A selective maintenance sequence analysis system and method for multi-task equipment with production requirements

Abstract

The present invention discloses a system and method for analyzing the selective maintenance sequence of multi-task equipment for production demand, and relates to the field of selective maintenance of multi-task equipment. The system includes a maintenance strategy and model building unit, an assumption rule building unit, and a production system state analysis unit, wherein the maintenance strategy and model building unit is used to formulate a production system maintenance strategy and build a selective maintenance model; the assumption rule building unit is used to set the constraint rules of the selective maintenance model based on the production system state degradation time and the maintenance time; the production system state analysis unit is used to predict the reliability of the next two consecutive tasks of the production system based on the constraint rules, and optimize the production system maintenance strategy using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability. The present invention constructs a new selective maintenance model by considering the next two consecutive tasks.

Description

Technical Field

[0001] The invention belongs to the field of selective maintenance of multi-task equipment, and in particular to a system and method for analyzing the selective maintenance sequence of multi-task equipment according to production requirements. Background Art

[0002] In production systems, equipment degradation phenomena such as cracks, wear, and corrosion are inevitable. Therefore, effective maintenance of failed or degraded production systems, reducing potential risks, and extending service life has become one of the important issues. However, in most industrial and military environments, due to the need to perform multiple tasks continuously, production systems can usually only be maintained in the interval between two tasks. For example, factories need to shut down for maintenance on weekends or at the end of the month, and military equipment will be repaired between tasks. This maintenance activity on some equipment under the condition of limited maintenance resources such as time, budget, and manpower is usually called selective maintenance. Selective maintenance can ensure that the production system can successfully complete the next task under limited resource conditions. It is a common and effective maintenance strategy with rich research accumulation.

[0003] At present, the research on selective maintenance in academia is mainly divided into two types: single-task model and multi-task model. The former only considers the current task demand and ignores the demand of subsequent tasks. Therefore, when the current task ends, the production system may fall into a poor state. If the demand of subsequent tasks is high, it will be difficult to meet the demand of subsequent tasks even if maintenance is carried out. The latter takes all subsequent task demands into consideration, or considers the demand of all tasks comprehensively, or ignores the uncertainty of maintenance time. It is impossible to respond quickly and accurately to the fluctuation of production system demand under the premise of uncertain maintenance time. On the one hand, the long-term task demand forecast can only provide a general direction. The larger the forecast deviation is, the less effective it is for the formulation of specific maintenance strategies. On the other hand, if the maintenance strategies of all tasks are considered comprehensively, the maintenance strategies of the current tasks will inevitably be sacrificed and adjusted to a certain extent, that is, the maintenance strategies currently formulated may not fully meet the current task needs. In addition, due to the uncertainty of maintenance time and production system degradation time, as multi-stage tasks continue, the higher the calculation cost of the actual state distribution of the production system in subsequent tasks.

[0004] In the existing technology, the single-task model used often has the disadvantage of short-sightedness, and the multi-task model used is not very applicable to the reliability assessment of the production system in the subsequent task stage. Therefore, there is an urgent need for a selective maintenance sequence analysis technology for multi-task equipment with production requirements, which can combine the rolling time window idea to construct a new rolling dual-task model, so as to formulate the current maintenance strategy on the basis of considering the state degradation time of the production system and the uncertainty of the maintenance time, and predict the reliability of the subsequent two consecutive tasks, greatly improving the comprehensive reliability of the analysis results.

[0005] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[0006] Purpose of the invention: To provide a system and method for selective maintenance sequence analysis of multi-task equipment with production requirements, so as to overcome the above-mentioned technical problems existing in the existing related technologies.

[0007] Technical solution: According to one aspect of the present invention, a selective maintenance sequence analysis system for multi-task equipment with production requirements is provided, comprising a maintenance strategy and model building unit, a hypothesis rule building unit and a production system status analysis unit, wherein the production system status analysis unit comprises a maintenance task status analysis module, a first continuous task status analysis module, a second continuous task status analysis module and a multi-task comprehensive reliability evaluation module;

[0008] Among them, the maintenance strategy and model building unit is used to formulate the maintenance strategy of the production system and build a selective maintenance model;

[0009] A hypothesis rule building unit is used to set constraint rules of a selective maintenance model based on the state degradation time and maintenance time of the production system;

[0010] The production system status analysis unit is used to predict the reliability of the next two consecutive tasks of the production system based on constraint rules, and optimize the maintenance strategy of the production system using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability;

[0011] The maintenance task status analysis module is used to analyze the status distribution of the production system at the end of the kth maintenance interval;

[0012] The first continuous task state analysis module is used to analyze the state distribution of the production system at the end of the kth task;

[0013] The second continuous task state analysis module is used to analyze the state distribution of the production system at the end of the k+1th task;

[0014] The multi-task comprehensive reliability evaluation module is used to evaluate the comprehensive reliability of the subsequent two consecutive tasks (i.e., the kth task and the k+1th task) of the production system.

[0015] Furthermore, the system construction unit includes a maintenance interval status module, a maintenance target module, a maintenance sequence module and a maintenance strategy module;

[0016] Among them, the maintenance interval state module is used to indicate the state of the production system at the beginning of the kth maintenance interval;

[0017] Maintenance target module, used to construct maintenance target decision variables;

[0018] Maintenance sequence module, used to construct maintenance sequence decision variables;

[0019] The maintenance strategy module is used to record the maintenance strategy of the maintenance interval based on the maintenance target and maintenance sequence.

[0020] Further, the assumption rule establishing unit includes a first assumption rule module, a second assumption rule module, a third assumption rule module, a fourth assumption rule module and a fifth assumption rule module;

[0021] The first assumption rule module is used to represent the production capacity of the equipment. When the equipment is in state i, the production capacity of the equipment is represented by g l,i , when the production capacity of equipment l at any time t is expressed as G l (t);

[0022] The second assumption rule module is used to indicate that the maintenance task execution time of the equipment within the maintenance interval and the state degradation time within the task both obey exponential distribution;

[0023] The third assumption rule module is used to represent the production capacity of the entire production system at any time t;

[0024] The fourth assumption rule module is used to indicate that the selected maintenance actions are performed sequentially within the task interval, and the maintenance actions can only be performed within the task interval, and the equipment cannot be repaired within the task;

[0025] The fifth assumption rule module is used to indicate that the equipment state will not degrade within the task interval.

[0026] Further, the analysis of the production system status distribution at the end of the kth maintenance interval includes:

[0027] Based on the constraint rules of the selective maintenance model and combined with the maintenance strategy of the maintenance interval, the first state transfer equation is constructed;

[0028] According to the first state transfer equation, a first initial condition is set;

[0029] Calculate the maintenance cost required by the maintenance queue and analyze the status of equipment l at the end of the kth maintenance interval;

[0030] Analyze device l in state s l The probability of and the probability that the production system is in state s.

[0031] Furthermore, the first state transfer equation is expressed as:

[0032]

[0033] In the formula, α i,jrepresents the transition rate of the maintenance queue from state i to state j, α i-1,i represents the maintenance rate of the i-th equipment in the maintenance queue;

[0034] The expression of the first initial condition is:

[0035] P M (t M,k-1 )=[1,0,...,0];

[0036] In the formula, t M,k-1 represents the time when the kth maintenance interval starts;

[0037] The state expression of device l is:

[0038]

[0039] Device l is in state s l The probability expression is:

[0040]

[0041] The probability expression of the production system being in state s is:

[0042]

[0043] Where s∈S, S represents the complete set of production system states.

[0044] Further, the analysis of the production system status distribution at the end of the kth task includes:

[0045] Based on the constraint rules of the selective maintenance model, the second state transfer equation is constructed;

[0046] According to the second state transfer equation, a second initial condition is set;

[0047] Based on the second initial condition, calculate the probability that device l is in state i, and analyze the state distribution of device l;

[0048] Using the general generating function method, solve the u function of equipment l and calculate the u function of the production system;

[0049] Based on the u function of the production system, solve the reliability of the production system;

[0050] Based on the maintenance time of the equipment in the kth maintenance interval and the state degradation time of the equipment in the kth task, analyze the equipment l in state s l The probability that the production system is in state s=[s1,s2,…,s N ] probability.

[0051] Furthermore, the second state transfer equation is expressed as:

[0052]

[0053] In the formula, λ l,i,j represents the transition rate of device l from state i to state j;

[0054] The second initial condition expression is:

[0055]

[0056] The u function expression of device l is:

[0057]

[0058] The u function expression of the production system is;

[0059]

[0060] Where N CAP represents the total production capacity of the production system, represents the j-th production capacity of the production system, Indicates that in S(t B,k )=s condition, probability;

[0061] The reliability of the production system is expressed as:

[0062]

[0063] Where W k represents the required production capacity of the kth task;

[0064] Device l is in state s l The probability expression is:

[0065]

[0066] The production system is in state s = [s1, s2, …, s N The probability expression of ] is:

[0067]

[0068] Further, the analysis of the production system status distribution at the end of the k+1th task includes:

[0069] Based on the execution time of equipment maintenance tasks, the probability of the production system being in state i at the end of the k+1th maintenance interval is analyzed;

[0070] Based on the constraint rules and aiming at maximizing task reliability, the maintenance target of the production system within the k+1th maintenance interval is found.

[0071] Furthermore, the comprehensive reliability of two consecutive tasks of the production system is evaluated including:

[0072] Based on the uncertainty of the execution time of the maintenance task within the kth maintenance interval, the kth reliability is analyzed;

[0073] Based on the divergence of the production system status at the end of the kth task, the comprehensive reliability of the kth and k+1th tasks is analyzed.

[0074] According to another aspect of the present invention, a method for analyzing the selective maintenance sequence of a multi-task equipment with production requirements is provided, and the method for analyzing the selective maintenance sequence of a multi-task equipment with production requirements comprises the following steps:

[0075] S1. Develop a maintenance strategy for the production system and build a selective maintenance model;

[0076] S2. Based on the degradation time and maintenance time of the production system state, set the constraint rules of the selective maintenance model;

[0077] S3. Based on the constraint rules, the reliability of the next two consecutive tasks of the production system is predicted, and the maintenance strategy of the production system is optimized using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability.

[0078] Beneficial effects:

[0079] 1. The present invention constructs a new selective maintenance model by considering two subsequent continuous tasks. Under the premise of limited maintenance resources and uncertain maintenance time, a calculation method for the comprehensive reliability of two subsequent continuous tasks is proposed. The comprehensive reliability is used as the objective function, and the maintenance interval length and maintenance budget are used as constraints to achieve the optimization of the maintenance objectives and maintenance sequence of the equipment to be repaired.

[0080] 2. The selective maintenance model constructed by the present invention can take into account the needs of subsequent tasks, avoiding the short-sighted problem of the single-task model that only considers the reliability of the current task, which is conducive to improving the ability to cope with large fluctuations in production system demand.

[0081] 3. The present invention takes into account the uncertainty of the production system state degradation time and maintenance time, and can more accurately predict the production system state distribution, and then formulate a more robust maintenance strategy, which is more risk-resistant than the single-task model. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] 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 will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0083] Figure 1 is a principle block diagram of a selective maintenance sequence analysis system for multi-task equipment with production requirements according to an embodiment of the present invention;

[0084] Figure 2 is a schematic diagram of a multi-task selective maintenance cycle according to an embodiment of the present invention;

[0085] Figure 3 is a schematic diagram of the structure of a multi-state production system according to an embodiment of the present invention;

[0086] Figure 4 is a schematic diagram of the production system state and task reliability distribution at the start of the kth task in the dual-task model according to an embodiment of the present invention;

[0087] Figure 5 is a schematic diagram of the production system state and task reliability distribution at the start of the kth task in a single-task model according to an embodiment of the present invention;

[0088] Figure 6 is the state of the production system and the distribution of task reliability when the kth task starts when the maintenance time is determined according to an embodiment of the present invention;

[0089] Figure 7 It is a flow chart of a method for analyzing the selective maintenance sequence of multi-task equipment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0090] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features well known in the art are not described.

[0091] According to an embodiment of the present invention, a system and method for analyzing the selective maintenance sequence of multi-task equipment with production requirements are provided.

[0092] like Figure 1As shown, according to one embodiment of the present invention, a production demand multi-task equipment selective maintenance sequence analysis system is provided, the production demand multi-task equipment selective maintenance sequence analysis system comprises a maintenance strategy and model building unit 1, an assumption rule building unit 2 and a production system state analysis unit 3, the production system state analysis unit 3 comprises a maintenance task state analysis module 301, a first continuous task state analysis module 302, a second continuous task state analysis module 303 and a multi-task comprehensive reliability evaluation module 304;

[0093] Among them, the maintenance strategy and model building unit 1 is used to formulate the maintenance strategy of the production system and build a selective maintenance model;

[0094] Assumption rule establishment unit 2, used for setting constraint rules of the selective maintenance model based on the production system state degradation time and maintenance time;

[0095] The production system state analysis unit 3 is used to predict the reliability of the next two consecutive tasks of the production system based on the constraint rules, and optimize the maintenance strategy of the production system by using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability;

[0096] Maintenance task status analysis module 301, used to analyze the status distribution of the production system at the end of the kth maintenance interval;

[0097] The first continuous task state analysis module 302 is used to analyze the state distribution of the production system when the kth task is completed;

[0098] The second continuous task state analysis module 303 is used to analyze the state distribution of the production system when the k+1th task is completed;

[0099] The multi-task comprehensive reliability evaluation module 304 is used to evaluate the comprehensive reliability of two subsequent consecutive tasks of the production system.

[0100] In one embodiment, the system construction unit 1 includes a maintenance interval status module 101, a maintenance target module 102, a maintenance sequence module 103 and a maintenance strategy module 104;

[0101] Among them, the maintenance interval state module 101 is used to indicate the state of the production system at the beginning of the kth maintenance interval;

[0102] Maintenance target module 102, used to construct maintenance target decision variables;

[0103] A maintenance sequence module 103 is used to construct maintenance sequence decision variables;

[0104] The maintenance strategy module 104 is used to record the maintenance strategy of the maintenance interval based on the maintenance target and the maintenance sequence.

[0105] Specifically, the tasks and maintenance intervals of the production system are distributed as follows: Figure 2 As shown in the figure, there is a maintenance interval between two adjacent tasks. At present, the production system has completed k-1 tasks and is preparing to start the kth maintenance interval. The production system contains N devices, among which device l has n l states, and use represents the state of the production system at the beginning of the kth maintenance interval, represents the state of equipment l at the beginning of the kth maintenance interval, t B,k and t M,k They represent the kth maintenance interval and the time when the kth task ends. The maintenance plan needs to determine the maintenance goals of each device at this time. Y l TS,k represents the maintenance target of device l in the kth maintenance interval, that is, if the maintenance task for device l is completed, the state of device l will change from Change to Y l TS,k At the same time, due to the uncertainty of the execution time of equipment maintenance tasks, it cannot be guaranteed that all planned maintenance tasks can be completed within the maintenance interval. The equipment at the front of the maintenance queue has a higher probability of completing maintenance. Therefore, the maintenance order is also a very important decision variable. represents the maintenance order of all equipment to be repaired within the kth maintenance interval, Y l SE,k =1 means that equipment l is the first to be repaired in the kth maintenance interval, Y l SE,k =0 means that equipment l does not need to be maintained during the kth maintenance interval, and the maintenance strategy of the kth maintenance interval is recorded as Y k =[Y TS,k ,Y SE,k ]; The selective maintenance model proposed in this embodiment that simultaneously considers the reliability of two adjacent tasks is referred to as a dual-task model, and the selective maintenance model that considers the reliability of a single task is referred to as a single-task model.

[0106] In one embodiment, the assumption rule establishing unit 2 includes a first assumption rule module 201, a second assumption rule module 202, a third assumption rule module 203, a fourth assumption rule module 204 and a fifth assumption rule module 205;

[0107] The first assumption rule module 201 is used to represent the production capacity of the equipment. When the equipment is in state i, the production capacity of the equipment is represented by g l,i , when the production capacity of equipment l at any time t is expressed as G l (t);

[0108] The second assumption rule module 202 is used to indicate that the maintenance task execution time of the equipment within the maintenance interval and the state degradation time within the task both obey exponential distribution;

[0109] The third assumption rule module 203 is used to represent the production capacity of the entire production system at any time t;

[0110] The fourth assumption rule module 204 is used to indicate that the selected maintenance actions are performed sequentially within the task interval, and the maintenance actions can only be performed within the task interval, and the equipment cannot be repaired within the task;

[0111] The fifth assumption rule module 205 is used to indicate that the device state will not degrade within the task interval.

[0112] Specifically, without loss of generality, five assumptions are made in this embodiment;

[0113] The first assumption rule: When the device is in state i (i = 1, 2, ..., n l ), the production capacity of the equipment is g l,i , i=1 indicates a complete failure state, at which time g l,i =0, i=n l Indicates that the state is a brand new state; the production capacity of equipment l at any time t is represented by G l (t);

[0114] The second assumption rule: The execution time of the maintenance task within the maintenance interval and the state degradation time of the equipment within the task both obey the exponential distribution, so the maintenance task execution process and the equipment state degradation process can both be described by the Markov model;

[0115] The third assumption rule: The production capacity of the entire production system at any time t is expressed as G(t). G(t) is determined by the equipment status and the production system structure. in represents the production system structure function;

[0116] When two devices are connected in series, g2(t))=min{G1(t),G2(t)}; When two devices are connected in parallel, g2(t))=G1(t)+G2(t);

[0117] Fourth assumption rule: The selected maintenance actions are performed sequentially during the task interval, and maintenance actions can only be performed during the task interval, and equipment cannot be repaired during the task;

[0118] Fifth Assumption Rule: The equipment status will not degrade during the task interval.

[0119] In one embodiment, analyzing the production system status distribution at the end of the kth maintenance interval includes:

[0120] Based on the constraint rules of the selective maintenance model and combined with the maintenance strategy of the maintenance interval, the first state transfer equation is constructed;

[0121] According to the first state transfer equation, a first initial condition is set;

[0122] Calculate the maintenance cost required by the maintenance queue and analyze the status of equipment l at the end of the kth maintenance interval;

[0123] Analyze device l in state s l The probability of and the probability that the production system is in state s.

[0124] Specifically, according to the fourth assumption rule, the execution time of the maintenance task of each device follows an exponential distribution. Therefore, the number of devices that have completed maintenance at time t is a variable. N(t) is defined as the state of the maintenance queue. Then, according to the maintenance strategy Y k It can be seen that in the kth maintenance interval, there are H(k)=max(Y SE,k ) equipment needs repair; represents the probability that the maintenance queue is in state n at time t, that is, the probability that n equipment has been repaired. represents the state distribution of the maintenance queue at time t; according to The definition of and the state transfer relationship can give the expression of the first state transfer equation.

[0125] Specifically, let l(i) represent the equipment number corresponding to the i-th equipment to be repaired in the maintenance queue, and we can get:

[0126]

[0127] So we get α i,i+1 =μ l(i),(x,y) ; where μ l(i),(x,y) represents the maintenance rate of equipment l(i) from state x to state y,

[0128] Specifically, at the beginning of the kth maintenance interval (i.e., t=t M,k-1 ), the equipment in the maintenance queue begins to be repaired in sequence, thereby obtaining the initial condition of the first state transfer equation expression, which is represented by the first initial condition.

[0129] Specifically, combining the first state transfer equation expression with the first initial condition, we can obtain any t≥t M,k-1 The state distribution of the maintenance queue at the moment, in this embodiment, let P M,k =P M (tB,k ) indicates the end of the kth maintenance interval (i.e., t = t B ,k ) Status distribution of the maintenance queue.

[0130] Specifically, in this embodiment, when formulating the maintenance strategy, it is required that the maintenance cost required by the maintenance queue is not higher than the preset cost C of the kth maintenance interval. Budget,k , the expression is: In the formula, c l,(x,y) represents the cost required to repair equipment l from state x to state y, y=Y l TS,k .

[0131] Specifically, when the kth maintenance interval ends, the production system immediately starts the kth task. At this time, the maintenance queue state can be directly converted into the state of each device. Let S l (t) represents the state of device l at any time t, S(t) = [S1(t), S2(t), L, S N (t)] represents the state of the production system at any time t. B,k )=n, the state of device 1 is represented by the state expression of device 1.

[0132] Specifically, in Under the condition, when t = t B,k When the device l is in state s l The probability expression of Under the condition, when t = t B,k When , we get the probability expression that the production system is in state s.

[0133] In one embodiment, the first state transition equation is expressed as:

[0134]

[0135] In the formula, α i,j represents the transition rate of the maintenance queue from state i to state j, α i-1,i represents the maintenance rate of the i-th equipment in the maintenance queue;

[0136] Specifically, according to the fourth assumption rule, only one device in the maintenance queue can complete maintenance at a certain time, that is, only when j=i+1 i,j ≠0, other α i,j =0,i=1,2,...,H(k).

[0137] The expression of the first initial condition is:

[0138] P M (tM,k-1 )=[1,0,...,0];

[0139] In the formula, t M,k-1 represents the time when the kth maintenance interval starts;

[0140] The state expression of device l is:

[0141]

[0142] Specifically, the state expression of device 1 indicates that if the maintenance queue state (the number of repaired devices) is greater than or equal to the maintenance order of device 1, it means that device 1 has been repaired and its state has been restored to the target state, otherwise device 1 has not been repaired and remains in the initial state.

[0143] Device l is in state s l The probability expression is:

[0144]

[0145] The probability expression of the production system being in state s is:

[0146]

[0147] Where s∈S, S represents the complete set of production system states.

[0148] In one embodiment, analyzing the production system status distribution at the end of the kth task includes:

[0149] Based on the constraint rules of the selective maintenance model, the second state transfer equation is constructed;

[0150] According to the second state transfer equation, a second initial condition is set;

[0151] Based on the second initial condition, calculate the probability that device l is in state i, and analyze the state distribution of device l;

[0152] Using the general generating function method, solve the u function of equipment l and calculate the u function of the production system;

[0153] Based on the u function of the production system, solve the reliability of the production system;

[0154] Based on the maintenance time of the equipment in the kth maintenance interval and the state degradation time of the equipment in the kth task, analyze the equipment l in state s l The probability that the production system is in state s=[s1,s2,…,s N ] probability.

[0155] Specifically, let Q l,i (t) = Pr{Sl (t) = i} represents the probability that device l is in state i at time t, i = 1, 2, ..., n l , represents the state distribution of device l at time t; according to the fourth assumption rule, the equipment cannot be repaired within the task, so the device l within the task can only degenerate from a better state to a worse state, thus obtaining the second state transfer equation.

[0156] Specifically, if at the start of the kth task (i.e., t = t B,k ), device l is in state sl, that is, S l (t B,k )=s l , thus obtaining the initial condition of the second state transfer equation expression, expressed as the second initial condition.

[0157] Specifically, combining the second state transfer equation expression with the second initial condition, we can obtain l (t B,k )=s l Under the condition, any t ≥ t B,k The state distribution of device l at time instant is denoted as in, Indicates that in S l (t B,k )=s l Under the condition of t≥t B,k The probability that device l is in state i at the moment, so Indicates that in S l (t B,k )=s l Under the condition, at the end of the kth task (i.e. t = t M,k ), the state distribution of device l.

[0158] Specifically, the universal generating function method (UGF) is an effective tool for evaluating the production capacity of a multi-state system. In this embodiment, let Indicates that in S l (t B,k )=s l Under the condition, when t = t M,k When the u function of device l is obtained, the u function expression of device l is obtained; let U k (s) indicates that in S(t B,k )=s, when t=t M,k When S(t B,k )=s, when t=t M,k When the reliability of the production system is R M,k (s), and obtain the expression of the reliability of the production system.

[0159] Specifically, considering the uncertainty of the equipment maintenance time in the kth maintenance interval and the equipment state degradation time in the kth task, Under the condition, when t = t M,k When the device l is in state s l The probability expression of S(t M,k-1 )=X k Under the condition, when t = t M,k When , we get the probability expression that the production system is in state s = [s1, s2, …, sN].

[0160] In one embodiment, the second state transition equation is expressed as:

[0161]

[0162] In the formula, λ l,i,j represents the transition rate of device l from state i to state j;

[0163] The second initial condition expression is:

[0164]

[0165] The u function expression of device l is:

[0166]

[0167] The u function expression of the production system is;

[0168]

[0169] Where N CAP represents the total production capacity of the production system, represents the j-th production capacity of the production system, Indicates that in S(t B,k )=s condition, probability;

[0170] The reliability of the production system is expressed as:

[0171]

[0172] Where W k represents the required production capacity of the kth task;

[0173] Device l is in state s l The probability expression is:

[0174]

[0175] The production system is in state s = [s1, s2, …, s N The probability expression of ] is:

[0176]

[0177] In one embodiment, analyzing the production system status distribution at the end of the k+1th task includes:

[0178] Based on the execution time of equipment maintenance tasks, the probability of the production system being in state i at the end of the k+1th maintenance interval is analyzed;

[0179] Based on the constraint rules and aiming at maximizing task reliability, the maintenance target of the production system within the k+1th maintenance interval is found.

[0180] Specifically, the k+1th stage includes the k+1th maintenance interval and the k+1th task. Since the reliability of the k+1th task is predicted at the end of the k-1th task, the maintenance situation cannot be fully understood. Therefore, the maintenance process in the k+1th maintenance interval is calculated using a deterministic process, that is, the execution time of each equipment maintenance task is a constant. In this embodiment, the mean execution time of the maintenance task is used instead of the maintenance task execution time, so that in S(t M,k )=s, when the k+1th maintenance interval ends (i.e. t=t B,k+1 ), the production system is in state i=[i1,i2,...,i N The probability expression of ] is:

[0181]

[0182] In the formula, Indicates that device l changes from state s l Repair to l The average time; T B,k+1 =t B,k+1 -t M,k Indicates the length of the k+1th maintenance interval.

[0183] Specifically, the probability expression of the production system being in state i cannot uniquely determine the maintenance target of the production system in the k+1th maintenance interval. Therefore, it is necessary to use the system reliability of the k+1th task to determine the maintenance target. Under the constraint of satisfying the maintenance resources, find the state that enables the system to achieve the maximum task reliability in the k+1th task. In the above embodiment, let S TS,k+1 (s) indicates that in S(t M,k )=s, the maintenance target of the system in the k+1th maintenance interval is expressed as:

[0184]

[0185] In one embodiment, evaluating the combined reliability of two consecutive tasks of a production system includes:

[0186] Based on the uncertainty of the execution time of the maintenance task within the kth maintenance interval, the kth reliability is analyzed;

[0187] Based on the divergence of the production system status at the end of the kth task, the comprehensive reliability of the kth and k+1th tasks is analyzed.

[0188] Specifically, the production system optimizes the maintenance strategy at the beginning of the kth maintenance interval, which needs to be judged based on the reliability of the next two tasks. The reliability of the kth task takes into account the uncertainty of the execution time of the maintenance task within the kth maintenance interval, and the reliability of the k+1th task inherits the divergence of the state of the production system at the end of the kth task. In this embodiment, let R SYN,1 (k) indicates that in S(t M,k-1 )=X k Under this condition, the reliability of the kth task is expressed as:

[0189]

[0190] Then let R SYN,2 (k) indicates that in S(t M,k-1 )=X k Under the condition, the comprehensive reliability of the kth and k+1th tasks is expressed as:

[0191]

[0192] In order to facilitate understanding of the above technical solution of the present invention, the following example of a series-parallel production system consisting of four devices performing two consecutive tasks is used to demonstrate the effectiveness of the model constructed by the present invention, and the specific description is as follows:

[0193] like Figure 3 As shown, the production system includes two sub-production systems, each of which has two independent devices and each has a different number of states, where devices 1, 2, 3, 4, and 5 have 4, 4, 3, and 3 states respectively. The initial state of the production system is assumed to be X k =[1,1,1,3,2]; the sub-production system of equipment 1, equipment 2 and equipment 3 in parallel is connected in series with the sub-production system of equipment 4 and equipment 5 in parallel to form a series-parallel production system. Each device has a finite number of states. All possible states and corresponding production capacity values ​​are shown in Table 1.

[0194] Table 1 Average production capacity value g of each equipment under each state l,i(tons / hour)

[0195]

[0196] The maintenance time of each device is a random variable and obeys exponential distribution. The mean maintenance time of each device is shown in Table 2.

[0197] Table 2 Average time for maintenance status transfer of each equipment / (Hour)

[0198]

[0199] The maintenance cost of each equipment is shown in Table 3.

[0200] Table 3 Maintenance cost of each equipment c lxy / (10,000 yuan)

[0201]

[0202] Within the task, the transition rate of each device state degradation is shown in Table 4.

[0203] Table 4 Degradation transition rate of each device state / (0.01day-1)

[0204]

[0205] The two tasks are executed continuously, and the specific parameters of the tasks are shown in Table 5.

[0206] Table 5 Task parameters

[0207]

[0208] The optimization method adopts the composite particle swarm optimization algorithm, in which the number of particles is 40, the maximum number of iterations is 250,000, the maximum speed is 0.8, the inertia factor is 0.6, and the acceleration constant is 2.

[0209] According to the above model assumptions, the maintenance strategies of the dual-task model, single-task model and deterministic model can be obtained, as shown in Table 6. The deterministic model refers to the framework of the dual-task model without considering the uncertainty of the maintenance time.

[0210] Table 6 Optimal solutions of examples under various conditions

[0211]

[0212] In X k=[1,1,1,3,2], the dual-task model only needs to repair equipment 2 and equipment 3 from state 1 to state 2. Equipment 2 is repaired first, and then equipment 3 is repaired. Other equipment that are not repaired are sorted in order. This maintenance strategy is defined as strategy 1. In the kth task, the system task reliability R SYN,1 (k) = 0.8827, the comprehensive reliability of the two tasks R SYN,2 (k) = 1.5485; the single-task model only needs to repair device 2 from state 1 to state 2, and the other devices are not repaired. This maintenance strategy is defined as strategy 2; in the kth task, R SYN,1 (k) is also equal to 0.8827; Under the condition of maintenance uncertainty, find the R that the system can obtain from each state at the beginning of the k+1th maintenance interval. SYN,1 (k+1), such as Figure 4 and Figure 5 As shown in the figure, the main state distribution of the production system and the corresponding R at the beginning of the k+1th maintenance interval under different maintenance strategies are listed. SYN,1 (s,k+1), R SYN,1 (s,k+1) represents the B,k+1 )=s, the reliability of the k+1th task can be obtained by referring to the reliability expression of the kth task.

[0213] like Figure 4 and Figure 5 As shown in the figure, the main state distributions generated by the two maintenance strategies at the beginning of the k+1th maintenance interval are listed, where the probability of each state appearing at the end of the task is greater than 0.01. Figure 4 represents the results of the dual-task model. The broken line represents the distribution of the main states at the beginning of the k+1th maintenance interval, among which state 12232 is the most important state with a probability of 63.09%, and the mission reliability that can be achieved by this state is 0.7358; Figure 5 It represents the results produced by the single-task model, among which state 12132 is the most important state, with a probability of 70.34%. The mission reliability that this state can achieve is 0.6376. In addition, the sum of the probabilities of states 11132, 12112 and 11112 is nearly 18%. Even after the k+1th maintenance interval, the system cannot complete the k+1th mission.

[0214] If the uncertainty of maintenance time is not considered, the maintenance target Y l TS,k=[1,3,2,3,2], it is necessary to repair device 2 from state 1 to state 3, and device 3 from state 1 to state 2. Moreover, the repair sequence of device 2 and device 3 has no effect on the system task reliability; however, if the uncertainty of the repair time is introduced, two repair sequences will be generated, namely [3,1,2,4,5] and [3,2,1,4,5]. The first repair sequence corresponds to R SYN,1 (k) = 0.8696, R SYN,2 (k)=1.5364, R corresponding to the second maintenance sequence SYN,1 (k) = 0.8111, R SYN,2 (k) = 1.4991. Therefore, Y l SE,k =[3,1,2,4,5] is the maintenance sequence, and this maintenance strategy is defined as strategy 3. It can be seen that compared with Y1, Y3 has a certain improvement in maintenance target, which is reflected in the target state of equipment 2 being state 3, and the maintenance sequence has not changed. Because the maintenance target of Y3 is relatively high, it may not be achieved within the kth maintenance interval. Therefore, the production system state is dispersed at the beginning of the kth task, and then the production system state is more dispersed at the end of the kth task. The corresponding performance of Y3 is as follows Figure 6 As shown, at the end of the kth task, the state with the highest probability of occurrence is 13232, and the corresponding probability of occurrence is only 54.80%, and the number of states with a probability of occurrence exceeding 1% reaches 9, while the number of states of the other two strategies is 6. In general, not considering the uncertainty of maintenance time will lead to a more dispersed state of the production system, making the performance of the production system lower than expected. The comparison shows the effectiveness and superiority of the model constructed by the present invention.

[0215] like Figure 7 According to another embodiment of the present invention, a method for analyzing the selective maintenance sequence of a multi-task equipment with production requirements is provided. The method for analyzing the selective maintenance sequence of a multi-task equipment with production requirements comprises the following steps:

[0216] S1. Develop a maintenance strategy for the production system and build a selective maintenance model;

[0217] S2. Based on the degradation time and maintenance time of the production system state, set the constraint rules of the selective maintenance model;

[0218] S3. Based on the constraint rules, the reliability of the next two consecutive tasks of the production system is predicted, and the maintenance strategy of the production system is optimized using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability.

[0219] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A selective maintenance sequence analysis system for multi-task equipment with production requirements, characterized in that: The production demand multi-task equipment selective maintenance sequence analysis system includes a maintenance strategy and model building unit, an assumption rule building unit and a production system status analysis unit, wherein the production system status analysis unit includes a maintenance task status analysis module, a first continuous task status analysis module, a second continuous task status analysis module and a multi-task comprehensive reliability evaluation module; Wherein, the maintenance strategy and model building unit is used to formulate a maintenance strategy for the production system and build a selective maintenance model; The assumption rule establishment unit is used to set the constraint rules of the selective maintenance model based on the production system state degradation time and maintenance time; The production system status analysis unit is used to predict the reliability of two subsequent continuous tasks of the production system based on constraint rules, and optimize the maintenance strategy of the production system using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability; The maintenance task status analysis module is used to analyze the k The state distribution of the production system at the end of each maintenance interval; The first continuous task state analysis module is used to analyze the k The state distribution of the production system at the end of each task; The second continuous task state analysis module is used to analyze the k +1 The status distribution of the production system at the end of the task; The multi-task comprehensive reliability evaluation module is used to evaluate the comprehensive reliability of two subsequent consecutive tasks of the production system.

2. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 1, characterized in that: The maintenance strategy and model building unit includes a maintenance interval status module, a maintenance target module, a maintenance sequence module and a maintenance strategy module; Wherein, the maintenance interval status module is used to indicate the k The state of the production system at the beginning of each maintenance interval; The maintenance target module is used to construct maintenance target decision variables; The maintenance sequence module is used to construct maintenance sequence decision variables; The maintenance strategy module is used to record the maintenance strategy of the maintenance interval based on the maintenance target and the maintenance sequence.

3. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 2, characterized in that: The assumption rule establishment unit includes a first rule module, a second rule module, a third rule module, a fourth rule module and a fifth rule module; The first rule module is used to indicate the production capacity of the equipment. i The production capacity of the equipment is expressed as g l,i , when at any time t Time Equipment l The production capacity is expressed as G l ( t ); The second rule module is used to indicate that the maintenance task execution time of the equipment within the maintenance interval and the state degradation time within the task both obey exponential distribution; The third rule module is used to represent the entire production system at any time t production capacity; The fourth rule module is used to indicate that the selected maintenance actions are performed in sequence within the task interval, and the maintenance actions can only be performed within the task interval, and the equipment cannot be repaired within the task; The fifth rule module is used to indicate that the device state will not degrade within the task interval.

4. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 3, characterized in that: The analysis k The distribution of production system status at the end of each maintenance interval includes: Based on the constraint rules of the selective maintenance model and combined with the maintenance strategy of the maintenance interval, the first state transfer equation is constructed; According to the first state transfer equation, a first initial condition is set; Calculate the maintenance costs required for the maintenance queue and analyze the k At the end of each maintenance interval, the equipment l Status; Analytical equipment l In state s l The probability that the production system is in state s probability.

5. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 4, characterized in that: The first state transfer equation is expressed as: ; In the formula, α i,i+1 Indicates that the maintenance queue is in the state i Transfer to state i +1 transfer rate, α i-1,i Indicates that the maintenance queue is in the state i -1 transfer to state i The transfer rate, P i M ( t )express t The maintenance queue is in i The probability of the state, H ( k ) indicates the k The number of devices that need to be repaired within a maintenance interval; The expression of the first initial condition is: ; In the formula, P M ( t M,k-1 )express t M ,k-1 The state distribution of the maintenance queue at each moment, t M,k-1 Indicates k The time when a maintenance interval starts; The device l The state expression is: ; In the formula, S l ( t B,k ) indicates the k Maintenance interval equipment l status, t B,k Indicates k Maintenance intervals, Y l TS,k Indicates k Equipment within maintenance interval l The maintenance goal, X l k Indicates k At the beginning of each maintenance interval, the equipment l Status, Y l SE,k Indicates k Equipment within maintenance interval l The maintenance sequence, n Indicates the number of maintenance equipment; The device l In state s l The probability expression is: ; In the formula, S l ( t M,k-1 ) indicates the k At the beginning of each maintenance interval, the equipment l status, H ( Y k ) indicates the use of maintenance strategy Y k No. k The number of devices that need to be repaired within a maintenance interval, P n M,k Indicates k Maintenance at the end of the maintenance interval n The probability of a device; The production system is in state s The probability expression is: ; In the formula, S ( t B,k ) indicates that k The system status at the end of each maintenance interval, S ( t M,k-1 ) indicates that k The system status at the start of a maintenance interval, X k Indicates k The system status at the start of each maintenance interval, , represents the complete set of production system states, N Indicates the number of devices in the system.

6. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 5, characterized in that: The analysis k The status distribution of the production system at the end of each task includes: Based on the constraint rules of the selective maintenance model, the second state transfer equation is constructed; According to the second state transfer equation, a second initial condition is set; Based on the second initial condition, the computing device l In state i probability, and analyze the device l The state distribution of Using the general generating function method, solve the device l of u function, and calculate the production system u function; Based on production system u Function, solve the reliability of the production system; Based on k The maintenance time of the equipment within a maintenance interval is k The state degradation time of the equipment in each task is analyzed. l In state s l The probability that the production system is in state s probability.

7. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 6, characterized in that: The second state transfer equation is expressed as: ; In the formula, λ l,i,j Indicates the device l From the status i Transfer to state j The transfer rate, Q l,j ( t )express t Time equipment l In state j The probability of n l Indicates the device l The number of states; The second initial condition expression is: ; The device l of u The function expression is: ; In the formula, Indicates the device l of u function, Indicated in S l ( t B,k )= s l Under the conditions, k At the end of each task, the device l In state i l The probability of Indicates the device l In i l Status z function; the production system u The function expression is; , where U k ( s ) represents the production system u function, Indicates that the system is at production capacity [ g 1,j1 , g 2,j2 ,..., g N,jN ]of z function, G ( t M,k ) indicates the k The production capacity of the production system at the end of each task, R M,k ( s ) means in S ( t B,k )= s conditions, when t = t M,k The reliability of the system, N CAP represents the total production capacity of the production system, The production system j Production capacity, Indicated in S ( t B,k )= s conditions, probability; The expression of the reliability of the production system is: ; In the formula, W k Indicates k The required production capacity of each task; The device l In state s l The probability expression is: ; In the formula, S l ( t M,k ) indicates a device l In state s l The probability of Indicated in l ( t B,k )= X l Under the conditions, k At the end of each task, the device l In state s l The probability of Indicated in S l ( t B,k )= Y l TS Under the conditions, k At the end of each task, the device l In state s l probability; The production system is in state s The probability expression is: .

8. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 7, characterized in that: The analysis k +1 The status distribution of the production system at the end of the task includes: Based on the execution time of equipment maintenance tasks, analyze the k +1 Maintenance interval ends with the production system in state i probability; Based on the constraint rules, with the goal of maximizing task reliability, we find the production system in the k +1 repair target per repair interval.

9. A selective maintenance sequence analysis system for multi-task equipment according to production demand according to claim 8, characterized in that: The comprehensive reliability of two consecutive tasks of evaluating the production system includes: Based on k The uncertainty of the maintenance task execution time within the maintenance interval is analyzed. k Reliability of each task; Based on k The divergence of the state of the production system at the end of each task, and the analysis of the k The first k +1 mission's overall reliability.

10. A method for analyzing the selective maintenance sequence of multi-task equipment with production requirements, used to implement the system for analyzing the selective maintenance sequence of multi-task equipment with production requirements as claimed in any one of claims 1 to 9, characterized in that: The selective maintenance sequence analysis method for production demand multi-task equipment includes the following steps: S1. Develop a maintenance strategy for the production system and build a selective maintenance model; S2. Based on the degradation time and maintenance time of the production system state, set the constraint rules of the selective maintenance model; S3. Based on the constraint rules, the reliability of the next two consecutive tasks of the production system is predicted, and the maintenance strategy of the production system is optimized using the constructed selective maintenance model with the goal of maximizing the comprehensive reliability.

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