 1,1 , f 1,2 , …, f q,n ), the solution vector composed of decision variables;

[0066] m——the number of full-life repairs;

[0067] C b ——the fixed repair cost for the engine to be sent to the factory for repair;

[0068] N——natural number;

[0069] e i,k ——whether to overhaul at the kth time of sending for repair, taking the value of 1 for overhaul and 0 otherwise; i

[0070] f j,k ——whether to replace at the kth time of sending for repair, taking the value of 1 for replacement and 0 otherwise; j

[0071] Ω——Ω = {s|m ∈ N ∩ [0, T lim , T k ∈ N ∩ [0, T lim , e i,k ∈ {0, 1}, f j,k ∈ {0, 1}}

[0072] where i = 1, 2, …, p, j = 1, 2, …, q, k = 1, 2, …, m

[0073] The opportunity maintenance problem of a single engine belongs to a combinatorial optimization problem. According to the domain of each decision variable, it is not difficult to find the scale of the solution space of this problem, as shown in Equation (5).

[0074]

[0075] It can be seen that the scale of the problem solution space is extremely large, and the main influencing factors are the number p of unit bodies, the number q of life components, and the remaining life T of the unit bodies and life components lim ​​Even when the number of engine unit bodies and life components is not very large, it is almost impossible to obtain the optimal solution by traversing the solution space through a complete traversal method.

[0076] Analysis shows that even when the number of unit bodies and life components of the engine is relatively small, the scale of the solution space is very large, and it is simply impossible to solve the problem by using the traversal method. If some optimization algorithms are directly used for solving, such as the particle swarm optimization algorithm, the ant colony algorithm, etc., due to too many decision variables and too large a scale of the solution space, there will also be problems such as extremely long solution time consumption and poor solution results. Therefore, it is necessary to decouple the civil aviation engine maintenance decision-making problem.

[0077] Research finds that when the previous maintenance times T of the engine k are determined, the optimal maintenance strategy and its cost for the unit body over the entire life cycle and the optimal replacement strategy and its cost for the life components under the maintenance time plan can be solved according to certain rules or methods. According to the maintenance cost of the unit body and the replacement cost of the life components, it can be deduced whether this maintenance time is the optimal maintenance time. By iterating in this way, the optimal solution to the problem can be solved.

[0078] In order to improve the efficiency of the search algorithm, the following reduction rules are proposed to reduce the solution space:

[0079] (1) Reduction rule 1

[0080] According to formula (4), it can be known that for the next maintenance time, as long as the unit body does not exceed the hard time limit and the life components do not exceed their service life, there is an intuitive understanding: if there are no life components reaching the end of their service life when sending for repair, then the number of repair times will inevitably increase or there will be a waste of life components. Based on this, the following maintenance time reduction rule is given:

[0081] That is, if A = {T1, T2, …, T k} then

[0082] According to reduction rule 1, the next maintenance time can be reduced from a certain value range to multiple fixed values.

[0083] (2) Reduction rule 2

[0084] Since the unit body allows delayed maintenance while the life components must be maintained when reaching the end of their service life. The following reduction rule for finding the next maintenance time can be formulated:

[0085] Let its number of elements be s. Considering that there may be unit bodies and life components with the same remaining life, s ≤ p + q. Arrange the elements of S res in ascending order in a column, and denote them as r1, r2, …, r sLet the minimum remaining life of the life component be r m , and the minimum remaining life of the unit body be r n . If r1 = r m , since the life component must be repaired when its life expires, the next maintenance time T pot = r1. If r1 = r n , since the unit body allows delayed maintenance, r2 can also be used as the next potential maintenance time. Also, since the life component must be repaired when its life expires, T pot = {r|r = r1, r2,..., r m} is the potential maintenance time for the next maintenance. However, the potential maintenance time can be further reduced based on cost analysis, and r l can be found to satisfy and r l is the maximum maintenance time that satisfies the total penalty cost of delayed maintenance of the unit body not exceeding the disassembly and assembly cost C b . Let r k = min{r l , r m}, then the next potential maintenance time T pot = {r|r1, r2,..., r k}}.

[0086] According to reduction rule 2, the value range of the next maintenance time can be effectively reduced to several fixed values.

[0087] (3) Reduction rule 3

[0088] Based on the above two rules, the next potential maintenance time can be determined, and the maintenance strategy for each maintenance time can be determined by the following reduction rule. Define the average loss cost K n as follows:

[0089]

[0090] In the formula: l - the number of unit bodies with non-delayed maintenance in this maintenance;

[0091] m - the number of life component replacements in this maintenance;

[0092] n - the number of unit bodies with delayed maintenance in this maintenance;

[0093] T - this maintenance time;

[0094] s - the total number of unit bodies and replaced life components in this maintenance; s = l + m + n

[0095] The rationality of the current maintenance strategy can be evaluated through the average loss cost. The higher the average loss cost, the more cost is wasted in repairing a unit or replacing a life component, indicating that the maintenance strategy is less reasonable; the lower the average loss cost, the less cost is wasted in repairing a unit or replacing a life component, indicating that the maintenance strategy is reasonable. According to actual maintenance experience, when sending for repair each time, give priority to repairing the unit with a short remaining life and replacing the life component with a short remaining life. Therefore, the units and life components can be added to the current maintenance strategy in ascending order of their remaining lives. When the number of added components is small, the fixed disassembly and assembly cost C b and the number s of the units to be maintained and life components to be replaced in this maintenance are the main influencing factors of the average loss cost K s . When the number s of the units to be maintained and life components to be replaced increases, the average loss cost K s decreases. When the number of added components is large, the sum of the loss costs of the components is the main influencing factor of the average loss cost K s . When the number s of the units to be maintained and life components to be replaced increases, the average loss cost K s increases. Therefore, as the number s of the units to be maintained and life components to be replaced in this maintenance continuously increases, the average loss cost K s first decreases and then increases, and the maintenance strategy corresponding to the minimum point of the average loss cost K s is the optimal maintenance strategy under the current maintenance timing.

[0096] According to the above three reduction rules, the single - machine full - life maintenance strategy formulation algorithm can be developed as follows:

[0097] Step 1: According to Reduction Rule 1 and Reduction Rule 2, on the premise of knowing the remaining lives of all components, determine the potential next maintenance timing after simplification.

[0098] Step 2: According to Reduction Rule 3, determine the optimal maintenance strategy at each potential next maintenance timing, and calculate the average loss cost K s corresponding to each optimal maintenance strategy.

[0099] Step 3: According to the average loss cost K s corresponding to all optimal maintenance strategies, find the minimum average loss cost, and determine the maintenance timing and optimal maintenance strategy corresponding to it as the maintenance timing and maintenance strategy for this maintenance.

[0100] Step 4: Set the overhaul soft time limit for the units repaired in the maintenance strategy, set the remaining life of the life components replaced in the maintenance strategy as their limit life, and subtract the current maintenance timing from the remaining lives of all units and life components not in this maintenance strategy to complete the update of the remaining lives of all units and life components.

[0101] Step 5: Add up the maintenance times for each instance to obtain the sum of the maintenance time K, and compare it with the total life R of the engine. If K < R, repeat Steps 1 to 4. If K > R, output all the obtained maintenance times and maintenance strategies.

[0102] Convert the algorithm into a flowchart as Figure 3 shown below.

[0103] For both engines, use the above algorithm to calculate their minimum total loss cost C tem1 and C tem2 , and the minimum total loss cost sum C tem,sum = C tem1 + C tem2 can characterize the life loss degrees of the unit bodies and life components of the opportunistic maintenance of the two engines. Therefore, it can be used as an evaluation criterion for the unit body and life component exchange scheme of the two engines.

[0104] From the above example, it can be seen that using the heuristic search algorithm based on the reduction rule can quickly obtain the maintenance time and maintenance strategy of the engine, and then calculate the evaluation criterion for the unit body and life component exchange scheme of the two engines. If there are p (p≥1) unit bodies and q (q≥1) life components in the studied engine, the number of exchange schemes is 2 p+q-1 . When the number of unit bodies and life components is relatively large and the usage time of the two engines is considered to be long, it is impossible to use the traversal method to solve the optimal solution of the unit body and life component exchange scheme.

[0105] The problem of unit body and life component exchange between two engines is actually a combinatorial optimization problem. Currently, the main algorithms for solving combinatorial optimization problems include: genetic algorithm, particle swarm algorithm, dynamic programming method, ant colony algorithm, and heuristic search algorithm. The genetic algorithm has many advantages, including easy implementation, fast convergence speed, and high calculation accuracy, and has good superiority in engineering. In this example, the genetic algorithm will be used to solve the unit body and life component exchange scheme.

[0106] Genetic algorithm is a search algorithm based on natural selection and population genetics mechanism, which simulates the phenomena of reproduction, hybridization and mutation in natural selection and natural genetic processes. When using genetic algorithm to solve problems, each possible solution of the problem is encoded into a "chromosome", that is, an individual, and several individuals constitute a population (all possible solutions). At the beginning of the genetic algorithm, some individuals (i.e., initial solutions) are always randomly generated, and each individual is evaluated according to a predetermined objective function to give a fitness value. Based on this fitness value, some individuals are selected to produce the next generation. The selection operation embodies the principle of "survival of the fittest". Individuals with high fitness values are used to produce the next generation, while individuals with low fitness values are eliminated. Then, the selected individuals are recombined through crossover and mutation operators to generate a new generation. Since the individuals of this generation inherit some excellent traits of the previous generation, their performance is better than that of the previous generation, and thus they gradually evolve in the direction of the optimal solution. Therefore, genetic algorithm can be regarded as a process of the initial evolution of a population composed of feasible solutions.

[0107] (1) Encoding operation

[0108] When using genetic algorithm to solve problems, it is necessary to first determine the objective function and variables of the problem, and then encode the variables. The main reason for doing this is that in genetic algorithm, the solutions of the problem are represented by digital strings, and the genetic operators also directly operate on the digital strings. The encoding methods can be divided into binary encoding and real number encoding. Binary encoding is generally used to solve combinatorial optimization problems, and real number encoding is generally used to solve constrained optimization problems.

[0109] (2) Genetic operation

[0110] Genetic operation is to simulate the operation of biological genes. Its task is to impose certain operations on individuals according to their fitness, so as to realize the evolutionary process of survival of the fittest. From the perspective of optimization search, genetic operation can optimize the solutions of the problem generation by generation and approach the optimal solution. Genetic operation includes the following three basic genetic operators: selection, crossover, and mutation. Selection and crossover basically complete most of the search functions of genetic algorithm, and mutation increases the ability of genetic algorithm to find the optimal solution.

[0111] 1) Selection

[0112] Selection refers to the operation of selecting excellent individuals from the population and eliminating inferior individuals. It is based on fitness evaluation. The greater the fitness of an individual, the greater the possibility of being selected, and the more "offspring" it has in the next generation. The selected individuals are put into the pairing pool. Currently, the commonly used selection methods include roulette wheel algorithm, best individual retention method, expected value method, ranking selection method, competition method, and linear normalization method.

[0113] Roulette wheel selection algorithm: Roulette wheel selection is also known as proportional selection operator. Its basic idea is that the probability of each individual being selected is proportional to the value of its fitness function. Let the population size be n and the fitness of individual i be F i , then the probability that individual i is selected and inherited into the next generation population is:

[0114] 2) Crossover:

[0115] Crossover refers to the operation of replacing and recombining parts of the structures of two parent individuals to generate new individuals. The purpose of crossover is to produce new individuals in the next generation. Through the crossover operation, the search ability of the genetic algorithm has been improved by leaps and bounds. Crossover is an important means for the genetic algorithm to obtain excellent individuals. The crossover operation is randomly selecting two individuals from the matching library according to a certain crossover probability, and the crossover position is also random. The crossover probability P c is generally set to be very large, ranging from 0.6 to 0.9. Generate a random number rand between [0,1]. If rand < P c , then perform the crossover operation of the two parents at a random position.

[0116] 3) Mutation

[0117] Mutation is to randomly change the values of some genes of individuals in the population with a very small mutation probability P m . The basic process of the mutation operation is: generate a random number rand between [0,1]. If rand < P m , then perform the mutation operation. The mutation operation itself is a kind of local random search. Combined with the selection and crossover operators, it can avoid some permanent loss of information caused by the selection and crossover operators, ensure the effectiveness of the genetic algorithm, endow the genetic algorithm with local random search ability, and at the same time enable the genetic algorithm to maintain the diversity of the population to prevent premature convergence. In the mutation operation, the mutation probability should not be set too large. If Pm > 0.5, the genetic algorithm degenerates into a random search.

[0118] (3) Termination condition

[0119] When the fitness of the optimal individual reaches the given threshold, or the fitness of the optimal individual and the population fitness no longer increase, or the number of iterations reaches the preset number of generations, the algorithm terminates. The preset number of generations is generally set to 100 - 500 generations.

[0120] For the genetic algorithm to achieve global convergence, first, it is required that any initial population can reach the global optimal solution after a finite number of steps. Second, the algorithm must have an operation to preserve the optimal solution to prevent the loss of the optimal solution. The factors related to the algorithm convergence mainly include population size, selection operation, crossover probability, and mutation probability.

[0121] Generally, if the population is too small, it cannot provide enough sampling points, resulting in poor algorithm performance; if the population is too large, although it can increase the optimization information and prevent premature convergence, it will undoubtedly increase the computational amount, causing the convergence time to be too long, manifested as slow convergence speed.

[0122] The selection operation enables individuals with high fitness to survive with a greater probability, thus improving the global convergence of the genetic algorithm. If the optimal preservation strategy is adopted in the algorithm, that is, the best individual in the parental population is retained and does not participate in the crossover and mutation operations, but directly enters the next generation, the genetic algorithm can finally converge to the global optimal solution with probability 1.

[0123] The crossover operation is used for pairs of individuals to generate new individuals, which is essentially an effective search in the solution space. When the crossover probability is too large, the individuals in the population are updated quickly, and the individuals with high fitness values will be quickly destroyed; when the probability is too small, the crossover operation is rarely performed, which will cause the search to stagnate and the algorithm not to converge.

[0124] The mutation operation is a perturbation to the population pattern, which is beneficial to increasing the diversity of the population. However, if the mutation probability is too small, it is difficult to generate new patterns, and if the mutation probability is too large, the genetic algorithm will become a random search algorithm.

[0125] The genetic algorithm is essentially a series of operations on chromosome patterns, that is, the excellent patterns in the current population are inherited to the next generation population through the selection operator, pattern recombination is carried out using the crossover operator, and pattern mutation is carried out using the mutation operator. Through these genetic operations, the patterns gradually evolve in a better direction, and finally the optimal solution of the problem is obtained.

[0126] To calculate and find the optimal solution of the exchange scheme of two engine components, a study on the exchange problem of two engine unit bodies and life parts is carried out based on the genetic algorithm. According to the principle of the genetic algorithm, the relevant links are set as follows:

[0127] (1) Encoding link

[0128] The exchange situation of the unit bodies and life parts of the two engines is represented by binary codes. If there are p (p≥1) unit bodies and q (q≥1) life parts in the studied engine, the number of exchange schemes is 2 p+q-1 . Therefore, the exchange scheme of the unit bodies and life parts can be represented by p + q - 1 - bit binary codes.

[0129] (2) Exchange link

[0130] In the genetic algorithm, the setting of the fitness function is closely related to the selection process. For the selection process, the roulette wheel algorithm allows individuals with larger fitness values to have a higher probability of being selected as parents to generate new individuals, and a greater chance of obtaining better offspring. Therefore, the roulette wheel algorithm can be chosen for the selection process. Since the roulette wheel algorithm selects individuals with large fitness values as parents, and in this problem, the goal is to solve the swapping method that minimizes the total loss cost of two engines, the reciprocal of the sum of the total loss costs of the two engines can be used as the fitness function F for this problem. That is

[0131]

[0132] (3) Crossover process

[0133] Set a pc greater than 0 and less than 1 as the mating probability. If the random number generated from 0 to 1 is less than pc, then the adjacent two groups of solution vectors will be crossed. The crossover node is also randomly generated.

[0134] (4) Mutation process

[0135] Set a pm greater than 0 and less than 1 as the mutation probability. If the random number generated from 0 to 1 is less than pm, then a certain bit of the solution vector will change (from 0 to 1 or from 1 to 0).

[0136] The purpose of the crossover process and the mutation process is to increase the diversity of the population and avoid getting stuck in a local optimum and being unable to find the global optimum. Since this problem is a discrete problem, even if only 1 bit of the solution vector changes, the corresponding fitness function F may change greatly. Therefore, for the value of the fitness function F of a solution vector, it is impossible to judge the similarity degree between this solution vector and the optimal solution, and it is impossible to eliminate the solution vector according to the value of the fitness function. Therefore, in this problem, the elimination process of the genetic algorithm can be omitted.

[0137] In this problem, the genetic algorithm proceeds according to the following steps:

[0138] Step 1 Generation of the initial population: Randomly generate n binary codes with p + q - 1 bits as the initial population of the genetic algorithm, where n is the population size.

[0139] Step 2 Swap and calculate the fitness function F: Perform swapping based on the obtained population, calculate the corresponding fitness function values after swapping, and retain the generations and the best solution vectors and the reciprocals of the corresponding fitness function values in each generation.

[0140] Step 3 Generate a new population: Through the roulette wheel algorithm for the selection process, generate population 1, cross population 1 to generate population 2, and then mutate population 2 to generate a new population.

[0141] Step 4 Repeat Step 2 and Step 3, and record the optimal exchange scheme and the reciprocal of the corresponding fitness function value for each generation in the k-th generation.

[0142] Step 5 End the loop when the exchange scheme remains unchanged for k consecutive generations.

[0143] Next, verify the performance of the technical solution described in this example:

[0144] Use the optimization problem of unit body exchange when multiple units are randomly generated for repair simultaneously to evaluate the proposed algorithm. Let p = 10 and q = 15. The remaining life of the unit body and the remaining life of the life component follow a uniform distribution on the flight cycle in the interval (8000, 30000). For unit body M i the overhaul cost and for life component L j the replacement cost follow a uniform distribution on the interval (35000, 300000) US dollars. The soft time limit of the unit body the limited life of the life component Let p = 10 and q = 10, randomly generate 10 problems as Experiment 1, and then let p = 10 and q = 15, randomly generate 10 problems as Experiment 2. Let the disassembly and assembly cost C b = 30000 US dollars. The algorithm is implemented in Python. According to experience, when the population size n = 3000, the mating probability pc = 0.6, the mutation probability pm = 0.8, and the number of genetic generations k = 80, the genetic algorithm has a better solution effect. Solve the above 20 problems on a computer (CPU: AMD Ryzen 5 4600H, memory 16GB) using the above parameters, and record the average consumption time t, the optimization ratio D, the average relative deviation r from the optimal solution, the maximum relative deviation R from the optimal solution, and the average consumption time T of the exhaustive search for Experiment 1 and Experiment 2 using this genetic algorithm. The experimental results are shown in Table 1:

[0145] Table 1 Experimental Results

[0146]

[0147] Take a randomly generated problem as an example, and its relevant data are shown in Tables 2 and 3:

[0148] Table 2 Unit Body Related Data

[0149]

[0150]

[0151] Table 3 Life Component Related Data

[0152]

[0153] Among them, represents the remaining life of the i-th life component of the first engine, represents the remaining life of the i-th life component of the first engine. represents the remaining life of the j-th life component of the first engine, represents the remaining life of the j-th life component of the first engine. According to relevant calculations, the maintenance time of the first engine is [8459, 14649, 20144, 27869], and the total loss cost is $170,938.9. The maintenance time of the second engine is [8947, 15312, 22371, 27550], and the total loss cost is $265,008.8, with a total of $435,947.7. According to relevant calculations, an exchange plan can be obtained. After the exchange, the remaining life of the first engine unit is [17858, 27501, 15607, 12820, 13328, 13024, 12440, 20243, 23233, 29318], and the remaining life of the first engine life component is [12725, 16659, 12388, 13508, 8898, 8459, 26642, 27550, 8947, 8801]. After the exchange, the remaining life of the second engine unit is [22809, 22371, 21913, 18567, 23073, 29072, 15095, 25577, 25908, 29318], and the remaining life of the second engine life component is [18153, 28692, 27869, 20144, 17863, 15312, 20603, 16474, 14649, 17261]. After the exchange, the maintenance plan of the first engine is [8459, 13508, 26642], and the total loss cost is $163,781.2. After the exchange, the maintenance plan of the second engine is [14649, 20144, 27869], and the total loss cost is $183,602.2, with a total of $347,383.4, and the optimization rate is 20.3%.

[0154] In order to solve the problem of the exchange of two engine units and life components, this example conducts research on two aspects: the evaluation of the exchange scheme of two engine units and life components and the search algorithm for the exchange scheme of two engine units and life components, and uses numerical experiments to evaluate the proposed algorithm. The experimental results show that: the proposed algorithm can find the exchange scheme of the unit and the life component in a relatively short time, and the obtained exchange scheme of the unit and the life component can reduce the life loss of the unit and the life component caused by the maintenance of the two engines; at the same time, the proposed algorithm can also be applied to the problem of the exchange of two engine units and life components on a larger scale.

Claims

1. An optimization method for component exchange when two complex equipment are sent for repair simultaneously, characterized in that, First, establish the opportunistic maintenance model for a single complex equipment; secondly, construct an algorithm for quickly solving the opportunistic maintenance problem of a single complex equipment; finally, solve the opportunistic maintenance problems of two complex equipments respectively and formulate evaluation criteria; the opportunistic maintenance model for a single complex equipment is specifically as follows: A complex equipment includes p (p≥1) unit bodies and q (q≥1) life components. The disassembly and assembly costs required for repairing unit bodies and replacing life components are C b , which is independent of the number of replaced life components. Each unit body is denoted as M i , where i = 1, 2, …, p. The hard time limit for major overhaul is denoted as The soft time limit for major overhaul is denoted as The major overhaul cost is denoted as Each life component is denoted as L j , where j = 1, 2, …, q. The limited life is denoted as The replacement cost is denoted as The equipment usage time is denoted as T. The usage time of M i is denoted as The remaining life is denoted as L j The usage time is denoted as The remaining life is denoted as As T increases, and increase correspondingly, and decrease correspondingly; when occurs, M i must undergo major overhaul, and the cost incurred is When occurs, L j must be replaced, and the cost incurred is The unit body can be repaired with a time delay. The loss and waste per hour caused by delaying the repair of unit body M i is If M i is repaired at T k which is preventive maintenance, the cost of loss is C i , If M i is repaired at T k with a delay in repair, the loss cost is C i , If L j at T k is replaced, the loss cost is C j , The goal of opportunistic maintenance for a single complex equipment is to determine the opportunistic maintenance strategies for unit bodies and long-life components, that is, to determine \(m\) and \(T\). k For each repair, the unit bodies and long-life components to be overhauled are selected to minimize the total loss cost \(C\), which can be expressed as Equation (4). where: s——s = (m, T1, T2, …, T m , e 1,1 , e 1,2 , …, e p,m , f 1,1 , f 1,2 , …, f q,n ), the solution vector composed of decision variables; m - The total number of maintenance times during the whole life C b —— Fixed repair cost for complex equipment sent to the factory for repair N - Natural number e i,k —— M at the k-th repair i Whether it is a major repair, the value for major repair is 1, otherwise it is 0; f j,k —— L at the k-th repair j Whether to replace, the replacement value is 1, otherwise 0; Ω——Ω={s|m∈N∩[0,T lim ,T k ∈N∩[0,T lim ,e i,k ∈{0,1},f j,k ∈{0,1}} where i = 1, 2, …, p, j = 1, 2, …, q, k = 1, 2, …, m The solution space of the opportunistic maintenance problem of a single complex equipment is shown in Equation (5):

2. The optimized method for component exchange when two complex equipment are sent for repair simultaneously according to claim 1, characterized in that The algorithm for quickly solving the opportunistic maintenance problem of a single complex equipment specifically includes the following steps: Step 1-1: Based on reduction rule 1 and reduction rule 2, on the premise that the remaining life of all components is known, determine the potentially simplified next maintenance timing, where the reduction rule 1 is that if A = {T1, T2, …, T k}, then the reduction rule 2 is as follows: Let The number of its elements is s. Considering that there may be unit bodies and life components with the same remaining life, s ≤ p + q. Arrange the elements of S res in a column in ascending order, and denote them as r1, r2, …, r s . Let the minimum remaining life of the life component be r m , and the minimum remaining life of the unit body be r n . If r1 = r m , since the life component will definitely be repaired when it reaches the end of its life, the next maintenance time T pot = r1. If r1 = r n , since the unit body allows delayed maintenance, r2 can also be used as the next potential maintenance time. Also, since the life component will definitely be repaired when it reaches the end of its life, T pot = {r|r = r1, r2, …, r m} is the potential maintenance time for the next maintenance. However, the potential maintenance time can be further narrowed down based on cost analysis, and r l can be found to satisfy and r l is the maximum maintenance time that satisfies the total penalty cost of the unit body's delayed maintenance not exceeding the disassembly and assembly cost C b . Let r k = min{r l , r m}, then the next potential maintenance time T pot = {r|r1, r2, …, r k}; Step 1-2: According to reduction rule 3, determine the optimal maintenance strategy at each potential next maintenance time, and calculate the average loss cost K corresponding to each optimal maintenance strategy s , where the reduction rule 3 is: Define the average loss cost K n as follows: In the formula: l - The number of non-delay maintenance unit bodies in this maintenance m - The number of life parts replaced in this maintenance n - The number of delay maintenance unit bodies in this maintenance T - The timing of this maintenance s —— The total quantity of the maintenance unit and the replaced life parts in this maintenance; s = l + m + n. Step 1 - 3: According to the average loss cost K corresponding to all the optimal maintenance strategies s , find the minimum average loss cost, and determine the corresponding maintenance timing and the optimal maintenance strategy as the maintenance timing and maintenance strategy for this maintenance; Steps 1 - 4: Set the overhaul soft time limit for the unit bodies that have been maintained in the maintenance strategy, set the remaining life of the life parts replaced in the maintenance strategy as their limited life, and subtract the timing of this maintenance from the remaining life of all unit bodies and life parts not in this maintenance strategy to complete the update of the remaining life of all unit bodies and life parts; Steps 1 - 5: Add up the maintenance timings to get the maintenance timing sum K and compare it with the whole life R of the complex equipment. If K < R, repeat Steps 1 - 1 to Steps 1 - 4. If K > R, output all the obtained maintenance timings and maintenance strategies.

3. The component exchange optimization method when two complex equipments are sent for repair simultaneously according to claim 1, characterized in that, For two complex equipment, the above algorithm is used to calculate their minimum total loss cost C tem1 and C tem2 , the minimum total loss cost and C tem,sum = C tem1 + C tem2 can characterize the life loss degree of the unit body and life parts of the two complex equipment for opportunistic maintenance.

4. An optimization method for component exchange when two complex equipment are sent for repair simultaneously according to claim 1, characterized in that To calculate and obtain the optimal solution of the component exchange plan for two complex equipments, according to the genetic algorithm principle, it includes the following steps: Step 2-1: Encoding stage. Represent the exchange situations of the unit bodies and life components of two complex equipment with binary codes. If there are p, p≥1 unit bodies and q, q≥1 life components in the complex equipment under study, the number of exchange schemes is 2 p+q-1 , so the exchange schemes of the unit bodies and life components can be represented by (p + q - 1)-bit binary codes; Step 2 - 2: Exchange link. In the genetic algorithm, the setting of the fitness function is closely related to the selection link. The roulette wheel algorithm is selected in the selection link. Take the reciprocal of the sum of the total loss costs of the two complex equipments as the fitness function F of this problem, that is Step 2 - 3: Crossover link. Set a pc greater than 0 and less than 1 as the mating probability. If the random number generated from 0 to 1 is less than pc, then cross the adjacent two groups of solution vectors, and the crossover node is also randomly generated; Step 2 - 4: Mutation link. Set a pm greater than 0 and less than 1 as the mutation probability. If the random number generated from 0 to 1 is less than pm, then change a certain bit of the solution vector, changing from 0 to 1 or from 1 to 0.

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