Multi-component system opportunity maintenance optimization method based on differentiated maintenance time window and incomplete maintenance effect

Abstract

The invention provides a multi-component system opportunity maintenance optimization method based on a differentiated maintenance time window and an incomplete maintenance effect, and is applied to the technical field of operation and maintenance management of wind power equipment. According to the method, firstly, part faults are divided into a damage class and an essential fatigue class according to the maintenance effect, and a mixed fault rate model is established to accurately describe the incomplete maintenance effect; then, a maintenance or replacement decision criterion of the individual part is formulated; furthermore, a two-stage optimization framework is proposed initiatively: in the first stage, a system-level basic opportunity maintenance time window is determined, and in the second stage, a differentiated time window scale factor is optimized for each component, so that a customized opportunity maintenance time window is generated for each component. The method has the beneficial effects that through refined modeling and differential optimization, the total maintenance cost and downtime of the multi-component system in a planning period are remarkably reduced, and the scientificity and economy of a maintenance strategy are improved.

Description

Technical Field

[0001] This invention relates to the field of equipment maintenance for complex multi-component systems of wind turbine generators, and in particular to an optimization method for opportunistic maintenance strategies of wind turbine generators based on differentiated maintenance time windows and incomplete maintenance effects. Background Technology

[0002] As a high-value asset operating in harsh environments with poor maintenance accessibility, wind turbines face significant challenges in operation and maintenance management. The complex system comprised of multiple key components exhibits economic interdependence, making opportunistic maintenance-based collaborative maintenance strategies an effective way to reduce operation and maintenance costs. However, traditional opportunistic maintenance strategies have significant limitations when applied to the wind power sector: Firstly, existing methods typically set a uniform opportunistic maintenance time window for the system, ignoring the differences in fault characteristics, degradation rates, and maintenance costs among wind turbine components, and failing to differentiate window components. This can easily lead to premature maintenance of critical components, wasting their remaining lifespan, or causing minor components to miss their optimal maintenance window, increasing the risk of failure. Secondly, existing models generally ignore the differences in the effectiveness of preventative maintenance for different fault types. In actual operation, routine maintenance such as lubrication and cleaning can effectively alleviate wear-related faults, but has little effect on fundamental faults such as material fatigue. This difference in maintenance effectiveness is not fully considered in existing opportunistic maintenance models, causing maintenance strategies to deviate from engineering reality. Therefore, this invention proposes an opportunistic maintenance optimization method that can simultaneously consider component differences and the incompleteness of maintenance effects. Summary of the Invention

[0003] This invention addresses the problems of high maintenance costs and inaccurate strategies caused by the simplistic formulation and model distortion of traditional maintenance strategies. Specifically, it requires generating a maintenance calendar for wind power equipment operation, containing a series of maintenance time points, the component combinations involved in maintenance at each time point, the specific maintenance methods adopted for each component in the combination, and the system downtime caused by each maintenance. Based on this requirement, it is necessary to distinguish component failure types and optimize the size of the opportunistic maintenance time window and the specific maintenance decisions for each component.

[0004] To achieve the above-mentioned technical features, the objective of this invention is as follows: a method for optimizing the opportunistic maintenance of a multi-component system based on differentiated maintenance time windows and incomplete maintenance effects, the optimization method comprising the following steps: Step 1: Set input parameters to classify component failures into damage-related failures affected by preventive maintenance and inherent fatigue-related failures unaffected by preventive maintenance, and establish a mixed failure rate model based on the Weibull distribution. Step 2: Trigger preventive maintenance by setting a reliability threshold, and make a decision on whether to perform incomplete preventive maintenance or preventive replacement for the parts that have triggered maintenance and the parts that are opportunistically repairable, based on the expected number of failures after maintenance and related costs. Step 3: Establish a cost calculation model; Step 4: Optimize the solution for the system-level basic opportunity maintenance time window W, with the goal of minimizing the total system maintenance cost during the planning period; Step 5: Using the obtained W as a benchmark, and aiming to minimize the total system maintenance cost within the planning period, calculate the maintenance cost for each component in the system. i Optimize a differentiated opportunity repair time window ratio factor k i Thus determining the components i Personalized repair opportunity window k i W; Step 6: Based on the optimal W obtained from the solution... k i It generates a series of maintenance time points, the combination of components involved in maintenance at each time point, the specific maintenance method adopted for each component in the combination, and the system downtime caused by each maintenance.

[0005] Preferably, step 1 is specifically performed as follows: Based on the Weibull distribution, system modeling and parameter initialization are performed: the system is defined to consist of M components, and maintenance-related parameters are initialized for each component, including: initial failure rate distribution parameters, damage-type failure ratio factor, inherent fatigue-type failure ratio factor, corrective maintenance cost, incomplete preventive maintenance cost, preventive replacement cost, time required for various maintenance activities, system setup cost, unit downtime cost, and planning period. Based on the input initialization parameters, the components... i Initial failure rate function categorized into damage-related failures The initial failure rate function of intrinsic fatigue failure. The following formula: ; in: and Each represents a component i The shape and scale parameters, while assuming and Components i The ratio factor between damage-related failures and inherent fatigue failures satisfies ; For damage-related failures, a hybrid failure rate model is used to describe the effectiveness of incomplete preventative maintenance: in components i No.j After the preventive maintenance, the damage-related failure rate function is updated, incorporating both the service life regression factor and the failure rate adjustment factor. However, for fatigue-related failures, preventive maintenance has no effect on inherent fatigue-related failures; therefore, the component... i In the j Reliability function per maintenance cycle Represented as: ; in: , Indicates components i No. j -1 calendar time for preventative maintenance; Indicates components i No. j -1 year of service life before the first maintenance Indicates components i No. j The length of a maintenance cycle; Indicates components i No. j -1 preventive maintenance failure rate adjustment factor; Indicates components i No. j -Service life adjustment factor for one preventative maintenance; for any and ,when j When =0, , ;when j When it is a positive integer, , .

[0006] Preferably, step 2 specifically involves the following process: The determination of when to perform maintenance on a critical component is expressed as: setting a reliability threshold for the component. When the component i Reliability reaches [a certain level] at the end of the current maintenance cycle. If this occurs, preventative maintenance of the component will be triggered; For components that trigger preventative maintenance i The decision-making criterion formula for deciding whether to adopt incomplete preventive maintenance or preventive replacement is as follows: ; in: and Each represents a component i The expected number of damage-related failures and inherent fatigue-related failures in the next maintenance cycle when incomplete preventive maintenance is adopted. Indicates components iThe length of the next maintenance cycle when incomplete preventive maintenance is adopted; and Each represents a component i The expected number of damage-related failures and inherent fatigue-related failures within the first maintenance cycle after replacement measures are implemented. Indicates components i The length of the first maintenance cycle after replacement measures are taken; Indicates components i Number of damage-related failures Indicates components i The number of inherent fatigue-related failures was recorded. The determination of the timing of maintenance for non-initiating components can be expressed as determining whether to participate in opportunistic maintenance by judging whether the planned maintenance time falls within the time window of its own differentiated opportunity maintenance that is opened due to the maintenance of other components. For components that do not trigger preventative maintenance j The decision-making criterion formula for deciding whether to adopt incomplete preventive maintenance or preventive replacement is as follows: ; in, Indicates components j Downtime due to incomplete preventative maintenance Indicates components j The downtime for which replacement measures are taken is expressed by the following formulas.

[0007] .

[0008] Preferably, step 3 specifically involves the following process: Establish a cost model, assuming the system's planning period is PH, then the specific formula for the total maintenance cost incurred during the planning process is as follows: ; 1) C m It is the cost of restorative repairs. M The specific restorative maintenance cost of a system composed of individual components during the planning period is as follows: ; in: Indicates components i Repair costs for damage-related faults Indicates components i Repair costs for inherent fatigue-related faults Indicates components i The number of maintenance phases during the planning period (PH), that is, the period from when a component is put into use to when it is scrapped is considered one maintenance phase. Indicates components i In the k The number of preventative maintenance operations performed within a maintenance phase, including incomplete preventative maintenance and preventative replacements. Indicates components i In the k Within the first maintenance phase j The length of a preventative maintenance cycle; 2) C p It is the cost of preventative maintenance. M The incomplete preventive maintenance cost of a system composed of individual components during the planning period is expressed by the following formula: ; in: Indicates components i Costs of incomplete preventative maintenance; Indicates components i In the k The number of incomplete preventive maintenance operations performed in each maintenance phase; 3) C r It's the replacement cost. M The replacement cost of a system composed of individual components during the planning period is specifically described as follows: ; in: It is the cost of replacing parts; Indicates the first i The number of times each component will be replaced during the planning period; 4) C d It refers to downtime cost, the downtime cost per unit of time. c d If so, the total downtime cost of the system during the planning period can be expressed by the following formula: ; Among them: components i Incomplete preventive maintenance time is Preventive replacement time is When multiple components are repaired together, the downtime is taken as the maximum value of the repair time of each component. Assume the system performed a total of [number] operations during the planning period. N Second preventive maintenance, the first j The time required for each preventative maintenance is ; Components within the planning period i The total time spent on troubleshooting is expressed by the following formula: ; in: part i Repair time for damage-related faults This refers to the repair time for inherent fatigue-related faults; 5) C os It saves on setup costs; when multiple components are maintained together for preventative maintenance, setup costs can be reduced; and it saves costs during the planning period. C os It is represented by the following formula; ; in: N 0 represents the total number of opportunistic repairs that occur during the planning period. Indicates participation in the i Number of parts to be repaired per opportunity c s This indicates the setup cost.

[0009] Preferably, step 4 specifically involves the following process: The first phase of determining the system-level basic opportunity maintenance time window is specifically described as follows: W is proposed as the system-level basic opportunity maintenance time window, and the search range within the given system time window is... Within, the total system cost within the planning period PH. C Total (W) With the objective of minimizing the time window, we solve for the optimal system-level opportunistic maintenance time window W. The specific optimization model is shown in the following formula: .

[0010] Preferably, step 5 specifically involves the following process: The second stage of optimization differentiates the time window scaling factor for each component: using the optimal W* obtained in the first stage as a fixed input, a chance maintenance time window scaling factor is set for each component, and the chance maintenance time window for each component is adjusted. Assume the... i The adjustment factor for the opportunity repair time window of each component is: k i Within the given search range of scaling factors for each component Internally, based on the total system cost With the goal of minimizing costs, optimize the solution for each component. i Optimal Differentiation Ratio Factor The specific optimization model is as follows: .

[0011] Preferably, step 6 specifically involves the following process: Based on the final optimal parameter combination, a detailed maintenance plan for the system during the planning period PH is generated. The plan specifically includes: a series of maintenance time points, the combination of components involved in maintenance at each time point, the specific maintenance method adopted for each component in the combination, and the system downtime caused by each maintenance.

[0012] Preferably, the specific repair methods include incomplete repair and replacement.

[0013] The present invention has the following beneficial effects: 1. The present invention provides an opportunistic maintenance optimization method for multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects. It fully considers the problems of high maintenance costs and inaccurate strategies caused by the simple formulation and model distortion of traditional maintenance strategies, so that the maintenance strategy has high economy and rationality.

[0014] 2. This invention significantly reduces the total maintenance cost and downtime of multi-component systems during the planning period through refined modeling and differentiated optimization, improving the scientific and economical nature of maintenance strategies. It proposes an effective maintenance optimization method to address the problems of high maintenance costs and inaccurate strategies caused by the use of a uniform time window and neglect of differences in maintenance effects in traditional opportunistic maintenance strategies. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0016] Figure 1 A flowchart of an opportunistic maintenance optimization method for multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects.

[0017] Figure 2 A schematic diagram of the component system differentiation opportunity maintenance strategy in an embodiment of the present invention.

[0018] Figure 3 The flowchart of the algorithm for solving the two-stage optimization model of this invention.

[0019] Figure 4 Component maintenance plan calendar and maintenance decision diagram. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0021] Example: Wind energy, as a green energy source, is not only environmentally friendly but also offers significant economic benefits, making it a crucial force in driving energy transition and achieving sustainable development goals. Wind turbines, as the core equipment in wind energy development, are not only vital for environmental protection and climate change response but also key factors in promoting sustainable economic development and technological innovation. With the continuous growth of global demand for clean energy, wind turbines will continue to occupy an increasingly important position in the global energy structure. Taking wind turbines as an example, this paper selects four key components—the main shaft, main bearing, generator, and gearbox—and formulates an opportunistic maintenance strategy for wind turbines.

[0022] Considering the characteristics and manageability of the actual problem, the following reasonable assumptions are made about the problem: 1) The failure rate of each component of the system is zero at the initial moment.

[0023] 2) There are two types of faults in each component of the system: the first is damage-related faults, and the second is inherent fatigue-related faults. Preventive maintenance works for damage-related faults, but not for inherent fatigue-related faults.

[0024] 3) Sufficient spare parts are available for maintenance.

[0025] 4) The faults of each component are independent of each other.

[0026] The present invention first requires parameter initialization: defining the system as consisting of M components, and initializing the maintenance-related parameters for each component, including: initial failure rate distribution parameters, damage-related failure ratio factor, inherent fatigue-related failure ratio factor, corrective maintenance cost, incomplete preventive maintenance cost, preventive replacement cost, time required for various maintenance activities, system setup cost, unit downtime cost, and planning period.

[0027] First, set system-level parameters: set the cost. C s = $20,000, unit downtime cost C d = $10,000 / day, planning period PH = 20 years. Reliability models and maintenance cost parameters for four key components of the wind turbine were established. Based on literature references, the key parameters for each component are shown in Table 1: Table 1. Maintenance costs ($), maintenance time (days), and fault-related parameters for major components of wind turbine units.

[0028] To simplify the calculations appropriately, some references were made, and the following values ​​were adopted: Take the maximum opportunity to repair the window. sky, The search step size is 1 day; for any i,Pick ; Each component of the wind turbine j Failure rate adjustment factor for each maintenance a j and service age adjustment factor b j Set the formula as shown below: ; Based on the Weibull distribution, system modeling is performed, and a hybrid failure rate model is constructed for each component; the initial failure rate function for component i's damage class failure is... u The initial failure rate function of intrinsic fatigue failure. v The following formula: ; in: and Each represents a component i The shape and scale parameters, while assuming and Components i The ratio factor between damage-related failures and inherent fatigue failures satisfies ; For damage-related failures, a hybrid failure rate model is used to describe the effectiveness of incomplete preventative maintenance: in components i No. j After the preventive maintenance, the damage-related failure rate function is updated. The update method combines the service life regression factor and the failure rate adjustment factor, and the mathematical relationship is as follows: ; ; in: , Indicates components i No. j -1 calendar time for preventative maintenance; Indicates components i No. j -1 year of service life before the first maintenance Indicates components i No. j The length of a maintenance cycle; Indicates components i No. j -1 preventive maintenance failure rate adjustment factor; Indicates components i No. j -Service life adjustment factor for one preventative maintenance. For any and ,when j When =0, , When j is a positive integer, , .

[0029] For fatigue-related failures, since preventive maintenance is ineffective against inherently fatigue-related failures, the mathematical relationship is as follows: ; ; part i In the j Reliability function per maintenance cycle It can be represented as: ; in: , Indicates components i No. j -1 calendar time for preventative maintenance; Indicates components i No. j -1 year of service life before the first maintenance Indicates components i No. j The length of a maintenance cycle; Indicates components i No. j -1 preventive maintenance failure rate adjustment factor; Indicates components i No. j -Service life adjustment factor for one preventative maintenance; for any and ,when j When =0, , ;when j When it is a positive integer, , .

[0030] The determination of when to perform maintenance on a critical component is expressed as: setting a reliability threshold for the component. When the component i Reliability reaches [a certain level] at the end of the current maintenance cycle. If this occurs, preventative maintenance of the component will be triggered; For components that trigger preventative maintenance i The decision-making criterion formula for deciding whether to adopt incomplete preventive maintenance or preventive replacement is as follows: ; in: and Each represents a component iThe expected number of damage-related failures and inherent fatigue-related failures in the next maintenance cycle when incomplete preventive maintenance is adopted. Indicates components i The length of the next maintenance cycle when incomplete preventive maintenance is adopted; and Each represents a component i The expected number of damage-related failures and the number of inherent fatigue-related failures within the first maintenance cycle after replacement (complete repair) are implemented. Indicates components i The length of the first maintenance cycle after replacement measures are taken. Indicates components i Number of damage-related failures Indicates components i The number of inherent fatigue-related failures was recorded.

[0031] The determination of the timing of maintenance for non-initiating components can be expressed as follows: the first stage determines whether to participate in opportunistic maintenance if the planned maintenance time falls within the opportunistic maintenance time window opened due to the maintenance of other components; the second stage determines whether to participate in opportunistic maintenance if the planned maintenance time falls within the opportunistic maintenance time window with its own characteristics opened due to the maintenance of other components.

[0032] For components that do not trigger preventative maintenance j The decision is made regarding whether to adopt incomplete preventive maintenance or preventive replacement. The decision criterion formula is: ; in, Indicates components j Downtime due to incomplete preventative maintenance Indicates components j The downtime for which replacement measures are taken is expressed by the following formulas.

[0033] .

[0034] Simultaneously, a cost model is established. Assuming the system's planning period is PH, the specific formula for the total maintenance cost incurred during planning is as follows: ; 1) C m It is the cost of restorative repairs. M The specific restorative maintenance cost of a system composed of individual components during the planning period is as follows: ; in: Indicates components iRepair costs for damage-related faults Indicates components i Repair costs for inherent fatigue-related faults Indicates components i The number of maintenance phases experienced during the planning period (PH) (a maintenance phase is defined as the time from when a component is put into use until it is scrapped). Indicates components i In the k The number of preventive maintenance operations performed within a maintenance phase (including incomplete preventive maintenance and preventive replacements). Indicates components i In the k Within the first maintenance phase j The length of a preventative maintenance cycle; 2) C p It is the cost of preventative maintenance. M The incomplete preventive maintenance cost of a system composed of individual components during the planning period is expressed by the following formula: ; in: Indicates components i Costs of incomplete preventative maintenance; Indicates components i In the k The number of incomplete preventive maintenance operations performed in each maintenance phase; 3) C r It's the replacement cost. M The replacement cost of a system composed of individual components during the planning period is specifically described as follows: ; in: It is the cost of replacing parts; Indicates the first i The number of times each component will be replaced during the planning period; 4) C d It refers to downtime cost, the downtime cost per unit of time. c d If so, the total downtime cost of the system during the planning period can be expressed by the following formula: ; Among them: components i Incomplete preventive maintenance time is Preventive replacement time is When multiple components are repaired together, the downtime is taken as the maximum value of the repair time of each component. Assume the system performed a total of [number] operations during the planning period.N Second preventive maintenance, the first j The time required for each preventative maintenance is ; Components within the planning period i The total time spent on troubleshooting is expressed by the following formula: ; in: part i Repair time for damage-related faults This refers to the repair time for inherent fatigue-related faults; 5) C os It saves on setup costs; when multiple components are maintained together for preventative maintenance, setup costs can be reduced; and it saves costs during the planning period. C os It is represented by the following formula; ; in: N 0 represents the total number of opportunistic repairs that occur during the planning period. Indicates participation in the i Number of parts to be repaired per opportunity c s This indicates the setup cost.

[0035] like Figure 3 The flowchart shown is the solution algorithm for the two-stage optimization model of this invention.

[0036] The first phase of determining the system-level basic opportunity maintenance time window is specifically described as follows: W is proposed as the system-level basic opportunity maintenance time window, and the search range within the given system time window is... Within, the total system cost within the planning period PH. C Total (W) With the objective of minimizing the time window (W), we solve for the optimal system-level opportunistic maintenance time window. The optimization model is shown in the following formula: .

[0037] Based on the opportunistic maintenance strategy, with the objective of minimizing the total system maintenance cost within the planning period, the system-level basic opportunistic maintenance time window W* is optimized. Specifically, the maintenance cost rate and maintenance strategy are: C* = 1141242.8, W* = 346.

[0038] The second stage optimizes the differentiated time window scaling factor for each component: using the optimal W* obtained in the first stage as a fixed input, a chance maintenance time window scaling factor is set for each component, and the chance maintenance time window for each component is adjusted. Assume the... iThe adjustment factor for the opportunity repair time window of each component is: k i Within the given search range of scaling factors for each component Internally, based on the total system cost With the goal of minimizing the minimum, optimize the solution to find the optimal differentiation scaling factor for each component i. The optimization model is defined by the following formula: ; Based on the final optimal parameter combination, a detailed maintenance plan for the system during the planning period PH is generated. The plan includes: a series of maintenance time points, the combination of components involved in maintenance at each time point, the specific maintenance method (incomplete maintenance, replacement) for each component in the combination, and the system downtime caused by each maintenance.

[0039] Based on the proposed maintenance window W* value, for each component in the system... i Optimize a differentiated opportunity repair time window ratio factor k i Thus determining the components i Personalized repair opportunity window k i W*. Specific results and parameters are shown in Table 2: Table 2 Repair Time Window and Repair Time Window Ratio Factor for Each Component

[0040] The system generates a sequence of maintenance time points, the component combinations involved in maintenance at each time point, the specific maintenance methods used for each component in the combination, and the system downtime caused by each maintenance. The specific results are shown in Table 3. Table 3 Results of maintenance sequences and other maintenance strategies

[0041] Although the preferred embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many specific modifications under the guidance of the present invention without departing from the spirit of the invention and the scope of protection of the claims, and these modifications all fall within the scope of protection of the present invention.

Claims

1. A method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects, characterized in that, The optimization method includes the following steps: Step 1: Set input parameters to classify component failures into damage-related failures affected by preventive maintenance and inherent fatigue-related failures unaffected by preventive maintenance, and establish a mixed failure rate model based on the Weibull distribution. Step 2: Trigger preventive maintenance by setting a reliability threshold, and make a decision on whether to perform incomplete preventive maintenance or preventive replacement for the parts that have triggered maintenance and the parts that are opportunistically repairable, based on the expected number of failures after maintenance and related costs. Step 3: Establish a cost calculation model; Step 4: Optimize the solution for the system-level basic opportunity maintenance time window W, with the goal of minimizing the total system maintenance cost during the planning period; Step 5: Using the obtained W as a benchmark, and aiming to minimize the total system maintenance cost within the planning period, calculate the maintenance cost for each component in the system. i Optimize a differentiated opportunity repair time window ratio factor k i Thus determining the components i Personalized repair opportunity window k i W; Step 6: Based on the optimal W obtained from the solution... k i It generates a series of maintenance time points, the combination of components involved in maintenance at each time point, the specific maintenance method adopted for each component in the combination, and the system downtime caused by each maintenance.

2. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 1 is as follows: Based on the Weibull distribution, system modeling and parameter initialization are performed: the system is defined to consist of M components, and maintenance-related parameters are initialized for each component, including: initial failure rate distribution parameters, damage-type failure ratio factor, inherent fatigue-type failure ratio factor, corrective maintenance cost, incomplete preventive maintenance cost, preventive replacement cost, time required for various maintenance activities, system setup cost, unit downtime cost, and planning period. Based on the input initialization parameters, the components... i Initial failure rate function categorized into damage-related failures The initial failure rate function of intrinsic fatigue failure. The following formula: ； in: and Each represents a component i The shape and scale parameters, while assuming and Components i The ratio factor between damage-related failures and inherent fatigue failures satisfies ; For damage-related failures, a hybrid failure rate model is used to describe the effectiveness of incomplete preventative maintenance: in components i No. j After the preventive maintenance, the damage-related failure rate function is updated, incorporating both the service life regression factor and the failure rate adjustment factor. However, for fatigue-related failures, preventive maintenance has no effect on inherent fatigue-related failures; therefore, the component... i In the j Reliability function per maintenance cycle Represented as: ； in: , Indicates components i No. j -1 calendar time for preventative maintenance; Indicates components i No. j -1 year of service life before the first maintenance Indicates components i No. j The length of a maintenance cycle; Indicates components i No. j -1 preventive maintenance failure rate adjustment factor; Indicates components i No. j -Service life adjustment factor for one preventative maintenance; for any and ,when j When =0, , ;when j When it is a positive integer, , .

3. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 2 is as follows: The determination of when to perform maintenance on a critical component is expressed as: setting a reliability threshold for the component. When the component i Reliability reaches [a certain level] at the end of the current maintenance cycle. If this occurs, preventative maintenance of the component will be triggered; For components that trigger preventative maintenance i The decision-making criterion formula for deciding whether to adopt incomplete preventive maintenance or preventive replacement is as follows: ； in: and Each represents a component i The expected number of damage-related failures and inherent fatigue-related failures in the next maintenance cycle when incomplete preventive maintenance is adopted. Indicates components i The length of the next maintenance cycle when incomplete preventive maintenance is adopted; and Each represents a component i The expected number of damage-related failures and inherent fatigue-related failures within the first maintenance cycle after replacement measures are implemented. Indicates components i The length of the first maintenance cycle after replacement measures are taken; Indicates components i Number of damage-related failures Indicates components i The number of inherent fatigue-related failures was recorded. The determination of the timing of maintenance for non-initiating components can be expressed as determining whether to participate in opportunistic maintenance by judging whether the planned maintenance time falls within the time window of its own differentiated opportunity maintenance that is opened due to the maintenance of other components. For components that do not trigger preventative maintenance j The decision-making criterion formula for deciding whether to adopt incomplete preventive maintenance or preventive replacement is as follows: ； in, Indicates components j Downtime due to incomplete preventative maintenance Indicates components j The downtime for which replacement measures are taken is expressed by the following formulas. 。 4. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 3 is as follows: Establish a cost model, assuming the system's planning period is PH, then the specific formula for the total maintenance cost incurred during the planning process is as follows: ； 1) C m It is the cost of restorative repairs. M The specific restorative maintenance cost of a system composed of individual components during the planning period is as follows: ； in: Indicates components i Repair costs for damage-related faults Indicates components i Repair costs for inherent fatigue-related faults Indicates components i The number of maintenance phases during the planning period (PH), that is, the period from when a component is put into use to when it is scrapped is considered one maintenance phase. Indicates components i In the k The number of preventative maintenance operations performed within a maintenance phase, including incomplete preventative maintenance and preventative replacements. Indicates components i In the k Within the first maintenance phase j The length of a preventative maintenance cycle; 2) C p It is the cost of preventative maintenance. M The incomplete preventive maintenance cost of a system composed of individual components during the planning period is expressed by the following formula: ； in: Indicates components i Costs of incomplete preventative maintenance; Indicates components i In the k The number of incomplete preventive maintenance operations performed in each maintenance phase; 3) C r It's the replacement cost. M The replacement cost of a system composed of individual components during the planning period is specifically described as follows: ； in: It is the cost of replacing parts; Indicates the first i The number of times each component will be replaced during the planning period; 4) C d It refers to downtime cost, the downtime cost per unit of time. c d If so, the total downtime cost of the system during the planning period can be expressed by the following formula: ； Among them: components i Incomplete preventive maintenance time is Preventive replacement time is When multiple components are repaired together, the downtime is taken as the maximum value of the repair time of each component. Assume the system performed a total of [number] operations during the planning period. N Second preventive maintenance, the first j The time required for each preventative maintenance is ; Components within the planning period i The total time spent on troubleshooting is expressed by the following formula: ； in: part i Repair time for damage-related faults This refers to the repair time for inherent fatigue-related faults; 5) C os It saves on setup costs; when multiple components are maintained together for preventative maintenance, setup costs can be reduced; and it saves costs during the planning period. C os It is represented by the following formula; ； in: N 0 represents the total number of opportunistic repairs that occur during the planning period. Indicates participation in the i Number of parts to be repaired per opportunity c s This indicates the setup cost.

5. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 4 is as follows: The first phase of determining the system-level basic opportunity maintenance time window is specifically described as follows: W is proposed as the system-level basic opportunity maintenance time window, and the search range within the given system time window is... Within, the total system cost during the planning period (PH) is used. C Total (W) With the objective of minimizing the time window, we solve for the optimal system-level opportunistic maintenance time window W. The specific optimization model is shown in the following formula: 。 6. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 5 is as follows: The second stage of optimization differentiates the time window scaling factor for each component: using the optimal W* obtained in the first stage as a fixed input, a chance maintenance time window scaling factor is set for each component, and the chance maintenance time window for each component is adjusted. Assume the... i The adjustment factor for the opportunity repair time window of each component is: k i Within the given search range of scaling factors for each component Internally, based on the total system cost With the goal of minimizing costs, optimize the solution for each component. i Optimal Differentiation Ratio Factor The specific optimization model is as follows: 。 7. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects as described in claim 1, characterized in that, The specific process of step 6 is as follows: Based on the final optimal parameter combination, a detailed maintenance plan for the system during the planning period PH is generated. The plan specifically includes: a series of maintenance time points, the combination of components involved in maintenance at each time point, the specific maintenance method adopted for each component in the combination, and the system downtime caused by each maintenance.

8. The method for optimizing opportunistic maintenance of multi-component systems based on differentiated maintenance time windows and incomplete maintenance effects according to claim 7, characterized in that, Specific repair methods include incomplete repair and replacement.

Images