Multi-objective optimization maintenance decision-making method for turbine blade of gas turbine

Abstract

The invention relates to the technical field of gas turbines, and provides a gas turbine blade multi-objective optimization maintenance decision-making method, which comprises the following steps of: 1, training a life prediction result as a blade damage factor by adopting a Weibull model, and generating a failure probability curve through historical operation data to represent a change rule of the reliability of a blade along with time; step 2, designing a series of economic formulas related to maintenance, considering factors of maintenance cost, shutdown loss cost and fuel cost, and providing economic evaluation indexes for subsequent maintenance decisions; 3, optimizing the maintenance time point and the maintenance duration by using a multi-objective optimization algorithm in combination with the failure probability curve and the economic formula; and step 4, based on a result of the multi-objective optimization algorithm, setting a reliability threshold, selecting an optimal point and outputting a maintenance strategy. The method can provide an optimal decision for maintenance of the turbine blade of the gas turbine.

Description

Technical Field

[0001] The invention relates to the technical field of gas turbines, and in particular to a multi-objective optimization maintenance decision method for turbine blades of a gas turbine. Background Art

[0002] As an important equipment in modern industrial and power systems, the operating efficiency and reliability of gas turbines directly affect the stability and economy of production and power supply. Gas turbine blades are key components in gas turbines. Due to their long-term exposure to high temperature, high pressure and high-speed airflow, they are prone to wear, corrosion and fatigue damage. Therefore, scientific and effective maintenance decisions for gas turbine blades are of great significance for extending the service life of equipment and improving system reliability. The maintenance decision of gas turbine blades is a complex multi-objective optimization problem, which requires comprehensive consideration of multiple factors such as maintenance cost, safety risk and equipment operating status. Traditional single-objective or empirical maintenance methods are difficult to achieve the best maintenance effect in a complex industrial environment. Therefore, there is an urgent need for a multi-objective optimization maintenance decision method that can balance economy and safety to achieve scientific and refined maintenance of gas turbine blades. Summary of the invention

[0003] The content of the present invention is to provide a multi-objective optimization maintenance decision method for gas turbine turbine blades. It combines blade-related operation and maintenance data and life prediction model results, uses advanced optimization algorithms to optimize the maintenance time point and duration of gas turbine turbine blades, comprehensively considers the economy and safety of maintenance, and provides the optimal decision for gas turbine turbine blade maintenance.

[0004] A multi-objective optimization maintenance decision method for gas turbine blades according to the present invention comprises the following steps:

[0005] Step 1: Use the Weibull model to train the life prediction results as the blade damage factor, and generate a failure probability curve based on historical operation data to characterize the change law of blade reliability over time;

[0006] Step 2: Design a series of economic formulas related to maintenance, taking into account factors such as maintenance cost, downtime loss cost, and fuel cost, to provide economic evaluation indicators for subsequent maintenance decisions;

[0007] Step 3: Use a multi-objective optimization algorithm, combined with the failure probability curve and the economic formula, to optimize the maintenance time point and maintenance duration;

[0008] Step 4: Based on the results of the multi-objective optimization algorithm, set the reliability threshold, select the optimal point and output the maintenance strategy.

[0009] Preferably, in step 1, in order to solve the fluctuation problem of the initially generated failure probability curve, the cumulative sum control chart CUSUM method is applied to process the data; the processed data is further encrypted by interpolation technology to increase the density of data points.

[0010] Preferably, in step 2, the economic evaluation index includes maintenance cost, downtime loss and fuel combustion cost, and the calculation formula is as follows:

[0011] C total =C1+C2+C3#(1)

[0012] Among them, C1 represents the maintenance cost, C2 represents the downtime loss cost, and C3 represents the fuel combustion cost. The specific calculation formula is as follows:

[0013] C1=n×a#(2)

[0014] C2=m×b#(3)

[0015]

[0016] Where n is the number of maintenance times, a is the cost of a single maintenance, b is the downtime loss per unit time, and m is the downtime time. is the fuel flow rate, c f is the unit cost of fuel, LHV is the lower heating value of fuel, and t is the operating time of the gas turbine; the single maintenance cost includes labor cost, material cost, equipment and tool cost, inspection and testing cost, and transportation material cost; the downtime loss cost is composed of the loss of sales revenue caused by production interruption. Due to the confidentiality of actual data, we assume that the single maintenance cost is 3000, the downtime loss per unit time and the fuel-related loss are 1 each for preliminary analysis and model verification.

[0017] Preferably, in step 3, the optimized objective function includes two aspects:

[0018] Economic efficiency, i.e., the economic efficiency formula that integrates maintenance cost, downtime loss cost and fuel combustion cost;

[0019] Reliability, i.e., the failure probability curve generated based on the Weibull model;

[0020] The optimization variables include the number of maintenance times, the start time of each maintenance, and the duration of each maintenance. In the specific optimization problem, the duration of each maintenance is set to range from 0 to 5000 hours as the constraint of the optimization problem.

[0021] Preferably, in step 3, the multi-objective optimization algorithm includes a genetic algorithm and a particle swarm algorithm;

[0022] In the optimization process, the genetic algorithm generates a set of initial maintenance strategies through selection, crossover and mutation operations, and evaluates these strategies according to the fitness function. With the goal of minimizing the total cost and maximizing the reliability, the optimization is continuously iterated to finally obtain the best maintenance time point and maintenance duration plan.

[0023] The particle swarm algorithm gradually optimizes the maintenance strategy represented by each particle by simulating information sharing in the group and collaboration between individuals, making it gradually approach the global optimal solution.

[0024] During the optimization process, the position and velocity update formula of each particle will take into account both the failure probability curve and the economic formula to ensure that the optimization results can take into account both reliability and economy.

[0025] Preferably, in step 4, the reliability threshold is set to ensure a reasonable balance between economy and reliability, so that the gas turbine can maintain high reliability while controlling maintenance costs and downtime losses during operation.

[0026] The present invention proposes a multi-objective optimization maintenance decision method for gas turbines that combines blade-related operating data and life prediction model results. The method uses the life prediction model results as the gas turbine turbine blade damage factor and blade-related operating data to train the Weibull model, thereby generating a failure probability curve to characterize the reliability of the gas turbine turbine blades; at the same time, a series of economic formulas are combined to comprehensively consider the economic efficiency of maintenance; finally, the optimization algorithm is used to optimize the maintenance time point and the maintenance market to achieve the best balance between economy and reliability. The method is highly scientific and practical, can improve the reliability and economy of equipment, reduce maintenance costs and downtime losses, and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flowchart of a multi-objective optimization maintenance decision method for a gas turbine blade in an embodiment;

[0028] Figure 2 Schematic diagram of cumulative failure probability curve of blades in the embodiment;

[0029] Figure 3 This is a schematic diagram of the cumulative failure probability curve of the blade after CUSUM processing fluctuations in the embodiment;

[0030] Figure 4 It is a schematic diagram of the optimization results of the NSGA-Ⅱ algorithm in the embodiment;

[0031] Figure 5 This is a schematic diagram of the optimization results of the NSGA-III algorithm in the embodiment;

[0032] Figure 6 This is a schematic diagram of the optimization results of the MOPSO algorithm in the embodiment;

[0033] Figure 7 A schematic diagram of the Pareto frontier of the NSGA-Ⅱ algorithm in the embodiment;

[0034] Figure 8 A Pareto frontier diagram of the NSGA-III algorithm in the embodiment;

[0035] Fig. 9 A schematic diagram of the Pareto frontier of the MOPSO algorithm in the embodiment;

[0036] Fig.10 It is a schematic diagram of the maintenance time point and maintenance duration in the optimization result in the embodiment. DETAILED DESCRIPTION

[0037] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0038] Example

[0039] like Figure 1 As shown, this embodiment provides a multi-objective optimization maintenance decision method for gas turbine blades, which includes the following steps:

[0040] Step 1: Use the Weibull model to train the life prediction results as the blade damage factor, and generate the failure probability curve through historical operation data, such as Figure 2 As shown in the figure, the reliability of the blade is characterized by its changing pattern over time. Weibull distribution is a commonly used reliability analysis method that can effectively describe the failure pattern of the blade over time.

[0041] However, the initially generated failure probability curve may be unstable due to data noise and random fluctuations, affecting the accuracy of the prediction. In order to overcome this problem, the CUSUM (Cumulative Sum Control Chart) method is applied to process the data; the CUSUM method can effectively detect the changing trend in the data and perform smoothing, reduce noise interference, and make the failure probability curve more stable and smooth. The processed data is further encrypted through interpolation technology to increase the density of data points.

[0042] After the above steps, the resulting failure probability curve can accurately reflect the reliability changes of the blade at different time points, such as Figure 3 Using this high-precision failure probability curve, the remaining life of the blade and the time point when potential failures will occur can be predicted more accurately.

[0043] By combining accurate damage factor models, Weibull distribution fitting, CUSUM data processing, and interpolation encryption processing, this method greatly improves the prediction accuracy of gas turbine blade reliability changes, thus providing a solid data foundation for making maintenance decisions. This method can significantly improve the accuracy of maintenance decisions, ensure preventive maintenance at the best time, avoid premature or late maintenance operations, effectively reduce equipment failures and downtime, and optimize the use of maintenance resources.

[0044] In step 1, the calculation formula for blade failure probability using Weibull distribution fitting is as follows:

[0045] If the time when the blade fails is T, the failure rate λ(t) can be expressed as:

[0046] R(t)=P(T>t)#(1)

[0047] F(t)=P(T <t)=1-R(t)#(2)

[0048]

[0049] Where R(t) is the reliability function, F(t) is the cumulative failure probability function, and f(t) is the failure probability density function.

[0050] In summary, the conversion relationship between the four commonly used reliability indicators can be obtained as follows:

[0051]

[0052] R(t)=exp(-∫λ(t)dt)#(6)

[0053] f(t)=λ(t)exp(-∫λ(t)dt)#(7)

[0054] The failure problems faced in actual engineering projects give the most accurate failure forms of mechanical parts. Among them, the two-parameter Weibull distribution is widely used because it can give accurate analysis results using a small amount of sample data. Its failure rate expression is:

[0055]

[0056] According to equations (2), (6) and (7), the probability density function, reliability and cumulative failure probability of Weibull distribution can be obtained as follows:

[0057]

[0058] Where β is the shape parameter, which determines the overall shape of the curve; η is the scale parameter, which determines the distribution range of the curve.

[0059] The failure rate of the Proportional Hazard Model (PHM) is expressed as:

[0060] λ(t,X)=λ0(t)g(X)#(12)

[0061] In the formula, λ0(t) is the baseline failure rate, which is only related to the operating life t, and g(X) is the accompanying variable, which indicates the influence of many factors on the failure rate. To ensure that g(X)>0, it is usually taken So the common proportional hazard model is:

[0062]

[0063] Where X=(X1,X2,…,X k ) is the covariate that affects the performance of the mechanical system, α=(α1,α2,…,α k ) is the regression coefficient corresponding to the covariate X

[0064] In practical engineering applications, Weibull distribution is a distribution function commonly used to describe the change of mechanical equipment failure degree over time. Therefore, it is often used as a baseline failure function to substitute into the proportional hazard model to obtain the Weibull Proportional Hazard Model (WPHM), whose failure rate function expression is:

[0065]

[0066] Therefore, the corresponding reliability index of the WPHM model can be calculated as:

[0067]

[0068] The unknown parameters β, η and α in the WPHM model are usually estimated using the maximum likelihood estimation method.

[0069] According to equation (17), the WPHM model is used to perform reliability analysis on the blades, and the cumulative failure probability F(t,X) of the blades as the running time changes is calculated. The cumulative failure probability F(t,X) characterizes the failure degree of the blades. The greater the cumulative failure probability, the greater the possibility of blade failure. Therefore, this study uses the cumulative failure probability F(t,X) as a failure indicator to realize blade status monitoring and as a reliability indicator in subsequent multi-objective optimization.

[0070] In this study, the blade fatigue damage factor integrated with mathematics and physics was input into the Weibull proportional risk model, and the failure probability curve output by the model was used as the reliability indicator.

[0071] Step 2: Design a series of economic formulas related to maintenance, taking into account factors such as maintenance cost, downtime loss cost, and fuel cost, to provide economic evaluation indicators for subsequent maintenance decisions.

[0072] In step 2, the economic evaluation indicators include maintenance cost, downtime loss and fuel combustion cost, and the calculation formula is as follows:

[0073] C total =C1+C2+C3#(1)

[0074] Among them, C1 represents the maintenance cost, C2 represents the downtime loss cost, and C3 represents the fuel combustion cost. The specific calculation formula is as follows:

[0075] C1=n×a#(2)

[0076] C2=m×b#(3)

[0077]

[0078] Where n is the number of maintenance times, a is the cost of a single maintenance, b is the downtime loss per unit time, and m is the downtime time. is the fuel flow rate, c f is the unit cost of fuel, LHV is the lower heating value of fuel, and t is the operating time of the gas turbine; the single maintenance cost includes labor cost, material cost, equipment and tool cost, inspection and testing cost, and transportation material cost; the downtime loss cost is composed of the loss of sales revenue caused by production interruption.

[0079] Step 3: Use a multi-objective optimization algorithm, combined with the failure probability curve and economic formula, to optimize the maintenance time point and maintenance duration.

[0080] In step 3, the optimized objective function includes two aspects:

[0081] Economic efficiency, i.e., the economic efficiency formula that integrates maintenance cost, downtime loss cost and fuel combustion cost;

[0082] Reliability, that is, the failure probability curve generated based on the Weibull model.

[0083] The optimization variables include the number of maintenance times, the start time of each maintenance, and the duration of each maintenance.

[0084] In step 3, the multi-objective optimization algorithm includes genetic algorithm and particle swarm algorithm.

[0085] During the optimization process, the genetic algorithm generates a set of initial maintenance strategies through selection, crossover and mutation operations, and evaluates these strategies according to the fitness function. With the goal of minimizing total cost and maximizing reliability, it continuously iterates and optimizes, and finally obtains the optimal maintenance time point and maintenance duration plan.

[0086] The particle swarm algorithm gradually optimizes the maintenance strategy represented by each particle by simulating information sharing in the group and collaboration between individuals, making it gradually approach the global optimal solution.

[0087] During the optimization process, the position and velocity update formula of each particle will take into account both the failure probability curve and the economic formula to ensure that the optimization results can take into account both reliability and economy.

[0088] Step 4: Based on the results of the multi-objective optimization algorithm, set the reliability threshold, select the optimal point and output the maintenance strategy.

[0089] In step 4, the optimized maintenance time point and maintenance duration have been obtained through the previous multi-objective optimization algorithm; next, based on these optimization results, a reliability threshold is set to evaluate the effectiveness of different maintenance strategies. The reliability threshold is set to ensure a reasonable balance between economy and reliability, so that the gas turbine can maintain high reliability during operation while controlling maintenance costs and downtime losses.

[0090] The multi-objective optimization model of turbine blades is established by selecting maintenance once, maintenance twice, maintenance three times and maintenance four times, and the NSGA-II algorithm, NSGA-III algorithm and MOPSO algorithm are used to solve it. NSGA-II algorithm and NSGA-III algorithm are multi-objective genetic algorithms, and MOPSO algorithm is a multi-objective particle swarm algorithm.

[0091] In the optimization results, Figure 4 , Figure 5 and Figure 6 As shown in Figure 2, NSGA-II and NSGA-III algorithms provide a wider range of maintenance time and maintenance frequency options. They provide options from shorter maintenance time to longer maintenance time, and also include maintenance plans from frequent maintenance to fewer maintenance times. This flexibility allows the maintenance plan to be adjusted according to actual conditions to balance the needs of reliability and economy.

[0092] In contrast, the MOPSO algorithm may be more inclined to provide fewer maintenance plans, usually with longer maintenance time, but fewer overall maintenance times. This means that MOPSO may be more suitable for situations that are more sensitive to maintenance costs but have relatively low reliability requirements.

[0093] In the Pareto frontier diagram, if Figure 7 , Figure 8 , Fig. 9 As shown in the figure, the multi-objective optimization results based on different maintenance times of gas turbine turbine blades are shown, with the horizontal axis representing the economic cost and the vertical axis representing the failure probability of the blades. In the optimization model, each point on the Pareto frontier not only reflects a specific combination of economy and reliability, but also represents a complete maintenance strategy. Specifically, this includes the specific number of maintenance, the time point when each maintenance starts, and the expected maintenance time. For example, a point on the Pareto frontier may depict a scenario where, during the operating cycle, the first maintenance is performed on the 100th day, which is expected to take 8 hours, followed by a second maintenance on the 300th day, which is also expected to take 8 hours. Such a maintenance strategy design is derived from the analysis of the failure probability curve of the gas turbine, and aims to optimize the maintenance timing of the equipment to ensure the most efficient operating state while reducing production interruptions.

[0094] The goal of this method is to find the most economical maintenance strategy under the condition of meeting a certain reliability threshold. In the Pareto frontier diagram of the maintenance results, we can select a decision point for a single maintenance, and not only can we obtain its economy and failure probability, but the optimization algorithm can also output the ut (when to carry out maintenance, that is, the time point when maintenance starts) and ul (the number of hours the maintenance lasts) of this point. Fig.10 The decision point of a single maintenance is to perform maintenance at the time point of ut = 10121 hours, and the maintenance duration is ut = 1056 hours. This is the decision point of a single maintenance. In case of multiple maintenance, we can also get multiple sets of ut and ul, which represent the start time and maintenance duration of each maintenance respectively.

[0095] Therefore, when making the final choice, it is necessary to comprehensively consider specific economic indicators, such as maintenance costs, downtime losses, etc., as well as reliability indicators, such as the impact of equipment failure on production. This can quantitatively evaluate the comprehensive benefits of different solutions and make the best maintenance decision.

[0096] When applying the optimization model to the maintenance strategy formulation of gas turbines in practice, in addition to considering the indicators of economy and reliability provided by the model, the actual operating environment of the equipment must be carefully evaluated, which may require more frequent maintenance to adapt to operation under harsh conditions. At the same time, the availability of maintenance resources, including the skills, tools and spare parts of maintenance personnel, must also be taken into consideration. These factors directly affect the efficiency and cost of maintenance work. During maintenance, the potential impact of equipment downtime on production progress cannot be ignored, so the plan should minimize the disruption to production, such as performing it during off-peak hours. Safety and compliance must also be strictly followed, and all maintenance processes must ensure the safety of workers and the environment. With the help of historical and real-time maintenance data to support decision-making, maintenance strategies can be continuously optimized and adjusted in actual applications. In addition, the formulated strategy should be flexible so that it can respond quickly to changes in equipment performance and real-time monitoring data. After considering these comprehensive factors, a dynamic maintenance strategy framework is adopted, which not only reflects the balance between economy and reliability, but also has the feasibility and adaptability of implementation, so that the strategy can effectively support the continuous and stable operation of gas turbines under changing operating conditions.

[0097] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A multi-objective optimization maintenance decision method for gas turbine blades, characterized in that: The following steps are involved: Step 1: Use the Weibull model to train the life prediction results as the blade damage factor, and generate a failure probability curve based on historical operation data to characterize the change law of blade reliability over time; Step 2: Design a series of economic formulas related to maintenance, taking into account factors such as maintenance cost, downtime loss cost, and fuel cost, to provide economic evaluation indicators for subsequent maintenance decisions; Step 3: Use a multi-objective optimization algorithm, combined with the failure probability curve and the economic formula, to optimize the maintenance time point and maintenance duration; Step 4: Based on the results of the multi-objective optimization algorithm, set the reliability threshold, select the optimal point and output the maintenance strategy.

2. A multi-objective optimization maintenance decision method for gas turbine blades according to claim 1, characterized in that: In step 1, the cumulative sum control chart CUSUM method is used to process the data to address the fluctuation problem of the initially generated failure probability curve; the processed data is further encrypted through interpolation technology to increase the density of data points.

3. The multi-objective optimization maintenance decision method for gas turbine blades according to claim 2 is characterized by: In step 2, the economic evaluation indicators include maintenance cost, downtime loss and fuel combustion cost, and the calculation formula is as follows: C total =C1+C2+C3# (1) Among them, C1 represents the maintenance cost, C2 represents the downtime loss cost, and C3 represents the fuel combustion cost. The specific calculation formula is as follows: C1=n×a#(2) C2=m×b#(3) Where n is the number of maintenance times, a is the cost of a single maintenance, b is the downtime loss per unit time, and m is the downtime. is the fuel flow rate, c f is the unit cost of fuel, LHV is the lower heating value of fuel, and t is the operating time of the gas turbine; the single maintenance cost includes labor cost, material cost, equipment and tool cost, inspection and testing cost, and transportation material cost; the downtime loss cost is composed of the loss of sales revenue caused by production interruption.

4. The multi-objective optimization maintenance decision method for gas turbine blades according to claim 3 is characterized by: In step 3, the optimized objective function includes two aspects: Economic efficiency, i.e., the economic efficiency formula that integrates maintenance cost, downtime loss cost and fuel combustion cost; Reliability, i.e., the failure probability curve generated based on the Weibull model; The optimization variables include the number of maintenance times, the start time of each maintenance, and the duration of each maintenance.

5. A multi-objective optimization maintenance decision method for gas turbine blades according to claim 4, characterized in that: In step 3, the multi-objective optimization algorithm includes genetic algorithm and particle swarm algorithm; In the optimization process, the genetic algorithm generates a set of initial maintenance strategies through selection, crossover and mutation operations, and evaluates these strategies according to the fitness function. With the goal of minimizing the total cost and maximizing the reliability, the optimization is continuously iterated to finally obtain the best maintenance time point and maintenance duration plan. The particle swarm algorithm gradually optimizes the maintenance strategy represented by each particle by simulating information sharing in the group and collaboration between individuals, making it gradually approach the global optimal solution. During the optimization process, the position and velocity update formula of each particle will take into account both the failure probability curve and the economic formula to ensure that the optimization results can take into account both reliability and economy.

6. A multi-objective optimization maintenance decision method for gas turbine blades according to claim 5, characterized in that: In step 4, the reliability threshold is set to ensure a reasonable balance between economy and reliability, so that the gas turbine can maintain high reliability while controlling maintenance costs and downtime losses during operation.

Images