A method for gas turbine efficiency optimization

Abstract

This invention discloses a gas turbine energy efficiency optimization method, comprising: extracting multi-dimensional input features from gas turbine operating data, and standardizing and normalizing the data; using a gradient boosting regression model to perform regression prediction on each objective variable, and performing inverse standardization recovery on the prediction results to ensure prediction accuracy; establishing an upper-lower layer coupled multi-objective optimization model, with the upper layer aiming at maximizing efficiency, minimizing emissions, and optimizing economy, and the lower layer aiming at satisfying physical constraints and maximizing scheduling benefits, generating a Pareto front solution set through an improved adaptive NSGA-II; applying the TOPSIS decision method to calculate the weighted distance of the optimal solution set, sorting by proximity, selecting the optimal solution, and outputting the optimal operating parameters to support actual decision-making.

Description

Technical Field

[0001] This invention relates to the field of gas turbine technology, and in particular to a method for optimizing the energy efficiency of gas turbines. Background Technology

[0002] Gas turbines, as crucial power devices in fields such as electric power, marine propulsion, and distributed energy, are significantly affected by factors such as load demand, environmental conditions, and component status. In practical engineering applications, the overall energy efficiency, sustainability, emissions, and economic performance of gas turbines often exhibit interdependent relationships: for example, improving overall energy efficiency or sustainability may require increasing combustion temperature or adjusting the air-fuel ratio, leading to higher emissions; conversely, reducing emissions may result in decreased overall energy efficiency or increased operating costs, thus impacting economic efficiency. Therefore, how to synergistically optimize adjustable controllable parameters such as inlet guide vane opening, airflow, and fuel flow under different loads to achieve improved overall energy efficiency while balancing emissions and economic efficiency remains a key long-standing concern in the field of gas turbine operation optimization.

[0003] Existing gas turbine energy efficiency optimization methods mainly include mechanistic model-based optimization methods and data-driven optimization methods. Mechanism-based methods typically rely on thermodynamic cycle calculations and component characteristic models, evaluating performance indicators under a certain combination of control variables by solving nonlinear equations or calling complex simulation platforms. While these methods can reflect physical mechanisms, they often have the following shortcomings in engineering practice: First, model construction and calibration are costly, and they are highly dependent on the accuracy of component characteristic curves, correction coefficients, and sensors; second, simulation calculations are time-consuming, making it difficult to support large-scale iterative searches under multi-objective, strongly nonlinear, and strongly coupled conditions; third, when the unit experiences aging, scaling, or performance drift after maintenance, the mechanistic model needs to be recalibrated, resulting in insufficient model adaptability and real-time performance, thus affecting the stability and usability of the optimization results.

[0004] On the other hand, data-driven optimization methods utilize historical operating data or experimental data to establish input-output mapping relationships and perform optimization based on these relationships. While these methods can reduce reliance on mechanistic models and improve online adaptability, they still face several engineering challenges: First, gas turbine optimization typically involves multiple control variables and performance objectives. These objectives differ in dimensions, scales, and optimization directions, easily leading to unclear objective trade-offs. Second, some methods employ a single objective or simply weight and merge multiple objectives, with weight selection relying on experience, making it difficult to reliably obtain a comprehensive Pareto optimal solution set. Third, even if a Pareto solution set is obtained, the engineering site still needs to select an executable optimal operating point or form an optimal operating line that varies with load from the multiple solutions. Without unified and repeatable decision rules, inconsistent point selection results can easily occur, affecting the engineering implementation and widespread application of the optimization method.

[0005] Therefore, there is an urgent need for an energy efficiency optimization method for gas turbines: under different load conditions, a multi-objective performance prediction model can be established based on operating data to quickly assess the impact of control variable combinations on comprehensive energy efficiency, sustainability indicators, emission indicators, and economic indicators; a Pareto optimal solution set can be obtained by searching within dynamic constraints using a multi-objective evolutionary algorithm to achieve a synergistic trade-off between comprehensive energy efficiency improvement, emission reduction, and economic improvement; at the same time, a clear multi-index decision-making mechanism can be used to automatically select a single optimal solution or output the optimal operating point set from the Pareto solution set to form optimal operating condition parameters that can be directly used for operation control or setpoint guidance, thereby achieving the comprehensive goals of improving comprehensive energy efficiency, reducing emissions, and optimizing economic performance of gas turbines. Summary of the Invention

[0006] To address the limitations of existing gas turbine energy efficiency optimization methods, this invention provides a gas turbine energy efficiency optimization method, characterized by the following steps: S1. Extract multidimensional input features from gas turbine operating data, use standardization methods to convert the input feature data into a data distribution with zero mean and unit variance, and normalize the efficiency, emission and economic target variables to obtain the normalized target vector; S2. Based on the standardized feature data and normalized target variables, the gradient boosting regression model is used to perform regression prediction on multiple objectives in the energy efficiency optimization of gas turbines, and the prediction results are destandardized and recovered. S3. Establish a two-layer coupled multi-objective optimization model with upper and lower layers. The upper layer aims to maximize efficiency, minimize emissions, and optimize economics. The lower layer aims to satisfy physical constraints and maximize scheduling benefits. The Pareto front solution set is generated through the improved adaptive NSGA-II. S4. Apply the TOPSIS decision method to calculate the weighted distance of each objective to the optimized Pareto front solution, sort them by proximity, and select the candidate solution with the highest priority in the proximity sort as the final optimal solution to ensure that emissions are minimized and economic efficiency is optimized while improving efficiency.

[0007] Furthermore, S1 specifically includes: S11. Obtain historical operating data of the gas turbine, including: load. Intake guide vane opening airflow Fuel flow rate and the corresponding comprehensive efficiency indicators Emission indicators Economic indicators Construct input feature vectors based on runtime data. With the target vector :

[0008]

[0009] S12. Use standardization methods to transform the input feature vector Each feature is subjected to zero-mean and unit-variance transformation to obtain the standardized feature vector. Then, normalization is applied to compress the values ​​of the target variable to a predetermined range, resulting in the normalized target variable. .

[0010] Furthermore, S2 specifically includes the following steps: S21. Based on the standardized feature data vector and the normalized target variable The gradient boosting regression model is used to predict multiple objectives in the energy efficiency optimization of gas turbines, and the true target values ​​are obtained. Includes: efficiency indicators Emission indicators Economic indicators The trained regression model uses standardized feature data vectors. To predict the target value :

[0011] In the formula, For the first The prediction error term for the target conforms to a Gaussian distribution; The prediction function for the gradient boosting regression model is calculated using the following formula:

[0012] In the formula, It is the first in the regression model The weight coefficient of each tree, It is the first The base learner generated by the tree It is the number of decision trees used in the regression model; S22. The regression model for each objective is optimized using a loss function, with the optimization objective being: :

[0013] In the formula, For the set of model parameters, For sample index, The total number of training samples, For loss function, For the first The first sample A normalized target variable For the first The first sample One target predicted value, The regularization coefficient is . For the model The parameters of a decision tree, This is the multi-task coupling strength coefficient. For output For input features gradient, For output For input features The gradient; S23. Normalized predicted target value for each target The destandardization method is used to restore it from the normalized range to the scale of the original target variable; the destandardization process is as follows:

[0014] In the formula, This represents the prediction results of the regression model at a real physical scale. and These are the maximum and minimum values ​​of the target variable during normalization. and These are the maximum and minimum values ​​of the target variable in the original data, respectively.

[0015] Furthermore, the two-layer coupled multi-objective optimization model described in S3 uses the upper-layer input feature vector. To control for variables, a multi-objective function is constructed based on the output of the regression model:

[0016] In the formula, Let be the efficiency function. For emission functions, It is an economic function; Consider maximizing efficiency: ;in These are predicted values ​​for efficiency indicators; Consider minimizing emissions and adding a threshold penalty:

[0017] In the formula, The threshold penalty coefficient is... These are the predicted values ​​for emission indicators. Emission threshold; Consider minimizing economic costs, and include risk factors:

[0018] In the formula, These are forecast values ​​for economic indicators. For risk weighting coefficients, For an uncertain cost function, Conditional risk value; Given an upper-layer input feature vector Solve for the lower-level scheduling variables To satisfy physical constraints and maximize operational benefits:

[0019] In the formula, The objective function for the lower-level operation's revenue is... For the lower-level constraint set; The optimal value of the lower layer Degree of violation of constraints Feedback is sent to the higher-level objective to obtain the overall objective function:

[0020] In the formula, To incorporate feedback from lower levels to correct upper-level objectives, For the upper level One original objective function, For feasibility penalty weighting, Weighting for revenue feedback.

[0021] Furthermore, in S3, an adaptive improved NSGA-II is used to generate the Pareto front solution set; the population is randomly initialized, and the fitness is obtained by performing upper-level target calculation and lower-level verification feedback for each individual; the population is then sorted by non-dominated order and crowding distance is calculated to obtain the non-dominated hierarchy set. Define population diversity indicators and non-dominated layers Construct adaptive selection probability :

[0022] In the formula, , These are the lower and upper bounds of the adaptive probability, respectively. This is a reference value for the number of non-dominated layers. For diversity reference values, , These are the slope parameters; If the random number is less than the adaptive selection probability, random selection is performed to enhance exploration; otherwise, the elite retention strategy is followed. Simulated binary crossover and polynomial mutation are employed, and the mutation rate is... Adaptive adjustment based on diversity indicators:

[0023] In the formula, For the first The mutation rate of generations , These are the lower and upper bounds of the mutation rate, respectively. This is the attenuation coefficient of the variation rate as a function of diversity. Merge the parent and child generations and iterate until convergence, then output the Pareto front solution set.

[0024] Furthermore, S3 also includes the following steps: suppressing solution aggregation by calculating the sparsity of the solution set across each objective dimension, and preferentially retaining candidate solutions with a sparser distribution; the distribution sparsity The calculation formula is:

[0025] In the formula, For the target number, To solve In the The function value on each target To solve In the The function value on each target and The feasible solution set in the current iteration is at the th ... The maximum and minimum values ​​on each target; To prevent stable terms with a denominator of zero; The weighting coefficients are related to the sensitivity of the target dimension, and satisfy the following conditions: ; By non-dominated sorting and distribution sparsity calculation, the Pareto front solution set that best considers all objectives is selected. The Pareto front solution set contains multiple feasible combinations of control variables and their corresponding target prediction values.

[0026] Furthermore, S4 calculates the results of optimizing the Pareto front solution set and comparing it with the optimal reference solution. Worst-case reference solution Weighted distance between: The proximity of candidate solutions is calculated based on the weighted distance and sorted. The candidate solution with the highest priority in the proximity ranking is selected as the final optimal solution.

[0027] Furthermore, the optimal solution provides the gas turbine with the optimal combination of control variables and energy efficiency optimization indicators, ensuring the best trade-off in multi-objective optimization.

[0028] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1) This invention takes comprehensive efficiency indicators, emission indicators and economic indicators as optimization objectives, and realizes dynamic collaborative optimization between control decision and operational feasibility by constructing a two-layer coupled optimization structure and an adaptively improved NSGA-II multi-objective algorithm.

[0029] 2) This invention introduces an adaptive selection probability and adaptive mutation rate adjustment mechanism for non-dominated layer structure in the multi-objective evolution process, so that the algorithm maintains the uniformity of the solution set in the convergence phase and enhances the global search capability in the exploration phase, effectively overcoming the problems of premature convergence, uneven distribution of solution set and insufficient stability of standard NSGA-II.

[0030] 3) This invention utilizes historical operating data to construct a multi-objective performance prediction model, enabling rapid evaluation and iterative optimization of control quantity combinations under different loads. Compared with methods relying on thermodynamic cycle mechanism models and complex simulations, it significantly reduces modeling and calibration costs and computation time, and has better adaptability to unit performance drift.

[0031] 4) After obtaining the Pareto solution set, the present invention uses a multi-index decision-making mechanism to automatically screen a single optimal solution, thereby outputting the optimal combination of parameters such as intake guide vane opening, air flow rate, and fuel flow rate under different loads, solving the problem of having a solution set but being difficult to select, and improving the repeatability and feasibility of the optimization results.

[0032] 5) In the process of establishing the upper-lower layer coupled multi-objective optimization model, this invention adds a threshold penalty when calculating emission minimization and a risk term when calculating economic cost minimization, thereby more comprehensively considering optimization indicators and physical constraints to achieve model optimization. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 Overall flowchart of gas turbine energy efficiency optimization method; Detailed Implementation

[0035] The following is in conjunction with the instruction manual appendix. Figure 1 The present invention provides a more detailed description of a gas turbine energy efficiency optimization method. The method includes the following steps: S1. Extract multidimensional input features from gas turbine operating data, use standardization methods to convert the input feature data into a data distribution with zero mean and unit variance, and normalize the efficiency, emission and economic target variables to obtain the normalized target vector; S1 specifically includes: S11. Obtain historical operating data of the gas turbine, including: load. Intake guide vane opening airflow Fuel flow rate and the corresponding comprehensive efficiency indicators Emission indicators Economic indicators Construct input feature vectors based on runtime data. With the target vector :

[0036]

[0037] Among them, the comprehensive efficiency index This indicates the overall operating efficiency of the gas turbine under a given load, reflecting the unit's energy utilization level; emission indicators Indicates the level of pollutant emissions during unit operation, reflecting environmental performance; economic indicators It indicates the economic cost level of the unit under a given operating condition, including fuel cost per unit of electricity generated, operating cost, and emission treatment cost; S12. Use standardization methods to transform the input feature vector Each feature is subjected to zero-mean and unit-variance transformation to obtain the standardized feature vector. Then, normalization is applied to compress the values ​​of the target variable to a predetermined range, resulting in the normalized target variable. .

[0038] S2. Based on the standardized feature data and normalized target variables, the gradient boosting regression model is used to perform regression prediction on multiple objectives in the energy efficiency optimization of gas turbines, and the prediction results are destandardized and recovered. S2 specifically includes the following steps: S21. Based on the standardized feature data vector and the normalized target variable The gradient boosting regression model is used to predict multiple objectives in the energy efficiency optimization of gas turbines, and the true target values ​​are obtained. Includes: efficiency indicators Emission indicators Economic indicators The trained regression model uses standardized feature data vectors. To predict the target value :

[0039] In the formula, For the first The prediction error term for the target conforms to a Gaussian distribution; The prediction function for the gradient boosting regression model is calculated using the following formula:

[0040] In the formula, It is the first in the regression model The weight coefficient of each tree, It is the first The base learner generated by the tree It is the number of decision trees used in the regression model; S22. The regression model for each objective is optimized using a loss function, with the optimization objective being: :

[0041] In the formula, For the set of model parameters, For sample index, The total number of training samples, For loss function, For the first The first sample A normalized target variable For the first The first sample One target predicted value, The regularization coefficient is . For the model The parameters of a decision tree, This is the multi-task coupling strength coefficient. For output For input features gradient, For output For input features The gradient; S23. Normalized predicted target value for each target The destandardization method is used to restore it from the normalized range to the scale of the original target variable; the destandardization process is as follows:

[0042] In the formula, This represents the prediction results of the regression model at a real physical scale. and These are the maximum and minimum values ​​of the target variable during normalization. and These are the maximum and minimum values ​​of the target variable in the original data, respectively.

[0043] S3. Establish a two-layer coupled multi-objective optimization model with upper and lower layers. The upper layer aims to maximize efficiency, minimize emissions, and optimize economics. The lower layer aims to satisfy physical constraints and maximize scheduling benefits. The Pareto front solution set is generated through the improved adaptive NSGA-II. The specific steps are as follows: The aforementioned two-layer coupled multi-objective optimization model uses upper-layer input feature vectors. To control for variables, a multi-objective function is constructed based on the output of the regression model:

[0044] In the formula, Let be the efficiency function. For emission functions, It is an economic function; Consider maximizing efficiency: ;in These are predicted values ​​for efficiency indicators; Consider minimizing emissions and adding a threshold penalty:

[0045] In the formula, The threshold penalty coefficient is... These are the predicted values ​​for emission indicators. Emission threshold; Consider minimizing economic costs, and include risk factors:

[0046] In the formula, These are forecast values ​​for economic indicators. For risk weighting coefficients, For an uncertain cost function, Conditional risk value; Given an upper-layer input feature vector Solve for the lower-level scheduling variables To satisfy physical constraints and maximize operational benefits:

[0047] In the formula, The objective function for the lower-level operation's revenue is... For the lower-level constraint set; The optimal value of the lower layer Degree of violation of constraints Feedback is sent to the higher-level objective to obtain the overall objective function:

[0048] In the formula, To incorporate feedback from lower levels to correct upper-level objectives, For the upper level One original objective function, For feasibility penalty weighting, Weighting for revenue feedback.

[0049] An adaptive improved NSGA-II is used to generate the Pareto front solution set; the population is randomly initialized, and the fitness of each individual is obtained by performing upper-level target calculation and lower-level verification feedback; the population is then sorted by non-dominated order and crowding distance is calculated to obtain the non-dominated hierarchy set. Define population diversity indicators and non-dominated layers Construct adaptive selection probability :

[0050] In the formula, , These are the lower and upper bounds of the adaptive probability, respectively. This is a reference value for the number of non-dominated layers. For diversity reference values, , These are the slope parameters; If the random number is less than the adaptive selection probability, random selection is performed to enhance exploration; otherwise, the elite retention strategy is followed. Simulated binary crossover and polynomial mutation are employed, and the mutation rate is... Adaptive adjustment based on diversity indicators:

[0051] In the formula, For the first The mutation rate of generations , These are the lower and upper bounds of the mutation rate, respectively. This is the attenuation coefficient of the variation rate as a function of diversity. Merge the parent and child generations and iterate until convergence, then output the Pareto front solution set.

[0052] The sparsity of the solution set across each objective dimension is calculated to suppress solution clustering and preferentially retain candidate solutions with a sparser distribution; the sparsity of the distribution... The calculation formula is:

[0053] In the formula, For the target number, To solve In the The function value on each target To solve In the The function value on each target and The feasible solution set in the current iteration is at the th ... The maximum and minimum values ​​on each target; To prevent stable terms with a denominator of zero; The weighting coefficients are related to the sensitivity of the target dimension, and satisfy the following conditions: ; By non-dominated sorting and distribution sparsity calculation, the Pareto front solution set that best considers all objectives is selected. The Pareto front solution set contains multiple feasible combinations of control variables and their corresponding target prediction values.

[0054] S4. Apply the TOPSIS decision method to calculate the difference between the optimized Pareto front solution and the optimal reference solution. Worst-case reference solution Weighted distance between:

[0055]

[0056] In the formula, Candidate solutions With the optimal reference solution distance, Candidate solutions With worst reference solution distance, For the first The candidate solution at the th... The target value on each target, and The optimal reference solution and the worst reference solution are respectively at the th... Reference values ​​for each target; The target weight coefficients are and satisfy the following conditions: , For configurable distance order parameters, The target number.

[0057] The proximity of candidate solutions is calculated based on the weighted distance. :

[0058] The proximity is sorted, and the candidate solution with the highest priority in the proximity ranking is selected as the final optimal solution. The optimal combination of control variables and the corresponding target prediction value are output for each load point, thereby forming an optimal set of operating condition parameters that can be directly used for gas turbine operation control or setpoint guidance. Ultimately, the selected optimal solution will provide guidance for the optimized design of gas turbines, ensuring the best trade-offs are achieved in multi-objective optimization to meet practical application requirements.

[0059] Using gas turbine operating data as input, the regression model prediction results are shown in Table 1, and the performance optimization results are shown in Table 2. The analysis results show that the prediction model can accurately characterize the mapping relationship between control variables and various target indicators, meeting the need for rapid and stable evaluation of the objective function in subsequent multi-objective optimization solutions. This invention can achieve effective synergistic trade-offs among different objectives, improving overall energy efficiency and sustainability while reducing emissions and significantly improving economic performance, thus verifying the effectiveness and engineering application value of the method in optimizing gas turbine operating parameters.

[0060] Table 1

[0061] Table 2

[0062] In this specification, the same or similar parts between the various embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the descriptions of the embodiments described later are relatively simple, and relevant parts can be referred to the descriptions of the foregoing embodiments.

[0063] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for optimizing the energy efficiency of a gas turbine, characterized in that, The steps include the following: S1. Extract multidimensional input features from gas turbine operating data, use standardization methods to convert the input feature data into a data distribution with zero mean and unit variance, and normalize the efficiency, emission and economic target variables to obtain the normalized target vector; S2. Based on the standardized feature data and normalized target variables, the gradient boosting regression model is used to perform regression prediction on multiple objectives in the energy efficiency optimization of gas turbines, and the prediction results are destandardized and recovered. S3. Establish a two-layer coupled multi-objective optimization model with upper and lower layers. The upper layer aims to maximize efficiency, minimize emissions, and optimize economics. The lower layer aims to satisfy physical constraints and maximize scheduling benefits. The Pareto front solution set is generated through the improved adaptive NSGA-II. S4. Apply the TOPSIS decision method to calculate the weighted distance of each objective to the optimized Pareto front solution, sort them by proximity, and select the candidate solution with the highest priority in the proximity sort as the final optimal solution to ensure that emissions are minimized and economic efficiency is optimized while improving efficiency.

2. The method according to claim 1, characterized in that, S1 specifically includes: S11. Obtain historical operating data of the gas turbine, including: load. Intake guide vane opening airflow Fuel flow rate and the corresponding comprehensive efficiency indicators Emission indicators Economic indicators Construct input feature vectors based on runtime data. With the target vector : ； ； S12. Use standardization methods to transform the input feature vector Each feature is subjected to zero-mean and unit-variance transformation to obtain the standardized feature vector. Then, normalization is applied to compress the values ​​of the target variable to a predetermined range, resulting in the normalized target variable. .

3. The method according to claim 2, characterized in that, S2 specifically includes the following steps: S21. Based on the standardized feature data vector and the normalized target variable The gradient boosting regression model is used to predict multiple objectives in the energy efficiency optimization of gas turbines, and the true target values ​​are obtained. Includes: efficiency indicators Emission indicators Economic indicators The trained regression model uses standardized feature data vectors. To predict the target value : ； In the formula, For the first The prediction error term for the target conforms to a Gaussian distribution; The prediction function for the gradient boosting regression model is calculated using the following formula: ； In the formula, It is the first in the regression model The weight coefficient of each tree, It is the first The base learner generated by the tree It is the number of decision trees used in the regression model; S22. The regression model for each objective is optimized using a loss function, with the optimization objective being: : ； In the formula, For the set of model parameters, For sample index, The total number of training samples, For loss function, For the first The first sample A normalized target variable For the first The first sample One target predicted value, The regularization coefficient is . For the model The parameters of a decision tree, This is the multi-task coupling strength coefficient. For output For input features gradient, For output For input features The gradient; S23. Normalized predicted target value for each target The destandardization method is used to restore it from the normalized range to the scale of the original target variable; the destandardization process is as follows: ； In the formula, This represents the prediction results of the regression model at a real physical scale. and These are the maximum and minimum values ​​of the target variable during normalization. and These are the maximum and minimum values ​​of the target variable in the original data, respectively.

4. The method according to claim 3, characterized in that, The dual-layer coupled multi-objective optimization model described in S3 uses the upper layer as input feature vectors. To control for variables, a multi-objective function is constructed based on the output of the regression model: ； In the formula, Let be the efficiency function. For emission functions, It is an economic function; Consider maximizing efficiency: ;in These are predicted values ​​for efficiency indicators; Consider minimizing emissions and adding a threshold penalty: ； In the formula, The threshold penalty coefficient is... These are the predicted values ​​for emission indicators. Emission threshold; Consider minimizing economic costs, and include risk factors: ； In the formula, These are forecast values ​​for economic indicators. For risk weighting coefficients, For an uncertain cost function, Conditional risk value; Given an upper-layer input feature vector Solve for the lower-level scheduling variables To satisfy physical constraints and maximize operational benefits: ； In the formula, The objective function for the lower-level operation's revenue is... For the lower-level constraint set; The optimal value of the lower layer Degree of violation of constraints Feedback is sent to the higher-level objective to obtain the overall objective function: ； In the formula, To incorporate feedback from lower levels to correct upper-level objectives, For the upper level One original objective function, For feasibility penalty weighting, Weighting for revenue feedback.

5. The method according to claim 4, characterized in that, In S3, an adaptive improved NSGA-II is used to generate the Pareto front solution set; the population is randomly initialized, and the fitness is obtained by performing upper-level target calculation and lower-level verification feedback for each individual; the population is then sorted by non-dominated order and crowding distance is calculated to obtain the non-dominated hierarchy set. Define population diversity indicators and non-dominated layers Construct adaptive selection probability : ； In the formula, , These are the lower and upper bounds of the adaptive probability, respectively. This is a reference value for the number of non-dominated layers. For diversity reference values, , These are the slope parameters; If the random number is less than the adaptive selection probability, random selection is performed to enhance exploration; otherwise, the elite retention strategy is followed. Simulated binary crossover and polynomial mutation are employed, and the mutation rate is... Adaptive adjustment based on diversity indicators: ； In the formula, For the first The mutation rate of generations , These are the lower and upper bounds of the mutation rate, respectively. This is the attenuation coefficient of the variation rate as a function of diversity. Merge the parent and child generations and iterate until convergence, then output the Pareto front solution set.

6. The method according to claim 5, characterized in that, S3 further includes the following steps: suppressing solution aggregation by calculating the distribution sparsity of the solution set in each target dimension, and preferentially retaining candidate solutions with sparser distribution; the distribution sparsity The calculation formula is: ； In the formula, For the target number, To solve In the The function value on each target To solve In the The function value on each target and The feasible solution set in the current iteration is at the th ... The maximum and minimum values ​​on each target; To prevent stable terms with a denominator of zero; The weighting coefficients are related to the sensitivity of the target dimension, and satisfy the following conditions: ; By non-dominated sorting and distribution sparsity calculation, the Pareto front solution set that best considers all objectives is selected. The Pareto front solution set contains multiple feasible combinations of control variables and their corresponding target prediction values.

7. The method according to claim 6, characterized in that, S4 For the optimized Pareto front solution set, calculate its relationship with the optimal reference solution. Worst-case reference solution Weighted distance between: The proximity of candidate solutions is calculated based on the weighted distance and sorted. The candidate solution with the highest priority in the proximity ranking is selected as the final optimal solution.

8. The method according to claim 7, characterized in that, The optimal solution provides the best combination of control variables and energy efficiency optimization indicators for the gas turbine, ensuring the best trade-off in multi-objective optimization.

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