Three-gradient risk maintenance method for wind turbine generator system

Abstract

This invention discloses a three-gradient risk maintenance method for wind turbines. It establishes a comprehensive reliability model based on the bidirectional propagation effect of component failures, effectively solving the problem that traditional methods neglect fault propagation between components, leading to systematic biases in reliability assessments and unrealistic maintenance decisions, thus increasing the risk of sudden unit failures and unplanned downtime. The method designs a three-gradient risk maintenance system that integrates preventative replacement, opportunistic replacement, and opportunistic incomplete maintenance, using the comprehensive reliability of components as the decision variable. Combined with an opportunistic maintenance triggering mechanism based on failure risk, it avoids over-maintenance caused by blindly implementing opportunistic maintenance. This maintenance method can achieve synergistic optimization of unit operational reliability and operation and maintenance economy under different preventative replacement thresholds. Its calculation approach is clear and easy to implement in engineering, providing a feasible technical solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

Description

Technical Field

[0001] This invention belongs to the field of wind power generation system operation and maintenance technology, and relates to a three-gradient risk maintenance method for wind turbine units. Background Technology

[0002] Wind energy, as a clean and renewable energy source, has become one of the core pillars of the global energy transition. Wind turbines operate in complex and harsh environments for extended periods, which can easily lead to component failures. Their operation and maintenance costs account for approximately 20%-30% of the total life-cycle cost. Traditional reliability analyses of wind turbines mostly only consider the degradation factors of the components themselves, ignoring the two-way propagation effect of failures between components. This results in inaccurate estimates of the actual operational reliability of components, and maintenance decisions deviating from reality, which can easily increase the risk of sudden unit failures and unplanned downtime.

[0003] In terms of wind turbine maintenance strategies, practical engineering often employs a single preventative replacement maintenance approach. This approach suffers from two drawbacks: firstly, premature component replacement leads to wasted maintenance resources; secondly, it neglects opportunistic maintenance during turbine downtime, resulting in repeated downtime and additional maintenance costs. While some studies have introduced opportunistic replacement maintenance, they fail to consider low-cost, incomplete opportunistic maintenance methods and lack a fault risk-based triggering mechanism, making it difficult to achieve synergistic optimization of maintenance costs and turbine reliability. Therefore, how to consider and accurately quantify the bidirectional propagation intensity of faults between components to construct a comprehensive component reliability model, and design a gradient multi-mode maintenance strategy that balances economy and reliability, are critical technical issues that urgently need to be addressed in the current wind turbine operation and maintenance field. Summary of the Invention

[0004] The purpose of this invention is to provide a three-gradient risk maintenance method for wind turbines, which solves the problem in the prior art that the risk maintenance strategy for wind turbines deviates from the actual situation and is difficult to achieve a balance between maintenance cost and turbine reliability.

[0005] The technical solution adopted in this invention is a three-gradient risk maintenance method for wind turbine generators, comprising: Step 1: Construct a comprehensive reliability model based on the bidirectional propagation effect of wind turbine component failures; Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; Step 3: Construct a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method; Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components.

[0006] The invention is further characterized by: Step 1 includes step 11, constructing a directed fault propagation graph based on wind turbine component fault correlation analysis and directed graph theory, where each node represents a component, each directed edge represents a fault propagation path, and each directed edge represents the fault propagation impact of the source component on the target component. The weight of the directed edge is the fault propagation impact factor. , indicating component For components Based on the propagation intensity, a fault propagation influence factor matrix is ​​constructed, as shown below: (1) in, The range of values ​​is , This indicates no impact on transmission. ; Step 12: Based on the Gumbel Copula function, solve the problem using maximum likelihood estimation combined with excess conditional probability. The specific solution steps are as follows: Step 121, Data Preparation: Collect the fault interval time series of each component after eliminating common cause faults, and obtain the Weibull distribution parameters and shape parameters through maximum likelihood fitting. Scale parameters For each directed edge in the fault propagation directed graph, the corresponding component pair Based on a complete operational observation cycle, the components... and components Synchronize and pair fault interval time samples: within the same observation period, components The Fault intervals and components The Each fault interval is paired with a two-dimensional sample to form a synchronous pairing sample set. ,in A unified number for both groups of samples; Step 122: Convert the failure interval time into a uniform marginal distribution: Estimate the Gumbel Copula parameters for each component pair using maximum likelihood estimation. The existing component failure interval time is transformed into a uniform marginal distribution, representing the standardized input for Copula parameter estimation: (2) (3) In the formula, Components The shape and scale parameters of the Weibull distribution Components Shape and scale parameters of the Weibull distribution; Get component pair Middle components and Uniformly distributed marginal distribution sample set ,in This represents the total number of valid sample sets for synchronous pairing of the two components, and is taken as the smaller of the effective fault interval sample sizes after common-cause faults have been removed from both components. A unique identifier for paired samples; Step 123: Construct the log-likelihood function: The joint distribution expression of the Gumbel Copula function is: (4) In the formula: Let f(x) represent the marginal cumulative distribution function values ​​of two random variables, both of which take values ​​in the range (0,1). The dependency parameters representing Gumbel Copula are the core parameters for quantifying the strength of fault propagation. This indicates that the two variables are independent. The larger the value, the stronger the correlation. The probability density function of Gumbel Copula The expression is: (5) In the formula: ; For the sample set Construct the log-likelihood function, expressed as: (6) By minimizing the negative log-likelihood function estimate Maximum likelihood estimate ; Step 124: Determine the reference time of the component: Select the component. achieve The time as a reference time Solve using the following formula: (7) Right now: (8) In the formula, The preset preventative replacement and maintenance threshold; Step 125: Calculate the marginal failure probability of the component: at the reference time... At this point, the marginal failure probability of each of the two components is calculated, representing the failure probability at a specific moment. part exist Marginal failure probability at time: (9) part exist Marginal failure probability at time: (10) Step 126: Solve for the fault propagation impact factor using excess conditional probability: (11) The conditional probability is calculated using the Gumbel Copula function: (12) In the formula, The solution is obtained by formula (6); Step 127, Verification of bidirectional propagation asymmetry: For the bidirectional propagation component... , respectively and Based on the reference time, calculate according to the above steps. and The two are not equal, which reflects the asymmetry of propagation, and finally the fault propagation influence factor matrix is ​​obtained after solving; Step 13: Calculate the overall component failure rate and overall reliability: The overall component failure rate is the sum of the inherent failure rate of the component and the change in failure rate caused by the propagation of failures from other components. At any moment The inherent failure rate, based on the Weibull distribution, can be expressed as: (13) In the formula, For components Shape parameters, For components Scale parameters; When components Affected by others When the failure propagation of a component has an impact, the change in its failure rate is: (14) In the formula, For components For components Fault propagation influencing factors For components At any moment The overall failure rate; part The overall failure rate is: (15) Substituting the above formula into the Weibull reliability formula, we obtain the component... At any moment Overall reliability after the propagation of failures from other components: (16).

[0007] In step 2, the three-gradient risk maintenance method uses the overall reliability of components as the decision-making basis, introduces failure risk triggering conditions, and integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to give the corresponding preventive replacement maintenance threshold for components. and for each component Define decision variable: Opportunity replacement threshold Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; When components Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point.

[0008] The maintenance cost structure in step 3 includes preventative replacement costs, opportunistic replacement costs, and opportunistic incomplete maintenance costs. The cost of a single maintenance service includes: transportation and hoisting fees. Incomplete maintenance material costs and replacement and maintenance material costs Labor costs Downtime losses ; part The cost of a single maintenance session under the three maintenance methods is as follows: Cost of preventative replacement: ; Opportunistic replacement costs:

[0009] Opportunistic incomplete maintenance costs:

[0010] Fault risk triggering model: To avoid blind opportunistic replacement and maintenance, a fault risk triggering model is defined, representing the time... part The risk of additional future costs due to not performing opportunistic maintenance: Opportunistic replacement failure risk triggering model: (17) Opportunistic incomplete maintenance failure risk triggering model: (18) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; when When the fault risk triggering conditions are met, opportunistic replacement is triggered; when When the fault risk triggering conditions are met, opportunistic incomplete maintenance is triggered.

[0011] In step 4, three progressive maintenance models are established, each with the objective of minimizing the total maintenance cost over the entire life cycle of the wind turbine. The optimal replacement maintenance threshold and risk factors under each model are solved using a genetic algorithm, and the three-gradient risk maintenance method is verified. The three progressive maintenance models include: Model 1: Single preventative replacement maintenance; For reliability lower than Preventative replacement of components, objective function: (twenty three) In the formula, This represents the total number of components. This refers to the total maintenance cost over the entire life cycle of the wind turbine. For components The number of preventative replacements indicates the number of components replaced during the entire lifespan of the wind turbine. The overall reliability degrades to the preventive replacement threshold. The total number of times preventative replacements are proactively triggered; This indicates that during the entire lifespan of the wind turbine, the components... The cost of a single preventative replacement; Model 2: Combining preventative replacement with opportunistic replacement maintenance; Preventative replacement during downtime for systems with reliability levels below [value missing] And components that meet the risk triggering conditions are replaced opportunistically. Objective function: (twenty four) Maintain threshold constraints: , Opportunistic replacement trigger constraints: (19) (20) In the formula, For components The number of opportunistic replacements indicates the number of components that need to be replaced during the downtime replacement window when preventative replacements are triggered by other components in the wind turbine. The overall reliability is less than or equal to the replacement threshold for that component. And it meets the opportunistic replacement failure risk triggering model. The risk of failure exceeding the opportunistic replacement threshold During the downtime replacement window, the total number of opportunistic replacements will be performed concurrently. This indicates that during the entire lifespan of the wind turbine, the components... Opportunistic replacement single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement; Model 2 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic replacement of risk factors Z i1 The optimization process is as follows: Decision variable construction: constructing all The opportunistic replacement threshold and opportunistic replacement risk factor for each component are concatenated into one. 3D decision variable vector: (25) Boundary constraints: to ensure opportunistic threshold replacement Strictly greater than the preventive replacement threshold And the risk factor is less than 1 and lies in the (0,1) interval. The upper and lower bounds of the genetic algorithm decision variables are set as follows: (26) Fitness function: based on the total maintenance cost of Model 2 Based on the basic fitness, a degeneracy penalty term is introduced to prevent the genetic algorithm from converging to a degeneracy state where no component triggers opportunistic replacement. In this case, Model 2 will degenerate into Model 1. First, let's record the total number of opportunistic replacements of all components throughout their entire lifespan: (27) Secondly, define the degeneration penalty item. : (28) Finally, the fitness function is: (29) In the formula, The penalty coefficient for degradation is equivalent in magnitude to the total maintenance cost, ensuring that degradation is effectively eliminated; Genetic algorithm parameters: population size 60, maximum number of generations 150, crossover probability 0.8, elite retention count 6, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To obtain the optimal parameters for each component: a multi-starting-point restart model is adopted, and a genetic algorithm search is performed independently 5 times with different random number seeds. The candidate solutions obtained in each search are then analyzed. Substitute the values ​​into the Model 2 maintenance simulation program to calculate the total maintenance cost and the opportunistic replacement frequency of each component. Select the candidate solution with the lowest total maintenance cost as the optimal solution for Model 2. This allows us to extract the optimal opportunistic replacement threshold for each component. With risk factors ; Model 3: Three-tiered risk maintenance, which combines preventative replacement maintenance, opportunistic replacement maintenance, and opportunistic incomplete maintenance; Preventive maintenance downtime for systems with reliability lower than Furthermore, components that meet the risk triggering conditions are replaced opportunistically, and components with an overall reliability between [a certain level] are replaced opportunistically. and Components that meet the risk triggering conditions undergo opportunistic incomplete maintenance. Objective function: (30) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic incomplete maintenance (OCI) refers to the number of component maintenance operations that occur during the wind turbine shutdown replacement window. The overall reliability is between the opportunistic replacement threshold of this component. Opportunistic Incomplete Maintenance Threshold Between, and satisfying the opportunistic incomplete maintenance failure risk triggering model. The risk of failure exceeds the threshold for opportunistic incomplete maintenance. The total number of times opportunistic incomplete maintenance is performed during the downtime window; For components throughout the entire life cycle Opportunistic incomplete maintenance single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; Model 3 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor The optimization process is as follows: Decision variable construction: constructing all The opportunistic replacement threshold, opportunistic incomplete maintenance threshold, opportunistic replacement risk factor, and opportunistic incomplete maintenance risk factor for each component are combined into one. 3D decision variable vector: (31) Boundary constraints: The upper and lower bounds of each decision variable are: (32) Multi-objective soft-constraint fitness function: The fitness function is set to consist of the sum of the total maintenance cost of Model 3 and two independent degradation penalty terms. The overall expression of the fitness function is as follows: (33) Opportunistic replacement of degradation penalty items To avoid Model 3 degenerating into a single preventative replacement: (34) Opportunistic incomplete maintenance degradation penalty item To avoid Model 3 degenerating into Model 2: (35) In the formula, This represents the total life-cycle maintenance cost obtained from discrete event simulations of the maintenance strategy under the current decision variables in Model 3. , Components The number of opportunistic replacements and opportunistic incomplete maintenance operations throughout the entire life cycle. , All of these are degradation penalty coefficients, with a magnitude comparable to the total maintenance cost, ensuring that degradation is effectively eliminated. Genetic algorithm parameters: population size 100, maximum number of generations 200, crossover probability 0.8, elite retention count 10, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To find the optimal parameters for each component: A genetic algorithm is independently executed 12 times using distinct random number seeds. For each candidate solution obtained in the search... Substitute the solutions into the Model 3 maintenance simulation program, and select the solution with the lowest total maintenance cost from all candidate solutions as the optimal solution for Model 3. This allows us to extract the optimal opportunistic replacement threshold for each component. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; An evaluation system was established using six dimensions: system average overall reliability, total maintenance cost, number of outages, total power generation, unit average availability, and maintenance cost per unit of power generation. The maintenance effects of each maintenance model were compared to verify the performance of the three-gradient risk maintenance strategy for wind turbine components. Under a unified preventive replacement threshold, the three-tier risk maintenance model is compared with Model 1 and Model 2 in a full life cycle simulation, and the performance of each maintenance model is compared from six dimensions. By adjusting the preventive replacement threshold within a reasonable range, the maintenance effects of each maintenance model are compared again to verify the performance of the three-gradient risk maintenance method.

[0012] The beneficial effects of this invention are: The three-gradient risk maintenance method for wind turbines proposed in this invention establishes a comprehensive reliability model based on the bidirectional propagation effect of component failures. This effectively solves the problem that traditional methods ignore the propagation of failures between components, leading to systematic biases in reliability assessments and unrealistic maintenance decisions, which in turn increase the risk of sudden unit failures and unplanned downtime. The method designs a three-gradient risk maintenance system that integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance, using the comprehensive reliability of components as the decision variable. Combined with an opportunistic maintenance triggering mechanism based on failure risk, it avoids the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. This maintenance method can achieve synergistic optimization of unit operation reliability and operation and maintenance economy under different preventive replacement thresholds. The calculation approach is clear and easy to implement in engineering, providing a feasible technical solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the three-gradient risk maintenance method for wind turbines of the present invention; Figure 2 This is a directed graph of fault propagation in wind turbine components according to an embodiment of the present invention; Figure 3 This is a maintenance flowchart of the three-gradient risk maintenance method for wind turbines according to the present invention. Figure 4 This is a comparison diagram of the evolution of the inherent reliability and overall reliability of typical components in an embodiment of the present invention; Figure 5 This is a comparison chart of the overall reliability evolution of related components of the control system before and after the first preventive maintenance according to an embodiment of the present invention; Figure 6 This is a Gantt chart showing the dynamic changes in overall system reliability and maintenance execution under three maintenance models in this embodiment of the invention. Figure 7 These are different preventative replacement thresholds in embodiments of the present invention. The following chart compares the total number of downtimes for the three models; Figure 8 These are different preventative replacement thresholds in embodiments of the present invention. Comparison chart of average availability for the three model units; Figure 9 These are different preventative replacement thresholds in embodiments of the present invention. The following is a comparison chart of the maintenance costs per unit of power generation for the three models. Detailed Implementation

[0014] The following detailed description is provided in conjunction with specific implementation methods.

[0015] Example 1 The three-gradient risk maintenance method for wind turbines disclosed in this embodiment is as follows: Figure 1 As shown, it includes: Step 1: Construct a comprehensive reliability model based on the bidirectional propagation effect of wind turbine component failures; Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; Step 3: Construct a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method; Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components.

[0016] In this embodiment, step 1 establishes a comprehensive reliability model based on the bidirectional propagation effect of wind turbine component failures to address the problem that traditional methods neglect the propagation of failures between components, leading to systematic biases in reliability assessments and deviations from reality in maintenance decisions, thereby increasing the risk of sudden unit failures and unplanned shutdowns. Step 2 uses the model from step 1 as the decision variable, introduces failure risk triggering conditions, and designs a three-gradient risk maintenance strategy for wind turbine components. Step 3 constructs a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method, avoiding the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. Step 4 establishes three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components, proving that it can achieve synergistic optimization of unit operation reliability and operation and maintenance economy, and can provide a solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

[0017] Example 2 The three-gradient risk maintenance method for wind turbines disclosed in this embodiment, based on Embodiment 1, includes the following step 1: Step 11, constructing a fault propagation directed graph based on wind turbine component fault correlation analysis and directed graph theory, where each node represents a component, each directed edge represents a fault propagation path, and each directed edge represents the fault propagation impact of the source component on the target component. The weight of the directed edge is the fault propagation impact factor. , indicating component For components Based on the propagation intensity, a fault propagation influence factor matrix is ​​constructed, as shown below: (1) in, The range of values ​​is , This indicates no impact on transmission. ; Step 12: Based on the Gumbel Copula function, solve the problem using maximum likelihood estimation combined with excess conditional probability. The specific solution steps are as follows: Step 121, Data Preparation: Collect the fault interval time series of each component after eliminating common cause faults, and obtain the Weibull distribution parameters (shape parameters) through maximum likelihood fitting. Scale parameters For each directed edge in the fault propagation directed graph, the corresponding component pair Based on a complete operational observation cycle, the components... and components Synchronize and pair fault interval time samples: within the same observation period, components The Fault intervals and components The Each fault interval is paired with a two-dimensional sample to form a synchronous pairing sample set. ,in A unified number for both groups of samples; Step 122: Convert the failure interval time into a uniform marginal distribution: Estimate the Gumbel Copula parameters for each component pair using maximum likelihood estimation. The existing component failure interval time is transformed into a uniform marginal distribution, representing the standardized input for Copula parameter estimation: (2) (3) In the formula, Components The shape and scale parameters of the Weibull distribution Components Shape and scale parameters of the Weibull distribution; Get component pair Middle components and Uniformly distributed marginal distribution sample set ,in This represents the total number of valid sample sets for synchronous pairing of the two components, and is taken as the smaller of the effective fault interval sample sizes after common-cause faults have been removed from both components. A unique identifier for paired samples; Step 123: Construct the log-likelihood function: The joint distribution expression of the Gumbel Copula function is: (4) In the formula: Let f(x) represent the marginal cumulative distribution function values ​​of two random variables, both of which take values ​​in the range (0,1). The dependency parameters representing Gumbel Copula are the core parameters for quantifying the strength of fault propagation. This indicates that the two variables are independent. The larger the value, the stronger the correlation. The probability density function of Gumbel Copula The expression is: (5) In the formula: ; For the sample set Construct the log-likelihood function, expressed as: (6) By minimizing the negative log-likelihood function estimate Maximum likelihood estimate ; Step 124: Determine the reference time of the component: Select the component. achieve The time as a reference time Solve using the following formula: (7) Right now: (8) In the formula, The preset preventative replacement and maintenance threshold; Step 125: Calculate the marginal failure probability of the component: at the reference time... At this point, the marginal failure probability of each of the two components is calculated, representing the failure probability at a specific moment. part exist Marginal failure probability at time: (9) part exist Marginal failure probability at time: (10) Step 126: Solve for the fault propagation impact factor using excess conditional probability: (11) The conditional probability is calculated using the Gumbel Copula function: (12) In the formula, The solution is obtained by formula (6); Step 127, Verification of bidirectional propagation asymmetry: For the bidirectional propagation component... , respectively and Based on the reference time, calculate according to the above steps. and The two are not equal, which reflects the asymmetry of propagation, and finally the fault propagation influence factor matrix is ​​obtained after solving; Step 13: Calculate the overall component failure rate and overall reliability: The overall component failure rate is the sum of the inherent failure rate of the component and the change in failure rate caused by the propagation of failures from other components. At any moment The inherent failure rate, based on the Weibull distribution, can be expressed as: (13) In the formula, For components Shape parameters, For components Scale parameters; When components Affected by others When the failure propagation of a component has an impact, the change in its failure rate is: (14) In the formula, For components For components Fault propagation influencing factors For components At any moment The overall failure rate; part The overall failure rate is: (15) Substituting the above formula into the Weibull reliability formula, we obtain the component... At any moment Overall reliability after the propagation of failures from other components: (16).

[0018] Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; Step 3: Construct a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method; Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components.

[0019] In this embodiment, step 1 constructs a directed fault propagation graph based on wind turbine component fault correlation analysis and directed graph theory. Each node represents a component, each directed edge represents a fault propagation path, and each directed edge represents the fault propagation impact of the source component on the target component. The weight of the directed edge is the fault propagation impact factor. , indicating component For components The propagation intensity is determined, and a fault propagation influence factor matrix is ​​constructed accordingly. Based on the Gumbel Copula function, maximum likelihood estimation combined with excess conditional probability is used to solve the problem. Based on the solved fault propagation influence factor matrix, a comprehensive reliability model for components is established. Step 2 uses the model from Step 1 as the decision variable, introduces fault risk triggering conditions, and designs a three-gradient risk maintenance method for wind turbine components. Step 3 constructs a maintenance cost structure and fault risk triggering model to verify the fault risk of the three-gradient risk maintenance method, avoiding the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. Step 4 establishes three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components, proving that it can achieve synergistic optimization of unit operation reliability and operation and maintenance economy, and can provide a solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

[0020] Example 3 The three-gradient risk maintenance method for wind turbines disclosed in this embodiment is based on Embodiment 2. Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; The three-tiered risk maintenance method uses the overall reliability of components as the decision-making basis, introduces failure risk triggering conditions, and integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to give the corresponding preventive replacement maintenance threshold for components. and for each component Define decision variable: Opportunity replacement threshold Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; When components Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point.

[0021] Step 3: Construct a maintenance cost structure and fault risk triggering model to verify the fault risk of the three-gradient risk maintenance method; Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components.

[0022] In this embodiment, step 2 integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to provide the preventive replacement and maintenance threshold for the corresponding components. And set the opportunistic replacement threshold for the corresponding components. Parameters, Opportunistic Incomplete Maintenance Threshold parameter; When components Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point. Step 3 constructs a maintenance cost structure and fault risk triggering model to verify the fault risk of the three-gradient risk maintenance method, avoiding the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. Step 4 establishes three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components, proving that it can achieve synergistic optimization of unit operation reliability and operation and maintenance economy, and can provide a solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

[0023] Example 4 The three-gradient risk maintenance method for wind turbines disclosed in this embodiment, based on embodiment 3, step 3: constructing a maintenance cost structure and a fault risk triggering model to verify the fault risk of the three-gradient risk maintenance method; part The cost of a single maintenance service includes: transportation and hoisting fees. Incomplete maintenance material costs and replacement and maintenance material costs Labor costs Downtime losses ; part The cost of a single maintenance session under the three maintenance methods is as follows: Cost of preventative replacement: ; Opportunistic replacement costs:

[0024] Opportunistic incomplete maintenance costs:

[0025] Failure Risk Trigger Model: To avoid blind opportunistic replacement and maintenance, a failure risk trigger model is defined, representing the time... part The risk of additional future costs due to not performing opportunistic maintenance: Opportunistic replacement failure risk triggering model: (17) Opportunistic incomplete maintenance failure risk triggering model: (18) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; when When the fault risk triggering conditions are met, opportunistic replacement is triggered; when When the fault risk triggering conditions are met, opportunistic incomplete maintenance is triggered.

[0026] In this embodiment, step 3 constructs a maintenance cost structure and a fault risk triggering model, providing the opportunity replacement fault risk triggering threshold and the opportunity incomplete maintenance fault risk triggering threshold for the three-gradient risk maintenance method in step 2, thus avoiding the over-maintenance problem caused by blindly carrying out opportunity maintenance.

[0027] Example 5 The three-gradient risk maintenance method for wind turbine units disclosed in this embodiment, based on embodiment 4, step 4: establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine unit components; Three progressive maintenance models are proposed, with the goal of minimizing the total maintenance cost over the entire life cycle of the wind turbine. Genetic algorithms are used to solve for the optimal replacement maintenance threshold and risk factors under each model, and the three-gradient risk maintenance method is validated. The three progressive maintenance models include: Model 1: Single preventative replacement maintenance; For reliability lower than Preventative replacement of components, objective function: (twenty three) In the formula, This represents the total number of components. This refers to the total maintenance cost over the entire life cycle of the wind turbine. For components The number of preventative replacements indicates the number of components replaced during the entire lifespan of the wind turbine. The overall reliability degrades to the preventive replacement threshold. The total number of times preventative replacements are proactively triggered; This indicates that during the entire lifespan of the wind turbine, the components... The cost of a single preventative replacement; Model 2: Combining preventative replacement with opportunistic replacement maintenance; Preventative replacement during downtime for systems with reliability levels below [value missing] And components that meet the risk triggering conditions are replaced opportunistically. Objective function: (twenty four) Maintain threshold constraints: , Opportunistic replacement trigger constraints: (19) (20) In the formula, For components The number of opportunistic replacements indicates the number of components that need to be replaced during the downtime replacement window when preventative replacements are triggered by other components in the wind turbine. The overall reliability is less than or equal to the replacement threshold for that component. And it meets the opportunistic replacement failure risk triggering model. The risk of failure exceeding the opportunistic replacement threshold During the downtime replacement window, the total number of opportunistic replacements will be performed concurrently. This indicates that during the entire lifespan of the wind turbine, the components... Opportunistic replacement single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement; Model 2 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic replacement of risk factors Z i1 The optimization process is as follows: Decision variable construction: constructing all The opportunistic replacement threshold and opportunistic replacement risk factor for each component are concatenated into one. 3D decision variable vector: (25) Boundary constraints: to ensure opportunistic threshold replacement Strictly greater than the preventive replacement threshold And the risk factor is less than 1 and lies in the (0,1) interval. The upper and lower bounds of the genetic algorithm decision variables are set as follows: (26) Fitness function: based on the total maintenance cost of Model 2 Based on the basic fitness, a degeneracy penalty term is introduced to prevent the genetic algorithm from converging to a degeneracy state where no component triggers opportunistic replacement. In this case, Model 2 will degenerate into Model 1. First, let's record the total number of opportunistic replacements of all components throughout their entire lifespan: (27) Secondly, define the degeneration penalty item. : (28) Finally, the fitness function is: (29) In the formula, The penalty coefficient for degradation is equivalent in magnitude to the total maintenance cost, ensuring that degradation is effectively eliminated; Genetic algorithm parameters: population size 60, maximum number of generations 150, crossover probability 0.8, elite retention count 6, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To obtain the optimal parameters for each component: a multi-starting-point restart model is adopted, and a genetic algorithm search is performed independently 5 times with different random number seeds. The candidate solutions obtained in each search are then analyzed. Substitute the values ​​into the Model 2 maintenance simulation program to calculate the total maintenance cost and the opportunistic replacement frequency of each component. Select the candidate solution with the lowest total maintenance cost as the optimal solution for Model 2. This allows us to extract the optimal opportunistic replacement threshold for each component. With risk factors ; Model 3: Three-tiered risk maintenance, which combines preventative replacement maintenance, opportunistic replacement maintenance, and opportunistic incomplete maintenance; Preventive maintenance downtime for systems with reliability lower than Furthermore, components that meet the risk triggering conditions are replaced opportunistically, and components with an overall reliability between [a certain level] are replaced opportunistically. and Components that meet the risk triggering conditions undergo opportunistic incomplete maintenance. Objective function: (30) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic incomplete maintenance (OCI) refers to the number of component maintenance operations that occur during the wind turbine shutdown replacement window. The overall reliability is between the opportunistic replacement threshold of this component. Opportunistic Incomplete Maintenance Threshold Between, and satisfying the opportunistic incomplete maintenance failure risk triggering model. The risk of failure exceeds the threshold for opportunistic incomplete maintenance. The total number of times opportunistic incomplete maintenance is performed during the downtime window; For components throughout the entire life cycle Opportunistic incomplete maintenance single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; Model 3 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor The optimization process is as follows: Decision variable construction: constructing all The opportunistic replacement threshold, opportunistic incomplete maintenance threshold, opportunistic replacement risk factor, and opportunistic incomplete maintenance risk factor for each component are combined into one. 3D decision variable vector: (31) Boundary constraints: The upper and lower bounds of each decision variable are: (32) Multi-objective soft-constraint fitness function: The fitness function is set to consist of the sum of the total maintenance cost of Model 3 and two independent degradation penalty terms. The overall expression of the fitness function is as follows: (33) Opportunistic replacement of degradation penalty items To avoid Model 3 degenerating into a single preventative replacement: (34) Opportunistic incomplete maintenance degradation penalty item To avoid Model 3 degenerating into Model 2: (35) In the formula, This represents the total life-cycle maintenance cost obtained from discrete event simulations of the maintenance strategy under the current decision variables in Model 3. , Components The number of opportunistic replacements and opportunistic incomplete maintenance operations throughout the entire life cycle. , All of these are degradation penalty coefficients, with a magnitude comparable to the total maintenance cost, ensuring that degradation is effectively eliminated. Genetic algorithm parameters: population size 100, maximum number of generations 200, crossover probability 0.8, elite retention count 10, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To find the optimal parameters for each component: A genetic algorithm is independently executed 12 times using distinct random number seeds. For each candidate solution obtained in the search... Substitute the solutions into the Model 3 maintenance simulation program, and select the solution with the lowest total maintenance cost from all candidate solutions as the optimal solution for Model 3. This allows us to extract the optimal opportunistic replacement threshold for each component. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; An evaluation system was established using four dimensions: total number of outages, total power generation, average availability of the unit, and maintenance cost per unit of power generation. The reliability and economic synergistic optimization effect of each model was evaluated, and the three-gradient risk maintenance method for wind turbine components was verified. Under a unified preventive replacement threshold, Model 3 is compared with Model 1 and Model 2 in a full life cycle simulation. The models are comprehensively evaluated from the dimensions of average overall system reliability, maintenance cost composition, number of outages and power generation loss. Within a reasonable range, the threshold for preventative replacement was adjusted and compared for verification.

[0028] In this embodiment, step 1 constructs a directed fault propagation graph based on wind turbine component fault correlation analysis and directed graph theory. Each node represents a component, each directed edge represents a fault propagation path, and each directed edge represents the fault propagation impact of the source component on the target component. The weight of the directed edge is the fault propagation impact factor. , indicating component For components The propagation intensity is determined, and a fault propagation influence factor matrix is ​​constructed accordingly. Based on the Gumbel Copula function, maximum likelihood estimation combined with excess conditional probability is used to solve the problem. A comprehensive reliability model for the component is established based on the solved fault propagation influence factor matrix. Step 2 integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to provide the preventive replacement maintenance threshold for the corresponding components. And set the opportunistic replacement threshold for the corresponding components. Parameters, Opportunistic Incomplete Maintenance Threshold parameter; When components Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point. Step 3 constructs a maintenance cost structure and fault risk triggering model, providing opportunistic replacement fault risk triggering thresholds and opportunistic incomplete maintenance fault risk triggering thresholds for the three-gradient risk maintenance method in Step 2. This avoids the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. Step 4 establishes three progressive maintenance models with the goal of minimizing the total maintenance cost over the entire life cycle of the wind turbine. A genetic algorithm is used to solve for the optimal replacement maintenance threshold and risk factors under each model. An evaluation system is established using four-dimensional indicators: total number of outages, total power generation, average availability of the unit, and maintenance cost per unit of power generation. This system verifies the three-gradient risk maintenance method for wind turbine components, proving that it can achieve synergistic optimization of unit operation reliability and operation and maintenance economy, and can provide a solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

[0029] Example 6 Based on Example 5, the three-gradient risk maintenance method for wind turbines disclosed in this example, taking the actual operating data of a 2MW wind turbine in a domestic wind farm as an example, includes: Step 1: Construct a comprehensive reliability model based on the bidirectional propagation effect of wind turbine component failures; like Figure 2 As shown, in this embodiment, step 1 includes step 11: constructing a fault propagation directed graph based on wind turbine component fault correlation analysis and directed graph theory. This involves constructing a fault propagation directed graph containing 10 core components: main bearing, yaw system, braking system, generator, pitch system, converter, blades and hub, control system, hydraulic system, and gearbox. Each node represents a component, and each directed edge represents a fault propagation path. A directed edge from one component to another indicates that the source component has a fault propagation impact on the target component. A bidirectional edge indicates that the faults of two components influence each other. The weight of the directed edge is the fault propagation influence factor. , indicating component For components Based on the propagation intensity, a fault propagation influence factor matrix is ​​constructed, as shown below:

[0030] in, The range of values ​​is , This indicates no impact on transmission. ; S2 is based on the Gumbel Copula function, using maximum likelihood estimation combined with excess conditional probability to solve the problem. ; S21 Data Preparation: Collect the fault interval time series of each component after eliminating common cause faults, and obtain the Weibull distribution parameters (shape parameters) through maximum likelihood fitting. Scale parameters As shown in Table 1; for each directed edge in the fault propagation directed graph, the corresponding component pair Based on a complete operational observation cycle, the components... and components Synchronize and pair fault interval time samples: within the same observation period, components The Fault intervals and components The Each fault interval is paired with a two-dimensional sample to form a synchronous pairing sample set. ,in A unified number for both groups of samples;

[0031] Table 1. Intrinsic Reliability Model Parameters for Wind Turbine Components Step 122: Convert the failure interval time into a uniform marginal distribution: Estimate the Gumbel Copula parameters for each component pair using maximum likelihood estimation. The existing component failure interval time is transformed into a uniform marginal distribution, representing the standardized input for Copula parameter estimation: (2) (3) In the formula, Components The shape and scale parameters of the Weibull distribution Components Shape and scale parameters of the Weibull distribution; Get component pair Middle components and Uniformly distributed marginal distribution sample set ,in This represents the total number of valid sample sets for synchronous pairing of the two components, and is taken as the smaller of the effective fault interval sample sizes after common-cause faults have been removed from both components. A unique identifier for paired samples; Step 123: Construct the log-likelihood function: The joint distribution expression of the Gumbel Copula function is: (4) In the formula: Let f(x) represent the marginal cumulative distribution function values ​​of two random variables, both of which take values ​​in the range (0,1). The dependency parameters representing Gumbel Copula are the core parameters for quantifying the strength of fault propagation. This indicates that the two variables are independent. The larger the value, the stronger the correlation. The probability density function of Gumbel Copula The expression is: (5) In the formula: ; For the sample set Construct the log-likelihood function, expressed as: (6) By minimizing the negative log-likelihood function estimate Maximum likelihood estimate ; Step 124: Determine the reference time of the component: Select the component. achieve The time as a reference time Solve using the following formula: (7) Right now: (8) In the formula, The preset preventative replacement and maintenance threshold; Step 125: Calculate the marginal failure probability of the component: at the reference time... At this point, the marginal failure probability of each of the two components is calculated, representing the failure probability at a specific moment. part exist Marginal failure probability at time: (9) part exist Marginal failure probability at time: (10) Step 126: Solve for the fault propagation impact factor using excess conditional probability: (11) The conditional probability is calculated using the Gumbel Copula function: (12) In the formula, The solution is obtained by formula (6); Step 127, Verification of bidirectional propagation asymmetry: For the bidirectional propagation component... , respectively and Based on the reference time, calculate according to the above steps. and The two are not equal, which reflects the asymmetry of propagation. Finally, the solved fault propagation influence factor matrix is ​​obtained, as shown below.

[0032] Step 13: Calculate the overall component failure rate and overall reliability: The overall component failure rate is the sum of the inherent failure rate of the component and the change in failure rate caused by the propagation of failures from other components. At any moment The inherent failure rate, based on the Weibull distribution, can be expressed as: (13) In the formula, For components Shape parameters, For components Scale parameters; When components When affected by the propagation of faults from other components, the change in its failure rate is: (14) In the formula, For components For components Fault propagation influencing factors For components At any moment The overall failure rate; part The overall failure rate is: (15) Substituting the above formula into the Weibull reliability formula, we obtain the component... At any moment Overall reliability after the propagation of failures from other components: (16).

[0033] Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; The three-tiered risk maintenance method uses the overall reliability of components as the decision-making basis, introduces failure risk triggering conditions, and integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to provide a unified threshold for preventive replacement maintenance of components. and for each component Define decision variable: Opportunity replacement threshold Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; like Figure 3 As shown, when the component Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point.

[0034] Step 3: Construct a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method; part The cost of a single maintenance service includes: transportation and hoisting fees. Incomplete maintenance material costs and replacement and maintenance material costs Labor costs Downtime losses ; Standard charges for each item: Transportation and hoisting costs: , Yuan / hour, labor cost , Yuan / (person·hour), wind power grid connection price: Yuan / kWh, component replacement requires 6 workers, incomplete maintenance requires 2 workers, transportation and hoisting time: Hours, downtime losses The wind farm's power generation capacity is The incomplete maintenance time for the same component is 50% of the replacement maintenance time; The prices of each component, replacement time, and incomplete maintenance costs are shown in Table 2.

[0035] Table 2. Statistics on the price, replacement time, and incomplete maintenance costs of each component. part The cost of a single maintenance session under the three maintenance methods is as follows: Cost of preventative replacement: ; Opportunistic replacement costs:

[0036] Opportunistic incomplete maintenance costs:

[0037] Fault risk triggering model: To avoid blind opportunistic replacement and maintenance, a fault risk triggering model is defined, representing the time... part The risk of additional future costs due to not performing opportunistic maintenance: Opportunistic replacement failure risk triggering model: (17) Opportunistic incomplete maintenance failure risk triggering model: (18) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; when When the fault risk triggering conditions are met, opportunistic replacement is triggered; when When the fault risk triggering conditions are met, opportunistic incomplete maintenance is triggered.

[0038] Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components; Three progressive maintenance models are proposed, with the goal of minimizing the total maintenance cost over the entire life cycle of the wind turbine. Genetic algorithms are used to solve for the optimal replacement maintenance threshold and risk factors under each model, and the three-gradient risk maintenance method is validated. The three progressive maintenance models include: Model 1: Single preventative replacement maintenance; For reliability lower than Preventative replacement of components, objective function: (twenty three) In the formula, This represents the total number of components. This refers to the total maintenance cost over the entire life cycle of the wind turbine. For components The number of preventative replacements indicates the number of components replaced during the entire lifespan of the wind turbine. The overall reliability degrades to the preventive replacement threshold. The total number of times preventative replacements are proactively triggered; This indicates that during the entire lifespan of the wind turbine, the components... The cost of a single preventative replacement; Model 2: Combining preventative replacement with opportunistic replacement maintenance; Preventative replacement during downtime for systems with reliability levels below [value missing] And components that meet the risk triggering conditions are replaced opportunistically. Objective function: (twenty four) Maintain threshold constraints: , Opportunistic replacement trigger constraints: (19) (20) In the formula, For components The number of opportunistic replacements indicates the number of components that need to be replaced during the downtime replacement window when preventative replacements are triggered by other components in the wind turbine. The overall reliability is less than or equal to the replacement threshold for that component. And it meets the opportunistic replacement failure risk triggering model. The risk of failure exceeding the opportunistic replacement threshold During the downtime replacement window, the total number of opportunistic replacements will be performed concurrently. This indicates that during the entire lifespan of the wind turbine, the components... Opportunistic replacement single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement; Model 2 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic replacement of risk factors Z i1 The optimization process is as follows: Construction of decision variables: Concatenate the opportunity replacement thresholds and opportunity replacement risk factors for all 10 components into a 20-dimensional decision variable vector: (25) Boundary constraints: to ensure opportunistic threshold replacement Strictly greater than the preventive replacement threshold And the risk factor is less than 1 and lies in the (0,1) interval. The upper and lower bounds of the genetic algorithm decision variables are set as follows: (26) Fitness function: based on the total maintenance cost of Model 2 Based on the basic fitness, a degeneracy penalty term is introduced to prevent the genetic algorithm from converging to a degeneracy state where no component triggers opportunistic replacement. In this case, Model 2 will degenerate into Model 1. First, let's record the total number of opportunistic replacements of all components throughout their entire lifespan: (27) Secondly, define the degeneration penalty item. : (28) Finally, the fitness function is: (29) In the formula, The penalty coefficient for degradation is equivalent in magnitude to the total maintenance cost, ensuring that degradation is effectively eliminated; Genetic algorithm parameters: population size 60, maximum number of generations 150, crossover probability 0.8, elite retention count 6, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To obtain the optimal parameters for each component: a multi-starting-point restart model is adopted, and a genetic algorithm search is performed independently 5 times with different random number seeds. The candidate solutions obtained in each search are then analyzed. Substitute the values ​​into the Model 2 maintenance simulation program to calculate the total maintenance cost and the opportunistic replacement frequency of each component. Select the candidate solution with the lowest total maintenance cost as the optimal solution for Model 2. This allows us to extract the optimal opportunistic replacement threshold for each component. With risk factors ; Model 3: Three-tiered risk maintenance, which combines preventative replacement maintenance, opportunistic replacement maintenance, and opportunistic incomplete maintenance; Preventive maintenance downtime for systems with reliability lower than Furthermore, components that meet the risk triggering conditions are replaced opportunistically, and components with an overall reliability between [a certain level] are replaced opportunistically. and Components that meet the risk triggering conditions undergo opportunistic incomplete maintenance. Objective function: (30) Opportunistic replacement trigger constraints: (19) (20) Opportunistic incomplete maintenance trigger constraints: (twenty one) (twenty two) In the formula, For components Opportunistic incomplete maintenance (OCI) refers to the number of component maintenance operations that occur during the wind turbine shutdown replacement window. The overall reliability is between the opportunistic replacement threshold of this component. Opportunistic Incomplete Maintenance Threshold Between, and satisfying the opportunistic incomplete maintenance failure risk triggering model. The risk of failure exceeds the threshold for opportunistic incomplete maintenance. The total number of times opportunistic incomplete maintenance is performed during the downtime window; For components throughout the entire life cycle Opportunistic incomplete maintenance single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; Model 3 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor The optimization process is as follows: Decision variable construction: constructing all The opportunistic replacement threshold, opportunistic incomplete maintenance threshold, opportunistic replacement risk factor, and opportunistic incomplete maintenance risk factor for each component are combined into one. 3D decision variable vector: (31) Boundary constraints: The upper and lower bounds of each decision variable are: (32) Multi-objective soft-constraint fitness function: The fitness function is set to consist of the sum of the total maintenance cost of Model 3 and two independent degradation penalty terms. The overall expression of the fitness function is as follows: (33) Opportunistic replacement of degradation penalty items To avoid Model 3 degenerating into a single preventative replacement: (34) Opportunistic incomplete maintenance degradation penalty item To avoid Model 3 degenerating into Model 2: (35) In the formula, This represents the total life-cycle maintenance cost obtained from discrete event simulations of the maintenance strategy under the current decision variables in Model 3. , Components The number of opportunistic replacements and opportunistic incomplete maintenance operations throughout the entire life cycle. , All of these are degradation penalty coefficients, with a magnitude comparable to the total maintenance cost, ensuring that degradation is effectively eliminated. Genetic algorithm parameters: population size 100, maximum number of generations 200, crossover probability 0.8, elite retention count 10, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To find the optimal parameters for each component: A genetic algorithm is independently executed 12 times using distinct random number seeds. For each candidate solution obtained in the search... Substitute the solutions into the Model 3 maintenance simulation program, and select the solution with the lowest total maintenance cost from all candidate solutions as the optimal solution for Model 3. This allows us to extract the optimal opportunistic replacement threshold for each component. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor .

[0039] The maintenance model of the wind turbine was simulated using MATLAB, and the results are shown in Tables 3-8. Figures 4-9 As shown; An evaluation system is established using six dimensions: system average overall reliability, total maintenance cost, number of outages, total power generation, unit average availability, and maintenance cost per unit of power generation. The maintenance effects of various maintenance models are compared to verify the superior performance of the three-gradient risk maintenance method for wind turbine components designed in this invention. First, under a unified preventive replacement threshold, the three-gradient risk maintenance model is compared with Model 1 and Model 2 in a full life cycle simulation, and the performance of each maintenance model is compared from six dimensions. Secondly, to prove that the three-gradient risk maintenance method consistently outperforms traditional maintenance strategies, the preventive replacement threshold was adjusted within a reasonable range, and the maintenance effects of each maintenance model were compared and verified again.

[0040]

[0041] Table 3. Statistical table of reliability changes of related components before and after control system maintenance.

[0042] Table 4. Statistical table of average comprehensive reliability of the system under three models.

[0043] Table 5. Maintenance Cost Statistics for Three Maintenance Models

[0044] Table 6. Statistical Results of Optimal Threshold Optimization for Opportunistic Maintenance Reliability of Each Component under Models 2 and 3

[0045] Table 7. Statistical Table of Risk Factors for Each Component under Model 2 and Model 3

[0046] Table 8. Statistical Table of Maintenance Performance Indicators for Three Maintenance Models Depend on Figure 4 It can be seen that within 365 days, the overall reliability of both the gearbox and the hydraulic system is significantly lower than their intrinsic reliability, and the gap between the two gradually widens as the operating time increases. The overall reliability of the gearbox, which is affected by the failure propagation of 7 components, decreases much more than that of the hydraulic system, which is affected by only a single component of the control system. This confirms that the decrease in the overall reliability of components is positively correlated with the number of components affected by failure propagation. Figure 5Table 3 and the simulation experiment conducted on the synergistic reliability improvement effect of component maintenance were performed. Figure 5 As shown in Table 3, after performing preventative maintenance on the control system, the system's own reliability jumped from 0.6500 to 0.9879, and the overall reliability of all components affected by its fault propagation also improved synchronously. Figure 6 As shown in Table 4, during the simulation, the overall system reliability fluctuated across the three maintenance models. The three-gradient risk maintenance method (Model 3) resulted in fewer maintenance outages compared to the other two models, and its average overall system reliability was higher than that of Models 1 and 2. Tables 6 and 7 show that the genetic algorithm achieved differentiated optimization of maintenance thresholds and risk factors based on the value and fault characteristics of different components, thus realizing the rational utilization of maintenance resources. Tables 5 and 8 show that Model 3 had a higher total power generation, higher average unit availability, and higher maintenance cost per unit of power generation compared to the other two models, achieving superior performance in both reliability and economy. Figures 7-9 It can be seen that, with the increase in the preventive replacement threshold... From 0.60 to 0.80, the total number of outages and maintenance cost per unit of power generation increased for all three maintenance models, while the average availability of the units decreased. Within the specified range, Model 3 consistently maintains a lower total number of outages, higher average unit availability, and better overall performance in terms of maintenance cost per unit of power generation, demonstrating significantly better robustness than the other two maintenance models.

[0047] Comprehensive analysis Figures 4-9 Tables 3-8 show that the three-gradient risk maintenance method for wind turbines based on bidirectional fault propagation of components proposed in this invention can accurately quantify the intensity of bidirectional fault propagation between components, establish a comprehensive reliability assessment model considering bidirectional fault propagation between components, and effectively solve the problem that traditional methods ignore fault propagation between components, leading to systematic biases in reliability assessment and deviations from reality in maintenance decisions, thereby increasing the risk of sudden unit failures and unplanned shutdowns. A three-gradient risk maintenance system integrating preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance is designed, combined with an opportunistic maintenance triggering mechanism based on fault risk, avoiding the problem of over-maintenance caused by blindly carrying out opportunistic maintenance. This maintenance method can achieve synergistic optimization of unit operation reliability and operation and maintenance economy under different preventive replacement thresholds. The calculation idea is clear and easy to implement in engineering, providing a feasible technical solution for refined operation and maintenance decision-making throughout the entire life cycle of wind farms.

Claims

1. A three-gradient risk maintenance method for wind turbine generators, characterized in that, include: Step 1: Construct a comprehensive reliability model based on the bidirectional propagation effect of wind turbine component faults; Step 2: Using the overall reliability of components as the decision variable, introduce failure risk triggering conditions and design a three-gradient risk maintenance method for wind turbine components; Step 3: Construct a maintenance cost structure and failure risk triggering model to verify the failure risk of the three-gradient risk maintenance method; Step 4: Establish three progressive maintenance models to verify the three-gradient risk maintenance method for wind turbine components.

2. The three-gradient risk maintenance method for wind turbine generators according to claim 1, characterized in that: Step 1 includes, Step 11: Construct a directed fault propagation graph based on wind turbine component fault correlation analysis and directed graph theory. Each node represents a component, each directed edge represents a fault propagation path, and each directed edge represents the fault propagation impact of the source component on the target component. The weight of the directed edge is the fault propagation impact factor. , indicating component For components Based on the propagation intensity, a fault propagation influence factor matrix is ​​constructed, as shown below: （1） in, The range of values ​​is , This indicates no impact on transmission. ; Step 12: Based on the Gumbel Copula function, solve the problem using maximum likelihood estimation combined with excess conditional probability. ; Step 13: Calculate the overall failure rate and overall reliability of the components.

3. The three-gradient risk maintenance method for wind turbine generators according to claim 2, characterized in that: Step 12 includes, Step 121, Data Preparation: Collect the fault interval time series of each component after eliminating common cause faults, and obtain the Weibull distribution parameters and shape parameters through maximum likelihood fitting. Scale parameters ; For each directed edge in the fault propagation directed graph, the corresponding component pair Based on a complete operational observation cycle, the components... and components Synchronize and pair fault interval time samples: within the same observation period, components The Fault intervals and components The Each fault interval is paired with a two-dimensional sample to form a synchronous pairing sample set. ,in A unified number for both groups of samples; Step 122: Convert the failure interval time into a uniform marginal distribution: Estimate the Gumbel Copula parameters for each component pair using maximum likelihood estimation. The existing component failure interval time is transformed into a uniform marginal distribution, representing the standardized input for Copula parameter estimation: （2） （3） In the formula, Components The shape and scale parameters of the Weibull distribution Components Shape and scale parameters of the Weibull distribution; Get component pair Middle components and Uniformly distributed marginal distribution sample set ,in This represents the total number of valid sample sets for synchronous pairing of the components, and is taken as the smaller of the effective fault interval sample sizes after common-cause faults have been removed from both components. A unique identifier for paired samples; Step 123: Construct the log-likelihood function: The joint distribution expression of the Gumbel Copula function is: （4） In the formula: Let f(x) represent the marginal cumulative distribution function values ​​of two random variables, both of which take values ​​in the range (0,1). The dependency parameters representing Gumbel Copula are the core parameters for quantifying the strength of fault propagation. This indicates that the two variables are independent. The larger the value, the stronger the correlation. The probability density function of Gumbel Copula The expression is: （5） In the formula: ; For the sample set Construct the log-likelihood function, expressed as: （6） By minimizing the negative log-likelihood function estimate Maximum likelihood estimate ; Step 124: Determine the reference time of the component: Select the component. achieve The time as a reference time Solve using the following formula: （7） Right now: （8） In the formula, The preset preventative replacement and maintenance threshold; Step 125: Calculate the marginal failure probability of the component: at the reference time... At this point, the marginal failure probability of each of the two components is calculated, representing the failure probability at a specific moment. part exist Marginal failure probability at time: （9） part exist Marginal failure probability at time: （10） Step 126: Solve for the fault propagation impact factor using excess conditional probability: （11） The conditional probability is calculated using the Gumbel Copula function: （12） In the formula, The solution is obtained by formula (6); Step 127, Verification of bidirectional propagation asymmetry: For the bidirectional propagation component... , respectively and Based on the reference time, calculate according to the above steps. and The two are not equal, which reflects the asymmetry of propagation, and finally the fault propagation influence factor matrix is ​​obtained.

4. The three-gradient risk maintenance method for wind turbine generators according to claim 3, characterized in that: The component comprehensive failure rate in step 13 is the sum of the component's inherent failure rate and the change in failure rate caused by the propagation of failures from other components. At any moment The inherent failure rate, based on the Weibull distribution, can be expressed as: （13） In the formula, For components Shape parameters, For components Scale parameters; When components Affected by others When the failure propagation of a component has an impact, the change in its failure rate is: （14） In the formula, For components For components Fault propagation influencing factors For components At any moment The overall failure rate; part The overall failure rate is: （15） Substituting the above formula into the Weibull reliability formula, we obtain the component... At any moment Overall reliability after the propagation of failures from other components: （16）。 5. The three-gradient risk maintenance method for wind turbine generators according to claim 4, characterized in that: Step 2 uses the overall reliability of the component as the decision-making basis, introduces failure risk triggering conditions, and integrates preventive replacement, opportunistic replacement, and opportunistic incomplete maintenance to give the corresponding preventive replacement and maintenance threshold for the component. and for each component Define decision variable: Opportunity replacement threshold Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor ; When components Overall reliability Reduced to the preventive replacement maintenance threshold When this is triggered, preventative replacement is initiated, the machine is automatically shut down, and all components are completely replaced. During the downtime replacement window, a reliability assessment is performed on all other components. If a certain component... Overall reliability Less than or equal to the opportunistic replacement threshold of the component Furthermore, the failure risk triggering conditions are met, triggering opportunistic replacement, and the components are completely replaced simultaneously during the downtime replacement window. If a certain component Overall reliability Given the opportunistic replacement threshold of this component Opportunistic Incomplete Maintenance Threshold If the conditions for triggering a fault risk are met, opportunistic incomplete maintenance is triggered, and low-cost incomplete maintenance is performed during the downtime replacement window; a certain component Overall reliability The incomplete maintenance threshold of this component is higher than If no maintenance is performed, the unit will resume operation and continue monitoring until the next preventative trigger point.

6. The three-gradient risk maintenance method for wind turbine generators according to claim 5, characterized in that: The maintenance cost structure in step 3 includes preventative replacement costs, opportunistic replacement costs, and opportunistic incomplete maintenance costs. The cost of a single maintenance service includes: transportation and hoisting fees. Incomplete maintenance material costs and replacement and maintenance material costs Labor costs Downtime losses ; part The cost of a single maintenance session under the three maintenance methods is as follows: Cost of preventative replacement: ; Opportunistic replacement costs: Opportunistic incomplete maintenance costs: Fault Risk Trigger Model: Define the fault risk trigger model, representing the time... part The risk of additional future costs due to not performing opportunistic maintenance: Opportunistic replacement failure risk triggering model: （17） Opportunistic incomplete maintenance failure risk triggering model: （18） Opportunistic replacement trigger constraints: （19） （20） Opportunistic incomplete maintenance trigger constraints: （21） （22） In the formula, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; when When the fault risk triggering conditions are met, opportunistic replacement is triggered; when When the fault risk triggering conditions are met, opportunistic incomplete maintenance is triggered.

7. The three-gradient risk maintenance method for wind turbine generators according to claim 6, characterized in that: The three progressive maintenance models in step 4 include Model 1, single preventive replacement maintenance; Model 2, a combination of preventive and opportunistic replacement maintenance; and Model 3, a three-tiered risk maintenance, which combines preventive replacement maintenance, opportunistic replacement maintenance, and opportunistic incomplete maintenance. The optimal replacement maintenance threshold and risk factors for each model are determined using a genetic algorithm, with the goal of minimizing the total maintenance cost over the entire lifespan of the wind turbine. The three-tiered risk maintenance method is then validated.

8. The three-gradient risk maintenance method for wind turbine generators according to claim 7, characterized in that: Model 1, single preventative replacement maintenance: for reliability levels below [specific value] Preventative replacement of components, objective function: （23） In the formula, This represents the total number of components. This refers to the total maintenance cost over the entire life cycle of the wind turbine. For components The number of preventative replacements indicates the number of components replaced during the entire lifespan of the wind turbine. The overall reliability degrades to the preventive replacement threshold. The total number of times preventative replacements are proactively triggered; This indicates that during the entire lifespan of the wind turbine, the components... The cost of a single preventative replacement.

9. The three-gradient risk maintenance method for wind turbine generators according to claim 7, characterized in that: Model 2 combines preventative replacement with opportunistic replacement maintenance: during preventative replacement downtime, maintenance is performed on equipment with reliability levels below a certain threshold. And components that meet the risk triggering conditions are replaced opportunistically. Objective function: （24） Maintain threshold constraints: , Opportunistic replacement trigger constraints: （19） （20） In the formula, For components Opportunistic replacement count refers to the number of component replacements during the downtime replacement window when preventative replacements are triggered by other components in the wind turbine. The overall reliability is less than or equal to the replacement threshold for that component. And it meets the opportunistic replacement failure risk triggering model. The risk of failure exceeding the opportunistic replacement threshold During the downtime replacement window, the total number of opportunistic replacements will be performed simultaneously. This indicates that during the entire lifespan of the wind turbine, the components... Opportunistic replacement single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement; Model 2 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic replacement of risk factors Z i1 The optimization process is as follows: Decision variable construction: Constructing all The opportunistic replacement threshold and opportunistic replacement risk factor for each component are concatenated into one. 3D decision variable vector: （25） Boundary constraints: to ensure opportunistic threshold replacement Strictly greater than the preventive replacement threshold And the risk factor is less than 1 and lies in the (0,1) interval. The upper and lower bounds of the genetic algorithm decision variables are set as follows: （26） Fitness function: based on the total maintenance cost of Model 2 Based on the basic fitness, a degeneracy penalty term is introduced to prevent the genetic algorithm from converging to a degeneracy state where no component triggers opportunistic replacement. In this case, Model 2 will degenerate into Model 1. First, let's record the total number of opportunistic replacements of all components throughout their entire lifespan: （27） Secondly, define the degeneration penalty item. : （28） Finally, the fitness function is: （29） In the formula, The penalty coefficient for degradation is equivalent in magnitude to the total maintenance cost, ensuring that degradation is effectively eliminated; Genetic algorithm parameters: population size 60, maximum number of generations 150, crossover probability 0.8, elite retention count 6, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To obtain the optimal parameters for each component: a multi-starting-point restart model is adopted, and a genetic algorithm search is performed independently 5 times with different random number seeds. The candidate solutions obtained in each search are then analyzed. Substitute the values ​​into the Model 2 maintenance simulation program to calculate the total maintenance cost and the opportunistic replacement frequency of each component. Select the candidate solution with the lowest total maintenance cost as the optimal solution for Model 2. This allows us to extract the optimal opportunistic replacement threshold for each component. With risk factors .

10. The three-gradient risk maintenance method for wind turbine generators according to claim 7, characterized in that: Model 3, a three-tiered risk maintenance approach, combines preventative replacement maintenance, opportunistic replacement maintenance, and opportunistic incomplete maintenance. Preventive maintenance downtime for systems with reliability lower than Furthermore, components that meet the risk triggering conditions are replaced opportunistically, and components with an overall reliability between [a certain level] are replaced opportunistically. and Components that meet the risk triggering conditions undergo opportunistic incomplete maintenance. Objective function: （30） Opportunistic replacement trigger constraints: （19） （20） Opportunistic incomplete maintenance trigger constraints: （21） （22） In the formula, For components Opportunistic incomplete maintenance (OCI) refers to the number of component maintenance operations that occur during the wind turbine shutdown replacement window. The overall reliability is between the opportunistic replacement threshold of this component. Opportunistic Incomplete Maintenance Threshold Between, and satisfying the opportunistic incomplete maintenance failure risk triggering model. The risk of failure exceeds the threshold for opportunistic incomplete maintenance. The total number of times opportunistic incomplete maintenance is performed during the downtime window; For components throughout the entire life cycle Opportunistic incomplete maintenance single maintenance cost, For components Opportunistic replacement failure risk trigger threshold For components Risk factors for opportunistic replacement For components Opportunistic incomplete maintenance failure risk trigger threshold For components Risk factors that require opportunistic, incomplete maintenance; Model 3 uses a genetic algorithm to determine the opportunistic replacement threshold for each component under boundary constraints. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor The optimization process is as follows: Decision variable construction: Constructing all The opportunistic replacement threshold, opportunistic incomplete maintenance threshold, opportunistic replacement risk factor, and opportunistic incomplete maintenance risk factor for each component are combined into one. 3D decision variable vector: （31） Boundary constraints: The upper and lower bounds of each decision variable are: （32） Multi-objective soft-constraint fitness function: The fitness function is set to consist of the sum of the total maintenance cost of Model 3 and two independent degradation penalty terms. The overall expression of the fitness function is as follows: （33） Opportunistic replacement of degradation penalty items To avoid Model 3 degenerating into a single preventative replacement: （34） Opportunistic incomplete maintenance degradation penalty item To avoid Model 3 degenerating into Model 2: （35） In the formula, This represents the total life-cycle maintenance cost obtained from discrete event simulations of the maintenance strategy under the current decision variables in Model 3. , Components The number of opportunistic replacements and opportunistic incomplete maintenance operations throughout the entire life cycle. , All of these are degradation penalty coefficients, with a magnitude comparable to the total maintenance cost, ensuring that degradation is effectively eliminated. Genetic algorithm parameters: population size 100, maximum number of generations 200, crossover probability 0.8, elite retention count 10, function convergence tolerance. Enable parallel computing to accelerate fitness evaluation; To find the optimal parameters for each component: A genetic algorithm is independently executed 12 times using distinct random number seeds. For each candidate solution obtained in the search... Substitute the solutions into the Model 3 maintenance simulation program, and select the solution with the lowest total maintenance cost from all candidate solutions as the optimal solution for Model 3. This allows us to extract the optimal opportunistic replacement threshold for each component. Opportunistic incomplete maintenance threshold Opportunistic replacement of risk factors Opportunistic incomplete maintenance risk factor .

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