Method for improving approximate model accuracy of water pump turbine runner based on target supplement

Abstract

The application discloses a pump-turbine runner approximate model precision improving method based on target sampling, belongs to the technical field of turbine optimization design, and comprises the following steps: selecting pump-turbine runner optimization variables and optimization targets, generating an initial sample point set by using a criterion-based improved Latin hypercube sampling method; obtaining CFD calculation data corresponding to the initial sample point set, composing an optimization sample set, and constructing an initial approximate model by using a neural network model; evaluating the precision of the initial approximate model by using a comprehensive error parameter; increasing sample points at positions with relatively large approximate model errors by using a Markov chain Monte Carlo method; and stopping until the set approximate model precision requirement is met. The application avoids the blindness problem of traditional sample space sampling, has the characteristics of strong sample utilization sequentiality, fast precision improving efficiency, controllable calculation cost and the like, and is helpful to the development of pump-turbine runner design optimization towards modern intelligentization and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of turbine optimization design technology, and in particular to a method for improving the accuracy of an approximate model of a pump-turbine runner based on targeted sampling. Background Technology

[0002] As the core power equipment of pumped storage power stations, pump-turbines play a crucial role in power grid peak shaving and valley filling, frequency and phase regulation, and emergency backup. Their operating efficiency and stability directly determine the energy conversion efficiency of the power station. The runner, as a core component of the pump-turbine, has geometric parameters closely related to the water flow state within the flow channel. Therefore, optimized runner design is a key aspect of improving the overall performance of the pump-turbine.

[0003] However, existing methods for constructing approximate models have significant drawbacks. First, while traditional Latin hypercube sampling can guarantee stratified uniformity in the univariate dimension, it is prone to uneven sample distribution in the variable space of multidimensional and multi-parameter optimization. In particular, there may be blank or dense samples in the critical variable intervals that are sensitive to the efficiency of the rotating wheel, which leads to a significant increase in the fitting error of the initial approximate model in these regions. Second, when the model accuracy is insufficient, the commonly used strategies of uniform densification or random supplementation of samples lack specificity, wasting a lot of valuable computational resources in the regions where the model has already fitted well, while failing to correct the critical regions with large errors. This results in slow improvement of model accuracy and low optimization efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a method for improving the accuracy of an approximate model of a water pump turbine runner based on targeted sampling. The improved Latin hypercube sampling method generates an initial sample set, ensuring the uniform distribution of samples in the multidimensional design space from the source, laying the foundation for building a high-precision initial approximation model. It constructs comprehensive error parameters to systematically evaluate the model accuracy and innovatively introduces the Markov chain Monte Carlo method to intelligently identify areas with large errors in the approximation model and perform targeted sample densification, avoiding the blind problem of traditional sample space supplementation.

[0005] To achieve the above objectives, this invention provides a method for improving the accuracy of an approximate model of a water pump turbine runner based on targeted sampling, comprising the following steps: S1: Select the optimization variables and objectives for the water pump turbine runner, and adopt a method with global uniformity of the sample space as a constraint. The criterion improves the Latin hypercube sampling method to generate an initial sample point set in a multidimensional design space; S2: Obtain the CFD calculation data corresponding to the initial sample point set, form an optimized sample set, and use a neural network model to construct an initial approximate model; S3: Use comprehensive error parameters to evaluate the accuracy of the initial approximate model. If the comprehensive error is lower than the preset threshold, then perform optimization algorithm based on the approximate model to find the best value; otherwise, proceed to S4. S4: The Markov chain Monte Carlo method is used to construct the target probability distribution function with the approximate model error, and new sample points are generated in a probability-guided manner in the high error region of the approximate model. S5: Incorporate the newly added sample points into the optimized sample set, return to S2 to iteratively update the approximate model, until the comprehensive error meets the accuracy requirements of the approximate model.

[0006] Preferably, in S1, variables strongly correlated with runner performance are selected as runner optimization variables, including the blade inlet angle. β 1. Blade outlet placement angle β 2. High-voltage side blade tilt angle α and blade wrap angle i The efficiency at the operating point is selected based on the pump-turbine pump mode. or 1. Efficiency at the operating point of the turbine design or 2 is the optimization objective.

[0007] Preferably, in S1, the specific logic underlying the improved Latin hypercube sampling method for generating the initial sample point set is as follows: Based on the random Latin hypercube, the size of the initial sample point set is determined. By swapping the order of the two factor levels in the matrix columns, a new matrix is ​​generated, and the total distance between the new points is calculated. The value, through continuous iteration, when Stop when the value change meets the set conditions; ; In the formula, d ( X i , X j ) is a sample point X i and X j The Euclidean distance between them; p It is a positive integer; N This represents the initial number of samples.

[0008] Preferably, in S2, the specific logic for constructing the initial approximate model using the neural network model is as follows: S21. Normalize the optimized sample set data and divide it into a training set and a validation set. The normalization formula is: in, These represent the normalized blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively. These represent the minimum values ​​of the blade inlet installation angle, blade outlet installation angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set. These represent the maximum values ​​of the blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set. S22. Divide the neural network model into an input layer, hidden layer, and output layer; divide the sample points... X i =[ As input to the input layer of a neural network model, it will optimize the target matrix. Y i =[ As the theoretical output of the output layer of a neural network model, where i Number the sample scheme; They represent the first i The following parameters were collected for each sample point: blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine-turbine design operating point efficiency; a clustering algorithm was used to generate the parameters. m Each sample center serves as the hidden layer function center node, and the number of such centers is greater than [a certain value]. , l The centrality coefficient of the sample is greater than 1 and less than or equal to 2. S23, Each hidden layer node h Corresponding to one data center X ch Its output It is obtained by calculating the distance between the input matrix and the data center and then performing a Gaussian function transformation: ; In the formula, X i For the first i 1 sample point; control the width of the basis function ; s h This represents the average distance between any two data centers. S24. A linear mapping is used from the hidden layer to the output layer, and its calculation formula is as follows: ; In the formula,y ki For the first i The output layer corresponding to the sample scheme is the first k Theoretical output of each unit; w kh For the first k The unit and the hidden layer h The connection weights between nodes; b k For the output layer k The bias of each unit; S25. Construct the hidden layer output matrix Φ and the parameter matrix from the hidden layer to the output layer. W Define the error function L , which is the predicted value matrix Φ W With optimization objective matrix Y The square of the Euclidean distance between them is as follows: ; ; ; In the formula, c The regularization coefficient is used to balance fitting accuracy and model complexity; its optimal value is determined through cross-validation. The Euclidean distance uses the L2 norm. express; , , They represent the 1st, 2nd, and 3rd respectively. N The input sample at the th ... m The output of each hidden layer neuron node; W Let be the parameter matrix from the hidden layer to the output layer, where b1 and b2 represent the biases of the first and second units of the output layer, respectively. w 1m This indicates that the first unit of the output layer and the first unit of the hidden layer are connected. m The weight of each node, w 2m This indicates that the second unit of the output layer and the second unit of the hidden layer are connected. m The weight of each node; S26. Use the least squares method and regularization formula to solve for the parameter matrix from the hidden layer to the output layer of the neural network model. W : ; ; ; In the formula, I It is the identity matrix; c The regularization coefficient is used. This is the regularized covariance matrix.

[0009] Preferably, in S3, the comprehensive error parameter E Global error considering the influence of sample size E g and local error parameters considering sample spatial density E l The composition, and the comprehensive error parameters, are applicable to each optimization objective: ; in, x This refers to the global error weights in the comprehensive error parameters; Global error considering the influence of sample size E g : ; In the formula, E g These are global error parameters; R 2 The coefficient of determination; N T This represents the number of samples in the test set. f To optimize variable dimensions; T i For the first i The true values ​​of each test set sample; t i For the first i Approximate model response values ​​for each sample; The average of the true values ​​in the test set; The specific calculation logic for local error involves sorting all sample points in descending order of their relative errors, selecting the top 10% of sample points, and considering the sample space density for calculation. ; ; In the formula, E l These are local error parameters; d i For the first i The distance between each sample point and its nearest neighbor. d max The maximum spatial distance between sample points. N TK 10% of the total sample size; w di The sample space density weights.

[0010] Preferably, in S3, the threshold range for judging the approximate model error is 0.08 ≤ dThe threshold of the approximate model error gradually increases as the number of iterations of the approximate model optimization increases. ≤0.05

[0011] Preferably, in S4, the specific logic underlying the use of the Markov chain Monte Carlo method to target and increase sample points is as follows: S41. Constructing the local error function for a single sample point Its core is the combination of local density and the average error of neighboring samples: ; In the formula, For new sample points The local density, with new sample points and s neighboring known samples x i The average distance is represented as, i.e. ; Indicates new sample points of s The average error of 10 adjacent known sample points, i.e. ; S42. Construct the target probability density function p ( x ): ; In the formula, Ω represents the feasible region, which is the space consisting of the range of values ​​for the optimization variables. e It is a very small positive value; S43. Select a point with significant local error from the existing sample points as the initial point. x 0, to avoid the initial point deviating from the target area; S44. Generate new sample points using the Gaussian proposal distribution: ; In the formula: Indicates starting from the current point x 0 Generate new sample points The probability of; Indicated by x The Gaussian distribution with mean 0 and covariance matrix Σ has its elements distributed as 1 / 10 squared of the range of each variable, with off-diagonal elements being 0. For new sample points Calculate the acceptance probability: ; From uniform distribution U A number is randomly selected from (0,1). u ,if u ≤ ψ Then accept the move. x z+1 = Otherwise, refuse to move. x z+1 = x 0, where z For iteration numbering; S45. Determine the range of iterations and the burning period; after the iteration is completed, remove the burning period samples from the MCMC chain, and select several points with high error estimates in the remaining chain as the final target supplementary sample points; perform CFD calculation on the new sample points, obtain the response values, and add them to the optimization sample set for retraining the approximate model.

[0012] The present invention also provides an operable computer program, which is stored in a computer-readable storage medium and, when executed by a processor, implements a method for improving the accuracy of an approximate model of a water pump turbine runner based on targeted sampling.

[0013] Therefore, this invention adopts the above-mentioned method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling. First, it adopts a method based on... The improved Latin hypercube sampling method generates the initial sample set, ensuring a uniform distribution of samples in the multidimensional design space from the source, laying a solid foundation for building a high-precision initial approximation model. Secondly, a comprehensive error evaluation index considering sample quantity, spatial distribution density, and prediction error distribution characteristics is constructed, overcoming the limitation that a single error parameter cannot accurately characterize the local distortion problem of the approximation model. Finally, a Markov chain Monte Carlo method is innovatively introduced to intelligently identify regions with large errors in the approximation model and perform targeted sample densification. This method avoids the blind sampling problem of traditional sample space replenishment, and features strong sequential sample utilization, rapid accuracy improvement, and controllable computational cost, contributing to the modern intelligent and efficient development of pump turbine runner design optimization.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of computer program storage and execution according to an embodiment of the present invention; Figure 3 These are the flow field conditions inside the runner before and after optimization in this embodiment of the invention. a represents the flow field before optimization, and b represents the flow field after optimization. Detailed Implementation

[0016] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0017] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Example 1 This invention provides a method for improving the accuracy of an approximate model of a water pump turbine runner based on targeted sampling, the process of which is as follows: Figure 1 As shown, it includes the following steps: S1: Select the optimization variables and objectives for the water pump turbine runner, and adopt a method with global uniformity of the sample space as a constraint. The criterion improves the Latin hypercube sampling method to generate an initial sample point set within a multidimensional design space.

[0019] The runner optimization variables are those strongly correlated with runner performance, including the blade inlet angle. β 1. Blade outlet placement angle β 2. High-voltage side blade tilt angle α and blade wrap angle i The efficiency at the operating point is selected based on the pump-turbine pump mode. or 1. Efficiency at the operating point of the turbine design or 2 is the optimization objective.

[0020] The specific logic underlying the improved Latin hypercube sampling method for generating the initial sample point set is as follows: Based on the random Latin hypercube, the size of the initial sample point set is determined. By swapping the order of the two factor levels in the matrix columns, a new matrix is ​​generated, and the total distance between the new points is calculated. The value, through continuous iteration, when Stop when the value change meets the set conditions; ; In the formula, d ( X i , X j ) is a sample point X iand X j The Euclidean distance between them; p It is a positive integer; N This represents the initial number of samples.

[0021] S2: Obtain the CFD calculation data corresponding to the initial sample point set, form an optimized sample set, and use a neural network model to construct an initial approximate model.

[0022] The specific logic for constructing the initial approximate model of the neural network model is as follows: S21. Normalize the optimized sample set data and divide it into a training set and a validation set. The normalization formula is: in, These represent the normalized blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively. These represent the minimum values ​​of the blade inlet installation angle, blade outlet installation angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set. These represent the maximum values ​​of the blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set.

[0023] In this embodiment, the normalization range is [0,1], and the ratio of the training set to the validation set is 7:3.

[0024] S22. Divide the neural network model into an input layer, hidden layer, and output layer; divide the sample points... X i =[ As input to the input layer of a neural network model, it will optimize the target matrix. Y i =[ As the theoretical output of the output layer of a neural network model, where i Number the sample scheme; They represent the first i The sample points include the blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine-turbine design operating point efficiency; clustering algorithms were used to generate the data. m Each sample center serves as the center node of the hidden layer function. l The centrality coefficient is the sample center coefficient; specifically: ,1< l ≤2.

[0025] S23, Each hidden layer node h Corresponding to one data center X ch Its output It is obtained by calculating the distance between the input matrix and the data center and then performing a Gaussian function transformation: ; In the formula, X i For the first i 1 sample point; control the width of the basis function ; s h This represents the average distance between any two data centers.

[0026] S24. A linear mapping is used from the hidden layer to the output layer, and its calculation formula is as follows: ; In the formula, y ki For the first i The output layer corresponding to the sample scheme is the first k Theoretical output of each unit; w kh For the first k The unit and the hidden layer h The connection weights between nodes; b k For the output layer k The bias of each unit.

[0027] S25. Construct the hidden layer output matrix Φ and the parameter matrix from the hidden layer to the output layer. W Define the error function L , which is the predicted value matrix Φ W With optimization objective matrix Y The square of the Euclidean distance between them is as follows: ; ; ; In the formula, c The regularization coefficient is used to balance fitting accuracy and model complexity; its optimal value is determined through cross-validation. The Euclidean distance uses the L2 norm. express; , , They represent the 1st, 2nd, and 3rd respectively. N The input sample at the th ... mThe output of each hidden layer neuron node; W Let be the parameter matrix from the hidden layer to the output layer, where b1 and b2 represent the biases of the first and second units of the output layer, respectively. w 1m This indicates that the first unit of the output layer and the first unit of the hidden layer are connected. m The weight of each node, w 2m This indicates that the second unit of the output layer and the second unit of the hidden layer are connected. m The weight of each node.

[0028] S26. Use the least squares method and regularization formula to solve for the matrix from the hidden layer to the output layer of the neural network model. W : ; ; ; In the formula, I It is the identity matrix; c The regularization coefficient is used. This is the regularized covariance matrix.

[0029] S3: Use comprehensive error parameters to evaluate the accuracy of the initial approximate model. If the comprehensive error is lower than the preset threshold, then perform optimization algorithm based on the approximate model to find the best option; otherwise, proceed to S4.

[0030] Comprehensive error parameters E Global error considering the influence of sample size E g and local error parameters considering sample spatial density E l The composition, and the comprehensive error parameters, are applicable to each optimization objective: ; in, x This refers to the global error weights in the comprehensive error parameters; Global error considering the influence of sample size E g : ; In the formula, E g These are global error parameters; R 2 The coefficient of determination; N T This represents the number of samples in the test set. f To optimize variable dimensions; T i For the first iThe true values ​​of each test set sample; t i For the first i Approximate model response values ​​for each sample; This is the average of the true values ​​in the test set.

[0031] The specific calculation logic for local error involves sorting the relative errors of all sample points in descending order, selecting the top 10% of sample points, and considering the sample spatial density for calculation. ; ; In the formula, E l These are local error parameters; d i For the first i The distance between each sample point and its nearest neighbor. d max The maximum spatial distance between sample points. N TK 10% of the total sample size; w di The sample space density weights.

[0032] The threshold range for the approximate model error is 0.08 ≤ δ ≤ 0.15. As the number of iterations of approximate model optimization increases, the threshold for the approximate model error gradually increases. The specific strategy in this embodiment is as follows: When the number of optimization repetitions is less than 3, the threshold δ1=0.08 is used; when the number of optimization repetitions is greater than 4 but less than 6, the threshold δ2=0.1 is used; when the number of optimization repetitions is greater than 7, the threshold δ2=0.15 is used.

[0033] S4. Using the Markov chain Monte Carlo method, a target probability distribution function is constructed based on the approximate model error. New sample points are then generated in a probability-guided manner within the high-error region of the approximate model. The specific logic is as follows: S41. Constructing the local error function for a single sample point Its core is the combination of local density and the average error of neighboring samples: ; In the formula, For new sample points The local density, with new sample points and s neighboring known samples x i The average distance is represented as... In this embodiment k The range of values ​​is 5≤ k ≤10; Indicates new sample points of s The average error of 10 adjacent known sample points, i.e. .

[0034] S42. Construct the target probability density function p ( x ): ; In the formula, Ω represents the feasible region, which is the space consisting of the range of values ​​for the optimization variables. e It is a very small positive value.

[0035] S43. Select a point with significant local error from the existing sample points as the initial point. x 0, to avoid the initial point deviating from the target area.

[0036] S44. Generate new sample points using the Gaussian proposal distribution: ; In the formula: Indicates starting from the current point x 0 Generate new sample points The probability of; Indicates x The Gaussian distribution with mean 0 and covariance matrix Σ has elements distributed as 1 / 10 of the range of each variable, with off-diagonal elements being 0.

[0037] For new sample points Calculate the acceptance probability: ; From uniform distribution U A number is randomly selected from (0,1). u ,if u ≤ ψ Then accept the move. x z+1 = Otherwise, refuse to move. x z+1 = x 0, where z This is the iteration number.

[0038] S45. In this embodiment, the range of iterations is determined to be: 1500≤ I t The values ​​are ≤2500, and the combustion period is B=20%. After iteration, the combustion period samples are removed from the MCMC chain, and several points with higher error estimates in the remaining chain are selected as the final target supplementary sample points. CFD calculations are performed on the new sample points to obtain the response values, which are then added to the optimized sample set for retraining the approximate model.

[0039] S5: Incorporate the newly added sample points into the optimized sample set, return to S2 to iteratively update the approximate model, until the comprehensive error meets the accuracy requirements of the approximate model.

[0040] like Figure 2 As shown, this embodiment also provides a computer program product. The computer program is stored in a computer-readable storage medium and, when executed by a processor, can improve the accuracy of the above-described method for improving the approximate model of a water pump turbine runner based on targeted sampling.

[0041] Table 1 shows the comparison of neural network model accuracy before and after optimization following the application of the approximate model accuracy improvement method proposed in this invention.

[0042] Table 1

[0043] As shown in Table 1, after optimization, the global error, local error and overall error of the model are significantly reduced, indicating that the method effectively improves the accuracy of the approximate model and can meet the requirements of subsequent optimization tasks.

[0044] This embodiment further compares the flow field inside the runner before and after optimization, and the results are as follows: Figure 3 As shown in the figure, after optimization, the flow splitting phenomenon at the runner inlet is significantly reduced, and the flow field distribution is more uniform. This indicates that the hydraulic losses inside the runner are effectively reduced, which is beneficial to improving the energy conversion efficiency of this component.

[0045] Therefore, this invention adopts the above-mentioned method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling, by employing a method based on... An improved Latin hypercube sampling method generates an initial sample set, ensuring a uniform distribution of samples in the multidimensional design space from the outset, laying a solid foundation for constructing a high-precision initial approximation model. Furthermore, a comprehensive error parameter is constructed to systematically evaluate the model's accuracy, and a Markov chain Monte Carlo method is innovatively introduced to intelligently identify regions with large approximation model errors and perform targeted sample densification. This method avoids the blind sampling problem of traditional sample space replenishment, and features strong sequential sample utilization, rapid accuracy improvement, and controllable computational costs. It contributes to the modern, intelligent, and efficient development of pump turbine runner design optimization.

[0046] 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 them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for improving the accuracy of an approximate model of a water pump turbine runner based on targeted sampling, characterized in that, Includes the following steps: S1: Select the optimization variables and objectives for the water pump turbine runner, and adopt a method with global uniformity of the sample space as a constraint. The criterion improves the Latin hypercube sampling method to generate an initial sample point set in a multidimensional design space; The runner optimization variables are those strongly correlated with runner performance, including the blade inlet angle. β 1. Blade outlet placement angle β 2. High-voltage side blade tilt angle α and blade wrap angle θ ; Selecting the pump-turbine pump mode for design operating point efficiency η 1. Efficiency at the operating point of the turbine design η 2 is the optimization objective; S2: Obtain the CFD calculation data corresponding to the initial sample point set, form an optimized sample set, and construct an initial approximate model using a neural network model; the specific logic of constructing the initial approximate model using the neural network model is as follows: S21. Normalize the optimized sample set data and divide it into a training set and a validation set. The normalization formula is: in, These represent the normalized blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively. These represent the minimum values ​​of the blade inlet installation angle, blade outlet installation angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set. These represent the maximum values ​​of the blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine design operating point efficiency, respectively, in the actual optimized sample set. S22. Divide the neural network model into an input layer, hidden layer, and output layer; divide the sample points... X i =[ As input to the input layer of a neural network model, it will optimize the target matrix. Y i =[ As the theoretical output of the output layer of a neural network model, where i Number the sample scheme; They represent the first i The following parameters were collected for each sample point: blade inlet angle, blade outlet angle, high-pressure side blade tilt angle, blade wrap angle, pump-turbine design operating point efficiency, and turbine-turbine design operating point efficiency; a clustering algorithm was used to generate the parameters. m Each sample center serves as the hidden layer function center node, and the number of such centers is greater than [a certain value]. , λ The centrality coefficient of the sample is greater than 1 and less than or equal to 2. S23, Each hidden layer node h Corresponding to one data center X ch Its output It is obtained by calculating the distance between the input matrix and the data center and then performing a Gaussian function transformation: ； In the formula, X i For the first i 1 sample point; control the width of the basis function , σ h This represents the average distance between any two data centers. S24. A linear mapping is used from the hidden layer to the output layer, and its calculation formula is as follows: ； In the formula, y ki For the first i The output layer corresponding to the sample scheme is the first k Theoretical output of each unit; w kh For the first k The unit and the hidden layer h The connection weights between nodes; b k For the output layer k The bias of each unit; S25. Construct the hidden layer output matrix Φ and the parameter matrix from the hidden layer to the output layer. W Define the error function L , which is the predicted value matrix Φ W With optimization objective matrix Y The square of the Euclidean distance between them is as follows: ； ； ； In the formula, γ The regularization coefficient is used to balance fitting accuracy and model complexity; its optimal value is determined through cross-validation. The Euclidean distance uses the L2 norm. express; , , They represent the 1st, 2nd, and 3rd respectively. N The input sample at the th ... m The output of each hidden layer neuron node; W Let be the parameter matrix from the hidden layer to the output layer, where b1 and b2 represent the biases of the first and second units of the output layer, respectively. w 1m This indicates that the first unit of the output layer and the first unit of the hidden layer are connected. m The weight of each node, w 2m This indicates that the second unit of the output layer and the second unit of the hidden layer are connected. m The weight of each node; S26. Use the least squares method and regularization formula to solve for the parameter matrix from the hidden layer to the output layer of the neural network model. W : ； ； ； In the formula, I It is the identity matrix; γ The regularization coefficient is used. This is the regularized covariance matrix; S3: Use comprehensive error parameters to evaluate the accuracy of the initial approximate model. If the comprehensive error is lower than the preset threshold, then perform optimization algorithm based on the approximate model to find the best value; otherwise, proceed to S4. S4: The Markov chain Monte Carlo method is used to construct the target probability distribution function with the approximate model error, and new sample points are generated in a probability-guided manner in the high error region of the approximate model. S5: Incorporate the newly added sample points into the optimized sample set, return to S2 to iteratively update the approximate model, until the comprehensive error meets the accuracy requirements of the approximate model.

2. The method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling according to claim 1, characterized in that, In S1, the specific logic underlying the improved Latin hypercube sampling method for generating the initial sample point set is as follows: Based on the random Latin hypercube, the size of the initial sample point set is determined. By swapping the order of the two factor levels in the matrix columns, a new matrix is ​​generated, and the total distance between the new points is calculated. The value, through continuous iteration, when Stop when the value change meets the set conditions; ； In the formula, d ( X i , X j ) is a sample point X i and X j The Euclidean distance between them; p It is a positive integer; N This represents the initial number of samples.

3. The method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling according to claim 2, characterized in that, In S3, the comprehensive error parameter E Global error considering the influence of sample size E g and local error parameters considering sample spatial density E l The composition, and the comprehensive error parameters, are applicable to each optimization objective: ； in, ξ This refers to the global error weights in the comprehensive error parameters; Global error considering the influence of sample size E g : ； In the formula, E g These are global error parameters; R 2 The coefficient of determination; N T This represents the number of samples in the test set. f To optimize variable dimensions; T i For the first i The true values ​​of each test set sample; t i For the first i Approximate model response values ​​for each sample; The average of the true values ​​in the test set; The specific calculation logic for local error involves sorting all sample points in descending order of their relative errors, selecting the top 10% of sample points, and considering the sample space density for calculation. ； ； In the formula, E l These are local error parameters; d i For the first i The distance between each sample point and its nearest neighbor. d max The maximum spatial distance between sample points. N TK 10% of the total sample size; w di The sample space density weights.

4. The method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling according to claim 3, characterized in that, In S3, the threshold range for judging the error of the approximate model is 0.08≤ δ The threshold of the approximate model error gradually increases as the number of iterations of the approximate model optimization increases. ≤0.05 5. The method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling according to claim 4, characterized in that, In S4, the specific logic behind using the Markov chain Monte Carlo method to target and increase sample points is as follows: S41. Constructing the local error function for a single sample point Its core is the combination of local density and the average error of neighboring samples: ； In the formula, For new sample points The local density, with new sample points and s neighboring known samples x i The average distance is represented as, i.e. ; Indicates new sample points of s The average error of 10 adjacent known sample points, i.e. ; S42. Construct the target probability density function p ( x ): ； In the formula, Ω represents the feasible region, which is the space consisting of the range of values ​​for the optimization variables. ε It is a very small positive value; S43. Select a point with significant local error from the existing sample points as the initial point. x 0, to avoid the initial point deviating from the target area; S44. Generate new sample points using the Gaussian proposal distribution: ； In the formula: Indicates starting from the current point x 0 Generate new sample points The probability of; Indicated by x The Gaussian distribution with mean 0 and covariance matrix Σ has its elements distributed as 1 / 10 squared of the range of each variable, with off-diagonal elements being 0. For new sample points Calculate the acceptance probability: ; From uniform distribution U A number is randomly selected from (0,1). u ,if u ≤ ψ Then accept the move. x z+1 = Otherwise, refuse to move. x z+1 = x 0, where z For iteration numbering; S45. Determine the range of iterations and the burning period; after the iteration is completed, remove the burning period samples from the MCMC chain, and select several points with high error estimates in the remaining chain as the final target supplementary sample points; perform CFD calculation on the new sample points, obtain the response values, and add them to the optimization sample set for retraining the approximate model.

6. An operable computer program, characterized in that, The computer program is stored in a computer-readable storage medium and, when executed by a processor, implements the method for improving the accuracy of the approximate model of a water pump turbine runner based on targeted sampling as described in any one of claims 1 to 5.

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