Design optimization method suitable for variable geometry turbine with variable number exceeding 100

Abstract

The invention provides a design optimization method suitable for a variable geometry turbine with more than 100 variables, which comprises the following steps: acquiring control parameters of a three-dimensional blade model of a variable geometry turbine part, and establishing a design space; the method comprises the following steps: selecting a set number of uniformly distributed design samples in a design space as an initial population, and sequentially performing differential operation, interlace operation guided by an RBF proxy model and selection operation based on a parent target evaluation value on the samples in the population to generate a plurality of child samples; a local search strategy based on an RBF proxy model is used for an optimal sample in the population, and a child sample is generated; combining all generated filial generation samples, performing performance evaluation, and updating the current population; the number of iterations is set for each optimization, and knowledge migration from a low-fidelity population to a high-fidelity population is realized by adopting a knowledge migration strategy based on a probability distribution model; and performing updating iteration on the high-fidelity population until the number of high-fidelity sample evaluation times reaches a set upper limit.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of variable geometry turbine optimization design, and particularly relates to a variable geometry turbine design optimization method suitable for a variable number exceeding 100. BACKGROUND

[0002] Optimization design is an effective way to improve the performance of turbomachinery, and has been the focus of the field of aerothermodynamics of turbomachinery at home and abroad. An aero-engine is a complex mechanical product with multiple components working cooperatively, and it goes through different working states, including stable working states and non-stable working states, in its entire working envelope. The variable geometry turbine involves non-stable working states in operation based on the rotation of guide vanes, and the adjustment of the rotatable guide vanes of the variable geometry turbine will affect the flow field distribution of the downstream blades. If the internal flow of the turbine is to be effectively organized, a detailed understanding of the mutual matching between the flow field of the rotatable guide vanes and the flow field after the rotation of the guide vanes is necessary. Due to the complex geometric structure and unsteady characteristics involved in the variable geometry turbine, the performance evaluation and analysis thereof faces the problems of long cycle and high cost, and therefore, the optimization design of the variable geometry turbine based on CFD simulation is a typical high-dimensional large-resource black box problem. The design of the turbine blades is complex, and often needs multiple cross-sectional profile control points plus three-dimensional accumulation modes such as bending, twisting and skimming for parameterization, and the number of design variables of a single blade can reach dozens or even hundreds. In the optimization design of the variable geometry turbine, in order to fully consider the interaction between the blades, multiple rows of blades are usually optimized at the same time, which will lead to a sharp increase in the number of design variables, and the number of design variables may exceed 100. At the same time, due to the strong unsteadiness of the internal flow of the variable geometry turbine, in order to accurately evaluate its performance, a higher fidelity evaluation method is sometimes needed, and a single CFD unsteady simulation needs to consume several or even dozens of hours, and the acceptable number of CFD evaluations in an engineering actual design cycle may only be several hundred or several thousand, which undoubtedly poses a great challenge to the existing optimization design method.

[0003] The methods currently applied in the field of optimal design of impeller machines mainly include evolutionary algorithms, optimization algorithms based on surrogate models, and intelligent evolutionary algorithms assisted by surrogate models. Although traditional evolutionary algorithms can solve 100-dimensional problems, they have the disadvantage of requiring a large number of samples. Optimization algorithms based on surrogate models can greatly reduce the number of required samples, but have the disadvantage of "dimensional disaster", and their performance deteriorates rapidly when the number of dimensions exceeds 30. Intelligent evolutionary algorithms assisted by surrogate models can combine the advantages of both, and are more advanced optimization algorithm ideas. However, the computational cost of high-fidelity performance evaluation increases sharply compared to low-fidelity performance evaluation, and both evolutionary algorithms and surrogate model-based algorithms face the problem of sample scarcity, and the most efficient intelligent evolutionary algorithm assisted by surrogate models cannot meet the requirements. In order to further alleviate the limitations of computational resources and achieve variable geometry turbine optimization design based on high-fidelity performance evaluation, more efficient super-large variable optimization algorithm research is urgently needed. SUMMARY

[0004] The purpose of the present application is to provide a variable geometry turbine design optimization method suitable for more than 100 variables, to solve the problem of high computational cost of CFD unsteady evaluation in variable geometry turbine optimization design.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows: In the first aspect, the present application provides a variable geometry turbine design optimization method suitable for more than 100 variables, comprising: Obtaining the control parameters of the three-dimensional blade modeling of the variable geometry turbine component, and establishing a design space; Selecting a set number of uniformly distributed design samples in the design space as the initial population, and sequentially performing difference operation, RBF surrogate model guided crossover operation, and selection operation based on parent target evaluation value on the samples in the population to generate a number of offspring samples; Using a local search strategy based on RBF surrogate model on the optimal sample in the population to generate an offspring sample; merging all the generated offspring samples, performing performance evaluation, and updating the current population; Every optimization set iteration, a knowledge transfer strategy based on a probability distribution model is used to realize knowledge transfer from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of high-fidelity sample evaluations reaches the set upper limit.

[0006] Further, the obtaining of the control parameters of the three-dimensional blade modeling of the variable geometry turbine component and the establishment of the design space comprise: In the established design space, a set of defined design parameters corresponds to a unique geometric design. The Latin hypercube sampling (LHS) method is used in the design space to select design samples with a relatively uniform distribution. These samples are used as low-fidelity initial samples for performance evaluation.

[0007] Furthermore, the step of selecting a uniformly distributed design sample in the design space as the initial population, and then sequentially performing a differencing operation, a crossover operation guided by the RBF surrogate model, and a selection operation based on the parent generation's target evaluation value on the samples in the population, generates several offspring samples, including: First, for each parent individual The best / 1 differential mutation strategy is executed to generate the corresponding mutated individuals. :

[0008] In the formula: Represents the optimal individual in the population; and For two random individuals in the population and ; As a mutation operator, we take in this paper... ; To balance the training time required for the surrogate model and the diversity of the population, we take [the population size] in this paper. ; Next, in each parent individual Construct a radial basis function surrogate model within the corresponding neighborhood and perform a local search to obtain the corresponding predicted individual. :

[0009] In the formula: This represents the predicted optimal solution of the radial basis function surrogate model; This represents the predicted value from the proxy model; set up , The dimension of the design space is denoted by , and the number of sample points used to train the surrogate model is denoted by ; the parent individual is denoted by . neighborhood radius Set to:

[0010] In the formula: Indicates the first individual parents The maximum distance between the parent individuals; The dimension of the design space; parent individual The neighborhood of can be represented as , and These represent the lower and upper limits of the design space, respectively. Finally, an exponential crossover strategy is used to predict individual... and mutated individuals Performing a crossover operation yields offspring individuals:

[0011] In the formula: Indicates a variant individual The One variable; Indicates the prediction of individuals The One variable; For the crossover operator, the default value is ; Finally, each offspring corresponds to a parent individual. The offspring are ranked according to the performance evaluation value of the parent, and the top-ranked individuals are selected as offspring.

[0012] Furthermore, the process of using a local search strategy based on the RBF surrogate model to generate a child sample for the optimal sample in the population, merging all generated child samples, evaluating performance, and updating the current population includes: First, in the optimal individual of the population Establish a local RBF proxy model within the defined area surrounding the location; set The number of sample points used to train the surrogate model is crucial in the early stages of the algorithm if the number of evaluated sample points is insufficient. Then, all sample points are used as training samples to construct a surrogate model; then, the particle swarm optimization algorithm is used to perform a local search on the surrogate model to find its local optimum. The offspring samples obtained from crossover operations and local search are evaluated for performance, and then sorted together with the original population. Based on the performance evaluation value of each sample, the top-ranked samples are selected to update the population.

[0013] Furthermore, for each optimization iteration, a knowledge transfer strategy based on a probability distribution model is used to achieve knowledge transfer from a low-fidelity population to a high-fidelity population, including: For low-fidelity populations, the location of the global optimum in the design space is determined by a probability distribution model. Approximately, the model satisfies:

[0014] In the formula: To optimize the objective function of the problem; This represents the global optimum of the optimization objective; For a small deviation threshold, when At that time, probability distribution model This strictly degenerates into a point in the design space, which is the global optimal solution to the optimization problem. First, effective information about the optimization process is extracted from the low-fidelity population, that is, a probability distribution model is trained using samples from the current low-fidelity population. A diagonal Gaussian probability distribution model is adopted:

[0015] In the formula: Represents a multivariate Gaussian probability distribution; Represents random variables The mean vector; Represents random variables The covariance matrix of the diagonal Gaussian probability distribution model is a diagonal matrix; then, random sampling is performed in the design space based on the probability distribution model obtained from training, and a total of 10 design samples are collected for each knowledge transfer.

[0016] Furthermore, the high-fidelity population undergoes an evolutionary process similar to that of the low-fidelity population, with the surrogate models involved being multi-fidelity radial basis function surrogate models, as detailed below: The multifidelity radial basis function surrogate model used is a product / difference hybrid multifidelity model, which consists of a low-fidelity surrogate model, scaling factors, and a difference function, and its expression is as follows:

[0017] In the formula: This is a multi-fidelity radial basis function surrogate model; This represents the scaling factor for a low-fidelity proxy model. As a low-fidelity proxy model, the RBF proxy model is used. It is a parameter vector; This represents high-fidelity training samples; Indicates the prediction point With high-fidelity training samples The basis function vectors between them.

[0018] Furthermore, this multi-fidelity radial basis function surrogate model includes two types of hyperparameters: scaling coefficients. and parameter vector These hyperparameters can be obtained by solving the following system of linear equations:

[0019] In the formula: This represents the performance evaluation value of the high-fidelity training samples. Since the coefficient matrix of this system of linear equations is a full-rank row matrix, there must exist a unique minimum norm solution:

[0020] In the formula: That is, the coefficient matrix of the linear equation system; The vector of constant terms in the system of linear equations: .

[0021] Secondly, the present invention provides a variable geometry turbine optimization system suitable for multiple variables, characterized in that it comprises: The data acquisition module is used to acquire the control parameters for the three-dimensional blade model of the variable geometry turbine component and establish the design space; The offspring sample generation module is used to select a set number of uniformly distributed design samples in the design space as the initial population, and then perform differential operation, RBF surrogate model-guided crossover operation, and selection operation based on the parent target evaluation value on the samples in the population in sequence to generate several offspring samples. The merging module is used to generate a child sample from the best sample in the population using a local search strategy based on the RBF surrogate model; all generated child samples are merged, their performance is evaluated, and the current population is updated. The iterative output module is used to perform a set number of iterations for each optimization, and adopts a knowledge transfer strategy based on a probability distribution model to achieve knowledge transfer from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of evaluations of the high-fidelity samples reaches the set upper limit.

[0022] Thirdly, the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the variable geometry turbine design optimization method applicable to more than 100 variables.

[0023] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method for optimizing variable geometry turbine design with more than 100 variables.

[0024] Compared with the prior art, the present invention has the following technical effects: This invention places the design variables related to different blades of a variable geometry turbine in the same high-dimensional design space for joint optimization. Using a surrogate model-assisted evolutionary algorithm as the basic framework, a transfer strategy based on a probabilistic model is incorporated. This fully utilizes the results of low-fidelity optimization, helping to quickly narrow the search range in the early stages of the algorithm, significantly reducing the number of performance evaluations required for high-fidelity samples, and promoting the high-fidelity optimization process. This effectively alleviates the limitations of computational resources and further improves the optimization efficiency of the algorithm.

[0025] Furthermore, since this invention involves samples with both high-fidelity and low-fidelity evaluation methods, and high-fidelity samples are relatively scarce while low-fidelity samples are relatively abundant, a multi-fidelity radial basis function surrogate model is constructed during the high-fidelity sample iteration process. This method fuses low-fidelity and high-fidelity samples, effectively compensating for the scarcity of high-fidelity samples and improving the prediction accuracy of the surrogate model.

[0026] In engineering practice, since the algorithm involves the evolution of populations with different fidelity levels, the iterative evolution of low-fidelity and high-fidelity populations can be carried out simultaneously. This enables the method proposed in this invention to have parallel computing capabilities, thereby significantly shortening the time required for optimization design. This method can typically find the globally optimal design within 200 high-fidelity sample evaluations. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of an embodiment of the present invention.

[0028] Figure 2 This is a schematic diagram of the geometric model of the meridional channel surface of PW-E3 as the optimization object in an embodiment of the present invention.

[0029] Figure 3 This is a flowchart of the present invention. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings: Example 1, please refer to Figure 3 This invention provides a method for optimizing variable geometry turbine design applicable to more than 100 variables, including: Obtain the control parameters for the 3D blade model of the variable geometry turbine component and establish the design space; In the design space, a set number of uniformly distributed design samples are selected as the initial population. Differentiation operation, crossover operation guided by RBF surrogate model, and selection operation based on the parent generation target evaluation value are performed on the samples in the population in sequence to generate several offspring samples. The optimal sample in the population is used to generate a offspring sample using a local search strategy based on the RBF surrogate model; all generated offspring samples are merged, their performance is evaluated, and the current population is updated. For each set number of optimization iterations, a knowledge transfer strategy based on a probability distribution model is used to transfer knowledge from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of evaluations of the high-fidelity samples reaches the set upper limit.

[0031] 1) By using a transfer strategy based on a probabilistic model, the information in the low-fidelity sample space can be fully utilized. Considering the similarity between the global optimal solution positions of low-fidelity and high-fidelity optimization problems, using a probabilistic distribution model to achieve knowledge transfer from the low-fidelity population to the high-fidelity population will help to quickly narrow the search range for optimization in the early stages of the algorithm and significantly reduce the number of performance evaluations required for high-fidelity samples.

[0032] 2) Considering the scarcity of high-fidelity samples, a multi-fidelity RBF surrogate model is established during the high-fidelity population iteration process. This model can integrate samples of different fidelities, make up for the lack of high-fidelity samples, and effectively improve the accuracy of the surrogate model.

[0033] 3) Considering the ability of parallel computing in engineering practice, two population evolutions with different fidelity can be carried out simultaneously in the algorithm framework, which greatly shortens the time required for optimization design.

[0034] This invention combines relatively inexpensive and readily available low-fidelity samples with high-fidelity samples. During the optimization process, it fully utilizes the space and optimization information of the low-fidelity samples for transfer learning, aiding the evolution of the high-fidelity population. Furthermore, it merges samples of two different fidelities to build a surrogate model, resulting in higher accuracy. These two strategies significantly improve the efficiency of optimization design.

[0035] The method proposed in this invention fully considers the advantages of parallel computing, enabling simultaneous iterative evolution of high-fidelity and low-fidelity populations within a single framework. This is an important consideration for optimization design problems in engineering practice. In engineering applications, it can significantly reduce the time required for population evolution and shorten the optimization design cycle.

[0036] Example 2: This invention provides a method for optimizing variable geometry turbine design with more than 100 variables, including: The first step is to take the variable geometry turbine component as the design object, obtain the control parameters of each three-dimensional blade shape, and establish the design space. The second step is to select a certain number of evenly distributed design samples in the design space as the initial population, and to conduct low-fidelity performance evaluation on all individuals in the population. The third step involves sequentially performing a difference operation, a crossover operation guided by the RBF surrogate model, and a selection operation based on the parent generation's target evaluation value on the samples in the population to generate several offspring samples. Step 4: Use a local search strategy based on the RBF surrogate model to generate a offspring sample from the best sample in the population; The fifth step is to merge all the offspring samples generated in the third and fourth steps together; The sixth step is to evaluate the performance of all obtained offspring samples and update the current population. Step 7: Repeat steps 3 to 6, and after a certain number of iterations, use a knowledge transfer strategy based on a probability distribution model to transfer knowledge from the low-fidelity population to the high-fidelity population.

[0037] Step 8: Determine whether to stop knowledge transfer, and set the maximum number of performance evaluations for low-fidelity optimization problems as the criterion.

[0038] Step 9: Repeat steps 3 through 6 for the high-fidelity population until the maximum number of evaluations of the high-fidelity samples is reached. It is worth noting that the surrogate model used in steps 3 and 4 is replaced by a multi-fidelity RBF surrogate model instead of the original single-fidelity RBF surrogate model.

[0039] Furthermore, within the established design space, a set of defined design parameters corresponds to a unique geometric design; Latin hypercube sampling (LHS) is used to select relatively uniformly distributed design samples within the design space. These samples serve as low-fidelity initial samples for performance evaluation.

[0040] Furthermore, the following steps are performed sequentially on the samples in the low-fidelity population: differencing, crossover guided by the RBF surrogate model, and selection based on the parent's target evaluation value: First, for each parent individual The best / 1 differential mutation strategy is executed to generate the corresponding mutated individuals. :

[0041] In the formula: Represents the optimal individual in the population; and For two random individuals in the population and ; As a mutation operator, we take in this paper... ; To balance the training time required for the surrogate model and the diversity of the population, we take [the population size] in this paper. .

[0042] Next, in each parent individual Construct a radial basis function surrogate model within the corresponding neighborhood and perform a local search to obtain the corresponding predicted individual. :

[0043] In the formula: This represents the predicted optimal solution of the radial basis function surrogate model; This represents the predicted value from the proxy model.

[0044] To balance the accuracy of the surrogate model with the computational cost required for its training, this paper sets... ( (The dimension of the design space) represents the number of sample points used to train the surrogate model. Parent individual neighborhood radius Set to:

[0045] In the formula: Indicates the first individual parents The maximum distance between the parent individuals; To determine the dimension of the design space. Therefore, the parent individual... The neighborhood of can be represented as , and These represent the lower and upper limits of the design space, respectively.

[0046] Finally, an exponential crossover strategy is used to predict individual... and mutated individuals Performing a crossover operation yields offspring individuals:

[0047] In the formula: Indicates a variant individual The One variable; Indicates the prediction of individuals The One variable; For the crossover operator, the default value is .

[0048] Finally, each offspring corresponds to a parent individual. The offspring are ranked according to the performance evaluation value of the parent, and the top-ranked individuals are selected as offspring.

[0049] Furthermore, a local search strategy based on a surrogate model is employed around the optimal individual in the population, as follows: First, in the optimal individual of the population Establish a local RBF proxy model within a certain area surrounding the model. This represents the number of sample points used to train the surrogate model. In the early stages of the algorithm, if the number of evaluated sample points is insufficient... Then, all sample points are used as training samples to construct a surrogate model. Next, a particle swarm optimization algorithm is used to perform a local search on this surrogate model to find its local optimum. The offspring samples obtained from crossover operations and local search are evaluated for performance. Then, they are sorted together with the original population. Based on the performance evaluation value of each sample, the top-ranked samples (population size) are selected to update the population.

[0050] Furthermore, after a certain number of generations of evolution in the low-fidelity samples, knowledge transfer is performed to the high-fidelity population, as follows: For a low-fidelity population, the location of its global optimum in the design space can be determined by a probability distribution model. Approximately, the model satisfies:

[0051] In the formula: To optimize the objective function of the problem; This represents the global optimum of the optimization objective; For a small deviation threshold, when At that time, probability distribution model This strictly degenerates into a point in the design space, which is the global optimal solution to the optimization problem.

[0052] First, effective information about the optimization process is extracted from the low-fidelity population, that is, a probability distribution model is trained using samples from the current low-fidelity population. Here, a diagonal Gaussian probability distribution model is used:

[0053] In the formula: Represents a multivariate Gaussian probability distribution; Represents random variables The mean vector; Represents random variables The covariance matrix of the Gaussian probability distribution model is a diagonal matrix. Then, based on the probability distribution model obtained through training, random sampling is performed in the design space, with 10 design samples collected for each knowledge transfer. Since the probability distribution model can approximately represent the current optimal solution position of the low-fidelity optimization problem, the sampled design samples all contain low-fidelity optimization information, which helps high-fidelity optimization converge quickly.

[0054] Furthermore, the evolutionary process for high-fidelity populations is similar to that for low-fidelity populations, except that the surrogate models involved are all multi-fidelity radial basis function surrogate models, as detailed below: The multifidelity radial basis function surrogate model used is a product / difference hybrid multifidelity model, which consists of a low-fidelity surrogate model, scaling factors, and a difference function, and its expression is as follows:

[0055] In the formula: This is a multi-fidelity radial basis function surrogate model; This represents the scaling factor for a low-fidelity proxy model. For low-fidelity proxy models, we directly use the RBF proxy model as the low-fidelity proxy model here. It is a parameter vector; This represents high-fidelity training samples; Indicates the prediction point With high-fidelity training samples The basis function vectors between them.

[0056] This multi-fidelity radial basis function surrogate model contains two types of hyperparameters: scaling coefficients. and parameter vector These hyperparameters can be obtained by solving the following system of linear equations:

[0057] In the formula: This represents the performance evaluation value of the high-fidelity training samples. Since the coefficient matrix of this system of linear equations is a full-rank row matrix, there must exist a unique minimum norm solution:

[0058] In the formula: That is, the coefficient matrix of the linear equation system; The vector of constant terms in the system of linear equations:

[0059] Example 3, as Figure 1 As shown, this embodiment provides a variable geometry turbine optimization design method applicable to more than 100 variables and applies it to the blade styling optimization design of PW-E3, specifically including the following steps: (1) Establishment of design space: In this embodiment, the PW-E3 airfoil is selected as the optimization target (see...). Figure 2This turbomachinery comprises two rows of blades, denoted as S1: stationary blade and R1: moving blade. Due to the strong three-dimensional effect of the flow within the turbomachinery blades, the blade profile changes significantly with the blade height, requiring numerous design variables to accurately describe the three-dimensional shape of the blades. This results in a large number of design variables in this embodiment, exceeding 100. Furthermore, because the unsteady characteristics of the blade flow field are significant, unsteady evaluation is necessary to accurately capture the fine flow field features. Therefore, this invention is applied to optimize the design of this blade.

[0060] Considering the potential for significant profile changes in the PW-E3 turbine blades during optimization, a geometric parameter method was employed for parameterization. First, six cross-sections were selected at 0%, 20%, 40%, 60%, 80%, and 100% blade height for each blade column, serving as characteristic sections for the design. Specific geometric parameters were then applied to these characteristic sections to fit the blade profile. Next, some of these geometric parameters were set as design variables for optimization. Specifically: S1 optimization variables: center-to-center angle, inlet upper wedge angle, effective exhaust angle, outlet deflection angle, outlet wedge angle, correlation coefficient, STE1, STE2. R1 optimization variables: center-to-center angle, inlet geometric angle, effective exhaust angle, outlet deflection angle, outlet wedge angle, correlation coefficient, STE1, STE2. Simultaneously, a parameter was set for each of the five S1 cross-sections other than the 0% blade height section to adjust the three-dimensional blade spatial stacking state. As mentioned above, each blade cross section contains 8 characteristic variables, and there are a total of 12 cross sections for the two rows of blades. In addition, there are 5 spatially superimposed variables for the stationary blade, for a total of 101 design variables, which significantly exceeds the range of design variables that are feasible for common optimization design methods.

[0061] (2) Establishment of the performance evaluation model: This embodiment selects the overall isentropic efficiency of the PW-E3 blade as the target parameter for optimization design, aiming to design a geometric model with higher overall isentropic efficiency. Commercial computational fluid dynamics (CFD) software is used to evaluate the overall isentropic efficiency of the geometric design model. Furthermore, constraints are imposed on the flow rate and the absolute outlet airflow angle to conduct unsteady aerodynamic performance optimization design. The mathematical expression of the optimization model is as follows:

[0062] In the formula: Indicates the parameter values ​​of design variables; This represents the isentropic overall efficiency of the low-pressure turbine. This is the penalty function used to handle constraints; For mass flow rate; Absolute outlet airflow angle; subscript This indicates the numerical calculation results of the reference design.

[0063] (3) Determine the user-defined variables in the algorithm: In this embodiment, the number of samples selected for the population is 50; the initial sampling method is Latin hypercube sampling (LHS); the mutation operator and crossover operator have default values ​​of 0.3 and 0.9, respectively; the total number of offspring samples generated in each iteration is 10; the maximum number of evaluations for low-fidelity samples is 550, and the maximum number of evaluations for high-fidelity samples is 150; every 10 generations (100 samples) of low-fidelity samples, a knowledge transfer is performed to the high-fidelity population, and each transfer is based on sampling 10 samples according to the probability distribution model.

[0064] The selector optimization algorithm and the particle swarm optimization algorithm have a population sample size of 50; an inertia factor of 0.5; a learning factor of 2.05; and a maximum number of iterations of 100.

[0065] (4) Reference for the optimization design process Figure 1 Specifically, it is as follows: a. In the established design space, the Latin hypercube sampling (LHS) method is used to select 50 design samples with relatively uniform distribution as the initial population, and the low-fidelity performance evaluation is performed on them to obtain the total isentropic efficiency of these 50 design samples.

[0066] b. For samples in the low-fidelity population, perform differential evolution guided by the RBF surrogate model and selection based on the parent's target evaluation value in sequence, generating a total of 9 offspring samples: First, for each sample in the population A corresponding differentially mutated sample is generated using the best / 1 differential mutation strategy. Next, in each population sample A local RBF surrogate model is established by selecting up to 250 existing samples from the vicinity (if the sample size is insufficient, all evaluated samples are used as training samples) and their total isentropic efficiency. A particle swarm optimization (PSO) algorithm is then used to perform a local search on the surrogate model to obtain the sample... Then, use the samples obtained from the search. With the corresponding differential variation samples Samples are obtained by performing exponential crossover. Finally, based on the samples obtained from each crossover... Corresponding population sample The samples are sorted by their total isentropic efficiency, and the top 9 samples are selected as the new offspring samples.

[0067] c. For the optimal sample in the low-fidelity population, a local search strategy based on the RBF surrogate model is used to generate one offspring sample; first, the total isentropic efficiency of all samples in the population is compared, and the individual with the optimal total isentropic efficiency value is found. Secondly, in the optimal sample of the population A local RBF surrogate model is established by selecting up to 250 existing samples from the vicinity (if the sample size is insufficient, all evaluated samples are used as training samples) and their total isentropic efficiency. Finally, a local search is performed on the surrogate model using the particle swarm optimization algorithm (PSO), with the search radius set to half the distance between the best and worst samples in the samples used to train the RBF surrogate model, thus obtaining a new offspring sample.

[0068] d. Combine all the offspring samples generated in b and c, resulting in a total of 10 samples; e. Evaluate the performance of all the obtained offspring samples, obtain the total isentropic efficiency of these 10 offspring samples, and update the current population: merge the 10 offspring samples with the parent population, sort them according to the total isentropic efficiency, and select the top 50 samples with the highest efficiency as the new population.

[0069] f. Steps b to e constitute a complete optimization process. Repeat the above optimization process until the maximum number of evaluations for the low-fidelity population reaches 550.

[0070] g. Every 10 generations of the low-fidelity population, a knowledge transfer strategy based on a probability model will be implemented. Based on the current population distribution of the low-fidelity samples, a probability distribution model will be established, and 10 samples will be selected from it to enter the high-fidelity population for high-fidelity performance evaluation.

[0071] h. Perform similar steps to those for the low-fidelity populations b through e on the high-fidelity population. It's worth noting that when optimizing the high-fidelity population, the surrogate models involved are all multi-fidelity RBF surrogate models. When building the surrogate model, select the 250 closest low-fidelity samples and 50 closest high-fidelity samples to the corresponding individual (if the sample size is insufficient, use all evaluated samples as training samples) for training. Repeat the above optimization process until the maximum number of evaluations for high-fidelity is 150.

[0072] Results of the optimized design: In this optimization process, a total of 550 low-fidelity samples and 150 high-fidelity samples were used. The final total isentropic efficiency was 89.475%, which is a significant improvement of 0.670% compared to the reference design's total isentropic efficiency of 88.805%.

[0073]

[0074] The principle of this invention is as follows: The most significant features and innovations of this invention are: 1) By using a transfer strategy based on a probability model, the information in the low-fidelity sample space can be fully utilized. Considering the similarity between the global optimal solution positions of low-fidelity and high-fidelity optimization problems, knowledge transfer from the low-fidelity population to the high-fidelity population through a probability distribution model helps to quickly narrow the search range in the early stages of the algorithm, significantly reducing the number of performance evaluations required for high-fidelity samples. 2) Considering the scarcity of high-fidelity samples, a multi-fidelity RBF surrogate model is established during the iteration process of the high-fidelity population. This model can integrate samples of different fidelities, compensate for the lack of high-fidelity samples, and effectively improve the accuracy of the surrogate model. 3) Considering the parallel computing capabilities in engineering practice, the evolution of two populations with different fidelities can be carried out simultaneously within the algorithm framework, significantly shortening the time required for optimization design.

[0075] The optimization process of variable geometry turbines requires multiple high-fidelity evaluations. Traditional evolutionary algorithms and surrogate model-based optimization algorithms face the problem of sample scarcity. Even advanced surrogate model-assisted intelligent evolutionary algorithms cannot meet this requirement. This invention combines relatively inexpensive and readily available low-fidelity samples with high-fidelity samples. During the optimization process, it fully utilizes the space and optimization information of the low-fidelity samples for transfer learning, aiding the evolution of the high-fidelity population. Furthermore, it fuses samples of two different fidelities to establish a surrogate model, resulting in higher accuracy. These two strategies significantly improve the efficiency of the optimization design.

[0076] The method proposed in this invention fully considers the advantages of parallel computing, enabling simultaneous iterative evolution of high-fidelity and low-fidelity populations within a single framework. This is an important consideration for optimization design problems in engineering practice. In engineering applications, it can significantly reduce the time required for population evolution and shorten the optimization design cycle.

[0077] In another embodiment of the present invention, a variable geometry turbine optimization system suitable for multiple variables is provided, which can be used to implement the above-mentioned variable geometry turbine design optimization method suitable for more than 100 variables. Specifically, the system includes: The data acquisition module is used to acquire the control parameters for the three-dimensional blade model of the variable geometry turbine component and establish the design space; The offspring sample generation module is used to select a set number of uniformly distributed design samples in the design space as the initial population, and then perform differential operation, RBF surrogate model-guided crossover operation, and selection operation based on the parent target evaluation value on the samples in the population in sequence to generate several offspring samples. The merging module is used to generate a child sample from the best sample in the population using a local search strategy based on the RBF surrogate model; all generated child samples are merged, their performance is evaluated, and the current population is updated. The iterative output module is used to perform a set number of iterations for each optimization, and adopts a knowledge transfer strategy based on a probability distribution model to achieve knowledge transfer from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of evaluations of the high-fidelity samples reaches the set upper limit.

[0078] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0079] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for operations applicable to variable geometry turbine design optimization methods with more than 100 variables.

[0080] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the variable geometry turbine design optimization method applicable to more than 100 variables in the above embodiments.

[0081] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0082] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0083] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0084] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the design of variable geometry turbines with more than 100 variables, characterized in that: include: Obtain the control parameters for the 3D blade model of the variable geometry turbine component and establish the design space; In the design space, a set number of uniformly distributed design samples are selected as the initial population. Differentiation operation, crossover operation guided by RBF surrogate model, and selection operation based on the parent generation target evaluation value are performed on the samples in the population in sequence to generate several offspring samples. The optimal sample in the population is used to generate a offspring sample using a local search strategy based on the RBF surrogate model; all generated offspring samples are merged, their performance is evaluated, and the current population is updated. For each set number of optimization iterations, a knowledge transfer strategy based on a probability distribution model is used to transfer knowledge from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of evaluations of the high-fidelity samples reaches the set upper limit.

2. The method for optimizing variable geometry turbine design with more than 100 variables as described in claim 1, characterized in that, The process of obtaining control parameters for the three-dimensional blade shape of the variable geometry turbine component and establishing a design space includes: In the established design space, a set of defined design parameters corresponds to a unique geometric design. The Latin hypercube sampling (LHS) method is used in the design space to select design samples with a relatively uniform distribution. These samples are used as low-fidelity initial samples for performance evaluation.

3. The method for optimizing variable geometry turbine design with more than 100 variables as described in claim 1, characterized in that, The process involves selecting a uniformly distributed number of design samples from the design space as the initial population. Then, the samples in the population are sequentially subjected to a differencing operation, a crossover operation guided by the RBF surrogate model, and a selection operation based on the parent generation's target evaluation value to generate several offspring samples, including: First, for each parent individual The best / 1 differential mutation strategy is executed to generate the corresponding mutated individuals. : In the formula: Represents the optimal individual in the population; and For two random individuals in the population and ; As a mutation operator, it is taken in this paper. ; To balance the training time required for the surrogate model and the diversity of the population, we take [the population size] in this paper. ; Next, in each parent individual Construct a radial basis function surrogate model within the corresponding neighborhood and perform a local search to obtain the corresponding predicted individual. : In the formula: This represents the predicted optimal solution of the radial basis function surrogate model; This represents the predicted value from the proxy model; set up , The dimension of the design space is denoted by , and the number of sample points used to train the surrogate model is denoted by ; the parent individual is denoted by . neighborhood radius Set to: In the formula: Indicates the first individual parents The maximum distance between the parent individuals; The dimension of the design space; parent individual The neighborhood of can be represented as , and These represent the lower and upper limits of the design space, respectively. Finally, an exponential crossover strategy is used to predict individual... and mutated individuals Performing a crossover operation yields offspring individuals: In the formula: Indicates a variant individual The One variable; Indicates the prediction of individuals The One variable; For the crossover operator, the default value is ; Finally, each offspring corresponds to a parent individual. The offspring are ranked according to the performance evaluation value of the parent, and the top-ranked individuals are selected as offspring.

4. The method for optimizing variable geometry turbine design with more than 100 variables as described in claim 1, characterized in that, The process involves using a local search strategy based on the RBF surrogate model to generate a child sample from the optimal sample in the population, merging all generated child samples, evaluating their performance, and updating the current population, including: First, in the optimal individual of the population Establish a local RBF proxy model within the defined area surrounding the location; set The number of sample points used to train the surrogate model is crucial in the early stages of the algorithm if the number of evaluated sample points is insufficient. Then, all sample points are used as training samples to construct a surrogate model; then, the particle swarm optimization algorithm is used to perform a local search on the surrogate model to find its local optimum. The offspring samples obtained from crossover operations and local search are evaluated for performance, and then sorted together with the original population. Based on the performance evaluation value of each sample, the top-ranked samples are selected to update the population.

5. The method for optimizing variable geometry turbine design with more than 100 variables as described in claim 1, characterized in that, Each optimization sets a predetermined number of iterations, employing a knowledge transfer strategy based on a probability distribution model to achieve knowledge transfer from a low-fidelity population to a high-fidelity population, including: For low-fidelity populations, the location of the global optimum in the design space is determined by a probability distribution model. Approximately, the model satisfies: In the formula: To optimize the objective function of the problem; This represents the global optimum of the optimization objective; For a small deviation threshold, when At that time, probability distribution model This strictly degenerates into a point in the design space, which is the global optimal solution to the optimization problem. First, effective information about the optimization process is extracted from the low-fidelity population, that is, a probability distribution model is trained using samples from the current low-fidelity population. A diagonal Gaussian probability distribution model is adopted: In the formula: Represents a multivariate Gaussian probability distribution; Represents random variables The mean vector; Represents random variables The covariance matrix of the diagonal Gaussian probability distribution model is a diagonal matrix; then, random sampling is performed in the design space based on the probability distribution model obtained from training, and a total of 10 design samples are collected for each knowledge transfer.

6. The method for optimizing variable geometry turbine design with more than 100 variables according to claim 1, characterized in that, The evolutionary process of a high-fidelity population is similar to that of a low-fidelity population. The surrogate models involved are all multi-fidelity radial basis function surrogate models, as detailed below: The multifidelity radial basis function surrogate model used is a product / difference hybrid multifidelity model, which consists of a low-fidelity surrogate model, scaling factors, and a difference function, and its expression is as follows: In the formula: This is a multi-fidelity radial basis function surrogate model; This represents the scaling factor for a low-fidelity proxy model. As a low-fidelity proxy model, the RBF proxy model is used. It is a parameter vector; This represents high-fidelity training samples; Indicates the prediction point With high-fidelity training samples The basis function vectors between them.

7. The method for optimizing variable geometry turbine design according to claim 6, applicable to more than 100 variables, is characterized in that... This multi-fidelity radial basis function surrogate model contains two types of hyperparameters: scaling coefficients. and parameter vector These hyperparameters can be obtained by solving the following system of linear equations: In the formula: This represents the performance evaluation value of the high-fidelity training samples; since the coefficient matrix of this system of linear equations is a full-rank row matrix, there must exist a unique minimum norm solution: In the formula: That is, the coefficient matrix of the linear equation system; The vector of constant terms in the system of linear equations: 。 8. A variable geometry turbine optimization system suitable for multiple variables, characterized in that, include: The data acquisition module is used to acquire the control parameters for the three-dimensional blade model of the variable geometry turbine component and establish the design space; The offspring sample generation module is used to select a set number of uniformly distributed design samples in the design space as the initial population, and then perform differential operation, RBF surrogate model-guided crossover operation, and selection operation based on the parent target evaluation value on the samples in the population in sequence to generate several offspring samples. The merging module is used to generate a child sample from the best sample in the population using a local search strategy based on the RBF surrogate model; all generated child samples are merged, their performance is evaluated, and the current population is updated. The iterative output module is used to perform a set number of iterations for each optimization, and adopts a knowledge transfer strategy based on a probability distribution model to achieve knowledge transfer from a low-fidelity population to a high-fidelity population; the high-fidelity population is updated and iterated until the number of evaluations of the high-fidelity samples reaches the set upper limit.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the variable geometry turbine design optimization method as described in any one of claims 1 to 7, applicable to a variable number of variables exceeding 100.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the variable geometry turbine design optimization method as described in any one of claims 1 to 7, applicable to a variable number of variables exceeding 100.

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