A gas turbine multi-objective performance optimization method based on improved schrodinger optimization technique

Abstract

The application belongs to the technical field of multi-objective optimization of gas turbines. The application provides a multi-objective performance optimization method for gas turbines based on an improved Schrodinger optimization technique. By introducing an improved Schrodinger optimization algorithm, the full global optimization ability of the algorithm in dealing with complex nonlinear problems is fully utilized, and the key control variables such as the guide vane angle of the high-pressure compressor and the low-pressure compressor are accurately adjusted, so that the unit consumption rate of fuel and the emission level of nitrogen oxide pollutants are effectively coordinated and reduced while better performance is achieved. The method has good working condition adaptability, significantly improves the real-time response ability of the system under the premise of ensuring the model accuracy and reliability, and provides solid and advanced technical support for the three-shaft gas turbine to realize efficient and low-carbon emission, smooth and stable operation in a wide load range.

Description

Technical Field

[0001] This disclosure relates to the field of multi-objective optimization technology for gas turbines, and more particularly to a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique. Background Technology

[0002] Three-shaft gas turbines, with their high power density, wide load adjustment range, and strong environmental adaptability, have become core power equipment in large-scale power generation, ship propulsion, and other fields. As energy conservation, environmental protection, and economic requirements become increasingly stringent, gas turbine performance optimization has shifted from single-objective to multi-objective comprehensive improvement, requiring a balance between efficiency, emissions, and other indicators. However, the complex coupling and nonlinear interactions between the low-pressure, high-pressure, and power turbine rotors in a three-shaft structure make it difficult to solve the multi-performance trade-off problem under varying operating conditions using traditional thermodynamic analysis or single-variable control strategies. Current research on multi-objective optimization of three-shaft gas turbines has made some progress: In terms of cycle thermodynamic analysis and static optimization, some studies have constructed closed-loop gas turbine models based on finite-time thermodynamics, using heat exchanger thermal conductivity distribution and compressor pressure ratio as variables, and employing the NSGA-II algorithm to achieve multi-objective optimization; others have conducted "energy-efficiency-economy-environment" analyses for gas turbine combined cycle power systems, improving efficiency and reducing costs by optimizing parameters such as turbine inlet temperature. In the field of dynamic optimization and control strategies, dynamic multi-objective optimization algorithms based on piecewise prediction have been developed to shorten optimization time and improve the uniformity of Pareto front distribution. Meanwhile, research has explored optimizing high-power mode control strategies for three-shaft gas turbines by adjusting variable turbine guide vanes, or employing multi-objective genetic algorithms to adjust guide vane positions, thereby improving thermal efficiency and reducing power generation costs under partial load. However, existing technologies still have significant shortcomings: on the one hand, traditional optimization relies heavily on component-level nonlinear models (CLMs), which require numerous iterations to ensure convergence, severely limiting optimization efficiency and failing to meet real-time engineering requirements; on the other hand, commonly used intelligent algorithms such as NSGA-II and MOPSO have limitations in balancing global optimization capabilities and efficiency, with some algorithms prone to getting trapped in local optima and lacking adaptability under varying load conditions, failing to balance optimization accuracy and engineering practicality, and thus failing to meet the actual operational requirements of high efficiency and low emissions for three-shaft gas turbines.

[0003] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0004] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0005] The purpose of this disclosure is to provide a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] According to embodiments of this disclosure, a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique is provided, comprising: S1, Construct the LPV proxy model for the gas turbine: Based on the CLM of a three-shaft gas turbine, and combined with real-time measurable scheduling parameters, an LPV proxy model for the gas turbine is constructed. S2, Determine the multi-objective optimization function and optimization variables: Using the guide vane angles of the high-pressure compressor and the low-pressure compressor as optimization variables, and minimizing the fuel consumption rate and nitrogen oxide emissions of the gas turbine as optimization objectives, a bi-objective optimization function including a penalty function is established. S3, Improved Schrödinger optimization algorithm: An improved Schrödinger optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set. S31, Algorithm Initialization: Set the algorithm parameters, randomly generate the initial population position, calculate the bi-objective fitness value of each individual in the population, and initialize the external archive for storing non-dominated solutions based on the multi-objective dominance criterion. S32, Multi-objective guidance for individual choice: Based on the sparsity of the distribution of non-dominated solutions in the external archives of the gas turbine multi-objective optimization technology field, a roulette wheel betting method is used to select multiple guiding individuals; S33, Population Iterative Update: The exploration and development phases are switched based on probability coefficients. During the exploration phase, the wave function characteristics were used as a basis to guide individuals to conduct a global search, combined with the technology of multi-objective optimization of gas turbines. During the development phase, individual units are guided to perform local optimization based on Newton's laws of motion and combined with the field of multi-objective optimization technology for gas turbines. Update the position of individuals in the population; S34, External file updates and iterations terminated: The external archive is updated based on the bi-objective fitness values ​​of individuals in the updated population and the multi-objective dominance relationship of the solutions in the external archive of the gas turbine multi-objective optimization technology field. Select a new guide individual from the updated external archives; Repeat steps S32 to S34 until the maximum number of iterations is reached, and output all non-dominated solutions in the external archive as the Pareto optimal solution set.

[0007] Furthermore, the state equation and output equation of the LPV proxy model are as follows:

[0008]

[0009] Where A is the state matrix, B is the input matrix, C is the output matrix, and D is the direct transfer matrix. For real-time measurable scheduling parameters, For small deviations of state variables, To control minute deviations in the input, For system noise, To measure noise, This represents a small deviation in the output parameters.

[0010] Furthermore, the fuel consumption rate of the gas turbine is:

[0011] Nitrogen oxide emissions are:

[0012] in, For fuel flow rate, For the output power of the gas turbine LPV model, The residence time of fuel in the combustion chamber. Indicates the combustion chamber temperature. This indicates the gas pressure at the combustion chamber inlet. This represents the pressure difference between the combustion chamber outlet and inlet. By introducing a penalty function to constrain the turbine temperature and shaft speed of the gas turbine to not exceed limits and to avoid surge, a bi-objective optimization function is constructed:

[0013]

[0014] in, For the penalty function, For the first goal; The second goal.

[0015] Furthermore, initializing external files includes: Non-dominated solutions in the initial population are selected and stored in an external archive based on the multi-objective domination criterion. If the number of solutions in the external archive exceeds the preset maximum capacity, a grid partitioning mechanism is adopted to delete some solutions based on the congestion of the solutions in the target space in order to maintain the capacity. The grid partitioning mechanism includes: uniformly dividing the solution space into several hypercubes, counting the number of solutions in each hypercube, randomly deleting one solution in the most congested hypercube, and ensuring that the file capacity does not exceed the limit.

[0016] Furthermore, step S32 specifically includes: The solution space corresponding to the external archive is divided into two objective dimensions ( f 1, f 2) Divide the hypercubes uniformly and calculate the number of non-dominated solutions within each hypercube. n i ; Based on the number of nondominated solutions within each hypercube n i Define the selection probability for each solution. Pr i = c / n i ;in, c =2; The guiding individuals, selected through three rounds of roulette, are of priority 1st, 2nd, and 3rd, respectively, and are denoted as... , and These correspond to the solutions with the best overall performance, the second best overall performance, and the best balance in the bi-objective optimization, respectively, and are used to guide the direction of subsequent population updates.

[0017] Furthermore, in step S33, when the probability coefficient ≥ Conversion Factor At this time, switch to the exploration phase; The individual position update formula during the exploration phase is used to optimally guide individuals. or the current individual Based on the wave function And calculate the information from 3 guiding individuals; To optimally guide individuals Based on:

[0018] Based on the current individual Based on:

[0019] in, h is Planck's constant. For the individual with the worst fitness among the two target groups in the current population, It is a random number.

[0020] Furthermore, in step S33, when the probability coefficient Small < Conversion Factor At that time, switch to the development phase; The individual position update during the development phase is based on Newton's laws of motion and is calculated using strategies based on historical position inertia or optimal individual guidance. Based on historical location inertia:

[0021] Based on optimal individual guidance:

[0022] in, This is the Planck particle wave designation. For historical position.

[0023] Further updates to external files include: Determine the multi-objective domination relationship between the new individual and the solutions in the file. Depending on whether the new individual is dominated by one solution, partially dominated by solutions, or not dominated, perform the operation of discarding the new individual, replacing the dominated solution, or adding the new individual. If the file size exceeds the limit, a grid congestion filtering mechanism is used to delete solutions in order to maintain diversity and capacity.

[0024] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: In the embodiments of this disclosure, the above-described method, on the one hand, by introducing an improved Schrödinger optimization algorithm, fully leverages its powerful global optimization capability in handling complex nonlinear problems to precisely adjust key control variables such as the guide vane angles of the high-pressure and low-pressure compressors. This achieves better performance while effectively coordinating and reducing fuel consumption and nitrogen oxide emissions. On the other hand, this method possesses excellent adaptability to various operating conditions, simultaneously covering full-load and partial-load conditions. It overcomes the inefficiencies and long computation times caused by multiple iterations in traditional modeling methods under varying operating conditions. While ensuring model accuracy and reliability, it significantly improves the system's real-time response capability, providing solid and advanced technical support for achieving efficient, low-carbon emissions, and stable operation of three-shaft gas turbines across a wide load range. Attached Figure Description

[0025] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0026] Figure 1The diagram illustrates the steps of a gas turbine multi-objective performance optimization method based on an improved Schrödinger optimization technique in an exemplary embodiment of this disclosure. Figure 2 A flowchart illustrating a gas turbine multi-objective performance optimization method based on an improved Schrödinger optimization technique in an exemplary embodiment of this disclosure is shown. Figure 3 This illustrates the load requirements of the simulation process in an exemplary embodiment of this disclosure; Figure 4 This diagram shows a comparison of the speed outputs of the CLM model and the LPV model in an exemplary embodiment of this disclosure. Figure 5 A power output comparison diagram of the CLM model and the LPV model in an exemplary embodiment of this disclosure is shown; Figure 6 This diagram shows a comparison of the optimal solutions of PF and TOPSIS based on the LPV model under different loads in an exemplary embodiment of this disclosure. Figure 7 The diagram shows a comparison of the PF and TOPSIS optimal solutions of the CLM model under different loads in an exemplary embodiment of this disclosure. Detailed Implementation

[0027] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0028] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0029] This example implementation provides a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique. (Reference) Figure 1 As shown, the gas turbine multi-objective performance optimization method based on the improved Schrödinger optimization technique may include: S1, Construct the LPV proxy model for the gas turbine: Based on the CLM of a three-shaft gas turbine, and combined with real-time measurable scheduling parameters, an LPV proxy model for the gas turbine is constructed. S2, Determine the multi-objective optimization function and optimization variables: Using the guide vane angles of the high-pressure compressor and the low-pressure compressor as optimization variables, and minimizing the fuel consumption rate and nitrogen oxide emissions of the gas turbine as optimization objectives, a bi-objective optimization function including a penalty function is established. S3, Improved Schrödinger optimization algorithm: An improved Schrödinger optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set. S31, Algorithm Initialization: Set the algorithm parameters, randomly generate the initial population position, calculate the bi-objective fitness value of each individual in the population, and initialize the external archive for storing non-dominated solutions based on the multi-objective dominance criterion. S32, Multi-objective guidance for individual choice: Based on the sparsity of the distribution of non-dominated solutions in the external archives of the gas turbine multi-objective optimization technology field, a roulette wheel betting method is used to select multiple guiding individuals; S33, Population Iterative Update: The exploration and development phases are switched based on probability coefficients. During the exploration phase, the wave function characteristics were used as a basis to guide individuals to conduct a global search, combined with the technology of multi-objective optimization of gas turbines. During the development phase, individual units are guided to perform local optimization based on Newton's laws of motion and combined with the field of multi-objective optimization technology for gas turbines. Update the position of individuals in the population; S34, External file updates and iterations terminated: The external archive is updated based on the bi-objective fitness values ​​of individuals in the updated population and the multi-objective dominance relationship of the solutions in the external archive of the gas turbine multi-objective optimization technology field. Select a new guide individual from the updated external archives; Repeat steps S32 to S34 until the maximum number of iterations is reached, and output all non-dominated solutions in the external archive as the Pareto optimal solution set.

[0030] The aforementioned multi-objective performance optimization method for gas turbines based on improved Schrödinger optimization technology achieves two key benefits. Firstly, by introducing an improved Schrödinger optimization algorithm, its powerful global optimization capability in handling complex nonlinear problems is fully utilized. This allows for precise adjustment of key control variables such as the guide vane angles of the high-pressure and low-pressure compressors, thereby achieving better performance while effectively coordinating and reducing fuel consumption and nitrogen oxide emissions. Secondly, this method possesses excellent adaptability to various operating conditions, simultaneously covering full-load and partial-load conditions. It overcomes the inefficiencies and long computation times caused by multiple iterations in traditional modeling methods under varying operating conditions. While ensuring model accuracy and reliability, it significantly improves the system's real-time response capability, providing solid and advanced technical support for achieving efficient, low-carbon emissions, and stable operation of three-shaft gas turbines across a wide load range.

[0031] Below, we will refer to Figures 1 to 7 The steps of the gas turbine multi-objective performance optimization method based on the improved Schrödinger optimization technique described in this example embodiment will be explained in more detail.

[0032] This application discloses a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization algorithm (SRA), which addresses the problems of low efficiency and insufficient optimization capability of traditional models in multi-objective optimization of three-axis gas turbines. Figure 2 The diagram shown is a flowchart of a multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique. The details are as follows: In step S1, based on the CLM of the three-shaft gas turbine and combined with real-time measurable scheduling parameters, an LPV proxy model of the gas turbine is constructed.

[0033] Specifically, a gas turbine LPV proxy model is constructed. Based on the three-shaft gas turbine CLM, and combined with real-time measurable scheduling parameters of the gas turbine... (low pressure shaft percentage speed) and power shaft percentage speed Construct a linear variable parameter (LPV) model, with its state equation and output equation as follows: (1) in, Representing small deviations of state variables, the selected state variables are respectively High-pressure shaft percentage speed ( )and . Indicates control input (fuel flow rate) High and low pressure compressor guide vane angles — , The small deviations of ( ). A represents the state matrix, B represents the input matrix, C represents the output matrix, and D represents the direct transfer matrix. These matrices follow The model changes with the operating conditions and is piecewise linearized at different operating points, thus approximating the nonlinear model of the gas turbine with a linear model. and These represent system noise and measurement noise, respectively. This represents a small deviation in the output parameters of the LPV model. This model maintains accuracy without requiring numerous iterations, simulates the dynamic characteristics of gas turbines across the entire operating range, and can replace CLM for optimization calculations to improve efficiency.

[0034] In step S2, a bi-objective optimization function containing a penalty function is established, with the high-pressure compressor guide vane angle and the low-pressure compressor guide vane angle as optimization variables, and the minimization of the gas turbine's fuel consumption rate and nitrogen oxide emissions as optimization objectives.

[0035] Specifically, determine the multi-objective optimization function and variables. (The sentence is incomplete and requires more context.) , To optimize the variables, their value ranges are -3°~10° and -3°~30° respectively; based on the gas turbine fuel consumption rate ( SFC Minimize nitrogen oxide emissions ( Minimize as the optimization objective: (2) (3) in, This represents the output power of the LPV model of the gas turbine. This represents the residence time of the fuel in the combustion chamber. Indicates the combustion chamber temperature. This indicates the gas pressure at the combustion chamber inlet. This represents the pressure difference between the combustion chamber outlet and inlet.

[0036] Introducing a penalty function To constrain the turbine temperature and shaft speed of the gas turbine to stay within limits and to avoid surge, an optimization function is constructed: (4) In step S3, an improved Schrödinger optimization algorithm is used to optimize the solution and obtain the Pareto optimal solution set: S31, Algorithm Initialization: Set algorithm parameters, randomly generate initial population positions, calculate the bi-objective fitness value of each individual in the population, and initialize the external archive used to store non-dominated solutions based on the multi-objective dominance criterion. S32, Multi-objective guided individual selection: Based on the sparsity of the distribution of non-dominated solutions in the external archives of the gas turbine multi-objective optimization technology field, multiple guided individuals are selected using the roulette wheel selection method; S33, Population Iterative Update: Switching between the exploration and development phases based on probability coefficients; In the exploration phase, guiding individuals to perform global searches based on wave function characteristics and combined with the technology of gas turbine multi-objective optimization; In the development phase, guiding individuals to perform local optimization based on Newton's laws of motion and combined with the technology of gas turbine multi-objective optimization; Updating the position of individuals in the population; S34, External File Update and Iteration Termination: Based on the bi-objective fitness values ​​of individuals in the updated population and the multi-objective dominance relationship of solutions in the external file in the field of gas turbine multi-objective optimization technology, update the external file; reselect guiding individuals from the updated external file; repeat steps S32 to S34 until the maximum number of iterations is reached, and output all non-dominated solutions in the external file as the Pareto optimal solution set.

[0037] Specifically, the optimization process of the improved Schrödinger optimization algorithm: To adapt to the multi-objective optimization requirements of gas turbines, a multi-objective optimization strategy is incorporated into the Schrödinger optimization algorithm (SRA). This is achieved by managing non-dominated solutions through external archives and improving the individual selection mechanism to achieve higher fuel efficiency. SFC ) and nitrogen oxide emissions ( The collaborative optimization of () involves the following steps: S31: Algorithm and External File Initialization ① Algorithm parameter initialization: Set the population size N (number of search agents) and the maximum number of iterations. Search dimension Dim=2 (corresponding to) , ), variable upper and lower bounds UB=[10° 30°], LB=[-3° -3°] -3°~10° (-3°~30°); randomly generate the initial population position using the formula: (5) ② Fitness calculation: Each individual in the initial population ( , (Combination) becomes Input into the LPV model and calculate the corresponding bi-objective fitness value. f 1, f 2).

[0038] ③ External file initialization: Select non-dominated solutions from the initial population based on the multi-objective dominance criterion—if no individual exists... satisfy" fk ( )≤ f k ( (k=1,2) and at least one k such that f k ( )< f k ( ", then the individual Non-dominated solutions. All non-dominated solutions are saved to an external file. If the number of solutions in the file exceeds the preset maximum capacity, Arc... max =100, using a grid partitioning mechanism: the solution space is evenly divided into several hypercubes, the number of solutions (congestion) in each hypercube is counted, and one solution in the most congested hypercube is randomly deleted to ensure that the file capacity does not exceed the limit.

[0039] S32: Multi-objective guidance for individual choice Three optimal guide individuals are selected from external archives to guide population updates. The specific strategy is as follows: ① Divide the solution space corresponding to the external archive into two objective dimensions ( f 1, f 2) Divide the hypercubes uniformly and count the number of non-dominated solutions within each hypercube. n i , n i The smaller the value, the sparser the solution distribution in that region.

[0040] ② Roulette wheel selection guides individuals: Defining the probability of selection Pr i = c / n i ,in c =2, the probability of selecting a solution in a sparse region is higher. The guiding individuals, ranked 1st, 2nd, and 3rd priority respectively, are selected through three rounds of roulette, denoted as... , , These correspond to the optimal, suboptimal, and balanced solutions in the bi-objective optimization, respectively, and are used to guide the direction of subsequent population updates.

[0041] S33: Exploration and Development of SRA ① Exploration phase (wave function driven, global search).

[0042] Calculate probability coefficients With conversion factor t is the current iteration number.

[0043] when At that time, with wave function The feature expands the search space, and the global solution space is explored through probabilistic updates. Combining the information from three guiding individuals to update the position, the formula is: To optimally guide individuals Based on: (6) Based on the current individual Based on: (7) in, h is Planck's constant. The individual with the worst fitness among the two target groups in the current population.

[0044] ② Development phase (driven by Newtonian mechanics, local optimization).

[0045] when At this point, switch to the development strategy, focusing on a refined search of the multi-objective optimal region surrounding the guided individual. Optimize the accuracy of local solutions based on Newton's laws of motion, and adjust the update direction according to the differences between guided individuals. The formula is: Based on historical location inertia: (8) Based on optimal individual guidance: (9) S34: Termination of External File Updates and Iterations ① Archive Update: After each population update, calculate the bi-objective fitness of all new individuals, compare it with the existing solutions in the external archive for dominance, and update the archive according to the following rules: If the new individual is dominated by any solution in the file (i.e., there exists a solution in the file that satisfies "the solution's f1 ≤ the new individual's f1, and f2 ≤ the new individual's f2, and at least one objective is better"), then discard the new individual directly. If the new individual dominates some solutions in the file (i.e., the new individual's f1 ≤ dominated solution f1 and f2 ≤ dominated solution f2, and at least one objective is better), then delete the dominated solutions in the file and add the new individual to the file. If the new individual has a non-dominant relationship with all solutions in the file (i.e., the new individual's f1 is better than some solutions, but f2 is worse than these solutions, or vice versa), then the new individual is directly added to the file. If the file size exceeds Arc max The repeated grid congestion screening mechanism involves dividing hypercubes, calculating congestion, and deleting one solution from the most congested hypercube to maintain the diversity and capacity stability of the archives.

[0046] ② Guide individual updates: From the updated external archives, reselect according to the "grid congestion + roulette wheel" strategy in S32. , , This provides the latest guiding direction for the next iteration.

[0047] ③ Iteration Termination: When the number of iterations reaches the preset threshold... T max When the time is up, the algorithm terminates and outputs all non-dominated solutions in the external archive—that is, the Pareto optimal solution set for the gas turbine multi-objective optimization, with each solution corresponding to a set of solutions. , The parameter combination can be optimized according to the priority requirements of "low fuel consumption" or "low nitrogen oxide emissions" in actual engineering projects.

[0048] In one specific embodiment, the proposed framework is validated through simulation experiments. The experiments include Implementation 1 (accuracy validation of the LPV model) and Implementation 2 (efficiency and accuracy validation of multi-objective optimization).

[0049] Example 1: The load requirements of the simulation process are as follows Figure 3 As shown.

[0050] Comparison of velocity output between CLM model and LPV model (e.g.) Figure 4 As shown.

[0051] Power output comparison between CLM model and LPV model, for example Figure 5 As shown.

[0052] Figure 4-5 The power axis percentage speed (PCNP), high voltage axis percentage speed (PCNC), and model output power of the two models are shown. P out The maximum error of PCNC was 0.86%, and the average error was 0.02%; the maximum error of PCNP was 1.68%, and the average error was 0.04%; the maximum error of power output was 2.95%, and the average error was 0.03%. The results show that the constructed LPV model can effectively simulate the characteristics of the CLM model and can be used for gas turbine performance optimization.

[0053] Example 2: First, this embodiment presents the algorithm parameter settings for multi-objective optimization of a three-shaft gas turbine. The method of this application and the MOPSO algorithm are used. For each algorithm, N is set to 20. Set to 50. Specific parameter configurations are as follows: the grid expansion parameter for this application is set to 0.1, the number of grids per search Tmax dimension is set to 10, the navigator selection pressure parameter is set to 4, and the additional (to be deleted) repository member selection pressure parameter is set to 2. The initial value of the inertia weight is set to 1, the learning factor is set to 2, and the upper and lower limits of particle velocity are set to 0.5 and -0.5, respectively.

[0054] Unoptimized parameters and Set to 0. The LPV model under 100% operating conditions. and The concentrations were 0.2517 kg / kWh and 66.5291 ppm, respectively. The LPV model under 60% operating conditions... and The concentrations were 0.2637 kg / kWh and 37.0533 ppm, respectively. The CLM model under 100% operating conditions... and The concentrations were 0.2515 kg / kWh and 66.4681 ppm, respectively. The CLM model under 60% operating conditions... and The values ​​were 0.2640 kg / kWh and 37.6356 ppm, respectively. This indicates that the constructed LPV model has high accuracy and can accurately simulate the performance of the CLM model.

[0055] Comparison of optimal solutions for PF and TOPSIS based on the LPV model under different loads. Figure 6 As shown. A comparison of the optimal solutions of PF and TOPSIS based on the CLM model under different loads is presented. Figure 7 As shown.

[0056] Figure 6-7 The power factor (PF) of the gas turbine is shown under 100% and 60% load conditions. Under 100% power (P) condition, Relatively high, while The fuel consumption is relatively low. This indicates that full-load operation based on the LPV model exhibits low fuel consumption and... The trade-off between emissions. When power drops to 60%, Significantly reduced, but Slightly higher. The PF obtained by MOPSO and the method of this application is comparable to the optimal solution of TOPSIS. and The distribution trends are quite similar across different models. Among them, the optimal solution of TOPSIS is the most ideal solution selected in PF. Under different models, algorithms, and load conditions, the TOPSIS solution consistently reflects the balance between emissions and fuel consumption.

[0057] Table 1 Optimization results based on the LPV model

[0058] Table 2 Optimization results based on the CLM model

[0059] Tables 1 and 2 list the TOPSIS optimal solutions for the LPV model and the CLM model, respectively, and provide their... , The optimization variables and optimization time were compared. Compared with the unoptimized results, the adjusted... and It can simultaneously reduce fuel consumption and NOx emissions. Under both operating conditions, the CLM model... Slightly higher than the LPV model, while the CLM model... Slightly lower than the LPV model. This indicates that the LPV model has better fuel economy under full power conditions, while the CLM model has better emissions reduction. This method has advantages in several aspects. Based on the CLM model, the method in this application has advantages at 100% power. and The results are better than those of the MOPSO algorithm. Under other operating conditions, the proposed method and the MOPSO algorithm show different results. In terms of optimization time, the CLM model is more time-efficient than the LPV model at 100% power. The CLM model's design point is 100% power, and it converges without a large number of iterations, but gas turbines cannot operate at the design point for extended periods. At 60% pressure, the optimization time of the CLM model is significantly longer than that of the LPV model. This indicates that the developed LPV model is applicable to a wider range of operating conditions, which is highly advantageous for practical engineering applications under load fluctuations. Based on the CLM model, the proposed method has a significantly shorter optimization time than the MOPSO algorithm under partial load.

[0060] As can be seen, by optimizing key parameters such as the guide vane angles of the high-pressure and low-pressure compressors, this framework achieves a dual reduction in fuel consumption rate and nitrogen oxide emissions under both full-load and partial-load conditions. Specifically, fuel consumption rate decreases by 1.01%, and nitrogen oxide emissions decrease by 2.03 ppm. It is worth noting that the LPV surrogate model not only possesses high accuracy but also enables rapid computation in partial-load optimization, significantly improving its practicality for engineering applications. The method in this application also demonstrates superior global optimization capabilities and operational efficiency. Experimental results show that this optimization framework exhibits excellent performance.

[0061] The aforementioned multi-objective performance optimization method for gas turbines based on improved Schrödinger optimization technology achieves two key benefits. Firstly, by introducing an improved Schrödinger optimization algorithm, its powerful global optimization capability in handling complex nonlinear problems is fully utilized. This allows for precise adjustment of key control variables such as the guide vane angles of the high-pressure and low-pressure compressors, thereby achieving better performance while effectively coordinating and reducing fuel consumption and nitrogen oxide emissions. Secondly, this method possesses excellent adaptability to various operating conditions, simultaneously covering full-load and partial-load conditions. It overcomes the inefficiencies and long computation times caused by multiple iterations in traditional modeling methods under varying operating conditions. While ensuring model accuracy and reliability, it significantly improves the system's real-time response capability, providing solid and advanced technical support for achieving efficient, low-carbon emissions, and stable operation of three-shaft gas turbines across a wide load range.

[0062] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0063] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A multi-objective performance optimization method for gas turbines based on an improved Schrödinger optimization technique, characterized in that, include: S1, Construct the LPV proxy model for the gas turbine: Based on the CLM of a three-shaft gas turbine, and combined with real-time measurable scheduling parameters, an LPV proxy model for the gas turbine is constructed. S2, Determine the multi-objective optimization function and optimization variables: Using the guide vane angles of the high-pressure compressor and the low-pressure compressor as optimization variables, and minimizing the fuel consumption rate and nitrogen oxide emissions of the gas turbine as optimization objectives, a bi-objective optimization function including a penalty function is established. S3, Improved Schrödinger optimization algorithm: An improved Schrödinger optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set. S31, Algorithm Initialization: Set the algorithm parameters, randomly generate the initial population position, calculate the bi-objective fitness value of each individual in the population, and initialize the external archive for storing non-dominated solutions based on the multi-objective dominance criterion. S32, Multi-objective guidance for individual choice: Based on the sparsity of the distribution of non-dominated solutions in the external archives of the gas turbine multi-objective optimization technology field, a roulette wheel betting method is used to select multiple guiding individuals; S33, Population Iterative Update: The exploration and development phases are switched based on probability coefficients. During the exploration phase, the wave function characteristics were used as a basis to guide individuals to conduct a global search, combined with the technology of multi-objective optimization of gas turbines. During the development phase, individual units are guided to perform local optimization based on Newton's laws of motion and combined with the field of multi-objective optimization technology for gas turbines. Update the position of individuals in the population; S34, External file updates and iterations terminated: The external archive is updated based on the bi-objective fitness values ​​of individuals in the updated population and the multi-objective dominance relationship of the solutions in the external archive of the gas turbine multi-objective optimization technology field. Select a new guide individual from the updated external archives; Repeat steps S32 to S34 until the maximum number of iterations is reached, and output all non-dominated solutions in the external archive as the Pareto optimal solution set.

2. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 1, characterized in that, The state equation and output equation of the LPV proxy model are as follows: Where A is the state matrix, B is the input matrix, C is the output matrix, and D is the direct transfer matrix. For real-time measurable scheduling parameters, For small deviations of state variables, To control minute deviations in the input, For system noise, To measure noise, This represents a small deviation in the output parameters.

3. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 2, characterized in that, The fuel consumption rate of a gas turbine is: Nitrogen oxide emissions are: in, For fuel flow rate, For the output power of the gas turbine LPV model, The residence time of fuel in the combustion chamber. Indicates the combustion chamber temperature. This indicates the gas pressure at the combustion chamber inlet. This represents the pressure difference between the combustion chamber outlet and inlet. By introducing a penalty function to constrain the turbine temperature and shaft speed of the gas turbine to not exceed limits and to avoid surge, a bi-objective optimization function is constructed: in, For the penalty function, For the first goal; The second goal.

4. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 3, characterized in that, Initializing external files includes: Non-dominated solutions in the initial population are selected and stored in an external archive based on the multi-objective domination criterion. If the number of solutions in the external archive exceeds the preset maximum capacity, a grid partitioning mechanism is adopted to delete some solutions based on the congestion of the solutions in the target space in order to maintain the capacity. The grid partitioning mechanism includes: uniformly dividing the solution space into several hypercubes, counting the number of solutions in each hypercube, randomly deleting one solution in the most congested hypercube, and ensuring that the file capacity does not exceed the limit.

5. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 4, characterized in that, Step S32 specifically includes: The solution space corresponding to the external archive is divided into two objective dimensions ( f 1, f 2) Divide the hypercubes uniformly and calculate the number of non-dominated solutions within each hypercube. n i ; Based on the number of nondominated solutions within each hypercube n i Define the selection probability for each solution. Pr i = c / n i ;in, c =2; The guiding individuals, selected through three rounds of roulette, are of priority 1st, 2nd, and 3rd, respectively, and are denoted as... , and These correspond to the solutions with the best overall performance, the second best overall performance, and the best balance in the bi-objective optimization, respectively, and are used to guide the direction of subsequent population updates.

6. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 5, characterized in that, In step S33, when the probability coefficient ≥ Conversion Factor At this time, switch to the exploration phase; The individual position update formula during the exploration phase is used to optimally guide individuals. or the current individual Based on the wave function And calculate the information from 3 guiding individuals; To optimally guide individuals Based on: Based on the current individual Based on: in, h is Planck's constant. For the individual with the worst fitness among the two target groups in the current population, It is a random number.

7. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 6, characterized in that, In step S33, when the probability coefficient Small < Conversion Factor At that time, switch to the development phase; The individual position update during the development phase is based on Newton's laws of motion and is calculated using strategies based on historical position inertia or optimal individual guidance. Based on historical location inertia: Based on optimal individual guidance: in, This is the Planck particle wave designation. For historical position.

8. The gas turbine multi-objective performance optimization method based on improved Schrödinger optimization technology according to claim 7, characterized in that, Updating external files includes: Determine the multi-objective domination relationship between the new individual and the solutions in the file. Depending on whether the new individual is dominated by one solution, partially dominated by solutions, or not dominated, perform the operation of discarding the new individual, replacing the dominated solution, or adding the new individual. If the file size exceeds the limit, a grid congestion filtering mechanism is used to delete solutions in order to maintain diversity and capacity.

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