A selective maintenance decision-making method for multi-state systems based on improved mountain climbing algorithm

Abstract

The present invention discloses a selective maintenance decision method for a polymorphic system based on an improved mountain climbing algorithm, using the Kolmogorov equation to obtain the probability that the health state level of a component is k at the end of a task to be performed; using the probability to obtain the performance of the component at the end of the task to be performed; using the performance to obtain the performance expectation P of the polymorphic system at the end of the task to be performed; taking minimizing the overall maintenance time T of the polymorphic system as the objective function and taking the performance expectation P greater than the minimum performance required by the task to be performed as the constraint condition, a selective maintenance decision model for the polymorphic system is constructed; using the improved mountain climbing algorithm to solve the selective maintenance decision model, a maintenance strategy for the polymorphic system before performing the task to be performed is obtained. The present invention can minimize the overall maintenance time of the polymorphic system under the premise of ensuring that the performance of the polymorphic system after maintenance meets the requirements of the task to be performed.

Description

Technical Field

[0001] The invention relates to the technical field of reliability engineering, and more particularly to a multi-state system selective maintenance decision method based on an improved mountain climbing algorithm. Background Art

[0002] Complex polymorphic systems require preventive maintenance before performing tasks to ensure that the health status level of the system at any time during the task meets the minimum requirements, thereby ensuring the performance of the system; since the system has multiple states, non-intact maintenance needs to be considered.

[0003] Specifically in practical applications, complex polymorphic systems may include power supply systems, satellite communication systems, industrial manufacturing automation systems, and so on.

[0004] The power supply system includes subsystems such as power generation units, substations, transmission lines and load equipment. Each subsystem includes several components. Preventive maintenance of the components is required before performing the task to ensure the performance of the system. Since the components exist in various states, non-intact maintenance needs to be considered.

[0005] The satellite communication system includes subsystems such as satellites, ground stations and links. Each subsystem includes several components. Preventive maintenance of the components is required before performing the mission to ensure the performance of the system. Since the components exist in various states, non-intact maintenance needs to be considered.

[0006] Industrial manufacturing automation systems include subsystems such as machine units (such as robots, conveyor belts, processing equipment, etc.), control systems and sensors. Each subsystem includes several components. Preventive maintenance of components is required before performing tasks to ensure the performance of the system. Since components exist in various states, non-intact maintenance needs to be considered.

[0007] At present, due to the constraints of personnel and resources, the maintenance of complex multi-state systems requires the adoption of a selective maintenance strategy in maintenance decision-making, so as to save maintenance time as much as possible and ensure that the maintenance effect meets the needs.

[0008] Therefore, how to provide a selective maintenance decision method for a polymorphic system, which can minimize the overall maintenance time of the polymorphic system while ensuring that the performance of the polymorphic system after maintenance meets the requirements of the task to be performed, is an urgent problem to be solved by technical personnel in this field. Summary of the invention

[0009] In view of this, an object of the present invention is to provide a multi-state system selective maintenance decision method based on an improved mountain climbing algorithm.

[0010] In order to achieve the above object, the present invention adopts the following technical solution:

[0011] A selective maintenance decision method for a multi-state system based on an improved mountain climbing algorithm comprises the following steps:

[0012] S1: Use the Kolmogorov equation to obtain the components at the end of the task to be executed The probability of health status level k ; Among them, the components represents the jth element in the i-th subsystem of a polymorphic system; k is a positive integer; Indicates the time when the task to be executed ends;

[0013] S2: Using the probability Get the component when the task to be executed is finished Performance ;

[0014] S3: Utilizing the performance Obtain the expected performance P of the polymorphic system at the end of the task to be executed;

[0015] S4: Taking minimizing the total maintenance time T of the multi-state system as the objective function, the performance expectation P is greater than the minimum performance required for the task to be executed. As constraints, a selective maintenance decision model for multi-state systems is constructed;

[0016] S5: Solving the selective maintenance decision model using an improved mountain climbing algorithm to obtain a maintenance strategy for the polymorphic system before executing the task to be executed; wherein the improved mountain climbing algorithm combines a simulated annealing algorithm and a mountain climbing search algorithm.

[0017] Preferably, based on the formula Obtain ;

[0018] Will Substitution In t, the probability ;

[0019] in, Represents the component at time t The probability of health status level k; Display element The highest health status level; Display element A constant rate of transition from health state level m to health state level k; Represents the component at time t The probability of health status level m; Display element A constant rate of transition from health state level k to health state level m.

[0020] Preferably, the performance Based on the following formula:

[0021] ;

[0022] in, Represents the components in the maintenance strategy The health status level after repair; Display element Task capability at health level k.

[0023] Preferably, the performance expectation P is obtained based on the following formula:

[0024] ;

[0025] in, Indicates the number of subsystems included in the polymorphic system; Represents the number of components included in the i-th subsystem.

[0026] Preferably, the expression of the selective maintenance decision model is:

[0027] ;

[0028] in, Display element maintenance time.

[0029] Preferably, The calculation formula is:

[0030] ;

[0031] In the formula, Display element Fixed maintenance time; Display element Variable maintenance time; wherein the fixed maintenance time is determined by the component The variable maintenance time is determined by the type of component Maintenance level Decide.

[0032] Preferably, the element Maintenance level Component-based Health status before maintenance And components The highest health status level Sure;

[0033] element Maintenance level Divided into levels; among them, A value equal to 0 means no maintenance is performed; Equal to 1 means Restore to ; equal Indicates that Restore to .

[0034] Preferably, S5 specifically includes the following steps:

[0035] S51: Randomly initialize the target solution in the mountain climbing search algorithm; wherein the target solution is a set of health status levels of all components after maintenance;

[0036] Substitute the randomly initialized target solution into the selective maintenance decision model to determine whether it satisfies the constraints. ;

[0037] If satisfied, execute S52, if not satisfied, execute S54;

[0038] S52: Set the binary variable CS to 1;

[0039] S53: Select the component with the minimum maintenance efficiency E from all components that are not set as the no-maintenance strategy, and reduce its maintenance level by one level to update the target solution; substitute the updated target solution into the selective maintenance decision model to determine whether it does not meet the constraint conditions ; Repeat S53 until the constraint condition is not met Set the binary variable CS to 0, and then execute S56;

[0040] S54: Set the binary variable CS to 0;

[0041] S55: Select the component with the highest maintenance efficiency E from all components that are not in the highest health status level, and increase its maintenance level by one level to update the target solution, and substitute the updated target solution into the selective maintenance decision model to determine whether it meets the constraint conditions. ; Repeat S55 until the constraints are met Set the binary variable CS to 1, and then execute S56;

[0042] S56: Calculate the overall maintenance time corresponding to the current target solution , and initialize the initial temperature of the simulated annealing algorithm ;

[0043] S57: Randomly select a component and change its maintenance level to update the target solution; use the updated target solution and initial temperature Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, execute S59;

[0044] S58: taking the current target solution as the final health status level of each component after repair;

[0045] S59: Randomly select a component to change its maintenance level to achieve the update of the target solution and change the initial temperature Reduce to temperature ; Wherein, w represents the number of times S59 is executed, w={1, 2, 3...};

[0046] Using the updated target solution and temperature Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, repeat S59.

[0047] Preferably, the calculation formula of the maintenance efficiency E is:

[0048] ;

[0049] In the formula, represents the performance expectation after the target solution is updated in S53 or S55, represents the performance expectation before updating the target solution in S53 or S55; represents the overall maintenance time after the target solution is updated in S53 or S55; Indicates the total maintenance time before the target solution is updated in S53 or S55.

[0050] Preferably, the probability of the updated target solution being accepted in S57 is calculated based on the following formula:

[0051] ;

[0052] ;

[0053] ;

[0054] in, represents the probability of the updated target solution in S57 being accepted; Indicates the overall maintenance time calculated by S56; represents the overall maintenance time after the target solution is updated in S57; represents the performance expectation after updating the target solution in S57; Indicates the performance expectation before updating the target solution in S57; CS takes a value of 0 or 1.

[0055] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a selective maintenance decision method for a polymorphic system based on an improved mountain climbing algorithm, which can minimize the overall maintenance time of the polymorphic system while ensuring that the performance of the polymorphic system after maintenance meets the requirements of the task to be performed. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0057] Figure 1 The present invention provides a flowchart of a multi-state system selective maintenance decision-making method based on an improved mountain climbing algorithm. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] like Figure 1 As shown, the embodiment of the present invention discloses a multi-state system selective maintenance decision method based on an improved mountain climbing algorithm, comprising the following steps:

[0060] S1: Use the Kolmogorov equation to obtain the components at the end of the task to be executed The probability of health status level k ; Among them, the components represents the jth element in the i-th subsystem of a polymorphic system; k is a positive integer; Indicates the time when the task to be executed ends;

[0061] Furthermore, based on the formula Obtain ;

[0062] Will Substitution In t, the probability ;

[0063] in, Represents the component at time t The probability of health status level k; Display element The highest health status level; Display element A constant rate of transition from health state level m to health state level k; Represents the component at time t The probability of health status level m; Display element A constant rate of transition from health state level k to health state level m.

[0064] It can be understood that a polymorphic system consists of several subsystems, each of which consists of several components. The probability that the health status level of all components in the polymorphic system is k at the end of the task to be executed can be obtained.

[0065] S2: Using the probability Get the component when the task to be executed is finished Performance ;

[0066] Furthermore, the performance Based on the following formula:

[0067] ;

[0068] in, Represents the components in the maintenance strategy The health status level after repair; Display element Task capability at health level k ( is a known quantity).

[0069] S3: Utilizing the performance Obtain the expected performance P of the polymorphic system at the end of the task to be executed;

[0070] Furthermore, the performance expectation P is obtained based on the following formula:

[0071] ;

[0072] in, Indicates the number of subsystems included in the polymorphic system; Represents the number of components included in the i-th subsystem.

[0073] S4: Taking minimizing the total maintenance time T of the multi-state system as the objective function, the performance expectation P is greater than the minimum performance required for the task to be executed. As constraints, a selective maintenance decision model for multi-state systems is constructed;

[0074] Furthermore, the expression of the selective maintenance decision model is:

[0075] ;

[0076] in, Display element maintenance time.

[0077] Furthermore, The calculation formula is:

[0078] ;

[0079] In the formula, Display element Fixed maintenance time; Display element Variable maintenance time; wherein the fixed maintenance time is determined by the component The variable maintenance time is determined by the type of component Maintenance level Decide.

[0080] Furthermore, the components Maintenance level Component-based Health status before maintenance And components The highest health status level Sure;

[0081] element Maintenance level Divided into levels; among them, A value equal to 0 means no maintenance is performed; Equal to 1 means Restore to ; equal Indicates that Restore to .

[0082] It can be understood that: assuming that the health status level of a component is {1, 2, 3, 4, 5, 6, 7}, its current health status level (i.e., the health status level before maintenance) is 3, and the highest health status level is 7;

[0083] The maintenance level of the component It is divided into 5 levels; among them, A value equal to 0 means no maintenance is performed; If it is equal to 1, it means that the health level of the component is restored from 3 to 4; Equal to 2 means that the health level of the component is restored from 3 to 5; If it is equal to 3, it means that the health level of the component is restored from 3 to 6; When it is equal to 4, it means that the health status level of the component is restored from 3 to 7 (that is, restored to the highest health status level).

[0084] S5: Solving the selective maintenance decision model using an improved mountain climbing algorithm to obtain a maintenance strategy for the polymorphic system before executing the task to be executed; wherein the improved mountain climbing algorithm combines a simulated annealing algorithm and a mountain climbing search algorithm.

[0085] Furthermore, S5 specifically includes the following steps:

[0086] S51: Randomly initialize the target solution in the mountain climbing search algorithm; wherein the target solution is a set of health status levels of all components after maintenance;

[0087] Substitute the randomly initialized target solution into the selective maintenance decision model to determine whether it satisfies the constraints. ;

[0088] If satisfied, execute S52, if not satisfied, execute S54;

[0089] S52: Set the binary variable CS to 1;

[0090] S53: Select the component with the minimum maintenance efficiency E from all components that are not set as unmaintained, and reduce its maintenance level by one level to update the target solution; substitute the updated target solution into the selective maintenance decision model to determine whether it does not meet the constraint condition ; Repeat S53 until the constraint condition is not met Set the binary variable CS to 0, and then execute S56;

[0091] S54: Set the binary variable CS to 0;

[0092] S55: Select the component with the highest maintenance efficiency E from all components that are not in the highest health status level, and increase its maintenance level by one level to update the target solution, and substitute the updated target solution into the selective maintenance decision model to determine whether it meets the constraint conditions. ; Repeat S55 until the constraints are met Set the binary variable CS to 1, and then execute S56;

[0093] S56: Calculate the overall maintenance time corresponding to the current target solution , and initialize the initial temperature of the simulated annealing algorithm ;

[0094] S57: Randomly select a component and change its maintenance level to update the target solution; use the updated target solution and initial temperature Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, execute S59;

[0095] S58: taking the current target solution as the final health status level of each component after repair;

[0096] S59: Randomly select a component to change its maintenance level to achieve the update of the target solution and change the initial temperature Reduce to temperature ; Wherein, w represents the number of times S59 is executed, w={1, 2, 3...};

[0097] Using the updated target solution and temperature Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, repeat S59.

[0098] Furthermore, the calculation formula of maintenance efficiency E is:

[0099] ;

[0100] In the formula, represents the performance expectation after the target solution is updated in S53 or S55, represents the performance expectation before updating the target solution in S53 or S55; represents the overall maintenance time after the target solution is updated in S53 or S55; Indicates the total maintenance time before the target solution is updated in S53 or S55.

[0101] Furthermore, the probability of the updated target solution being accepted in S57 is calculated based on the following formula:

[0102] ;

[0103] ;

[0104] ;

[0105] in, represents the probability of the updated target solution in S57 being accepted; Indicates the overall maintenance time calculated by S56; represents the overall maintenance time after the target solution is updated in S57; represents the performance expectation after updating the target solution in S57; Indicates the performance expectation before updating the target solution in S57; CS takes a value of 0 or 1.

[0106] It can be understood that: if jumping from S53 to S56, the CS value is 0; if jumping from S55 to S56, the CS value is 1;

[0107] Further, the probability of the updated target solution being accepted in S59 is calculated based on the following formula:

[0108] ;

[0109] ;

[0110] ;

[0111] in, represents the probability of the target solution being accepted after the w-th update in S59; Indicates the overall maintenance time calculated by S56; represents the total maintenance time after the w-th update of the target solution in S59; represents the performance expectation after the w-th update of the target solution in S59; Represents the performance expectation before the w-th update of the target solution in S59; CS takes the value of 0 or 1.

[0112] It can be understood that: if jumping from S53 to S56, the CS value is 0; if jumping from S55 to S56, the CS value is 1.

[0113] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0114] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A selective maintenance decision method for a multi-state system based on an improved mountain climbing algorithm, characterized in that: The following steps are involved: S1: Use the Kolmogorov equation to obtain the component C at the end of the task to be executed ij The probability p of health status level k ij，k (t end ); wherein component C ij represents the jth element in the i-th subsystem of a polymorphic system; k is a positive integer; t end Indicates the time when the task to be executed ends; Specific: Based on the formula Find p ij，k (t); t end Substitute p ij，k (t) in t, obtain the probability p ij，k (t end ); Among them, p ij，k (t) represents the component C at time t ij The probability of health status level k; Indicates component C ij The highest health status level; Indicates component C ij A constant transition rate from health state level m to health state level k; p ij，m (t) represents the component C at time t ij The probability of health status level m; Indicates component C ij A constant rate of transition from health state level k to health state level m; S2: Using the probability p ij，k (t end ) Get component C when the task to be executed is completed ij Performance Specific: The performance Based on the following formula: in, Represents the component C in the maintenance strategy ij The health status level after repair; Indicates component C ij Mission capability at health status level k; S3: Utilizing the performance Obtain the expected performance P of the polymorphic system at the end of the task to be executed; Specifically: the performance expectation P is obtained based on the following formula: Among them, N s Indicates the number of subsystems included in the polymorphic system; N i represents the number of components included in the i-th subsystem; S4: Taking minimizing the total maintenance time T of the multi-state system as the objective function, the performance expectation P is greater than the minimum performance P required for the task to be executed. min As constraints, a selective maintenance decision model for multi-state systems is constructed; Specifically: The expression of the selective maintenance decision model is: subject to:P>P min Among them, t ij Indicates component C ij Maintenance time; S5: solving the selective maintenance decision model using an improved mountain climbing algorithm to obtain a maintenance strategy for the polymorphic system before executing the task to be executed; wherein the improved mountain climbing algorithm combines a simulated annealing algorithm and a mountain climbing search algorithm; S5 specifically includes the following steps: S51: randomly initializing the target solution in the hill climbing search algorithm; wherein the target solution is a set of health status levels of all components after maintenance; Substitute the randomly initialized target solution into the selective maintenance decision model to determine whether it satisfies the constraint condition P>P min ; If satisfied, execute S52, if not satisfied, execute S54; S52: Set the binary variable CS to 1; S53: Select the component with the lowest maintenance efficiency E from all components that are not set as the no-maintenance strategy, and reduce its maintenance level by one level to update the target solution; substitute the updated target solution into the selective maintenance decision model to determine whether it does not satisfy the constraint condition P>P min ; Repeat S53 until the constraint condition P>P is not satisfied min Set the binary variable CS to 0, and then execute S56; S54: Set the binary variable CS to 0; S55: Select the component with the highest maintenance efficiency E from all components that are not in the highest health status level, and increase its maintenance level by one level to update the target solution. Substitute the updated target solution into the selective maintenance decision model to determine whether it satisfies the constraint condition P>P min ; Repeat S55 until the constraint condition P>P is satisfied min Set the binary variable CS to 1, and then execute S56; S56: Calculate the overall maintenance time T(best) corresponding to the current target solution and initialize the initial temperature T of the simulated annealing algorithm p ; S57: Randomly select a component and change its maintenance level to update the target solution; use the updated target solution and initial temperature T p Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, execute S59; S58: taking the current target solution as the final health status level of each component after repair; S59: Randomly select a component and change its maintenance level to achieve the update of the target solution, and change the initial temperature T p Reduce to temperature α w *T p ; Wherein, w represents the number of times S59 is executed, w={1, 2, 3...}; Using the updated target solution and temperature α w *T p Calculate the probability of the updated target solution being accepted; if the probability of the updated target solution being accepted is within the randomly generated numerical range, execute S58; if the probability of the updated target solution being accepted is not within the randomly generated numerical range, repeat S59.

2. The method for selective maintenance decision of a multi-state system based on an improved mountain climbing algorithm according to claim 1, characterized in that: t ij The calculation formula is: In the formula, Indicates component C ij Fixed maintenance time; Indicates component C ij Variable maintenance time; wherein the fixed maintenance time is composed of element C ij The variable maintenance time is determined by the type of component C ij The maintenance level l determines the maintenance level.

3. The method for selective maintenance decision of a multi-state system based on an improved mountain climbing algorithm according to claim 2, characterized in that: Component C ij Maintenance level, based on component C ij Health status before maintenance And component C ij The highest health status level Sure; Component C ij Maintenance level Divided into where l = 0 means no maintenance is performed; l = 1 means Restore to l is equal to Indicates that Restore to 4. According to the method for selective maintenance decision-making of a multi-state system based on an improved mountain climbing algorithm as claimed in claim 1, the calculation formula of the maintenance efficiency E is: E=(P(new)-P(old))(T(new)-T(old)); Wherein, P(new) represents the expected performance after the target solution is updated in S53 or S55, and P(old) represents the expected performance before the target solution is updated in S53 or S55; T(new) represents the total maintenance time after the target solution is updated in S53 or S55; T(old) represents the total maintenance time before the target solution is updated in S53 or S55.

5. The method for selective maintenance decision of a multi-state system based on an improved mountain climbing algorithm according to claim 1, characterized in that: The probability of the updated target solution being accepted in S57 is calculated based on the following formula: ΔT′=T(new′)-T(best); ΔP′=|P(new′)-P(old′)|; Among them, P sa represents the probability of accepting the updated target solution in S57; T(best) represents the overall maintenance time calculated in S56; T(new) represents the overall maintenance time after the target solution is updated in S57; p(new′) represents the performance expectation after the target solution is updated in S57; P(old′) represents the performance expectation before the target solution is updated in S57; CS takes the value of 0 or 1.

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