Artificial intelligence-based turbine blade design parameter optimization method and system

Abstract

The application discloses a turbine blade design parameter optimization method and system based on artificial intelligence, and relates to the technical field of turbine blade optimization design. A double-layer proxy model combining a physical benchmark and a residual neural network is constructed. Sobol sensitivity partition and adaptive acquisition function guided evolution search are used to form a closed-loop optimization through on-demand CFD verification and incremental updating, so that the physical consistency and optimization efficiency are improved. The application has the following advantages: a double-layer proxy model architecture combining a physical benchmark model and a physical residual neural network is constructed. The learning task of the proxy model is simplified from complex nonlinear mapping of design parameters to full-quantity performance values to residual learning of physical residuals. The training data requirement can be effectively reduced, and the model training efficiency is improved. At the same time, the double protection of the bottom output of the physical benchmark model and the embedded multi-dimensional physical constraint regularization items such as continuity constraint, thermodynamic compatibility constraint and smoothness constraint ensures the normal operation of the model.

Description

Technical Field

[0001] This invention relates to the field of turbine blade optimization design technology, specifically to a method and system for optimizing turbine blade design parameters based on artificial intelligence. Background Technology

[0002] Turbine blades are core hot-end components of turbine machinery such as gas turbines and steam turbines, and their aerodynamic design directly affects the overall efficiency, power output, and operational stability of the machine. Turbine blade design involves the coordinated optimization of multiple geometric and aerodynamic parameters, such as the airfoil curvature, thickness distribution, installation angle, and inlet / outlet airflow angle. There are complex nonlinear coupling relationships between these parameters, and traditional methods based on iterative corrections based on design experience are insufficient to efficiently obtain globally optimal solutions in high-dimensional parameter spaces.

[0003] In recent years, data-driven optimization methods combining surrogate models and evolutionary algorithms have been increasingly applied to turbine blade design. For example, the authorized invention patent CN106874542B (authorization announcement date November 13, 2020) discloses a multi-condition, multi-objective optimization design method for hydraulic turbine impellers. This method uses an optimized Latin hypercube design to generate training samples, obtains performance data through CFD simulation, trains a BP neural network as an approximate surrogate model, and embeds it into the NSGA-II multi-objective genetic algorithm for Pareto optimization. Finally, a combined weighting method is used to select the optimal solution from the Pareto solution set. This approach represents the current mainstream technical paradigm of multi-objective optimization combining neural network surrogate models and genetic algorithms.

[0004] However, the aforementioned existing technical solutions have the following shortcomings: First, BP neural networks are purely data-driven models. Training the network requires learning a complex nonlinear mapping from design parameters to full performance values. In high-dimensional parameter spaces, the demand for training samples is large, and the acquisition cost is high. Furthermore, the prediction results lack physical constraints, and abnormal predictions that violate the basic physical laws of turbomachinery are prone to occur in sparse training data regions, resulting in insufficient engineering reliability. Second, during the optimization process, a uniform sampling density and fixed evolutionary operator parameters are used for all design variables, without considering the differences in sensitivity of different design parameters to the optimization objective. This leads to low efficiency in the allocation of computational resources, and the fixed crossover and mutation probabilities make it difficult for the algorithm to balance global exploration and local convergence. It is prone to getting trapped in local extrema in the early stages and has insufficient convergence accuracy in the later stages. Third, the surrogate model remains frozen after the initial training is completed and cannot use the new data generated during the optimization iteration process to improve itself. The optimization results need to rely on additional posterior CFD verification to confirm their engineering reliability.

[0005] Therefore, there is an urgent need for a turbine blade design parameter optimization method that can reduce training data requirements, adopt adaptive scheduling search strategies, and continuously improve the accuracy of surrogate models and the reliability of optimization results through a closed-loop mechanism while ensuring physical consistency. To this end, we propose an artificial intelligence-based turbine blade design parameter optimization method and system. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for optimizing turbine blade design parameters based on artificial intelligence.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for optimizing turbine blade design parameters based on artificial intelligence, comprising the following steps: Step 1: Determine the design variables, multi-condition optimization objectives and parameter constraint boundaries of the turbine blade, generate an initial sample set using the optimized Latin hypercube experimental design method, complete the three-dimensional viscous flow field high-fidelity CFD simulation of all samples, and construct an initial training sample database containing geometric parameters and corresponding performance labels. Step 2: Construct a coarse-grained physical benchmark model based on one-dimensional average streamline analysis and two-dimensional S2 flow surface flow calculation, input design parameters and output benchmark performance prediction values ​​with natural physical consistency; Step 3: Construct a physical residual neural network with embedded multi-dimensional physical constraint regularization terms. Use the performance residual between the high-fidelity CFD simulation results and the physical benchmark model as the training target to complete the initial training, and then superimpose the combined performance prediction results. Step 4: Based on the trained physical residual neural network, calculate the Sobol global sensitivity index of each design parameter using the quasi-Monte Carlo method, adaptively divide the parameter space into three levels, and configure the search resolution and evolution operator step size differently. Step 5: Estimate the prediction uncertainty of the physical residual neural network based on the Monte Carlo random deactivation mechanism, construct an adaptive balance between exploration and utilization composite acquisition function, and embed it as an additional optimization dimension into the framework of the third-generation non-dominated sorting genetic multi-objective evolutionary algorithm. Step 6: During the optimization iteration process, high-fidelity CFD verification is triggered for candidate solutions whose prediction uncertainty exceeds the threshold. The physical residual neural network is updated online in an incremental learning manner, the sensitivity index is recalculated synchronously, and the parameter partitions are dynamically adjusted to form a closed-loop optimization mechanism. Step 7: Perform multiple rounds of closed-loop iterations until the preset convergence criteria are met, output the final Pareto non-dominated solution set, and select the design parameter scheme applicable to the project.

[0008] As a further aspect of the present invention: in step one, the design variables include five types of geometric and aerodynamic parameters, namely, the airfoil arc control parameters, the airfoil thickness distribution parameters, the blade installation angle, the number of blades, and the inlet and outlet airflow angles; the optimization objectives cover two types of multi-objective directions: the highest efficiency and the lowest load under design conditions and variable conditions; the parameter constraint boundaries are set with upper and lower limits based on the turbine blade engineering design specifications; the high-fidelity CFD simulation outputs the isentropic efficiency, total pressure recovery coefficient, outlet airflow angle, and aerodynamic load performance parameters under all operating conditions corresponding to each set of design parameters.

[0009] As a further aspect of the present invention: In step two, the coarse-grained physical benchmark model is used to solve the flow path based on simplified forms of the mass conservation equation, momentum conservation equation, and energy conservation equation; the model takes no more than 1 second for a single evaluation, and its prediction results naturally satisfy the Euler equation, continuity equation, and basic thermodynamic constraints of turbomachinery, providing a physically sound benchmark for subsequent residual learning; the model output parameters include the isentropic efficiency, total pressure recovery coefficient, and outlet airflow angle benchmark performance prediction values ​​under the corresponding design parameters.

[0010] As a further aspect of the present invention: in step three, the formula for calculating the performance residual is: ; In the formula, The performance residual between high-fidelity CFD simulation results and physical baseline model predictions, These are the calculated performance parameters obtained from high-fidelity CFD simulations. The baseline performance prediction is the output of the physical baseline model; the total loss function for training the physical residual neural network is calculated using the following formula: ; In the formula, This represents the total loss function value during the training of the physical residual neural network. This is the mean squared error loss term for residual prediction. As a continuous residual penalty term, a mass conservation constraint is imposed on the partial derivative of the output with respect to the mass flow rate parameter using automatic differentiation techniques. As a thermodynamic compatibility penalty term, a soft constraint is imposed on the physically feasible interval of the efficiency prediction value. As a smoothness penalty term, regularization is applied to the Frobenius norm of the Hessian matrix of the output with respect to geometric parameters to suppress numerical noise overfitting. , , The weight coefficients corresponding to each constraint term are adaptively determined through Bayesian hyperparameter optimization.

[0011] As a further aspect of the present invention: in step four, the Sobol global sensitivity index includes a first-order sensitivity index. Sensitivity index of total effect The calculation formula is as follows: ; In the formula, For the first The first-order sensitivity index of each design parameter For the first The overall effect sensitivity index of each design parameter To optimize the target's performance predictions, For the first One design parameter, To exclude the first All other design parameters besides the one parameter, This is the variance operator. The conditional expectation operator is used; the parameter space has three levels: the core parameter region, the intermediate parameter region, and the marginal parameter region. The partition thresholds are the 70th and 30th quantiles of the total effect sensitivity index distribution. The core parameter region is configured with a dense search grid and a small variable asynchronous length, the marginal parameter region is configured with a coarse search grid and a large variable asynchronous length, and the intermediate parameter region maintains the baseline search resolution.

[0012] As a further aspect of the present invention: in step five, the prediction uncertainty is addressed by maintaining the activation of the random deactivated layer during the inference phase and performing 20 to 50 random forward propagations, using the standard deviation of multiple prediction results as the parameter point. Corresponding forecast uncertainty The composite acquisition function is calculated using the following formula: ; In the formula, Design parameter points The corresponding composite acquisition function value, For any parameter point in the design parameter space, For parameter points The predicted combined performance value at the location, This represents the maximum predicted performance value in the current population. For parameter points The predicted standard deviation at that location The maximum prediction standard deviation in the current population. To achieve adaptive balance, the initial optimization coefficient is set to 0.2 and then linearly increases to 0.8 with each iteration. The third-generation non-dominated sorting genetic algorithm uses the DasandDennis systematic method to generate reference points, and the step size of the crossover operator and mutation operator is configured differently according to the parameter space partitioning results.

[0013] As a further aspect of the present invention: in step six, the condition for triggering high-fidelity CFD verification is the uncertainty in the neural network prediction of the physical residual corresponding to the candidate solution. Exceeding the preset uncertainty threshold The preset uncertainty threshold is set in advance according to the accuracy requirements of the engineering design; the new sample data obtained from the verification is directly added to the training set, and the physical residual neural network is fine-tuned and updated in a small number of rounds using the stochastic gradient descent method with an exponentially decaying learning rate, without the need to perform full retraining; after each update of the physical residual neural network, the Sobol global sensitivity index is recalculated, and the three-layer partitioning results of the parameter space and the evolution operator parameters are dynamically adjusted synchronously.

[0014] As a further aspect of the present invention: in step seven, the convergence determination condition includes two quantitative indicators: first, the rate of change of the hypervolume index of the Pareto non-dominated front for two consecutive generations is lower than a preset convergence threshold; second, the uncertainty of the physical residual neural network prediction corresponding to all solutions of the Pareto non-dominated front is lower than a preset accuracy threshold; after the iteration terminates, a complete Pareto non-dominated parameter solution set is output, and the final turbine blade design parameter scheme is obtained by screening from the solution set based on the combination weighting method combined with engineering design requirements.

[0015] In addition, this application also provides an artificial intelligence-based turbine blade design parameter optimization system, which includes a sample construction module, a physical benchmark model module, a residual network training module, a sensitivity partitioning module, an evolutionary search module, a closed-loop update module, and a convergence output module. The sample construction module is used to determine the design variables, multi-condition optimization objectives and parameter constraint boundaries of the turbine blade, generate an initial sample set using the optimized Latin hypercube experimental design method, complete the three-dimensional viscous flow field high-fidelity CFD simulation of all samples, and construct an initial training sample database containing geometric parameters and corresponding performance labels. The physical benchmark model module receives data transmitted from the sample construction module and is used to construct a coarse-grained physical benchmark model based on one-dimensional average streamline analysis and two-dimensional S2 flow surface flow calculation. It inputs design parameters and outputs benchmark performance prediction values ​​with natural physical consistency. The residual network training module is used to construct a physical residual neural network with embedded multi-dimensional physical constraint regularization terms. The initial training is completed with the performance residual between the high-fidelity CFD simulation results and the physical benchmark model as the training target, and the combined performance prediction results are superimposed and output. The sensitivity partitioning module is used to calculate the global sensitivity index of each design parameter based on the trained physical residual neural network using the quasi-Monte Carlo method, adaptively divide the parameter space into three levels and differentiate the search resolution and evolution operator step size. The evolutionary search module is used to estimate the prediction uncertainty of the physical residual neural network based on the Monte Carlo random inactivation mechanism, construct an adaptive balance between exploration and utilization composite acquisition function, and embed it as an additional optimization dimension into the framework of the third-generation non-dominated sorting genetic multi-objective evolutionary algorithm. The closed-loop update module is used to trigger high-fidelity CFD verification for candidate solutions whose prediction uncertainty exceeds the threshold during the optimization iteration process. It updates the physical residual neural network online in an incremental learning manner, synchronously recalculates the sensitivity index and dynamically adjusts the parameter partitions to form a closed-loop optimization mechanism. The convergence output module is used to perform multiple rounds of closed-loop iteration until the preset convergence judgment condition is met, output the final Pareto non-dominated solution set, and filter to obtain the design parameter scheme applicable to the project.

[0016] Compared with the prior art, the beneficial effects of the present invention by adopting the above technical solution are as follows: 1. This invention constructs a two-layer surrogate model architecture that combines a physical benchmark model and a physical residual neural network. This simplifies the learning task of the surrogate model from the complex nonlinear mapping from design parameters to full performance values ​​to residual learning from design parameters to physical residuals. This can effectively reduce the amount of training data required and improve the model training efficiency. At the same time, through the double guarantee of the fallback output of the physical benchmark model and the embedding of regularization terms for multiple physical constraints such as continuity constraints, thermodynamic compatibility constraints, and smoothness constraints, the prediction results of the physical residual neural network in the sparse region of training data naturally conform to the basic physical laws of turbomachinery. This effectively improves the problem that the prediction results of existing pure data-driven surrogate models are prone to deviating from physical laws and have insufficient engineering credibility. 2. This invention employs a three-layer adaptive partitioning mechanism in the parameter space driven by the Sobol global sensitivity index. It differentiates the search resolution and evolutionary operator step size based on the contribution of each design parameter to the optimization objective, automatically focusing computational resources on high-sensitivity core parameter dimensions. This effectively compensates for the low search efficiency caused by existing methods using uniform sampling density and fixed evolutionary operators for all design variables. Furthermore, an adaptive composite acquisition function based on the Monte Carlo random deactivation mechanism achieves a smooth dynamic transition from exploration to utilization during the optimization process. In the early stages of optimization, it prioritizes exploring high-uncertainty regions to build global awareness, while in the later stages, it focuses on high-performance regions for fine-grained convergence. This alleviates the contradiction between insufficient early-stage exploration and insufficient late-stage convergence accuracy caused by fixed evolutionary parameters, improving the convergence accuracy and distribution uniformity of the Pareto non-dominated front. 3. This invention constructs a multi-stage dynamic closed-loop mechanism encompassing optimized search, uncertainty triggering, on-demand CFD verification, online incremental learning, surrogate model updating, sensitivity recalculation, and search partition adjustment. During the optimization iteration process, high-fidelity CFD verification is automatically triggered in regions where the uncertainty of the physical residual neural network prediction exceeds a threshold. New data is used to update the surrogate model in real time through incremental learning, and sensitivity and parameter space partitioning are recalculated synchronously. This effectively improves upon the shortcomings of existing methods where the surrogate model remains fixed after one-time training and cannot self-optimize using new data during the optimization process. This closed-loop mechanism can reduce the number of high-fidelity CFD evaluations and improve the engineering reliability of the output non-dominated solution set while achieving the same convergence accuracy. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method steps in an embodiment of the present invention; Figure 2 This is a schematic diagram of the system flow in an embodiment of the present invention. Detailed Implementation

[0018] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that the description of these embodiments is for the purpose of helping to understand the present invention, but does not constitute a limitation of the present invention.

[0019] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0020] Please see the appendix Figure 1 - Appendix Figure 2 The present invention provides a method for optimizing turbine blade design parameters based on artificial intelligence, comprising the following steps: Step 1: Determine the design variables, multi-condition optimization objectives and parameter constraint boundaries of the turbine blade, generate an initial sample set using the optimized Latin hypercube experimental design method, complete the three-dimensional viscous flow field high-fidelity CFD simulation of all samples, and construct an initial training sample database containing geometric parameters and corresponding performance labels. Step 2: Construct a coarse-grained physical benchmark model based on one-dimensional average streamline analysis and two-dimensional S2 flow surface flow calculation, input design parameters and output benchmark performance prediction values ​​with natural physical consistency; Step 3: Construct a physical residual neural network with embedded multi-dimensional physical constraint regularization terms. Use the performance residual between the high-fidelity CFD simulation results and the physical benchmark model as the training target to complete the initial training, and then superimpose the combined performance prediction results. Step 4: Based on the trained physical residual neural network, calculate the Sobol global sensitivity index of each design parameter using the quasi-Monte Carlo method, adaptively divide the parameter space into three levels, and configure the search resolution and evolution operator step size differently. Step 5: Estimate the prediction uncertainty of the physical residual neural network based on the Monte Carlo random deactivation mechanism, construct an adaptive balance between exploration and utilization composite acquisition function, and embed it as an additional optimization dimension into the framework of the third-generation non-dominated sorting genetic multi-objective evolutionary algorithm. Step 6: During the optimization iteration process, high-fidelity CFD verification is triggered for candidate solutions whose prediction uncertainty exceeds the threshold. The physical residual neural network is updated online in an incremental learning manner, the sensitivity index is recalculated synchronously, and the parameter partitions are dynamically adjusted to form a closed-loop optimization mechanism. Step 7: Perform multiple rounds of closed-loop iteration until the preset convergence criteria are met, output the final Pareto non-dominated solution set, and select the design parameter scheme applicable to the project. Example

[0021] This embodiment takes the aerodynamic optimization of the first-stage moving blade of a certain type of heavy-duty gas turbine as the application scenario, and carries out parameter optimization with the goal of improving the isentropic efficiency of the blade. The specific implementation process is as follows.

[0022] The first step is to determine the design variables, optimization objectives, and constraint boundaries.

[0023] Twelve geometric and aerodynamic parameters were selected as design variables: radial coordinates of four control points on the blade profile arc, three control parameters of blade profile thickness distribution, blade installation angle, inlet airflow angle, outlet airflow angle, number of blades, and tip clearance. The optimization objective was to achieve the highest isentropic efficiency of the blade under the design conditions. The constraint boundaries of each design variable were set with upper and lower limits based on the engineering design specifications of the blade stage, and all parameters were taken within the engineering feasible range.

[0024] An optimized Latin hypercube experimental design method was used to generate 120 initial samples. Numerical calculations of all samples were completed using three-dimensional viscous flow field CFD simulation software to obtain performance parameters such as isentropic efficiency, total pressure recovery coefficient, and outlet airflow angle for each sample, thus constructing an initial training sample database.

[0025] In this embodiment, the isentropic efficiency of the initial baseline design is 91.20%, and the highest isentropic efficiency in the initial sample set is 91.82%.

[0026] The second step is to construct a coarse-grained physical baseline model.

[0027] Based on the one-dimensional average streamline analysis method and the two-dimensional S2 flow surface flow calculation method, a physical benchmark model of the stage blade is constructed. The above 12 design parameters are input, and the flow is solved based on the simplified form of the mass conservation, momentum conservation and energy conservation equations. The benchmark performance prediction values ​​of isentropic efficiency, total pressure recovery coefficient and outlet airflow angle are output.

[0028] The model takes no more than 1 second for a single evaluation, and the prediction results naturally satisfy the Euler equation, continuity equation and basic thermodynamic constraints of turbomachinery, providing a physically sound baseline for subsequent residual learning.

[0029] Taking the initial baseline design as an example, the physical baseline model predicts an isentropic efficiency of 90.35%, with a relative deviation of 0.93% from the CFD calculation value, demonstrating reliable baseline accuracy.

[0030] The third step is to train a physical residual neural network with embedded physical constraint regularization.

[0031] Using 12 design parameters as network inputs and the performance residual between CFD simulation results and physical baseline model predictions as the fitting target, a physical residual neural network with four hidden layers was constructed, with the number of hidden layer neurons being 64, 32, 16, and 8, respectively, and the LeakyReLU function was used as the activation function.

[0032] The formula for calculating performance residuals is: ; In the formula, The performance residual between high-fidelity CFD simulation results and physical baseline model predictions, These are the calculated performance parameters obtained from high-fidelity CFD simulations. The baseline performance predictions are output by the physical baseline model.

[0033] Taking the initial baseline design as an example, the calculation is performed as follows: , The performance residuals were calculated. The residual amplitude is approximately 0.93% of the total performance value, which is consistent with the characteristic that the residual amplitude is much smaller than the total performance value.

[0034] The formula for calculating the total loss function during network training is: ; In the formula, This represents the total loss function value during the training of the physical residual neural network. This is the mean squared error loss term for residual prediction. As a continuous residual penalty term, a mass conservation constraint is imposed on the partial derivative of the output with respect to the mass flow rate parameter using automatic differentiation techniques. As a thermodynamic compatibility penalty term, a soft constraint is imposed on the physically feasible interval of the efficiency prediction value. As a smoothness penalty term, regularization is applied to the Frobenius norm of the Hessian matrix of the output with respect to geometric parameters to suppress numerical noise overfitting. , , The weight coefficients corresponding to each constraint term are adaptively determined through Bayesian hyperparameter optimization, and their initial optimized values ​​are 0.15, 0.10, and 0.05, respectively.

[0035] After training, the total loss on the test set is 2.1 × 10⁻⁵, of which the mean squared error loss term is 1.6 × 10⁻⁵. -5 The three constraint terms contribute a total of 0.5 × 10 -5 The mean absolute error of the network residual prediction is 0.12%.

[0036] The network was initially trained using the initial sample database, with 200 training rounds. After training, the residual predictions from the network were superimposed with the outputs from the physical baseline model to obtain the final combined performance prediction results.

[0037] The fourth step is to calculate the global sensitivity of Sobol and partition the parameter space.

[0038] Based on the trained physical residual neural network, 50,000 sampling points were generated using the quasi-Monte Carlo sampling method, and the first-order sensitivity index and the total effect sensitivity index of each design parameter to the isentropic efficiency target were calculated.

[0039] First-order sensitivity index Sensitivity index of total effect The calculation formula is as follows: ; In the formula, To optimize the target's performance predictions, For the first One design parameter, To exclude the first All other design parameters besides the one parameter, This is the variance operator. This is the conditional expectation operator.

[0040] In this embodiment, the calculated total effect sensitivity index of the outlet airflow angle is 0.342, the blade installation angle is 0.276, the mid-curve trailing edge control point is 0.158, the blade tip clearance is 0.021, and the thickness leading edge control point is 0.017; the 70th percentile threshold of the total effect sensitivity index distribution is 0.120, and the 30th percentile threshold is 0.035.

[0041] Using the 70th and 30th percentiles of the total effect sensitivity index distribution as partition thresholds, the 12 design parameters are divided into three levels: the three parameters with a total effect index not lower than the 70th percentile (exit airflow angle, blade installation angle, and mid-curve trailing edge control point) are the core parameter zone, configured with a denser search grid and a smaller variable asynchrony length; the four parameters with a total effect index lower than the 30th percentile (blade tip clearance, thickness leading edge control point, thickness trailing edge control point, and number of blades) are the edge parameter zone, configured with a coarser search grid and a larger variable asynchrony length; the remaining five parameters are the medium parameter zone, maintaining the baseline search resolution.

[0042] The fifth step is to construct a composite acquisition function and embed an evolutionary algorithm.

[0043] Monte Carlo random deactivation mechanism is used to estimate the prediction uncertainty of the network. During the inference phase, the randomly deactivated layers are kept active with a deactivation probability of 0.1. 30 random forward propagations are performed, and the standard deviation of the 30 prediction results is used as the corresponding parameter points. Corresponding forecast uncertainty .

[0044] Construct an adaptive composite acquisition function, the calculation formula is as follows: ; In the formula, Design parameter points The corresponding composite acquisition function value, For any parameter point in the design parameter space, For parameter points The predicted combined performance value at the location, This represents the maximum predicted performance value in the current population. For parameter points The predicted standard deviation at that location The maximum prediction standard deviation in the current population. To achieve an adaptive balance coefficient, the initial optimization stage uses a value of 0.2, which is linearly increased by 0.1 after each outer iteration cycle, and finally increased to 0.8 in the final iteration stage.

[0045] Taking a candidate solution from the first outer iteration cycle as an example, we substitute it into the calculation: ; Calculated acquisition function value .

[0046] The composite acquisition function is embedded as an additional optimization dimension into the third-generation non-dominated sorting genetic algorithm framework. The algorithm uses the DasandDennis systematic method to generate reference points, the population size is set to 200, and the step size of the crossover operator and mutation operator is configured differently according to the parameter space partitioning results. The step size of the core parameter area is 0.5 times the baseline value, and the step size of the marginal parameter area is 2 times the baseline value.

[0047] Step 6: Perform closed-loop incremental update.

[0048] During the algorithm iteration process, when the prediction uncertainty corresponding to the candidate solution... When the uncertainty threshold of 0.005 is exceeded, high-fidelity CFD simulation verification is automatically triggered. The newly obtained sample data is added to the training set, and the network is fine-tuned for 10 rounds using the stochastic gradient descent method with an exponentially decaying learning rate. The initial learning rate is 0.0001, and full retraining is not required.

[0049] After each network update, the Sobol global sensitivity index is recalculated, and the three-layer partitioning results of the parameter space and the evolution operator parameters are adjusted synchronously to ensure that the search strategy continuously adapts to the current model accuracy and parameter sensitivity distribution.

[0050] In this embodiment, 52 on-demand CFD verifications were triggered in 6 outer layer iteration cycles, and a total of 172 sets of high-fidelity CFD calculations were completed. The average absolute error of the surrogate model in the Pareto front region decreased from the initial 0.18% to 0.07%.

[0051] Step 7: Convergence determination and result output.

[0052] This embodiment executes a total of 6 outer iteration cycles. The iteration terminates when two convergence conditions are met: first, the rate of change of the hypervolume index of two consecutive generations of Pareto non-dominated fronts is less than 1%, and the rate of change of the hypervolume index of the 5th to 6th generations in this embodiment is 0.72%; second, the prediction uncertainty of all solutions of the front is less than 0.002, and the maximum prediction uncertainty of the final front solution is 0.0016.

[0053] After the iteration terminates, the Pareto non-dominated parameter solution set is output. The isentropic efficiency of the optimal solution in the solution set is 92.47%, which is 1.27 percentage points higher than the initial baseline design. Applicable blade design schemes can be obtained by combining the engineering design requirements and using the combined weighting method. Example

[0054] This embodiment takes the multi-objective optimization of the long blades of the last stage of a certain type of steam turbine as the application scenario, while taking into account both aerodynamic efficiency and structural strength performance. The specific implementation process is as follows.

[0055] The first step is to determine the design variables, multi-objective optimization functions, and constraint boundaries.

[0056] Ten geometric parameters were selected as design variables, including impeller outlet diameter, front and rear cover plate inclination angle, front and rear cover plate arc radius, blade inlet width, blade outlet placement angle, blade wrap angle, and number of blades. The optimization objectives included two aspects: maximizing isentropic efficiency under design conditions and minimizing maximum equivalent stress on the blades. The constraint boundaries of each design variable were set based on the strength design specifications and aerodynamic design criteria for the last-stage long blades.

[0057] One hundred initial samples were generated using an optimized Latin hypercube experimental design method. The performance of all samples was calculated through gas-thermal-solid coupling simulation. The isentropic efficiency and maximum equivalent stress data of each sample were obtained, and an initial training sample database was constructed.

[0058] The second step is to construct a coarse-grained physical benchmark model with multiple physical quantities.

[0059] For aerodynamic performance targets, a one-dimensional flow method is used to construct an aerodynamic benchmark model; for structural strength targets, a simplified cantilever beam mechanical model is used to construct a strength benchmark model.

[0060] Both types of benchmark models take design parameters as input and output efficiency benchmark values ​​and stress benchmark values ​​respectively. Their calculation results naturally satisfy the basic physical constraints of fluid mechanics and materials mechanics, providing a two-dimensional benchmark for dual-objective residual learning.

[0061] The third step is to train a multi-output physical residual neural network.

[0062] Using 10 design parameters as network inputs and the two-dimensional residuals of the physical baseline values ​​corresponding to the CFD and structural simulation results as the fitting target, a multi-output physical residual neural network was constructed. Three hidden layers and two output channels were set, and the LeakyReLU function was used as the activation function.

[0063] The total loss function for network training includes a mean squared error term for the two objectives and a constraint regularization term corresponding to the two types of physical quantities. The weights of each constraint term are adaptively determined through Bayesian hyperparameter optimization.

[0064] After initial training, the network outputs bi-objective residual predictions, which are then superimposed with the corresponding physical baseline values ​​to obtain the combined performance prediction results.

[0065] The fourth step is multi-target sensitivity calculation and dynamic partitioning.

[0066] Based on the trained multi-output physical residual neural network, the sensitivity index of the total effect of each design parameter on the two objectives of isentropic efficiency and maximum equivalent stress is calculated by quasi-Monte Carlo sampling. The weighted comprehensive value of the sensitivity of the two objectives is taken as the basis for partitioning.

[0067] The parameter space is divided into three levels—core, intermediate, and peripheral—based on the distribution quantiles of overall sensitivity. Fine-grained evolution step sizes are configured for core parameters, while coarser evolution step sizes are configured for peripheral parameters, thereby achieving a biased allocation of computing resources towards parameters with high impact.

[0068] Step 5: Guided search using acquisition functions in multi-target scenarios.

[0069] The Monte Carlo random deactivation mechanism is used to estimate the prediction uncertainty of two targets. A composite acquisition function adapted to multiple targets is constructed, and the adaptive balance coefficient is gradually increased with the iteration process to achieve a smooth transition from global exploration to local refinement.

[0070] The composite acquisition function and the two original optimization objectives are used together as the optimization dimensions of the evolutionary algorithm. The third-generation non-dominated sorting genetic algorithm is used to perform multi-objective evolutionary search. The population size is set to 180, and the number of reference points is adapted to the population size.

[0071] Step 6: Two-dimensional closed-loop incremental update.

[0072] During the iteration process, when the prediction uncertainty of any optimization objective exceeds the corresponding threshold, coupled simulation verification is triggered, new samples are added to the training set, and the network is incrementally fine-tuned.

[0073] After the network is updated, the dual-objective sensitivity index is recalculated synchronously, and the parameter partitioning strategy and evolution operator parameters are dynamically adjusted so that the search strategy continuously adapts to the parameter sensitivity distribution of the current optimization stage.

[0074] Step 7: Convergence and output of results.

[0075] This embodiment executes a total of 5 outer iteration cycles, and outputs the Pareto non-dominated solution set after the convergence condition is met.

[0076] All solutions within this solution set have been directly or indirectly verified by high-fidelity coupled simulation and can be directly used for engineering selection without the need for additional large-scale post-hoc verification work.

[0077] Summarize In summary, this invention improves the physical consistency of the surrogate model's predictions and the efficiency of data utilization from the root by constructing a two-layer surrogate architecture that combines a physical benchmark and a residual network; it achieves precise allocation of computing resources and intelligent balancing of the optimization process through sensitivity-driven adaptive partitioning and dynamic acquisition functions; and it continuously improves the accuracy of the surrogate model and the reliability of the optimization results with iteration through a closed-loop optimization mechanism involving multiple links.

[0078] This invention is adaptable to various turbine blade optimization scenarios, including single-objective and multi-objective optimization. It can effectively shorten the design cycle and reduce R&D costs, providing a reliable technical path for the intelligent design and optimization of turbine blades. It has good engineering application value and promotion prospects.

[0079] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any variations and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the invention, fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for optimizing turbine blade design parameters based on artificial intelligence, characterized in that, The process includes the following steps: Step 1: Determine the design variables, multi-condition optimization objectives and parameter constraint boundaries of the turbine blade, generate an initial sample set using the optimized Latin hypercube experimental design method, complete the three-dimensional viscous flow field high-fidelity CFD simulation of all samples, and construct an initial training sample database containing geometric parameters and corresponding performance labels. Step 2: Construct a coarse-grained physical benchmark model based on one-dimensional average streamline analysis and two-dimensional S2 flow surface flow calculation, input design parameters and output benchmark performance prediction values ​​with natural physical consistency; Step 3: Construct a physical residual neural network with embedded multi-dimensional physical constraint regularization terms. Use the performance residual between the high-fidelity CFD simulation results and the physical benchmark model as the training target to complete the initial training, and then superimpose the combined performance prediction results. Step 4: Based on the trained physical residual neural network, calculate the Sobol global sensitivity index of each design parameter using the quasi-Monte Carlo method, adaptively divide the parameter space into three levels, and configure the search resolution and evolution operator step size differently. Step 5: Estimate the prediction uncertainty of the physical residual neural network based on the Monte Carlo random deactivation mechanism, construct an adaptive balance between exploration and utilization composite acquisition function, and embed it as an additional optimization dimension into the framework of the third-generation non-dominated sorting genetic multi-objective evolutionary algorithm. Step 6: During the optimization iteration process, high-fidelity CFD verification is triggered for candidate solutions whose prediction uncertainty exceeds the threshold. The physical residual neural network is updated online in an incremental learning manner, the sensitivity index is recalculated synchronously, and the parameter partitions are dynamically adjusted to form a closed-loop optimization mechanism. Step 7: Perform multiple rounds of closed-loop iterations until the preset convergence criteria are met, output the final Pareto non-dominated solution set, and select the design parameter scheme applicable to the project.

2. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step one, the design variables include five types of geometric and aerodynamic parameters: blade profile arc control parameters, blade profile thickness distribution parameters, blade installation angle, number of blades, and inlet / outlet airflow angle. The optimization objectives cover two multi-objective directions: maximizing efficiency and minimizing load under design conditions and variable conditions. The parameter constraint boundaries are set with upper and lower limits based on turbine blade engineering design specifications. The high-fidelity CFD simulation outputs the isentropic efficiency, total pressure recovery coefficient, outlet airflow angle, and aerodynamic load performance parameters for each set of design parameters under all operating conditions.

3. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step two, the coarse-grained physical benchmark model is used to solve the flow path problem based on simplified forms of the mass conservation equation, momentum conservation equation, and energy conservation equation. The model takes no more than 1 second for a single evaluation, and its prediction results naturally satisfy the Euler equation, continuity equation, and basic thermodynamic constraints of turbomachinery, providing a physically sound benchmark for subsequent residual learning. The model output parameters include the isentropic efficiency, total pressure recovery coefficient, and outlet airflow angle benchmark performance prediction values ​​under the corresponding design parameters.

4. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step three, the formula for calculating the performance residual is: ； In the formula, The performance residual between high-fidelity CFD simulation results and physical baseline model predictions, These are the calculated performance parameters obtained from high-fidelity CFD simulations. The baseline performance prediction is the output of the physical baseline model; the total loss function for training the physical residual neural network is calculated using the following formula: ； In the formula, This represents the total loss function value during the training of the physical residual neural network. This is the mean squared error loss term for residual prediction. As a continuous residual penalty term, a mass conservation constraint is imposed on the partial derivative of the output with respect to the mass flow rate parameter using automatic differentiation techniques. As a thermodynamic compatibility penalty term, a soft constraint is imposed on the physically feasible interval of the efficiency prediction value. As a smoothness penalty term, regularization is applied to the Frobenius norm of the Hessian matrix of the output with respect to geometric parameters to suppress numerical noise overfitting. , , The weight coefficients corresponding to each constraint term are adaptively determined through Bayesian hyperparameter optimization.

5. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step four, the Sobol global sensitivity index includes a first-order sensitivity index. Sensitivity index of total effect The calculation formula is as follows: ； In the formula, For the first The first-order sensitivity index of each design parameter For the first The overall effect sensitivity index of each design parameter To optimize the target's performance predictions, For the first One design parameter, To exclude the first All other design parameters besides the one parameter, This is the variance operator. The conditional expectation operator is used; the parameter space has three levels: the core parameter region, the intermediate parameter region, and the marginal parameter region. The partition thresholds are the 70th and 30th quantiles of the total effect sensitivity index distribution. The core parameter region is configured with a dense search grid and a small variable asynchronous length, the marginal parameter region is configured with a coarse search grid and a large variable asynchronous length, and the intermediate parameter region maintains the baseline search resolution.

6. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step five, the prediction uncertainty is addressed by maintaining the activation of the random deactivated layer during the inference phase and performing 20 to 50 random forward propagations, using the standard deviation of multiple prediction results as the parameter point. Corresponding forecast uncertainty The composite acquisition function is calculated using the following formula: ； In the formula, Design parameter points The corresponding composite acquisition function value, For any parameter point in the design parameter space, For parameter points The predicted combined performance value at the location, This represents the maximum predicted performance value in the current population. For parameter points The predicted standard deviation at that location The maximum prediction standard deviation in the current population. To achieve adaptive balance, the initial optimization coefficient is set to 0.2 and then linearly increases to 0.8 with each iteration. The third-generation non-dominated sorting genetic algorithm uses the DasandDennis systematic method to generate reference points, and the step size of the crossover operator and mutation operator is configured differently according to the parameter space partitioning results.

7. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step six, the condition for triggering high-fidelity CFD verification is the uncertainty in the neural network prediction of the physical residual corresponding to the candidate solution. Exceeding the preset uncertainty threshold The preset uncertainty threshold is set in advance according to the accuracy requirements of the engineering design; the new sample data obtained from the verification is directly added to the training set, and the physical residual neural network is fine-tuned and updated in a small number of rounds using the stochastic gradient descent method with an exponentially decaying learning rate, without the need to perform full retraining; after each update of the physical residual neural network, the Sobol global sensitivity index is recalculated, and the three-layer partitioning results of the parameter space and the evolution operator parameters are dynamically adjusted synchronously.

8. The method for optimizing turbine blade design parameters based on artificial intelligence according to claim 1, characterized in that, In step seven, the convergence judgment condition includes two quantitative indicators: first, the rate of change of the hypervolume index of the Pareto non-dominated front for two consecutive generations is lower than the preset convergence threshold; second, the uncertainty of the physical residual neural network prediction corresponding to all solutions of the Pareto non-dominated front is lower than the preset accuracy threshold. After the iteration terminates, a complete Pareto non-dominated parameter solution set is output. Based on the combination weighting method and combined with the engineering design requirements, the final turbine blade design parameter scheme is obtained by screening from the solution set.

9. The artificial intelligence-based turbine blade design parameter optimization system according to any one of claims 1-8, characterized in that, The system includes a sample construction module, a physical benchmark model module, a residual network training module, a sensitivity partitioning module, an evolutionary search module, a closed-loop update module, and a convergence output module. The sample construction module is used to determine the design variables, multi-condition optimization objectives and parameter constraint boundaries of the turbine blade, generate an initial sample set using the optimized Latin hypercube experimental design method, complete the three-dimensional viscous flow field high-fidelity CFD simulation of all samples, and construct an initial training sample database containing geometric parameters and corresponding performance labels. The physical benchmark model module is used to construct a coarse-grained physical benchmark model based on one-dimensional average streamline analysis and two-dimensional S2 flow surface flow calculation, input design parameters and output benchmark performance prediction values ​​with natural physical consistency. The residual network training module is used to construct a physical residual neural network with embedded multi-dimensional physical constraint regularization terms. The initial training is completed with the performance residual between the high-fidelity CFD simulation results and the physical benchmark model as the training target, and the combined performance prediction results are superimposed and output. The sensitivity partitioning module is used to calculate the global sensitivity index of each design parameter based on the trained physical residual neural network using the quasi-Monte Carlo method, adaptively divide the parameter space into three levels and differentiate the search resolution and evolution operator step size. The evolutionary search module is used to estimate the prediction uncertainty of the physical residual neural network based on the Monte Carlo random inactivation mechanism, construct an adaptive balance between exploration and utilization composite acquisition function, and embed it as an additional optimization dimension into the framework of the third-generation non-dominated sorting genetic multi-objective evolutionary algorithm. The closed-loop update module is used to trigger high-fidelity CFD verification for candidate solutions whose prediction uncertainty exceeds the threshold during the optimization iteration process. It updates the physical residual neural network online in an incremental learning manner, synchronously recalculates the sensitivity index and dynamically adjusts the parameter partitions to form a closed-loop optimization mechanism. The convergence output module is used to perform multiple rounds of closed-loop iteration until the preset convergence judgment condition is met, output the final Pareto non-dominated solution set, and filter to obtain the design parameter scheme applicable to the project.

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