A turbine blade geometry uncertainty quantification analysis system

Abstract

The application discloses a kind of turbine blade geometry structure uncertainty quantification analysis system, the system includes CAD model construction module, uncertainty sampling module, CFD batch calculation module, DNN model training module, uncertainty analysis module and turbine performance optimization module.The analysis system of the application improves the efficiency and stability of CFD calculation of large batch uncertainty design sample set to a great extent, and helps to promote the application of uncertainty optimization design technology in practical engineering.On the other hand, by virtue of the structural parameterization of the geometry model of the turbine blade, up to dozens of parameters can be simultaneously subjected to uncertainty design sampling calculation, and the subsequent screening of relatively important parameters based on sensitivity analysis can achieve the goal of dimension reduction, solving the problem of "dimension disaster" in traditional uncertainty analysis and improving the accuracy and comprehensiveness of turbine blade uncertainty analysis.

Description

Technical Field

[0001] This invention relates to a quantitative analysis system for the geometric uncertainty of turbine blades, belonging to the field of turbomachinery technology. Background Technology

[0002] In aero-engines, turbines play a crucial role in energy conversion and directly impact the overall aerodynamic performance and service life. Because turbines operate under harsh conditions of high temperature, high pressure, and high speed, temperature, thermal stress, and ablation severely affect turbine blade performance. In recent years, with increasingly stringent operating requirements, turbine materials themselves cannot withstand such high-temperature flow. Therefore, turbine cooling performance has become critical. Manufacturing geometric uncertainties directly affect the internal flow and heat transfer processes of turbines, leading to aerodynamic and thermal performance degradation and reliability issues, resulting in significant lifespan variations for hot-end components in aero-engines. Simultaneously, as requirements for turbine performance indicators and service life continue to increase, the demands for refined turbine design are becoming increasingly stringent. Identifying and minimizing the impact of various geometric uncertainties on performance is of great significance. In recent years, various uncertainty quantification (UQ) methods have yielded a series of research results in turbine performance design.

[0003] Current research on the quantification of uncertainties in turbine blades mainly falls into two categories: one focuses on the impact of key geometric parameters on the blade surface, while the other focuses on the impact of geometric parameters in the cooling system. Most research solutions select a small number of geometric uncertainty parameters as inputs and some key performance indicators as outputs. After collecting uncertainty samples using numerical methods such as Latin hypercube sampling (LHS), CFD calculations are manually performed on the geometric models corresponding to the sample sets one by one to obtain the results. Finally, the calculation results are used as training and validation sets to establish and train a surrogate model, performing uncertainty quantification analysis and multidisciplinary optimization on the geometric parameters of the selected area.

[0004] Most existing studies on uncertainty quantification analysis of turbine blades only consider a few parameters. However, the complexity of turbine machinery itself and the numerous geometric uncertainties introduced during manufacturing and use not only affect performance individually, but their interactions further lead to performance changes. Therefore, considering only a few parameters is neither comprehensive nor accurate. On the other hand, uncertainty quantification studies for complex multivariate problems not only require a large amount of manual CFD calculations, resulting in long design cycles, but also suffer from the "curse of dimensionality" due to the excessively high dimensionality of the parameter space, making the computational time and cost prohibitive in engineering.

[0005] Therefore, developing suitable high-dimensional reduction methods is of great significance and can be applied to practical engineering fields. Meanwhile, since turbine design objectives involve constraints from multiple disciplines and objectives, including aerodynamics, heat transfer, and structure, developing suitable multidisciplinary and multi-objective optimization methods is crucial for turbine design. Summary of the Invention

[0006] To address the problems existing in the aforementioned background technology, this invention provides a turbine blade geometry uncertainty quantification analysis system. This system can serve as an automated design platform for multidisciplinary uncertainty analysis of turbine blades. The system integrates multiple modules, allowing users to easily complete uncertainty quantification analysis without manually calling each module or integrating various algorithms and software. This significantly improves the efficiency and stability of CFD calculations for large-scale uncertainty design sample sets, facilitating the application of uncertainty optimization design technology in practical engineering. Furthermore, by parameterizing the turbine blade's geometric model, this system can simultaneously perform uncertainty design sampling calculations on up to dozens of parameters. Subsequently, based on sensitivity analysis, relatively important parameters are selected to achieve dimensionality reduction, solving the "curse of dimensionality" problem in traditional uncertainty analysis and improving the accuracy and comprehensiveness of turbine blade uncertainty analysis.

[0007] This invention is achieved using the following technical solution:

[0008] A system for quantifying and analyzing the uncertainty of turbine blade geometry includes a CAD model construction module, an uncertainty sampling module, a CFD batch calculation module, a DNN model training module, an uncertainty analysis module, and a turbine performance optimization module. The CAD model construction module parameterizes the structure of the turbine blade's geometric model. The uncertainty sampling module selects geometric parameters based on the research objective and determines the uncertainty range of these parameters according to manufacturing and usage conditions, then samples within the uncertainty range. The CFD batch calculation module performs batch processing on the sampling results from the uncertainty sampling module, specifically including mesh generation, preprocessing, solving, and post-processing. The DNN model training module trains a DNN model based on the calculation results from the CFD batch calculation module; the DNN model takes geometric parameters as input and outputs target physical quantities. The uncertainty analysis module performs sensitivity analysis on the geometric parameters selected by the uncertainty sampling module based on the target physical quantities and extracts key geometric parameters. The turbine performance optimization module performs deterministic and uncertainty optimization on the key geometric parameters.

[0009] Furthermore, in the above technical solution, the geometric model of the turbine blade can be a model of a fully cooled turbine blade with a combination of impact and film cooling, etc.

[0010] Furthermore, the CAD model building module is used to parameterize the structure of the geometric model of the turbine blade. Specifically, the structure of the geometric model of the turbine blade includes: blade internal cavity curvature; blade thickness distribution; blade tip shape; blade tail shape; diameter, angle, distribution gap, and number of film cooling holes; diameter, angle, distribution gap, and number of impact holes; thickness, distribution gap, and number of ribs; and radius, distribution gap, and number of turbulence columns.

[0011] Furthermore, the uncertainty sampling module may specifically employ the Latin hypercube sampling method to randomly sample the selected geometric parameters.

[0012] Furthermore, the deterministic optimization specifically involves selecting an optimal set of key geometric parameters based on the target physical quantity; the uncertainty optimization specifically involves selecting a set of key geometric parameters based on the performance dispersion under the uncertainties brought about by manufacturing and use, thereby maximizing the robustness of the turbine system.

[0013] Furthermore, the mesh generation specifically involves meshing the geometric model of the turbine blade to discretize the solution domain; the preprocessing specifically includes defining initial and boundary conditions and material properties; the solution specifically involves numerically solving the fluid equations; and the post-processing involves statistically analyzing and visualizing the numerical solution results.

[0014] Furthermore, the DNN model training module is used to train a DNN model based on the computation results of the CFD batch computation module. Specifically, the computation results of the CFD batch computation module are randomly divided into K folds based on K-fold cross-validation, and each fold is used as a validation set to train the DNN model multiple times. The hyperparameters of the hidden layer node combinations in the DNN model are optimized using the Grid Search method. Key geometric parameters extracted by the uncertainty analysis module are used as input to the new DNN model for further training until the model accuracy reaches a set threshold and the retained parameter dimensions meet the computational requirements. This inner-loop dimensionality reduction method between the DNN model and the uncertainty analysis module can filter out key geometric parameters, solving the following problems: insufficient neural network accuracy due to a large number of parameters and the sparsity of the dataset, resulting in uncertain sensitivity relationships between two closely spaced parameters in the SHAP mean plot; and low computational efficiency due to the complex geometric features of turbine cooling blades.

[0015] Furthermore, the uncertainty analysis module is used to perform sensitivity analysis on the geometric parameters selected by the uncertainty sampling module based on the SHAP analysis method (specifically, the SHAP value of the geometric parameters can be calculated using the Kernel Explainer in Python's SHAP library), and extract key geometric parameters. The specific method is as follows: calculate the SHAP value of the geometric parameters selected by the uncertainty sampling module; the larger the SHAP value of a geometric parameter, the greater its sensitivity. Based on the SHAP value, select the geometric parameters with greater sensitivity as key geometric parameters. The specific formula for calculating the SHAP value of the geometric parameters is:

[0016]

[0017] δ i (S)=EY k (S∪(x i ))-EY k (S)

[0018] EY k (S)=E(Y(x k )|S)

[0019] Where, x i X represents the i-th input feature vector, which is composed of geometric parameters; X does not contain x. i The set of all other input feature vectors, where N represents the set of all feature vectors; Y(x k ) is x k The corresponding output vector.

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] This invention establishes a multi-module-integrated system for quantifying and analyzing the uncertainty of turbine blade geometry. In terms of efficiency, the system performs extensive uncertainty sampling calculations through automated processes and algorithms, eliminating the time and labor costs of manual sampling and accelerating the calculation process through parallel computing technology, thus improving computational efficiency. Regarding result processing, the system can generate visualized results and reports, summarizing analysis results and data for easier subsequent decision-making and communication. In terms of repeatability and scalability, the system establishes standardized uncertainty analysis processes and tools, allowing for repeated analysis of the same problem and rapid application to other projects. Regarding integration and collaboration, the system can integrate with existing engineering software and data systems to achieve automated data transmission and processing, supporting multi-user collaboration and enabling distributed uncertainty analysis and design. The system also parameterizes the turbine blade's geometric model. In parametric design, these parameters can be adjusted to change the shape, size, and features of the object without recreating the entire geometric model. Geometric parameterization improves design flexibility, efficiency, and accuracy, accelerates the design process, reduces complexity, and makes design work more systematic and engineering-oriented. A Latin hypercube sampling method is employed for uncertainty sampling calculations. This method uniformly divides the sample space into continuous regions and selects a sample value from each region to construct a sampling set. Compared to traditional sampling methods, the Latin hypercube sampling method improves sampling efficiency and increases the diversity of sampling points, thus better exploring and representing the entire sample space. A surrogate model is trained using the Grid Search method and K-fold cross-validation. Addressing the data sparsity challenge in training deep neural network (DNN) models, K-fold cross-validation can more fully utilize the data and reduce the bias in model evaluation results. Dimensionality reduction is performed using an inner-loop approach based on SHAP analysis. Traditional black-box models such as deep neural networks typically possess a large number of parameters and complex computational structures, making their internal operating mechanisms difficult to understand and interpret. The selected SHAP (Shapley Additive Explanations) value analysis method can effectively interpret the model and provide sensitivity to individual geometric variables. Furthermore, this inner-loop dimensionality reduction method resolves the contradiction between a large number of selected parameters and a sparse dataset leading to insufficient accuracy in neural networks, thereby obtaining the geometric features most influential on turbine cooling blades and significantly improving computational efficiency. This invention integrates the interactions of multiple disciplines (aerodynamics, heat transfer, structure, etc.), while simultaneously considering design variables and uncertainties in the system, to optimize target physical quantities. Multidisciplinary optimization establishes synergistic relationships between different disciplines and simplifies the coupling between design variables and performance indicators through machine learning methods, comprehensively considering all factors to obtain the optimal design. Attached Figure Description

[0022] Figure 1This is a flowchart of the turbine blade geometry uncertainty quantification analysis system of the present invention.

[0023] Figure 2 It is a parameterized model of turbine cooling blades.

[0024] Figure 3 The left chart shows the SHAP mean of 15 parameters, and the right chart shows the sum of SHAP values.

[0025] Figure 4 This is a flowchart of dimensionality reduction and optimization of neural networks.

[0026] Figure 5 During the dimensionality reduction process, R 2 Change diagram.

[0027] Figure 6 It is a Pareto plot in the sample space.

[0028] Figure 7 This is a Pareto curve based on a genetic algorithm. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0030] like Figure 1 As shown, the present invention provides a turbine blade geometry uncertainty quantification analysis system, which integrates multiple modules, including a CAD model construction module, an uncertainty sampling module, a CFD batch calculation module, a DNN model training module, an uncertainty analysis module, and a turbine performance optimization module.

[0031] This invention comprises two main functional parts. The first part is uncertainty sampling calculation based on a commercial design software, CAESE (corresponding to the CAD model building module, uncertainty sampling module, and CFD batch calculation module). The second part is uncertainty analysis and multidisciplinary performance optimization based on the sampling results (corresponding to the DNN model training module, uncertainty analysis module, and turbine performance optimization module).

[0032] In the first functional section, the CAD model building module is used to parameterize the geometric model of the turbine blade. This system can collect uncertainty sample sets with a single click. Specifically, the CAD model building module imports a model of a fully cooled turbine blade with a typical industrial configuration combining impact and film cooling. The geometric model of the turbine cooling blade is then parameterized, including: blade internal cavity curvature; blade thickness distribution; blade tip shape; blade tail shape; diameter, angle, distribution gap, and number of 11 exhaust film holes; diameter, angle, distribution gap, and number of 20 rows of cooling holes; thickness, distribution gap, and number of 4 sets of ribs; radius, distribution gap, and number of 4 sets of baffles, etc. This essentially covers all the cooling structures in the turbine cooling blade, setting initial design values ​​and appropriate value ranges for each parameter to ensure that the parameter values ​​vary within acceptable ranges. By changing the geometric parameter values ​​of the blade structure within the system, the corresponding CAD model will also adjust accordingly. This improves the flexibility, efficiency, and accuracy of the design, while accelerating the design process, reducing complexity, and making the design work more systematic and engineering-oriented. The parameterized model is shown below. Figure 2 .

[0033] Secondly, by writing scripts to call the interfaces provided by the CAESES software, interaction with other software is achieved. Based on CAESES, the CAD model building module, uncertainty sampling module, and CFD batch calculation module are integrated. The uncertainty sampling module is used to select geometric parameters according to the research objectives and determine the uncertainty range of the geometric parameters according to manufacturing and usage conditions, and then perform sampling within the uncertainty range of the geometric parameters. The CFD batch calculation module is used to batch process the sampling results of the uncertainty sampling module, specifically including mesh generation, preprocessing, solving, and post-processing.

[0034] The CAESES software uses ANSYS ICEM for mesh generation, CFX-Pre for preprocessing, CFX-Solver for solving, and CFX-Post for post-processing. The entire workflow is as follows:

[0035] (1) Model creation and import: Create a CAD model based on the geometry of the actual flow problem and import it into the fluid calculation software, including the solid domain and the fluid domain.

[0036] (2) Mesh generation: The geometric model is meshed to discretize the solution domain. Commonly used mesh generation methods include structured meshes and unstructured meshes.

[0037] (3) Preprocessing: Define initial and boundary conditions, including information such as flow rate, temperature, and pressure at the fluid inlet, as well as boundary conditions at the fluid outlet or other surfaces; define material properties.

[0038] (4) Solver solution: Select appropriate numerical methods and solvers to solve the fluid equations numerically, perform fluid simulation calculations and monitor the convergence.

[0039] (5) Post-processing: Obtain the simulation calculation results data and perform statistical analysis and visualization.

[0040] To reduce the number of computational examples required during the sampling process within the uncertainty range of the geometric parameters, the uncertainty sampling module employs the Latin Hypercube Sampling (LHS) method for uncertainty sampling calculation. This sampling method uniformly divides the sample space into continuous regions and selects a sample value from each region to construct a sample set. Compared with traditional random sampling methods, LHS has advantages such as high sampling efficiency, strong coverage, and small sampling bias.

[0041] Finally, leveraging CAESES's built-in design optimization capabilities, before using the uncertainty sampling module, appropriate parameter selection and uncertainty range settings are required. Then, the desired output and the number of data points to be collected can be determined for one-click sampling and calculation. The entire process is as follows:

[0042] (1) Determining the target parameters for uncertainty quantification: Determine the target of uncertainty research, select appropriate parameters or variables, and determine the range of uncertainty variation.

[0043] (2) Establish the parameter distribution function: Set an appropriate distribution function for the selected parameters.

[0044] (3) Select sampling method to generate samples: The uncertainty sampling module uses the Latin hypercube sampling method to generate a certain number of samples to represent its uncertainty range.

[0045] (4) Simulation calculation and result collection: Apply the sample set of uncertainty parameters to the CFD batch calculation module and perform a large number of simulation calculations.

[0046] In the second part, a deep neural network (DNN) is selected as a surrogate model for uncertainty analysis. A DNN model with one input layer, two hidden layers, and one output layer is constructed. Important blade geometric parameters are selected as inputs, and relevant blade physical quantities of interest are selected as outputs. The arctangent function tanh is selected as the activation function for nonlinear mapping. The root mean square error function RSME is selected as the loss function to measure the error between the model's predicted output and the true value, and its expression is as follows:

[0047]

[0048] Where n is the number of samples, y i For the sample true value, These are the model's predicted values.

[0049] When training a DNN model using the sample set obtained from the uncertainty sampling module, the Grid Search method is used to optimize the combination of node numbers in the two hidden layers of the constructed DNN model. Other hyperparameters include: learning rate (controlling the step size or magnitude of parameter updates in each iteration, set to 0.01); and weight decay rate (penalizing weight parameters to prevent overfitting, set to 0.1). On the other hand, even though the uncertainty sampling module significantly improves the efficiency of uncertainty sampling calculations, the CFD simulation calculations for each set of geometric parameters are extremely computationally intensive. To address the problem of data sparsity in DNN model training, the K-fold CrossValidation method is considered for model evaluation. Its principle is to divide the dataset into K equal subsets, with one subset serving as the validation set and the remaining K-1 subsets as the training set. This process is repeated K times, iterating through all subsets, and the final evaluation result is the average of the K iterations. This method can make fuller use of the data and reduce the bias of the model evaluation results. This system uses the coefficient of determination R0. 2 The following formula is used as an indicator to evaluate the goodness of fit of the regression model.

[0050]

[0051] Where y i For the sample true value, y is the model's predicted value, and y is the sample's true average value.

[0052] The training steps for a DNN model are as follows:

[0053] (1) Wide-range search for node combinations to narrow down the appropriate node range. Select a large node range and evaluate the fit of different DNN models (training set R). 2 Mean and generalization ability (validation set R) 2 The number of nodes should be determined within a reasonable small range.

[0054] (2) Determine the narrowed node search range and remove problematic data based on K-fold cross-validation. Since CFD calculations inevitably produce large errors in the calculation results due to issues such as model quality and mesh quality, such data will interfere with the real physical input-output relationship during model training. Therefore, problematic data needs to be removed through posterior methods.

[0055] (3) Select the optimal node combination based on the training results. Evaluate the R-values ​​of different node combinations comprehensively. 2 The optimal node combination is selected based on the mean and the loss function RSME value.

[0056] After the DNN model is trained, the uncertainty analysis module is used to perform sensitivity analysis and dimensionality reduction on the selected geometric parameters. Specifically, the SHAP (Shapley Additive Explanations) value analysis method is used for sensitivity analysis. The Shapley value is defined as the average marginal contribution rate of a certain feature value among all possible combinations. For the i-th input feature vector x... i To output vector Y(x) i The correlation between the Shapley value and the Shapley value is derived as follows:

[0057] Let S represent a subset of all eigenvectors, N represent the set of all eigenvectors, and x i Let x represent the i-th input feature vector (specifically, a vector composed of geometric parameters). i The marginal contribution added to subset S is:

[0058] δ i (S)=EY k (S∪(x i ))-EY k (S)

[0059] Prediction of the contribution value of removing eigenvalues ​​from S:

[0060] EY k (S)=E(Y(x k )|S)

[0061] δ is calculated consistently for all subsets. i (S), the final Shapley value formula can be derived by weighted summation of all possible eigenvalues:

[0062]

[0063] As can be easily seen from the above formula, by calculating the SHAP value and finding the average change in the prediction result after each feature is added, we can understand the degree of influence of each feature on the prediction result, thereby better understanding the model's decision-making process and the importance of features.

[0064] Sensitivity analysis of the selected geometric parameters is performed using the uncertainty analysis module. The Kernel Explainer from Python's SHAP library is used to calculate the SHAP values ​​of all features. The Kernel Explainer is used to interpret any machine learning model by estimating the sensitivity of input features through an approximation method in the feature space. Since the SHAP value calculation method involves calculating for all possible subsets of features, this is very time-consuming when the number of features is large. This system uses an approximate calculation method, estimating the Shapley value through random sampling and then approximating the true Shapley value using the sample mean. The number of iterations (i.e., the number of random samples) is set to 100. Generally, a SHAP mean plot and a SHAP value summary plot are used for model interpretation. The former is the result of averaging the absolute values ​​of the SHAP values ​​for each feature, which can be considered a ranking of feature importance; the latter is a visualization of the SHAP values ​​of all features, with each point representing a SHAP value and the color representing the magnitude of the value (gradually increasing from blue to red). The horizontal axis represents the magnitude of the SHAP value, and the vertical axis represents all features; that is, features with a wider horizontal distribution in the plot indicate greater influence. Figure 3 This is an analysis chart of the SHAP values ​​corresponding to a certain set of geometric parameters.

[0065] Considering the possibility of a large number of selected geometric parameters, including some less important ones, and the potential for insufficient neural network accuracy due to dataset sparsity, the sensitivity relationship between two closely adjacent parameters in the SHAP mean plot cannot be determined. On the other hand, due to the complex geometric features of turbine cooling blades, improved computational efficiency is required; therefore, only information from key features needs to be retained. This system employs an inner loop to reduce the dimensionality of the selected geometric parameters, as illustrated in the diagram. Figure 4 .

[0066] (1) Train using the selected geometric parameters and optimize step by step to improve R. 2 The deviation between the value and the predicted average temperature of the inner wall of the blade.

[0067] (2) Perform SHAP value analysis on the selected parameters and rank their sensitivity to the inner wall temperature of the blade. Then delete the geometric parameters with too low sensitivity.

[0068] (3) Retrain and optimize the neural network using the selected geometric parameters, and observe whether the quality of the neural network is optimized.

[0069] (4) If the quality of the neural network is improved, it means that the deleted geometric parameters have little impact on the output physical quantity, thus achieving dimensionality reduction and continuing the loop; if the quality of the neural network decreases, it means that the deleted geometric parameters are more important, thus failing to reduce dimensionality, ending the loop and completing the dimensionality reduction process.

[0070] For example, dimensionality reduction is performed based on the 29 sets of geometric parameters selected in the example. The optimal node combination neural network with K-fold cross-validation is used in the dimensionality reduction loop, with a training set R... 2 With validation set R 2 See the changes in the mean and maximum values. Figure 5 .Depend on Figure 5 It can be seen that the first and second dimensionality reductions improved the quality of the neural network to some extent. However, the quality of the neural network dropped significantly when parameters were removed in the third reduction. Therefore, it is concluded that when the 29 sets of turbine cooling blade geometric parameters selected in this example are reduced to 8 sets, both the model accuracy and parameter dimensionality meet the requirements. Further dimensionality reduction results in the loss of important physical quantities, failing to reflect the nonlinearity and geometric integrity of the system. Therefore, based on the final results, 8 sets of turbine cooling geometric parameters were selected as the final input.

[0071] Finally, based on the dimensionality-reduced key geometric parameters and the DNN model, deterministic and uncertain optimizations are performed to propose an optimization scheme for improving turbine cooling performance. Taking into account performance and cost objectives, and combining the uncertainty quantification results, the optimized design of turbine cooling performance is achieved.

[0072] This system uses a genetic algorithm for the final multidisciplinary optimization. Multidisciplinary Uncertainty Optimization (MUO) is a widely used optimization method in engineering and science, aiming to integrate the interactions of multiple disciplines while considering design variables and uncertainties in the system to optimize the objective function. Multidisciplinary Design Optimization (MDO) is the core foundation of MUO, emphasizing collaborative design and optimization between different disciplines. In multidisciplinary systems, design variables and performance indicators are often coupled between disciplines. In the research object of this invention, changing structural parameters may affect hydrodynamic properties, which in turn affect the system's heat transfer and performance.

[0073] Genetic Algorithm (GA) is an optimization method that simulates the process of biological evolution. Its core idea is to search for the optimal solution in the solution space of a problem through processes such as natural selection, genetic mutation, and crossover. Genetic Algorithms can be used to solve complex optimization problems and are highly applicable to nonlinear, high-dimensional, multimodal, and difficult-to-solve optimization problems.

[0074] For example, considering the trade-off between the selected blade surface average temperature and the ratio of cooling gas to inlet flow rate, the goal is to find a solution that achieves the lowest possible temperature while minimizing cooling gas usage. Two trained DNN models (one outputting the blade surface average temperature and the other outputting the cooling gas ratio) are used to predict both the blade surface average temperature and the cooling gas ratio. By using DNN models to predict combinations of each output physical quantity, the entire design space is effectively sampled. Figure 6 As shown, Pareto optimal solutions are identified by searching for points within the sample space and simultaneously minimizing two objectives (average temperature of the blade surface and the ratio of cooling gas to inlet flow rate). These solutions form a set of Pareto front design points, such as... Figure 6 As shown by the red dots in the diagram. A genetic algorithm (GA) is employed, iteratively approximating the Pareto optimal solution through crossover and mutation operations within the initial population, thus achieving a more accurate fit to the Pareto front. Through the evolutionary process, the initial sample set gradually converges towards the Pareto front, effectively approximating the Pareto curve, as shown in the diagram. Figure 7 As shown. The algorithm parameters are set as follows: crossover probability CXPB = 0.8, mutation probability MUTPB = 0.1, number of generations NGEN = 200, population size pop = 1000.

Claims

1. A system for quantitative analysis of uncertainties in the geometric structure of turbine blades, characterized in that, It includes a CAD model building module, an uncertainty sampling module, a CFD batch calculation module, a DNN model training module, an uncertainty analysis module, and a turbine performance optimization module; the CAD model building module is used to parameterize the structure of the geometric model of the turbine blade; the uncertainty sampling module is used to select geometric parameters according to the research objectives, determine the uncertainty range of the geometric parameters according to the manufacturing and usage conditions, and perform sampling within the uncertainty range of the geometric parameters; The CFD batch computation module is used to batch process the sampling results of the uncertainty sampling module, specifically including mesh generation, preprocessing, solving, and post-processing; the DNN model training module is used to train a DNN model based on the computation results of the CFD batch computation module, wherein the DNN model takes geometric parameters as input and outputs the target physical quantity; the uncertainty analysis module is used to perform sensitivity analysis on the geometric parameters selected by the uncertainty sampling module based on the target physical quantity and extract key geometric parameters; the turbine performance optimization module is used to perform deterministic optimization and uncertainty optimization on the key geometric parameters. The geometric model of the turbine blade is a model of a fully cooled turbine blade with a combination of impact and film cooling configuration; The CAD model building module is used to parameterize the structure of the geometric model of the turbine blade. The specific parameters after structural parameterization include: blade internal cavity curvature; blade thickness distribution; blade tip shape; blade tail shape; diameter, angle, distribution gap, and number of film cooling holes; diameter, angle, distribution gap, and number of impact holes; thickness, distribution gap, and number of ribs; radius, distribution gap, and number of turbulence columns. The DNN model training module is used to train a DNN model based on the calculation results of the CFD batch calculation module. Specifically, the calculation results of the CFD batch calculation module are randomly divided into K folds based on K-fold cross-validation, and each fold is used as a validation set to train the DNN model in multiple rounds. The hyperparameters of the hidden layer node combinations in the DNN model are optimized using the Grid Search method. Key geometric parameters extracted by the uncertainty analysis module are used as input to the new DNN model for further training until the model accuracy reaches a set threshold and the retained parameter dimensions meet the computational requirements. The uncertainty analysis module is used to perform sensitivity analysis on the geometric parameters selected by the uncertainty sampling module based on the SHAP analysis method, and to extract key geometric parameters. The specific method is as follows: Calculate the SHAP value of the geometric parameters selected by the uncertainty sampling module. The larger the SHAP value of the geometric parameter, the greater its sensitivity. Select the geometric parameter with greater sensitivity as the key geometric parameter based on the SHAP value. The deterministic optimization specifically involves selecting the optimal set of key geometric parameters based on the target physical quantity; the uncertainty optimization specifically involves selecting a set of key geometric parameters based on the performance dispersion under the uncertainties brought about by manufacturing and use, thereby maximizing the robustness of the turbine system.

2. The turbine blade geometry uncertainty quantification analysis system according to claim 1, characterized in that, The mesh generation specifically involves dividing the geometric model of the turbine blade into a mesh to discretize the solution domain; the preprocessing specifically includes defining initial and boundary conditions and material properties; the solution specifically involves numerically solving the fluid equations; and the post-processing involves statistically analyzing and visualizing the numerical solution results.

3. The turbine blade geometry uncertainty quantification analysis system according to claim 1, characterized in that, The derivation of the formula for calculating the SHAP value of geometric parameters is as follows: Let S denote a subset of all feature vectors and N the set of all feature vectors; x i denotes the i-th input feature vector, in particular a vector composed of geometric parameters; x i The marginal contribution added to the subset S is: Prediction of the contribution value of removing eigenvalues ​​from S: The computation is consistent across all subsets. The final SHAP value formula is derived by weighted summation of all possible eigenvalues: Where X does not contain x i The set of all other input feature vectors, Y(x k ) is x k The corresponding output vector.

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