Numerical control machine tool multistage maintenance strategy optimization method considering fault correlation

Abstract

The invention discloses a numerical control machine tool multi-stage maintenance strategy optimization method considering fault correlation, which comprises the following steps: acquiring a historical fault data record of a numerical control machine tool, and performing fault correlation analysis on each subsystem of the numerical control machine tool; reliability modeling is carried out on each subsystem, and a reliability model under fault independence is established; establishing a comprehensive fault rate model considering fault correlation; determining the optimal preventative maintenance frequency and the optimal reliability by taking the minimum maintenance cost rate in unit time as a target; a multi-stage maintenance mode is introduced, the minimum maintenance cost rate and the maximum availability serve as targets, and a numerical control machine tool multi-target opportunity maintenance model considering fault correlation is established; and optimizing the multi-target opportunity maintenance model to obtain an optimal opportunity maintenance threshold value of each subsystem and a corresponding optimal maintenance cost rate and availability, and determining an optimal maintenance plan. The fault correlation in the subsystem is considered, the maintenance cost is reduced, the usability is improved, and the optimal maintenance strategy of the numerical control machine tool is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability maintenance, and in particular to a method for optimizing a multi-level maintenance strategy for a CNC machine tool considering fault correlation. Background Art

[0002] In recent years, with the rapid development of my country's manufacturing industry, CNC machine tools have become an indispensable core equipment in modern industrial production. Its efficient and precise processing capabilities are crucial to improving production efficiency and product quality. However, CNC machine tools often fail during long-term operation due to factors such as complex working environment, human operating errors, and aging of parts. These failures not only cause machine tool shutdowns and affect production progress, but may also cause equipment damage and economic losses. At present, the maintenance of CNC machine tools mainly relies on a combination of regular inspections and post-repairs. However, this traditional maintenance model has some obvious shortcomings, such as high maintenance costs and unreasonable maintenance frequency, which may lead to over-maintenance or under-maintenance. Therefore, in order to improve the operating reliability and maintenance efficiency of CNC machine tools, it is urgent to conduct an in-depth analysis of the laws in the maintenance process, and formulate more reasonable and effective maintenance strategies guided by scientific maintenance theories. Therefore, studying and implementing advanced maintenance strategies is of great practical significance for improving the maintenance level of CNC machine tools, reducing failure rates, and ensuring production stability.

[0003] Preventive maintenance is a strategy for pre-inspection and maintenance of CNC machine tools before a failure occurs. It ensures that the equipment is always in the best operating state by promptly discovering signs of potential failures. Opportunistic maintenance is based on the maintenance and economic correlation between subsystems, allowing multiple subsystems to be repaired simultaneously at the right time to improve maintenance efficiency. However, this maintenance method often ignores the correlation between subsystems, while there is a coupling effect of correlation in actual operation. Under the influence of correlation, the failure rate of subsystems changes differently. Ignoring the correlation between subsystems will make it difficult to reasonably estimate the changes in component reliability and the number of random failures. Summary of the invention

[0004] In order to overcome the shortcomings of the above technologies, the present invention provides a method for optimizing the multi-level maintenance strategy of CNC machine tools considering fault correlation. The present invention aims at the problems of single maintenance mode of CNC machine tools, excessive maintenance of components and little consideration of subsystem correlation. On the basis of meeting the operational reliability, the present invention fully considers the fault correlation within the subsystem, reduces the maintenance cost and improves the availability, so as to effectively obtain the best maintenance strategy for CNC machine tools.

[0005] Terminology explanation:

[0006] 1. TOPSIS: Technique for Order of Preference by Similarity to Ideal Solution, which is a method of multiple attribute decision making.

[0007] The technical solution adopted by the present invention to overcome the technical problems is:

[0008] A method for optimizing a multi-level maintenance strategy for a CNC machine tool considering fault correlation comprises the following steps:

[0009] S1. Obtain historical fault data records of CNC machine tools and perform fault correlation analysis on each subsystem of the CNC machine tool;

[0010] S2. According to the historical fault data of CNC machine tools, reliability modeling is performed on each subsystem to establish a reliability model under independent faults;

[0011] S3, according to the reliability model under independent faults obtained in step S2, calculate the fault correlation coefficients between subsystems, and use the fault chain theory to establish a comprehensive failure rate model considering fault correlation;

[0012] S4. Introduce a multi-level maintenance model, with the goal of minimizing the maintenance cost rate per unit time, and determine the optimal number of preventive maintenance and the best reliability;

[0013] S5. Taking the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is established based on the optimal preventive maintenance strategy of the subsystem;

[0014] S6. Use a multi-objective genetic algorithm to optimize the multi-objective opportunity maintenance model obtained in step S5, so as to obtain the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability, and determine the optimal maintenance plan through a multi-attribute decision-making method.

[0015] Furthermore, step S1 specifically includes the following:

[0016] S11, obtaining historical fault data records of the CNC machine tool, and classifying and counting the historical fault data of the CNC machine tool according to different subsystems, calculating the fault interval time of each subsystem, and performing fault correlation analysis on the subsystems of the CNC machine tool;

[0017] S12. Collect statistics on the related fault data of the CNC machine tool subsystems, clarify the hierarchical structure of the fault transmission direction of the subsystems for the fault correlation existing in the subsystems.

[0018] Furthermore, step S2 specifically includes the following:

[0019] The failure data of CNC machine tools conforms to the Weibull distribution law. The Weibull distribution model is used for parameter estimation to obtain the reliability model of each subsystem under independent failure, including the failure rate function and reliability function , which is expressed as follows:

[0020] (1)

[0021] R(t)=exp[-( t or ) β ] (2)

[0022] In formula (1) and formula (2), represents the shape parameter and ; represents the scale parameter and ; Indicates the running time.

[0023] Furthermore, step S3 specifically includes the following:

[0024] S31. The correlation between fault-related subsystems is studied through the Gumbel Copula function, the fault correlation coefficient between subsystems is calculated, and then the fault joint distribution function of fault-related subsystems is established. The expression is as follows:

[0025] C(θ; u 1 , u 2 )= exp -[(- ln u 1 ) i +(- ln u 2 ) i ] 1 / θ (3)

[0026] In formula (3), It indicates the correlation between variables. The value range of is [1,+∞); and represents two variables; when When it approaches +∞, the variable With variables tends to be completely correlated; when When With variables Independent of each other;

[0027] S32, Converted to [0,1], the fault correlation coefficient is obtained. According to the fault chain theory, when the subsystem Other subsystems When the subsystem The comprehensive failure rate model is expressed as follows:

[0028] (4)

[0029] In formula (4), and Represents subsystems and subsystems The comprehensive failure rate; Representation Subsystem Independent failure rate; Representation Subsystem Subsystem The fault correlation coefficient of the action; when the subsystem Subsystem When there is a fault correlation, 0 ≤ ≤ 1; when the subsystem Subsystem If there is no fault correlation, =0, then .

[0030] Further, step S4 includes the following:

[0031] Introduce multi-level incomplete preventive maintenance strategies for each subsystem and establish a comprehensive failure rate evolution model;

[0032] When the subsystem reaches the specified reliability threshold, the preventive maintenance method is multi-level incomplete maintenance, and the failure rate of the CNC machine tool is improved; when a sudden failure occurs during the preventive maintenance cycle, the maintenance method is minor repair, which does not change the failure rate of the CNC machine tool;

[0033] Taking the minimum maintenance cost rate per unit time as the objective function, the maintenance cost rate per unit time of the subsystem based on reliability during the operating time is calculated to determine the optimal number of preventive maintenance times and the best reliability within the maintenance cycle of the subsystem.

[0034] Furthermore, step S4 specifically includes the following:

[0035] S41. Introduce an incomplete preventive maintenance strategy for each subsystem and establish a comprehensive failure rate evolution model, that is, add an age attenuation model and a failure rate increase model; then the subsystem No. Evolution model of comprehensive failure rate after incomplete maintenance for:

[0036] (5)

[0037] In formula (5), The value of ; The value of ,in, represents the optimal number of preventive maintenance; Representation Subsystem No. The interval between preventive maintenance; Representation Subsystem No. The failure rate function for each preventive maintenance is: and Represents subsystems The service age attenuation factor and failure rate increase factor of 1, ;

[0038] S42. When the reliability of a subsystem drops to a specified reliability threshold, preventive maintenance of the subsystem is required. The failure rate function is proportional to the specified reliability threshold. The relationship between them satisfies the following formula:

[0039] (6)

[0040] (7)

[0041] In formula (6) and formula (7), Indicates Failure rate function at the time of preventive maintenance;

[0042] S43, adopt multi-level preventive maintenance to perform maintenance work, divided into primary maintenance and advanced maintenance, and determine the optimal number of preventive maintenance with the minimum maintenance cost rate per unit time as the objective function, then the subsystem Maintenance cost rate per unit time based on reliability during operation time , which is expressed as follows:

[0043] (8)

[0044] In formula (8), It represents the cost of minor repair for a single sudden failure; represents the optimal preventive maintenance threshold; represents the replacement cost; For preventive maintenance costs; for downtime; represents the unit downtime cost; represents the fault impact factor; represents the risk cost per failure; It represents the sum of maintenance time, replacement time and normal working time; among which, , and They are respectively expressed as follows:

[0045] & C p = ∑ i=1 N [(1- oh i ) c j + oh i c s ] & oh i = 0 1 (9)

[0046] T= ∑ i=1 N T i + t r + ∑ i=1 N-1 [(1- oh i ) t j + oh i t s ]+N⋅(- ln R best )⋅ t cm (10)

[0047] T d = T fd + T pd + T rd =N⋅(- ln R best )⋅ t cm + t r + ∑ i=1 N-1 [(1- oh i ) t j + oh i t s ] (11)

[0048] Formula (9)-Formula (11), Indicates the preventive maintenance mode, 0 indicates primary maintenance, 1 indicates advanced maintenance, and the maintenance mode is selected by comparing the ratio of maintenance cost of different levels of investment to the failure rate recovery value; and They represent the cost of primary maintenance and the cost of advanced maintenance respectively; and They represent primary maintenance time and advanced maintenance time respectively; Indicates The interval between preventive maintenance; Indicates replacement time; Indicates the unit minor repair time; Indicates the total minor repair time; Indicates the replacement time; Indicates preventive maintenance time;

[0049] right Perform minimization calculation when When the minimum value is obtained, the optimal number of preventive maintenance times within the subsystem maintenance cycle is determined. and the optimal preventive maintenance threshold .

[0050] Further, step S5 includes the following:

[0051] Based on the optimal preventive maintenance strategy of a single subsystem, the idea of ​​opportunistic maintenance is introduced. When a subsystem in the whole machine undergoes preventive maintenance or replacement, it is determined whether the remaining subsystems undergo opportunistic maintenance.

[0052] Establish an opportunity maintenance model of CNC machine tools with minimum maintenance cost rate based on reliability within a limited operating time domain;

[0053] Establish an opportunistic maintenance model of CNC machine tools with maximum availability based on reliability within a limited operating time domain;

[0054] With the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is finally obtained.

[0055] Furthermore, step S5 specifically includes the following:

[0056] S51. When a subsystem in the whole machine is undergoing preventive maintenance or replacement, the remaining subsystems are given a maintenance opportunity due to maintenance shutdown, and it is determined whether the remaining subsystems are undergoing opportunistic maintenance;

[0057] S52, CNC machine tools in the limited operating time domain [0,T] The opportunity maintenance model based on the maintenance cost rate per unit time of reliability is:

[0058] (12)

[0059] In formula (12), Indicates the number of subsystems; Representation Subsystem Number of preventive maintenance shutdowns; represents direct maintenance cost; Representation Subsystem Equivalent reliability life cost; Representation Subsystem Conduct the Instantaneous reliability during second-chance preventive maintenance; Representation Subsystem The optimal reliability threshold of

[0060] Direct repair costs Included subsystems Preventive maintenance costs , minimum maintenance cost and replacement costs ;

[0061] & C pk = ∑ i=1 m k [(1- oh k,i )( c p y + t p y c d )+ oh k,i ( c p s + t p s c d )] & oh k,i = 0 1 (13)

[0062] C mk = c cm ∑ i=1 m k [ ∫ 0 T i l k,i (t)dt] (14)

[0063] (15)

[0064] Formula (13)-Formula (15), Representation Subsystem In the The preventive maintenance method, 0 represents primary maintenance, 1 represents advanced maintenance; It represents the cost of a single primary repair; Indicates the cost of a single advanced repair; Indicates primary maintenance downtime; downtime for advanced maintenance; Representation Subsystem In the Failure rate at the time of first repair;

[0065] S53, CNC machine tools in the limited operating time domain [0,T] The opportunistic maintenance model with maximum availability based on reliability is:

[0066] A R =1- ∑ k=1 M [ n r ⋅ t cm ∑ i=1 N k ∫ 0 T i l k,i t dt+ t r ∑ i=1 q ∫ 0 T i l k,i t dt+ t pk ] T (16)

[0067] In formula (16), Representation Subsystem The optimal number of preventive maintenance; Represents a subsystem in a finite runtime domain Number of preventive replacements; Representation Subsystem The number of preventive maintenance operations during the remaining time after the last preventive replacement; Representation Subsystem The downtime for preventive maintenance is the longest maintenance time in the maintenance subsystem;

[0068] In order to unify the function objective minimization, the maximum availability model is transformed into the minimum unavailability model, which is expressed as follows:

[0069] = ∑ k=1 M [ n r ⋅ t cm ∑ i=1 N k ∫ 0 T i l k,i t dt+ t r ∑ i=1 q ∫ 0 T i l k,i t dt+ t pk ] T (17)

[0070] S54. Finally, the multi-objective opportunistic maintenance model of CNC machine tools considering fault correlation is obtained as follows:

[0071] (18).

[0072] Furthermore, in step S51, the reliability of the subsystem is used as a criterion to determine whether the remaining subsystems can be repaired opportunistically, as follows:

[0073] (1) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem If no fault occurs, no maintenance measures will be taken; and Represents subsystems The start and end time of the run, Represents the reliability function of the CNC machine tool subsystem over time, represents the reliability threshold corresponding to the opportunity maintenance of each subsystem, Indicates the upper limit of the reliability threshold corresponding to the opportunistic maintenance of each subsystem;

[0074] (2) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem No failure has occurred, but the subsystem For preventive maintenance, the subsystem Follow Perform one-opportunity repairs;

[0075] (3) When subsystem Run to After the time, , then the subsystem must be preventive maintenance.

[0076] Further, step S6 includes the following:

[0077] S61. According to the maintenance mode of each subsystem, determine the preventive maintenance time, calculate the maintenance cost rate and unavailability of the CNC machine tool, use a multi-objective genetic algorithm to optimize the objective function, and determine the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability solution set;

[0078] S62. Through the multi-attribute decision-making method, the optimal maintenance plan is determined by distinguishing the advantages and disadvantages based on the evaluation index and the approximate distance between the optimal ideal solution.

[0079] The beneficial effects of the present invention are:

[0080] The present invention uses historical fault data of CNC machine tools to analyze the fault correlation between subsystems, considers the fault risk cost and the penalty cost of incomplete reliability utilization, adopts a multi-level maintenance model, achieves a large improvement in failure rate with a small investment cost, and considers opportunistic maintenance. The maintenance events that meet the interval conditions are integrated to construct a multi-objective opportunistic maintenance model for CNC machine tools that considers fault correlation, reasonably estimates the reliability change, avoids the deviation of the maintenance strategy from the actual situation, and takes into account the trade-off between reliability, availability and maintenance cost, providing more options for maintenance strategies and better meeting resource constraints and customer preferences. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 The present invention is a flowchart of a method for optimizing a multi-level maintenance strategy for a CNC machine tool taking fault correlation into consideration according to an embodiment of the present invention.

[0082] Figure 2 A fault relationship transfer diagram described in an embodiment of the present invention.

[0083] Figure 3 It is a comparison diagram of the comprehensive failure rate function and the independent failure rate function of the feeding system described in the embodiment of the present invention.

[0084] Figure 4 This is a schematic diagram of the opportunistic maintenance principle described in an embodiment of the present invention.

[0085] Figure 5 This is a schematic diagram of the relationship between the maintenance cost of a CNC machine tool and a subsystem opportunity maintenance threshold according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to facilitate those skilled in the art to better understand the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The following is only exemplary and does not limit the protection scope of the present invention.

[0087] The present invention discloses a method for optimizing a multi-level maintenance strategy for a CNC machine tool considering fault correlation, comprising the following steps:

[0088] S1. Obtain historical fault data records of CNC machine tools and perform fault correlation analysis on each subsystem of the CNC machine tool;

[0089] S2. According to the historical fault data of CNC machine tools, reliability modeling is performed on each subsystem to establish a reliability model under independent faults;

[0090] S3, according to the reliability model under independent faults obtained in step S2, calculate the fault correlation coefficients between subsystems, and use the fault chain theory to establish a comprehensive failure rate model considering fault correlation;

[0091] S4. Introduce a multi-level maintenance model, with the goal of minimizing the maintenance cost rate per unit time, and determine the optimal number of preventive maintenance and the best reliability;

[0092] S5. Taking the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is established based on the optimal preventive maintenance strategy of the subsystem;

[0093] S6. Use a multi-objective genetic algorithm to optimize the multi-objective opportunity maintenance model obtained in step S5, so as to obtain the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability, and determine the optimal maintenance plan through a multi-attribute decision-making method.

[0094] In order to better understand the above technical solution, the exemplary embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. These are only exemplary embodiments of the present invention. However, it should be understood that the present invention can also be implemented in various forms and is not limited to the embodiments described herein. These embodiments are intended to enable those skilled in the art to understand the present invention more clearly and thoroughly.

[0095] The present embodiment describes a method for optimizing a multi-level maintenance strategy for a CNC machine tool considering fault correlation, such as Figure 1 As shown, the following steps are included:

[0096] S1. Obtain the historical fault data records of the CNC machine tool and perform fault correlation analysis on each subsystem of the CNC machine tool.

[0097] In this embodiment, step S1 specifically includes the following:

[0098] S11. Obtain historical fault data records of the CNC machine tool, classify and count the historical fault data of the CNC machine tool according to different subsystems, calculate the fault interval time of each subsystem, and perform fault correlation analysis on the subsystems of the CNC machine tool.

[0099] S12. Count the associated fault data of CNC machine tool subsystems. For the fault correlation of subsystems, the hierarchical structure of the subsystem fault transmission direction is clarified based on the associated fault analysis and directed graph theory. Taking the four subsystems of electrical system E, hydraulic system D, tool magazine F and feed system J as examples, the fault relationship transmission diagram between them is given, as shown in Figure 2 shown.

[0100] S2. According to the historical failure data of CNC machine tools, reliability modeling is performed on each subsystem separately to establish a reliability model under independent failure.

[0101] In this embodiment, step S2 specifically includes:

[0102] The failure data of CNC machine tools conforms to the Weibull distribution law. The Weibull distribution model is used for parameter estimation to obtain the parameters and failure rate functions corresponding to the four subsystems, as shown in Table 1.

[0103] Table 1 Distribution parameters and failure rate function table of four subsystems

[0104]

[0105] S3. According to the reliability model under independent faults obtained in step S2, the fault correlation coefficients between subsystems are calculated, and a comprehensive failure rate model considering fault correlation is established using the fault chain theory.

[0106] In this embodiment, step S3 specifically includes the following:

[0107] S31. The correlation between fault-related subsystems is studied through the Gumbel Copula function, the fault correlation coefficient between subsystems is calculated, and then the fault joint distribution function of fault-related subsystems is established. The expression is as follows:

[0108] C(θ; u 1 , u 2 )= exp -[(- ln u 1 ) i +(- ln u 2 ) i ] 1 / θ (1)

[0109] In formula (1), It indicates the correlation between variables. The value range of is [1,+∞); and represents two variables; when When it approaches +∞, the variable With variables tends to be completely correlated; when When With variables Independent of each other.

[0110] The Kendall rank correlation coefficient is introduced, and the fault distribution function under fault independence is used as the marginal distribution function value to solve the Kendall rank correlation coefficient of the fault-related subsystem. Then, according to the rank correlation coefficient and the Gumbel Copula function, the element relationship is determined ;

[0111] (2)

[0112] (3)

[0113] In formula (2) and formula (3), represents the generator of the Gumbel Copula function, Express A derivative of ;

[0114] Combining formulas (2) and (3), we can get the unknown parameters The expression is:

[0115] (4).

[0116] S32, Converted to [0,1], the fault correlation coefficient is obtained. Taking the feed system J as an example, the feed system J is affected by the electrical system E and the hydraulic system D. The fault correlation coefficient of the electrical system E on the feed system J is =0.1565, the fault correlation coefficient of the hydraulic system D on the feed system J =0.1174, after the fault correlation coefficient is brought in, the comprehensive failure rate function of the feed system J is for:

[0117] 0.00013 +0.00015 (5)

[0118] The comprehensive failure rate function and independent failure rate function of feed system J are compared as follows: Figure 3 As shown, it can be seen that the failure rate function considering fault correlation grows faster than the failure rate function under fault independence.

[0119] S4. Introduce a multi-level maintenance model, with the goal of minimizing the maintenance cost rate per unit time, and determine the optimal number of preventive maintenance times and the best reliability.

[0120] In this embodiment, step S4 specifically includes the following:

[0121] S41. Introduce an incomplete preventive maintenance strategy for each subsystem and establish a comprehensive failure rate evolution model, that is, add an age attenuation model and a failure rate increase model; then the subsystem No. Evolution model of comprehensive failure rate after incomplete maintenance for:

[0122] (6)

[0123] In formula (6), The value of ; The value of ,in, represents the optimal number of preventive maintenance; Representation Subsystem No. The interval between preventive maintenance; Representation Subsystem No. The failure rate function for each preventive maintenance is: and Represents subsystems The service age attenuation factor and failure rate increase factor of 1, .

[0124] S42. When the reliability of a subsystem drops to a specified reliability threshold, preventive maintenance of the subsystem is required. The failure rate function is proportional to the specified reliability threshold. The relationship between them satisfies the following formula:

[0125] (7)

[0126] (8)

[0127] In formula (7) and formula (8), Indicates Failure rate function of each preventive maintenance visit.

[0128] S43, adopt multi-level preventive maintenance to perform maintenance work, divided into primary maintenance and advanced maintenance, and determine the optimal number of preventive maintenance with the minimum maintenance cost rate per unit time as the objective function, then the subsystem Maintenance cost rate per unit time based on reliability during operation time , which is expressed as follows:

[0129] (9)

[0130] In formula (9), It represents the cost of minor repair for a single sudden failure; represents the optimal preventive maintenance threshold; represents the replacement cost; For preventive maintenance costs; for downtime; represents the unit downtime cost; represents the fault impact factor; represents the risk cost per failure; It represents the sum of maintenance time, replacement time and normal working time; among which, , and They are respectively expressed as follows:

[0131] & C p = ∑ i=1 N [(1- oh i ) c j + oh i c s ] & oh i = 0 1 (10)

[0132] T= ∑ i=1 N T i + t r + ∑ i=1 N-1 [(1- oh i ) t j + oh i t s ]+N⋅(- ln R best )⋅ t cm (11)

[0133] T d = T fd + T pd + T rd =N⋅(- ln R best )⋅ t cm + t r + ∑ i=1 N-1 [(1- oh i ) t j + oh i t s ] (12)

[0134] Formula (10)-Formula (12), Indicates the preventive maintenance mode, 0 indicates primary maintenance, 1 indicates advanced maintenance, and the maintenance mode is selected by comparing the ratio of maintenance cost of different levels of investment to the failure rate recovery value; and They represent the cost of primary maintenance and the cost of advanced maintenance respectively; and They represent primary maintenance time and advanced maintenance time respectively; Indicates The interval between preventive maintenance; Indicates replacement time; Indicates the unit minor repair time; Indicates the total minor repair time; Indicates the replacement time; Indicates preventive maintenance time;

[0135] right Perform minimization calculation when When the minimum value is obtained, the optimal number of preventive maintenance times within the subsystem maintenance cycle is determined. and the optimal preventive maintenance threshold , that is, the optimal reliability is represented by the optimal preventive maintenance threshold.

[0136] S5. Taking the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is established based on the optimal preventive maintenance strategy of the subsystem.

[0137] In this embodiment, step S5 specifically includes:

[0138] S51. Based on the optimal number of preventive maintenance of subsystems, the idea of ​​opportunistic maintenance is introduced. When a subsystem in the whole machine undergoes preventive maintenance or replacement, the remaining subsystems are given a maintenance opportunity due to maintenance shutdown, and it is determined whether the remaining subsystems can undergo opportunistic maintenance. Specifically, the reliability of the subsystem is used as the criterion to determine whether the remaining subsystems can undergo opportunistic maintenance. The principle of opportunistic maintenance is as follows: Figure 4 As shown, the details are as follows:

[0139] (1) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem If no fault occurs, no maintenance measures will be taken; and Represents subsystems The start and end time of the run, Represents the reliability function of the CNC machine tool subsystem over time, represents the reliability threshold corresponding to the opportunity maintenance of each subsystem, It represents the upper limit of reliability threshold corresponding to the opportunity maintenance of each subsystem. Indicates the time domain in which each subsystem can be repaired opportunistically;

[0140] (2) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem No failure has occurred, but the subsystem For preventive maintenance, the subsystem Follow Perform one-opportunity repairs;

[0141] (3) When subsystem Run to After the time, , then the subsystem must be preventive maintenance.

[0142] S52, CNC machine tools in the limited operating time domain [0,T] Opportunity maintenance model based on the maintenance cost rate per unit time of reliability for:

[0143] (13)

[0144] In formula (13), Indicates the number of subsystems; Representation Subsystem Number of preventive maintenance shutdowns; represents direct maintenance cost; Representation Subsystem Equivalent reliability life cost; Representation Subsystem Conduct the Instantaneous reliability during second-chance preventive maintenance; Representation Subsystem The optimal reliability threshold of

[0145] Direct repair costs Included subsystems Preventive maintenance costs , minimum maintenance cost and replacement costs ;

[0146] & C pk = ∑ i=1 m k [(1- oh k,i )( c p y + t p y c d )+ oh k,i ( c p s + t p s c d )] & oh k,i = 0 1 (14)

[0147] C mk = c cm ∑ i=1 m k [ ∫ 0 T i l k,i (t)dt] (15)

[0148] (16)

[0149] Formula (14)-Formula (16), Representation Subsystem In the The preventive maintenance method, 0 represents primary maintenance, 1 represents advanced maintenance; It represents the cost of a single primary repair; Indicates the cost of a single advanced repair; Indicates primary maintenance downtime; downtime for advanced maintenance; Representation Subsystem In the Failure rate during maintenance.

[0150] S53, CNC machine tools in the limited operating time domain [0,T] Opportunistic maintenance model based on reliability and maximum availability for:

[0151] A R =1- ∑ k=1 M [ n r ⋅ t cm ∑ i=1 N k ∫ 0 T i l k,i t dt+ t r ∑ i=1 q ∫ 0 T i l k,i t dt+ t pk ] T (17)

[0152] In formula (17), Representation Subsystem The optimal number of preventive maintenance; Represents a subsystem in a finite runtime domain Number of preventive replacements; Representation Subsystem The number of preventive maintenance operations during the remaining time after the last preventive replacement; Representation Subsystem The downtime for preventive maintenance is the longest maintenance time in the maintenance subsystem;

[0153] In order to unify the function objective minimization, the maximum availability model is transformed into the minimum unavailability model , which is expressed as follows:

[0154] = ∑ k=1 M [ n r ⋅ t cm ∑ i=1 N k ∫ 0 T i l k,i t dt+ t r ∑ i=1 q ∫ 0 T i l k,i t dt+ t pk ] T (18)

[0155] S54. Finally, the multi-objective opportunistic maintenance model of CNC machine tools considering fault correlation is obtained as follows:

[0156] (19).

[0157] S6. Use a multi-objective genetic algorithm to optimize the multi-objective opportunity maintenance model obtained in step S5, so as to obtain the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability, and determine the optimal maintenance plan through a multi-attribute decision-making method.

[0158] Specifically, in step S6, a multi-objective genetic algorithm is used to optimize and solve the multi-objective opportunity maintenance model obtained in step S5. The specific solution process is as follows:

[0159] (1) Clarify the subsystem maintenance time and maintenance cost parameters and solve the optimal preventive maintenance plan;

[0160] (2) Set the initial opportunity maintenance threshold. When the preventive maintenance time comes, a choice is made based on the maintenance method, and it is determined whether other subsystems are undergoing opportunistic maintenance at the same time. If so, the number of the corresponding maintenance method is increased by 1; otherwise, only the subsystem Preventive maintenance;

[0161] (3) According to the maintenance method of each subsystem, the longest maintenance time is selected as the downtime of this system, and the next subsystem preventive maintenance time is updated after this downtime.

[0162] (4) Continuously looping step (2) to step (3), and when the running time is greater than the specified running cycle, stopping the loop;

[0163] (5) Calculate the maintenance cost rate and unavailability, change different opportunity maintenance thresholds for iteration, recalculate steps (2) to (5), and find the optimal opportunity maintenance threshold and the corresponding maintenance cost rate and unavailability.

[0164] Reliability threshold for opportunistic maintenance Related to the advance maintenance time of the subsystem, such as Figure 5 As shown, The larger it is, the more the preventive maintenance time will be advanced relative to the original schedule, which will lead to an increase in preventive maintenance costs and excessive maintenance; The smaller it is, the less effective the preventive maintenance will be, and the fault repair cost and downtime will also increase. Based on the multi-objective opportunity maintenance model solution process, a multi-objective genetic algorithm is used to optimize the two objective functions of maintenance cost rate and unavailability, and output the optimal opportunity maintenance threshold and the corresponding minimum maintenance cost rate and minimum unavailability. Since the sum of availability and unavailability is 1, the minimum unavailability is also determined by the availability; the multi-objective optimization solution obtains a set of optimal solutions, which are equal to each other, so an objective evaluation method can be used to select the expected global optimal solution. TOPSIS is a comprehensive and objective evaluation method that distinguishes between the evaluation index and the optimal ideal solution based on the proximity distance. as follows:

[0165] = (20)

[0166] In formula (20), represents the Euclidean distance to the negative ideal solution, represents the Euclidean distance to the positive ideal solution.

[0167] Comparison of approach distance , the minimum approach distance is selected as the optimal preference, thus obtaining the optimal maintenance plan.

[0168] In this embodiment, the optimized maintenance strategy results are compared with the other two strategies. The results are shown in Table 2, where strategy one is a multi-level opportunity maintenance strategy considering fault correlation, strategy two is a traditional preventive maintenance strategy, and strategy three is an opportunity maintenance strategy that does not consider fault correlation.

[0169] Table 2 Comparison of maintenance cost, downtime and availability of three maintenance strategies

[0170]

[0171] It can be seen from Table 2 that compared with Strategy 1 and Strategy 2, the strategy that takes into account opportunistic maintenance can effectively reduce the number of downtimes and reduce maintenance costs, and improve availability; compared with Strategy 1 and Strategy 3, the number of downtimes of the strategy that does not consider fault-related factors is slightly reduced, which is consistent with the fact that the maintenance time under independent faults lags behind the actual maintenance time, but this will lead to an increase in the number of sudden failures of CNC machine tools, and the resulting sudden failure maintenance costs and downtime costs will also increase.

[0172] In summary, the reliability model established in this embodiment describes the maintenance time more accurately, and the established multi-level maintenance strategy model is more in line with actual maintenance needs and the expectations of decision makers, has high economic benefits, and can provide a reference for the formulation of maintenance strategies.

[0173] The above only describes the basic principles and preferred embodiments of the present invention. Those skilled in the art may make many changes and improvements based on the above description, and these changes and improvements should fall within the protection scope of the present invention.

Claims

1. A method for optimizing multi-level maintenance strategies for CNC machine tools considering fault correlation, characterized in that: The steps include: S1. Obtain historical fault data records of CNC machine tools and perform fault correlation analysis on each subsystem of the CNC machine tool; S2. According to the historical fault data of CNC machine tools, reliability modeling is performed on each subsystem to establish a reliability model under independent faults; S3, according to the reliability model under independent faults obtained in step S2, calculate the fault correlation coefficients between subsystems, and use the fault chain theory to establish a comprehensive failure rate model considering fault correlation; S4. Introduce a multi-level maintenance model, with the goal of minimizing the maintenance cost rate per unit time, and determine the optimal number of preventive maintenance and the best reliability; S5. Taking the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is established based on the optimal preventive maintenance strategy of the subsystem; S6. Use a multi-objective genetic algorithm to optimize the multi-objective opportunity maintenance model obtained in step S5, so as to obtain the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability, and determine the optimal maintenance plan through a multi-attribute decision-making method.

2. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 1 is characterized in that: Step S1 specifically includes the following: S11, obtaining historical fault data records of the CNC machine tool, and classifying and counting the historical fault data of the CNC machine tool according to different subsystems, calculating the fault interval time of each subsystem, and performing fault correlation analysis on the subsystems of the CNC machine tool; S12. Collect statistics on the related fault data of the CNC machine tool subsystems, clarify the hierarchical structure of the fault transmission direction of the subsystems for the fault correlation existing in the subsystems.

3. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 1, characterized in that: Step S2 specifically includes the following: The failure data of CNC machine tools conforms to the Weibull distribution law. The Weibull distribution model is used for parameter estimation to obtain the reliability model of each subsystem under independent failure, including the failure rate function and reliability function , which is expressed as follows: （1） （2） In formula (1) and formula (2), represents the shape parameter and ; represents the scale parameter and ; Indicates the running time.

4. The method for optimizing multi-level maintenance strategies for CNC machine tools considering fault correlation according to claim 1 is characterized in that: Step S3 specifically includes the following: S31. The correlation between fault-related subsystems is studied through the Gumbel Copula function, the fault correlation coefficient between subsystems is calculated, and then the fault joint distribution function of fault-related subsystems is established. The expression is as follows: （3） In formula (3), It indicates the correlation between variables. The value range of is [1,+∞); and represents two variables; when When it approaches +∞, the variable With variables tends to be completely correlated; when When With variables Independent of each other; S32, Converted to [0,1], the fault correlation coefficient is obtained. According to the fault chain theory, when the subsystem Other subsystems When the subsystem The comprehensive failure rate model is expressed as follows: （4） In formula (4), and Represents subsystems and subsystems The comprehensive failure rate; Representation Subsystem Independent failure rate; Representation Subsystem Subsystem The fault correlation coefficient of the action; when the subsystem Subsystem When there is a fault correlation, 0 ≤ ≤ 1; when the subsystem Subsystem If there is no fault correlation, =0, then .

5. The method for optimizing multi-level maintenance strategies for CNC machine tools considering fault correlation according to claim 1, characterized in that: Step S4 includes the following: Introduce multi-level incomplete preventive maintenance strategies for each subsystem and establish a comprehensive failure rate evolution model; When the subsystem reaches the specified reliability threshold, the preventive maintenance method is multi-level incomplete maintenance, and the failure rate of the CNC machine tool is improved; when a sudden failure occurs during the preventive maintenance cycle, the maintenance method is minor repair, which does not change the failure rate of the CNC machine tool; Taking the minimum maintenance cost rate per unit time as the objective function, the maintenance cost rate per unit time of the subsystem based on reliability during the operating time is calculated to determine the optimal number of preventive maintenance times and the best reliability within the maintenance cycle of the subsystem.

6. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 5 is characterized in that: Step S4 specifically includes the following: S41. Introduce an incomplete preventive maintenance strategy for each subsystem and establish a comprehensive failure rate evolution model, that is, add an age attenuation model and a failure rate increase model; then the subsystem No. Evolution model of comprehensive failure rate after incomplete maintenance for: （5） In formula (5), The value of ; The value of ,in, represents the optimal number of preventive maintenance; Representation Subsystem No. The interval between preventive maintenance; Representation Subsystem No. The failure rate function for each preventive maintenance is: and Represents subsystems The service age attenuation factor and failure rate increase factor of 1, ; S42. When the reliability of a subsystem drops to a specified reliability threshold, preventive maintenance of the subsystem is required. The failure rate function is proportional to the specified reliability threshold. The relationship between them satisfies the following formula: （6） （7） In formula (6) and formula (7), Indicates Failure rate function at the time of preventive maintenance; S43, adopt multi-level preventive maintenance to perform maintenance work, divided into primary maintenance and advanced maintenance, and determine the optimal number of preventive maintenance with the minimum maintenance cost rate per unit time as the objective function, then the subsystem Maintenance cost rate per unit time based on reliability during operation time , which is expressed as follows: （8） In formula (8), It represents the cost of minor repair for a single sudden failure; represents the optimal preventive maintenance threshold; represents the replacement cost; For preventive maintenance costs; for downtime; represents the unit downtime cost; represents the fault impact factor; represents the risk cost per failure; It represents the sum of maintenance time, replacement time and normal working time; among which, , and They are respectively expressed as follows: （9） （10） （11） Formula (9)-Formula (11), Indicates the preventive maintenance mode, 0 indicates primary maintenance, 1 indicates advanced maintenance, and the maintenance mode is selected by comparing the ratio of maintenance cost of different levels of investment to the failure rate recovery value; and They represent the cost of primary maintenance and the cost of advanced maintenance respectively; and They represent primary maintenance time and advanced maintenance time respectively; Indicates The interval between preventive maintenance; Indicates replacement time; Indicates the unit minor repair time; Indicates the total minor repair time; Indicates the replacement time; Indicates the preventive maintenance time; right Perform minimization calculation when When the minimum value is obtained, the optimal number of preventive maintenance times within the subsystem maintenance cycle is determined. and the optimal preventive maintenance threshold .

7. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 6 is characterized in that: Step S5 includes the following: Based on the optimal preventive maintenance strategy of a single subsystem, the idea of ​​opportunistic maintenance is introduced. When a subsystem in the whole machine undergoes preventive maintenance or replacement, it is determined whether the remaining subsystems undergo opportunistic maintenance. Establish an opportunity maintenance model of CNC machine tools with minimum maintenance cost rate based on reliability within a limited operating time domain; Establish an opportunistic maintenance model of CNC machine tools with maximum availability based on reliability within a limited operating time domain; With the minimum maintenance cost rate and maximum availability as the goals, a multi-objective opportunistic maintenance model for CNC machine tools considering fault correlation is finally obtained.

8. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 7, characterized in that: Step S5 specifically includes the following: S51. When a subsystem in the whole machine is undergoing preventive maintenance or replacement, the remaining subsystems are given a maintenance opportunity due to maintenance shutdown, and it is determined whether the remaining subsystems are undergoing opportunistic maintenance; S52, CNC machine tools in the limited operating time domain The opportunity maintenance model based on the maintenance cost rate per unit time of reliability is: （12） In formula (12), Indicates the number of subsystems; Representation Subsystem Number of preventive maintenance shutdowns; represents direct maintenance cost; Representation Subsystem Equivalent reliability life cost; Representation Subsystem Conduct the Instantaneous reliability during second-chance preventive maintenance; Representation Subsystem The optimal reliability threshold of Direct repair costs Included subsystems Preventive maintenance costs , minimum maintenance cost and replacement costs ; （13） （14） （15） Formula (13)-Formula (15), Representation Subsystem In the The preventive maintenance method, 0 represents primary maintenance, 1 represents advanced maintenance; represents the cost of a single primary repair; Indicates the cost of a single advanced repair; Indicates primary maintenance downtime; downtime for advanced maintenance; Representation Subsystem In the Failure rate at the time of first repair; S53, CNC machine tools in the limited operating time domain The opportunistic maintenance model with maximum availability based on reliability is: （16） In formula (16), Representation Subsystem The optimal number of preventive maintenance; Represents a subsystem in a finite runtime domain Number of preventive replacements; Representation Subsystem The number of preventive maintenance operations during the remaining time after the last preventive replacement; Representation Subsystem The downtime for preventive maintenance is the longest maintenance time in the maintenance subsystem; In order to unify the function objective minimization, the maximum availability model is transformed into the minimum unavailability model, which is expressed as follows: = （17） S54. Finally, the multi-objective opportunistic maintenance model of CNC machine tools considering fault correlation is obtained as follows: （18）。 9. The method for optimizing the multi-level maintenance strategy of a CNC machine tool considering fault correlation according to claim 8, characterized in that: In step S51, the reliability of the subsystem is used as a criterion to determine whether the remaining subsystems can be repaired opportunistically, as follows: (1) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem If no fault occurs, no maintenance measures will be taken; and Represents subsystems The start and end time of the run, Represents the reliability function of the CNC machine tool subsystem over time, represents the reliability threshold corresponding to the opportunity maintenance of each subsystem, Indicates the upper limit of the reliability threshold corresponding to the opportunistic maintenance of each subsystem; (2) When subsystem In the time interval When running within ; If the subsystem In case of sudden failure, the minimum maintenance method is used to complete the repair; if the subsystem No failure has occurred, but the subsystem For preventive maintenance, the subsystem Follow Perform one-opportunity repairs; (3) When subsystem Run to After the time, , then the subsystem must be preventive maintenance.

10. The method for optimizing multi-level maintenance strategy for CNC machine tools considering fault correlation according to claim 1, 8 or 9, characterized in that: Step S6 includes the following: S61. According to the maintenance mode of each subsystem, determine the preventive maintenance time, calculate the maintenance cost rate and unavailability of the CNC machine tool, use a multi-objective genetic algorithm to optimize the objective function, and determine the optimal opportunity maintenance threshold of each subsystem and the corresponding optimal maintenance cost rate and availability solution set; S62. Through the multi-attribute decision-making method, the optimal maintenance plan is determined by distinguishing the advantages and disadvantages based on the evaluation index and the approximate distance between the optimal ideal solution.

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