Joint optimization method of production and maintenance of multi-equipment system considering dynamic working conditions

Abstract

The present invention provides a joint optimization method for production and maintenance of a multi-equipment system considering dynamic working conditions, comprising the following steps: S1: establishing a reliability model of a multi-equipment system based on different working conditions caused by dynamic working conditions; S2: analyzing the maintenance costs and production costs of the multi-equipment system based on the reliability model of the multi-equipment system, wherein the maintenance costs and production costs include preventive maintenance costs, fault maintenance costs, usage penalty costs, and maintenance resource mobilization costs; S3: establishing a joint optimization model for production and maintenance of a multi-equipment system with the goal of minimizing the maintenance costs and production costs; S4: using a dynamic decision algorithm to obtain a better maintenance plan based on the joint optimization model for production and maintenance of a multi-equipment system. The joint optimization method for production and maintenance of a multi-equipment system considering dynamic working conditions of the present invention has lower costs than existing joint optimization methods.

Description

Technical Field

[0001] The present invention relates to the technical field of system reliability, and in particular to a joint optimization method for production and maintenance of a multi-equipment system considering dynamic working conditions. Background Art

[0002] With the rapid development of China's manufacturing industry, the number of equipment in manufacturing production is increasing, the workload of equipment maintenance plants is increasing, and the total cost of equipment maintenance is also very large. In the actual production process, dynamic working conditions fluctuate greatly throughout the year, which not only affects the operating conditions, but also affects the production loss costs of downtime maintenance.

[0003] The current maintenance model is difficult to take into account various influencing factors, and there are widespread problems of "insufficient maintenance" or "excessive maintenance", resulting in huge cost waste. Therefore, how to reduce the total cost while ensuring the smooth production of equipment is an urgent problem to be solved. Summary of the invention

[0004] In view of the deficiencies in the above-mentioned prior art, the present invention provides a method for joint optimization of production and maintenance of a multi-equipment system taking into account dynamic working conditions, which can establish an equipment reliability model based on the impact of dynamic working conditions on equipment degradation; based on the reliability model, a joint optimization model for production and maintenance of a multi-equipment system is established with the goal of minimizing the production and maintenance costs of the multi-equipment system; and for the joint optimization model, a dynamic decision algorithm is used to obtain the optimized maintenance decision result.

[0005] In order to achieve the above object, the present invention provides a method for joint optimization of production and maintenance of a multi-equipment system considering dynamic working conditions, comprising the steps of:

[0006] S1: Establish a reliability model for a multi-device system based on different operating conditions caused by dynamic operating conditions;

[0007] S2: analyzing the maintenance costs and production costs of the multi-device system based on the multi-device system reliability model, wherein the maintenance costs and production costs include preventive maintenance costs, failure repair costs, usage penalty costs, and maintenance resource mobilization costs;

[0008] S3: Establishing a joint optimization model for production and maintenance of a multi-equipment system with the goal of minimizing the maintenance cost and production cost;

[0009] S4: Based on the multi-equipment system production and maintenance joint optimization model, a dynamic decision-making algorithm is used to obtain a better maintenance plan.

[0010] Preferably, the S1 step further comprises the steps of:

[0011] S11: Decision variables required to analyze maintenance decisions:

[0012]

[0013]

[0014] in, The decision variable indicating whether equipment m starts maintenance at time t; The decision variable indicating whether the device m is in maintenance state at time t;

[0015] S12: Analyze the failure rate evolution function:

[0016] Assuming that the benchmark failure rate of the equipment follows a two-parameter Weibull distribution, the benchmark failure rate λ0(t) is expressed as follows:

[0017]

[0018] Among them, α represents the scale parameter; β represents the shape parameter; t represents the time;

[0019] Assume that the entire time window is divided into θ intervals according to dynamic conditions:

[0020] [0,T]=[t1,t2]∪[t2,t3]∪...∪[t θ , t θ+1 ];

[0021] Among them, [0,T] represents the interval set within time T; t θ represents the θth moment;

[0022] Assuming that the operating condition factors affect the evolution of failure rate by accelerating the failure mode, the equivalent service age of interval i is analyzed. for:

[0023]

[0024] Among them, T i represents the length of interval i, ε i represents the operating factor;

[0025] The failure rate λ(t) of the equipment before the first preventive maintenance and in the nth interval is:

[0026]

[0027] Among them, ε n represents the operating factor of the nth interval; t begin represents the initial service age of the equipment; n is a natural number;

[0028] When the equipment has undergone k preventive maintenance, assuming that the last preventive maintenance ended at The interval is the n′th interval, n′ is a natural number; assuming that the time is t, the interval is the nth interval, n≥n′; the failure rate is:

[0029]

[0030] Preferably, each of the devices has an initial service life t begin , the reliability of the initial service age is not 1.

[0031] Preferably, each preventive maintenance repairs the system to be as good as new. Preventive maintenance takes d days, where d is a natural number. Fault repair does not change reliability, and maintenance time is ignored.

[0032] Preferably,

[0033] Among them, τ represents a temporary variable.

[0034] Preferably, the S2 step further comprises the steps of:

[0035] S21: Analyze the preventive maintenance cost C of the multi-device system P for:

[0036]

[0037] Among them, c up represents unit preventive maintenance cost; T represents time; m represents a natural number, V train represents the set of EMUs;

[0038] S22: Analyze the fault repair cost of the multi-device system:

[0039] Assume that the start time of the i-th preventive maintenance of the m-th equipment is And the end time is The number of preventive maintenance is n m , analyze the failure repair cost of the mth equipment

[0040]

[0041] Among them, c uc represents the unit failure repair cost;

[0042] Analyze the total failure repair cost C of the multi-device system c for:

[0043]

[0044] S23: Analyze the usage penalty cost c of the multi-device system fd (t) is:

[0045]

[0046] Among them, ρ n Indicates the usage rate of the interval, c uf represents the unit penalty cost, N train Indicates the number of the devices in the multi-device system;

[0047] S24: Analyze the maintenance resource mobilization cost c of the multi-device system sd (t) is:

[0048]

[0049] Among them, c us Represents the unit maintenance resource mobilization cost; N accept Represents the constraint on the number of devices that can start maintenance at the same time.

[0050] Preferably, the S3 step further comprises the steps of:

[0051] With the goal of minimizing the maintenance costs and production costs, and taking the maintenance plan of each equipment as the quantity to be optimized, the following optimization model is established:

[0052] min C total =C c +C p +C f +C s

[0053]

[0054]

[0055] Among them, minC total Indicates the minimum maintenance cost and production cost; C f represents the total usage penalty cost; C s Represents the total maintenance resource mobilization cost.

[0056] Preferably, the S4 step further comprises the steps of:

[0057] S401: sort the multiple equipment systems in ascending order of initial service age V age =(1, 2, ..., N train , V age Represents a set of devices arranged in order; set ω1, ω2, ..., is the coefficient for allocating the number of equipment maintenance times. The coefficient for allocating the number of equipment maintenance times in the multi-equipment system is ω j The equipment is repaired j times within the time window, that is, This is equivalent to dividing the multi-device system into N max Segments:

[0058]

[0059] S402: For the mth device, it has n repairs within the time window. m times, assuming that the starting point of each maintenance is The end points are Calculating preventive maintenance costs Calculate the cost of repairing a breakdown:

[0060]

[0061] S403: Analyze a sub-problem of the mth device:

[0062]

[0063]

[0064]

[0065] S404: Calculate the maintenance decision optimization result of each of the equipment using the interior point method, and combine them to obtain the preliminary maintenance decision result of the multi-equipment system;

[0066] S405: t=0;

[0067] S406: Determine whether the number of the devices to be repaired exceeds a threshold, if so, proceed to step S407, otherwise proceed to step S409;

[0068] S407: Calculate the number N of the equipment that needs to be delayed for maintenance de :

[0069]

[0070] S408: Sort by equivalent service age from smallest to largest, and take the top N de The devices constitute a set V de Delay maintenance by one day:

[0071]

[0072] S409: Calculate the number of equipment that can be repaired in advance N ad :

[0073]

[0074] S410: Repair equipment that can be repaired in advance:

[0075]

[0076] Among them, represents the originally scheduled maintenance start time of the multiple unit train m; V ad represents the set of all equipment that needs to be maintained in advance;

[0077] S411: The updated and adjusted maintenance decision, let t = t + 1;

[0078] S412: Determine whether the time window has ended. If t < T, go to step S406; otherwise, go to step S413;

[0079] S413: Output the final maintenance plan.

[0080] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0081] The joint optimization method provided by the present invention can analyze the evolution of equipment reliability based on the actual dynamic working conditions in the actual production and maintenance decision-making of equipment, and at the same time consider the production requirements caused by the dynamic working conditions to establish a joint optimization model for the production and maintenance of a multi-equipment system. And a dynamic decision optimization algorithm applicable to this model is provided, which can effectively reduce costs, and further provide an accurate and powerful scientific basis for scientific decision-making in the later stage.

[0082] Other features and advantages of the present invention will be described in the following specification, and, in part, will be obvious from the specification, or will be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained by the structures specifically pointed out in the specification, claims, and drawings. Brief Description of the Drawings

[0083] Figure 1 is a flowchart of the joint optimization method for the production and maintenance of a multi-equipment system considering dynamic working conditions according to an embodiment of the present invention;

[0084] Figure 2 is a flowchart of the dynamic decision algorithm in step S4 of the embodiment of the present invention;

[0085] Figure 3 is a comparison chart of the algorithm calculation time consumption according to an embodiment of the present invention. Detailed Embodiment

[0086] The following gives a preferred embodiment of the present invention according to the drawings Figure 1 to Figure 3 , and describes it in detail to better understand the functions and features of the present invention.

[0087] Please refer to Figure 1, a method for joint optimization of production and maintenance of a multi-equipment system considering dynamic working conditions according to an embodiment of the present invention, the method establishes a reliability model of a multi-equipment system based on dynamic working conditions; analyzes equipment maintenance and production costs based on the reliability model of the multi-equipment system; establishes a joint optimization model of production and maintenance of a multi-equipment system with the goal of minimizing the production and maintenance costs of the multi-equipment system; and uses a dynamic decision-making algorithm based on the joint optimization model of production and maintenance of a multi-equipment system to obtain a better maintenance plan. The method specifically includes the following steps:

[0088] S1: Establishing a multi-device system reliability model based on different working conditions caused by dynamic working conditions; Step S1 further includes the steps of:

[0089] S11: Decision variables required to analyze maintenance decisions:

[0090]

[0091]

[0092] in, The decision variable indicating whether equipment m starts maintenance at time t; The decision variable indicating whether the device m is in maintenance state at time t;

[0093] S12: Analyze the failure rate evolution function:

[0094] Assume that the benchmark failure rate of the equipment follows a two-parameter Weibull distribution, and the benchmark failure rate λ0(t) is expressed as follows:

[0095]

[0096] Among them, α represents the scale parameter; β represents the shape parameter; t represents the time;

[0097] Assume that the entire time window is divided into θ intervals according to dynamic conditions:

[0098] [0,T]=[t1,t2]∪[t2,t3]∪...∪[t θ , t θ+1 ];

[0099] Among them, [0,T] represents the interval set within time T; t θ represents the θth moment;

[0100] Assuming that the operating condition factors affect the evolution of failure rate by accelerating the failure mode, the equivalent service age of interval i is analyzed. for:

[0101]

[0102] Among them, T irepresents the length of interval i, ε i represents the operating factor;

[0103] The failure rate λ(t) of the analyzed equipment before the first preventive maintenance and in the nth interval is:

[0104]

[0105] Among them, ε n represents the operating factor of the nth interval; t begin Indicates the initial service life of the equipment; n is a natural number;

[0106] When the equipment has undergone k preventive maintenance, assuming that the last preventive maintenance ended at The interval is the n′th interval, n′ is a natural number; assuming that the time is t, the interval is the nth interval, n ≥ n′; the failure rate at this time is:

[0107]

[0108] Each device has an initial service life t begin , the reliability of the initial service age is not 1.

[0109] Each preventive maintenance repairs the product as good as new. Preventive maintenance takes d days, where d is a natural number. Fault repair does not change the reliability, and the maintenance time is ignored.

[0110]

[0111] Among them, τ represents a temporary variable.

[0112] S2: Analyze the maintenance cost and production cost of the multi-device system based on the multi-device system reliability model, the maintenance cost and production cost include preventive maintenance cost, failure repair cost, usage penalty cost and maintenance resource mobilization cost; wherein step S2 further includes the steps:

[0113] S21: Analyze the preventive maintenance cost of a multi-equipment system C P for:

[0114]

[0115] Among them, c up represents unit preventive maintenance cost; T represents time; m represents a natural number, V train represents the set of EMUs;

[0116] S22: Analyze the failure repair cost of multi-device systems:

[0117] Assume that the start time of the i-th preventive maintenance of the m-th equipment is And the end time is The number of preventive maintenance is n m , analyze the failure repair cost of the mth equipment

[0118]

[0119] Among them, c uc represents the unit failure repair cost;

[0120] Analyze the total failure repair cost C of a multi-device system c for:

[0121]

[0122] S23: Analyzing the usage penalty cost c of a multi-device system fd (t) is:

[0123]

[0124] Among them, ρ n Indicates the usage rate of the interval, c uf represents the unit penalty cost, N train Indicates the number of devices in a multi-device system;

[0125] S24: Analyze the maintenance resource mobilization cost of multi-equipment systems sd (t) is:

[0126]

[0127] Among them, c us Represents the unit maintenance resource mobilization cost; N accept Represents the constraint on the number of devices that can start maintenance at the same time.

[0128] S3: To minimize maintenance and production costs, a joint optimization model for production and maintenance of multi-equipment systems is established:

[0129] min C total =C c +C p +C f +C s

[0130]

[0131]

[0132] Among them, minC total Indicates the minimum maintenance cost and production cost; C f represents the total usage penalty cost; C sRepresents the total maintenance resource mobilization cost.

[0133] S4: Based on the joint optimization model of production and maintenance of multi-equipment systems, a dynamic decision-making algorithm is used to obtain a better maintenance plan; wherein step S4 further includes the following steps:

[0134] S401: sort the multiple equipment systems in ascending order of initial service age V age =(1, 2, ..., N train ), V age Represents a set of devices arranged in order; set ω1, ω2, ..., is the coefficient for allocating equipment maintenance times. The coefficient for allocating equipment maintenance times in a multi-equipment system is ω j The equipment is repaired j times within the time window, that is, This is equivalent to dividing the multi-device system into N max Segments:

[0135]

[0136] S402: For the mth device, it has n repairs within the time window. m times, assuming that the starting point of each maintenance is The end points are Calculating preventive maintenance costs Calculate the cost of repairing a breakdown:

[0137]

[0138] S403: Analyze a sub-problem of the mth device:

[0139]

[0140]

[0141]

[0142] S404: using the interior point method to calculate the maintenance decision optimization result of each device, and merging them to obtain the preliminary maintenance decision result of the multi-device system;

[0143] S405: t=0;

[0144] S406: Determine whether the number of the devices to be repaired exceeds a threshold, if so, proceed to step S407, otherwise proceed to step S409;

[0145] S407: Calculate the number of equipment that needs to be delayed for repair N de :

[0146]

[0147] S408: Arrange in ascending order of equivalent service age, and select the first N de devices to form a set V de Delay the maintenance by one day:

[0148]

[0149] S409: Calculate the number N of devices that can be maintained in advance ad :

[0150]

[0151] S410: Maintain in advance the devices that can be maintained in advance:

[0152]

[0153] Among them, represents the originally scheduled maintenance start time of the EMU m; V ad represents the set of all devices that need to be maintained in advance;

[0154] S411: Update the adjusted maintenance decision, and let t = t + 1;

[0155] S412: Determine whether the time window ends. If t < T, go to step S406; otherwise, go to step S413;

[0156] S413: Output the final maintenance plan.

[0157] Next, taking a specific numerical example as an object, the specific implementation steps of the present invention and the obtained optimization results are described. This experiment uses Matlab2019a as the software platform for optimization and solution to perform simulation and solution.

[0158] Considering a multi-device system, the failure functions of the devices all follow the same Weibull distribution, with a shape parameter of 3 and a scale parameter of 300. For the convenience of calculation, the time window is set to [1, 360], the maintenance time d = 5 days, and the initial service age of the devices is a random number between [0, 300]. The coefficients regarding cost are: c up = 500, c uc = 8000, c uf = 500, c us = 1000, c fix = 200, and the coefficients regarding constraints are: N max = 3, N accept = 5.

[0159] The selection of ρ is shown in Table 1:

[0160]

[0161] Table 1. ρ value selection table

[0162] Using the above dynamic decision algorithm, changing the number of devices, optimizing the model, and comparing it with the simulated annealing algorithm, the cost results are shown in Table 2.

[0163]

[0164] Table 2. Cost results comparison table

[0165] In this embodiment, the dynamic decision algorithm can effectively reduce costs, especially when the number of devices is 120, the cost of the simulated annealing algorithm is 675283, and the cost of the dynamic decision algorithm is 444033, saving 34%. The simulated annealing algorithm is greater than the dynamic decision algorithm in both preventive maintenance cost and fault repair cost.

[0166] For a comparison of the calculation time of this embodiment, please refer to Figure 3 , the dynamic decision algorithm is stable within 150s, while the simulated annealing algorithm increases linearly with the number of devices, especially when N train When =140, the calculation time reaches 608s.

[0167] The present invention is described in detail above in conjunction with the embodiments of the accompanying drawings. A person skilled in the art can make various variations of the present invention according to the above description. Therefore, certain details in the embodiments should not constitute a limitation of the present invention, and the scope of protection of the present invention shall be defined by the scope of the attached claims.

Claims

1. A joint optimization method for production and maintenance of a multi - device system considering dynamic working conditions, comprising the steps: S1: Establish a reliability model of the multi - device system based on different working conditions caused by dynamic working conditions; S2: Analyze the maintenance cost and production cost of the multi - device system based on the reliability model of the multi - device system, where the maintenance cost and production cost include preventive maintenance cost, breakdown maintenance cost, usage rate penalty cost, and maintenance resource mobilization cost; S3: Establish a joint optimization model for production and maintenance of the multi - device system with the goal of minimizing the maintenance cost and production cost; S4: Based on the joint optimization model for production and maintenance of the multi - device system, use a dynamic decision - making algorithm to obtain an optimal maintenance plan; The step S1 further includes the steps: S11: Analyze the decision variables required for maintenance decision - making; in, The decision variable indicating whether equipment m starts maintenance at time t; The decision variable indicating whether the device m is in maintenance state at time t; S12: Analyze the failure rate evolution function; Let the baseline failure rate of the device follow a two - parameter Weibull distribution, and the baseline failure rate λ0(t) is expressed as follows: where α represents the scale parameter; β represents the shape parameter; t represents the time; Suppose the entire time window is divided into θ intervals according to dynamic working conditions; [0,T]=[t1,t2]∪[t2,t3]∪...∪[t Θ ,t Θ+1 ]; Among them, [0,T] represents the interval set within time T; t θ represents the θth moment; Assuming that the operating condition factors affect the evolution of failure rate by accelerating the failure mode, the equivalent service age of interval i is analyzed. for: Among them, T i represents the length of interval i, ε i represents the operating factor; Analyze the failure rate λ(t) of the device when it is in the nth interval before the first preventive maintenance as: Among them, ε n represents the operating factor of the nth interval; t begin represents the initial service age of the equipment; n is a natural number; When the equipment has undergone k preventive maintenance, assuming that the last preventive maintenance ended at The interval is the n'th interval, n' is a natural number; assuming that the time is t, the interval is the n'th interval, n ≥ n'; the failure rate is:

2. The joint optimization method for production and maintenance of a multi - device system considering dynamic working conditions according to claim 1, wherein: Each of the equipment has an initial service life t begin , the reliability of the initial service age is not 1.

3. The joint optimization method for production and maintenance of a multi - device system considering dynamic working conditions according to claim 1, wherein: Each preventive maintenance restores the device to as - new condition. Preventive maintenance takes d days, where d is a natural number. Breakdown maintenance does not change the reliability, and the maintenance time is ignored.

4. The joint optimization method for production and maintenance of a multi - device system considering dynamic working conditions according to claim 1, wherein: where τ represents a temporary variable.

5. The method for joint optimization of production and maintenance of a multi-equipment system considering dynamic working conditions according to claim 1 is characterized in that: The step S2 further includes the steps: S21: Analyze the preventive maintenance cost C of the multi-device system P for: Among them, c up represents unit preventive maintenance cost; T represents time; m represents a natural number, V train represents the set of all EMUs; S22: Analyze the breakdown maintenance cost of the multi - device system; Assume that the start time of the i-th preventive maintenance of the m-th equipment is And the end time is The number of preventive maintenance is n m , analyze the failure repair cost of the mth equipment Among them, c uc represents the unit failure repair cost; Analyze the total failure repair cost C of the multi-device system c for: S23: Analyze the usage penalty cost c of the multi-device system fd (t) is: Among them, ρ n Indicates the usage rate of the interval, c uf represents the unit penalty cost, N train Indicates the number of the devices in the multi-device system; S24: Analyze the maintenance resource mobilization cost c of the multi-device system sd (t) is: Among them, c us Represents the unit maintenance resource mobilization cost; N accept Represents the constraint on the number of devices that can start maintenance at the same time.

6. The method for joint optimization of production and maintenance of a multi-equipment system considering dynamic working conditions according to claim 5 is characterized in that: The step S3 further includes the steps: With the goal of minimizing the maintenance cost and production cost, and taking the maintenance plans of each device as the quantities to be optimized, establish the following optimization model: my C total =C c +C p +C f +C s Among them, minC total Indicates the minimum maintenance cost and production cost; C f represents the total usage penalty cost; C s Represents the total maintenance resource mobilization cost.

7. The method for joint optimization of production and maintenance of a multi-equipment system considering dynamic working conditions according to claim 6 is characterized in that: The step S4 further includes the steps: S401: sort the multiple equipment systems in ascending order of initial service age V age =(1,2,...,N train ), V age Represents a collection of devices in order; set is the coefficient for allocating the number of equipment maintenance times. The coefficient for allocating the number of equipment maintenance times in the multi-equipment system is ω j The equipment is repaired j times within the time window, that is, This is equivalent to dividing the multi-device system into N max Segments: S402: For the mth device, it has n repairs within the time window. m times, assuming that the starting point of each maintenance is The end points are Calculating preventive maintenance costs Calculate the cost of repairing a breakdown: S403: Analyze a sub - problem of the m - th device; S404: Use the interior - point method to calculate the optimized results of the maintenance decisions of each device, and combine them to obtain the preliminary maintenance decision results of the multi - device system; S405: t = 0; S406: Judge whether the number of devices to be maintained exceeds the threshold. If it exceeds, enter step S407; otherwise, enter step S409; S407: Calculate the number N of the equipment that needs to be delayed for maintenance de : S408: Sort by equivalent service age from smallest to largest, and take the top N de The devices constitute a set V de Delay maintenance by one day: S409: Calculate the number of equipment that can be repaired in advance N ad : S410: Advance the maintenance of the devices that can be maintained in advance; in, V represents the original maintenance start time of EMU m; ad Represents the set of all equipment that needs to be repaired in advance; S411: Update the adjusted maintenance decision, and let t = t + 1; S412: Judge whether the time window ends. If t < T, enter step S406; otherwise, enter step S413; S413: Output the final maintenance plan.

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