A turbine cooling blade optimization method and system based on a proxy model and uncertainty quantification
By using a proxy model and uncertainty quantification approach, combined with a multi-objective genetic algorithm to optimize the key geometric parameters of turbine cooling blades, the problem of insufficient robustness in traditional methods is solved, and stable performance optimization and computational efficiency improvement are achieved under varying operating conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-03-06
- Publication Date
- 2026-06-12
AI Technical Summary
Traditional turbine cooling blade optimization methods lack robustness analysis, have low optimization efficiency, are sensitive to operating condition fluctuations and manufacturing tolerances, and rely on high-fidelity CFD simulation, resulting in high computational costs and difficulty in maintaining stable performance under varying operating conditions.
A surrogate model-based and uncertainty quantification approach is adopted, combined with a multi-objective genetic algorithm. By establishing a global surrogate model and unstructured mesh partitioning, the influence of design parameters and operating condition fluctuations is quantified, the key geometric parameters of turbine cooling blades are optimized, and iterative optimization is performed using a multi-objective genetic algorithm. Combined with uncertainty propagation analysis, robust design is achieved.
It significantly improves the design stability and computational efficiency of turbine cooling blades, can suppress performance fluctuations under fluctuating operating conditions and manufacturing tolerances, provides a visualized performance-stability trade-off, and enables efficient and robust design.
Smart Images
Figure CN122197705A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computational fluid dynamics (CFD) and turbine cooling structure optimization technology, specifically involving a turbine cooling blade optimization method and system based on surrogate model and uncertainty quantification. Background Technology
[0002] The improvement of modern aero-engine performance largely depends on the continuous increase in the temperature of the high-pressure turbine inlet gas. With the increase in thrust-to-weight ratio and combustion efficiency, turbine inlet temperatures have far exceeded the temperature resistance limits of metal blade materials, placing extremely high demands on blade thermal protection design. To ensure the safe operation of blades under high-temperature conditions, cooling technology has become a key means. Among these, film cooling (FSU) involves injecting cool gas onto the blade surface to form a low-temperature gas film between the high-temperature gas and the metal wall, effectively reducing heat flux density and wall temperature gradient, thereby significantly improving blade life and thermal efficiency. Therefore, the design and performance optimization of the film cooling structure of turbine blades is one of the core aspects of aero-engine design.
[0003] Optimization of turbine cooling blades is a typical multivariable, strongly nonlinear, and multi-objective coupled problem. Cooling structure parameters and operating condition parameters jointly determine the blade's heat load distribution and cooling efficiency. Traditional optimization methods are mostly based on deterministic assumptions, assuming that geometric parameters and operating conditions remain constant. Under this assumption, designers typically analyze the cooling effect of different parameter combinations through extensive CFD simulations and seek the optimal solution using surrogate models or multi-objective algorithms. However, in actual engineering, blade geometry has manufacturing errors, and cooling airflow and combustion conditions fluctuate, leading to significant changes in cooling performance under different conditions. This makes it difficult to maintain the stability of traditional deterministic optimization results in practical applications. In other words, traditional methods ignore uncertainties in the design and cannot guarantee the robust performance of blades under varying operating conditions. Furthermore, traditional optimization processes heavily rely on high-fidelity CFD simulations. Due to the numerous micro-channels and complex flow regions in the cooling structure, high-density meshing is usually required in the cooling holes and film cooling regions to ensure accuracy, resulting in a huge time consumption for a single simulation. If thousands of sample points need to be evaluated in the optimization, the computational cost will increase exponentially, severely limiting the efficiency of design iteration. Summary of the Invention
[0004] The purpose of this invention is to address the problems of lack of robustness analysis, low optimization efficiency, and sensitivity to tolerance and operating condition fluctuations in existing blade cooling optimization methods. This invention provides a robust optimization method and system for turbine cooling blades based on a surrogate model and a multi-objective genetic algorithm, which takes into account blade machining errors and operating condition fluctuations.
[0005] In a first aspect, the present invention provides a turbine cooling blade optimization method based on a surrogate model and uncertainty quantification, comprising:
[0006] Sampling intervals were established for the key geometric parameters and operating condition parameters of the turbine cooling blades. Sampling was performed in each sampling interval to form a dataset containing multiple samples.
[0007] For each sample, a corresponding blade geometry model was established, and computational fluid dynamics simulation was performed to obtain the key thermal response quantities of different samples.
[0008] A global proxy model for predicting key thermal response quantities based on key geometric parameters and operating condition parameters is established and trained using a dataset.
[0009] A multi-objective genetic algorithm was used to iteratively optimize the key geometric parameters of the turbine cooling blades, yielding the optimized results. The fitness of individuals in the multi-objective genetic algorithm was obtained as follows: based on the probability distribution of machining errors and operating condition fluctuations in the key geometric parameters of each individual, corresponding perturbation points were generated. A global surrogate model was then used to predict the key thermal response quantity corresponding to each perturbation point. The expected value and / or variance of the key thermal response quantity at each perturbation point were used as the fitness of the corresponding individual.
[0010] Preferably, the multi-objective genetic algorithm uses a bi-objective fitness function based on minimizing the expectation and variance of key thermal response quantities. The optimization results of the key geometric parameters of the turbine cooling blades are selected from the Pareto front solution set obtained by iterative optimization.
[0011] Preferably, the expectation and variance of the key thermal response quantities are obtained by performing uncertainty propagation analysis on the prediction results of the global proxy model.
[0012] Preferably, the global surrogate model employs a Kriging model based on Gaussian process regression, and hyperparameters are optimized using maximum likelihood estimation or cross-validation. The key geometric parameters of each sample in the dataset are normalized before training the global surrogate model.
[0013] Preferably, before computational fluid dynamics simulation, a three-dimensional computational domain is constructed for the blade geometric model and unstructured mesh generation is performed. During the unstructured mesh generation process, local mesh refinement is performed on the leading edge, trailing edge, and around the film cooling holes, and the minimum element size is refined in high-gradient regions including the film cooling hole outlet and hole wall.
[0014] Preferably, the key geometric parameters include the diameter of the air film pore, the expansion angle, the angle between the pore axis and the Z-axis, and the width of the impact pore.
[0015] Preferably, the operating conditions include the total temperature and total pressure at the front air inlet.
[0016] Preferably, the key thermal response quantity is the average temperature of the blade surface.
[0017] As a preferred method, samples that are evenly distributed in each sampling interval are obtained by using the Latin hypercube sampling method.
[0018] Secondly, the present invention provides a turbine cooling blade optimization system for performing the aforementioned turbine cooling blade optimization method. The turbine cooling blade optimization system includes a sampling module, a modeling module, a simulation module, a surrogate prediction module, and a robust optimization module.
[0019] The sampling module is used to establish multiple samples containing key geometric parameters and operating condition parameters, as well as to establish the probability distribution of key geometric parameters under the influence of machining errors and the probability distribution of operating condition parameters under operating condition fluctuations.
[0020] The modeling module is used to establish blade geometric models with different key geometric parameters and to perform unstructured mesh generation.
[0021] The simulation module is used to perform computational fluid dynamics simulation on each sample to obtain the corresponding key thermal response quantities.
[0022] The surrogate prediction module is used to establish a global surrogate model based on the key geometric parameters, operating condition parameters and corresponding key thermal response quantities of different samples, and to use the global surrogate model to predict the key thermal response quantities of different disturbance points.
[0023] The robustness optimization module is used to iteratively optimize key geometric parameters using the expectation and / or variance of key thermal response quantities at different disturbance points as fitness.
[0024] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program that can run on the processor; when the processor executes the computer program stored in the memory, it implements the aforementioned turbine cooling blade optimization method.
[0025] Fourthly, the present invention provides a readable storage medium storing a computer program; when the computer program is executed by a processor, it implements the aforementioned turbine cooling blade optimization method.
[0026] The present invention has the following beneficial effects.
[0027] 1. Achieving robust optimization design and improving design stability. This invention introduces an uncertainty quantification mechanism on the basis of traditional deterministic optimization. By quantifying the impact of design parameters and operating condition fluctuations on cooling performance, the output mean and variance are directly used as optimization targets. Compared with traditional methods that only pursue optimal performance, this invention can effectively suppress performance fluctuations under operating condition fluctuations and manufacturing tolerance conditions, thereby significantly improving the robustness and stability of blade cooling design.
[0028] 2. Significantly improved computational efficiency. This invention uses a surrogate model to replace high-fidelity CFD simulation, enabling rapid prediction of cooling performance indicators from input parameters and avoiding a large amount of repetitive calculations. Based on this, multi-objective optimization and uncertainty analysis in high-dimensional design spaces can be completed under limited resource conditions, resulting in a significant improvement in overall efficiency.
[0029] 3. Efficient Integration of Uncertainty Quantification and Multi-Objective Optimization. This invention embeds the uncertainty analysis process into a multi-objective genetic algorithm framework, enabling simultaneous uncertainty propagation and optimization iteration. This integrated design avoids the fragmented process of "quantification before optimization," and can dynamically evaluate the average performance level and stability during the optimization process, thereby obtaining a robust design scheme with optimal overall performance.
[0030] 4. The optimization results are quantifiable and highly interpretable. This invention obtains the mean and variance of the output through uncertainty quantification, which can directly characterize the sensitivity of blade performance to geometric and operating condition fluctuations; combined with the Pareto front obtained by the genetic algorithm, it can clearly show the trade-off between performance and stability, providing a visualized and interpretable decision-making basis for engineering design. Attached Figure Description
[0031] Figure 1 This is an optimized flowchart of an embodiment of the present invention.
[0032] Figure 2 This is a fitness calculation graph based on the combination of uncertainty quantization in an embodiment of the present invention.
[0033] Figure 3 This is a schematic diagram of the fluid domain of the simulation model in an embodiment of the present invention.
[0034] Figure 4 This is a sampling result diagram of key geometric parameters in an embodiment of the present invention.
[0035] Figure 5 This is a diagram showing the accuracy evaluation results for the global proxy model in an embodiment of the present invention.
[0036] Figure 6 The image shows the Pareto front results obtained through optimization in an embodiment of the present invention.
[0037] Figure 7 This is a comparison diagram of the blade surface temperature before and after optimization in an embodiment of the present invention. Detailed Implementation
[0038] The present invention will be further described below with reference to the accompanying drawings.
[0039] Example
[0040] A turbine cooling blade optimization method based on surrogate models and uncertainty quantification is proposed to achieve efficient uncertainty analysis and optimization of cooling structure design under limited computational resources. Given the high computational cost and difficulty in using traditional high-fidelity CFD for large-scale multi-parameter searches, this embodiment introduces surrogate models and uncertainty quantification methods, and utilizes a multi-objective genetic algorithm to construct a robust design process suitable for turbine blade cooling structures.
[0041] In this embodiment, the optimized object is the high-pressure turbine guide vane, and optimization is performed on four key geometric parameters in the film cooling structure. The four key geometric parameters are the film cooling orifice diameter, expansion angle, the angle between the orifice axis and the Z-axis, and the impact orifice width.
[0042] The optimization objective of this embodiment is to obtain the optimal combination of geometric parameters that maintains stable cooling performance under varying operating conditions, given fluctuations in the total temperature and pressure at the front air inlet and manufacturing errors in the geometric parameters. The optimization indices are the mean and variance of the average temperature on the blade surface, used to measure the cooling performance level and its stability, respectively.
[0043] like Figure 1 As shown, the turbine cooling blade robustness optimization method provided in this embodiment includes four main stages: sampling of optimization variables and uncertainty parameters, generation of geometric and operating condition samples, establishment of a global surrogate model, and robustness optimization calculation. This embodiment achieves a closed loop from input uncertainty description to robust design solution through multi-stage coupling. The specific processes of the above four main stages are as follows:
[0044] Phase 1: Sampling of Optimization Variables and Uncertainty Parameters
[0045] In this phase, key design and operating condition variables affecting the thermal-flow behavior of turbine cooling blades are first sampled across the entire input parameter space. The ranges of the four key geometric parameters used as inputs are determined based on blade structural design requirements, typical operating conditions, and empirical statistical data. Simultaneously, considering typical manufacturing errors, appropriate probability distributions are established according to the physical sources of variation for each key geometric parameter to characterize uncertainties such as manufacturing deviations and operating condition fluctuations. To reflect fluctuations in engine operating conditions, corresponding uncertainty ranges and probability distributions are set for the total temperature and total pressure at the front cooling air inlet.
[0046] To ensure that a limited number of samples can fully reflect the changing characteristics of the high-dimensional input space, this embodiment employs the Latin hypercube sampling method to generate sample points. This type of sampling method can evenly distribute samples within each parameter interval, thereby reducing sample clustering or gaps caused by randomness and improving overall sampling efficiency. The number of samples is determined based on a comprehensive consideration of the input dimension, the degree of parameter coupling, and the strength of nonlinearity in the system response to ensure sufficient information for subsequent surrogate modeling and uncertainty propagation analysis. The sampling results of this embodiment are as follows: Figure 4 As shown.
[0047] Phase Two: Generation of Geometry and Corresponding Working Condition Samples
[0048] After sampling the input parameters, a corresponding blade geometric model is generated for each set of samples. To accommodate the modeling needs brought about by a large number of samples, this embodiment constructs an automated generation strategy for blade cooling geometry based on parametric description. By embedding optimization variables into the parametric framework of the blade's 3D geometry, the update of geometric features can be directly driven according to the input samples, enabling batch model construction.
[0049] After the 3D geometry is generated, a 3D computational domain is constructed for each sample and meshed. Considering the complex 3D structure of the blade, such as... Figure 3 As shown, this embodiment uses an unstructured mesh to discretize the computational domain, improving the geometric matching capability for high-curvature surfaces and micro-cooling hole regions. Local mesh refinement is applied to the leading and trailing edges of the blades and around the film cooling holes to enhance the analytical capability for temperature gradients, shear layers, and mixing regions. The minimum element size is further refined in high-gradient regions such as the film cooling hole outlet and hole walls to ensure accurate capture of the jet flow structure and film adhesion behavior.
[0050] High-fidelity CFD simulations were performed on the blade geometric models corresponding to different samples after mesh generation to extract key thermal response quantities, thereby constructing an input-output dataset for training the surrogate model. The dataset includes key geometric parameters and corresponding key thermal response quantities for multiple different samples. The key thermal response quantities include the average surface temperature of the blade.
[0051] Phase 3: Establishment of the Global Proxy Model
[0052] After completing batch geometry construction and high-fidelity CFD simulation, this embodiment uses the data obtained in step two to establish and train a global surrogate model for the turbine cooling blades, replacing the computationally expensive numerical solution process. To satisfy the highly nonlinear characteristics of the turbine cooling system, this embodiment employs a Kriging method based on Gaussian process regression to construct a mapping relationship between input parameters and the average surface temperature of the blades, serving as the surrogate model.
[0053] The Kriging agent model views the system response as consisting of a globally deterministic trend term and a spatially correlated stochastic process, which can be expressed as:
[0054]
[0055] in, For input parameters The predicted value below, For global regression terms, It is a random process with zero mean and controlled by Gaussian covariance.
[0056] To ensure the accuracy and robustness of the surrogate model, this embodiment normalizes the input parameters before modeling to reduce the impact of dimensional differences on modeling stability. At the same time, based on the range of variation and physical meaning of the input parameters, an appropriate covariance function is selected to provide a basic structure for model building.
[0057] Subsequently, the hyperparameters of the model are optimized using maximum likelihood estimation or cross-validation. This process iteratively solves for the optimal parameters, ensuring the global surrogate model can both fit the training samples and maintain good generalization performance. To evaluate model accuracy, this embodiment uses metrics such as the coefficient of determination, root mean square error, and prediction error distribution to test the performance of the global surrogate model on the sample set. The model evaluation results of this embodiment are as follows: Figure 5 As shown, once the surrogate model achieves the predetermined accuracy requirements across all metrics, it can be used as a rapid prediction tool for subsequent robust optimization calculations.
[0058] After model training is complete, the surrogate model can perform a cooling performance prediction within milliseconds, reducing computation time by hundreds to thousands of times compared to CFD calculations. Through this surrogate model, this invention enables rapid evaluation of a large number of perturbation samples during robust optimization, significantly reducing computational costs and providing efficient support for uncertainty quantification and multi-objective optimization.
[0059] Phase 4: Robust Optimization Calculation
[0060] After constructing a high-precision global surrogate model, the process moves to the multi-objective genetic algorithm optimization stage based on uncertainty quantification. This stage combines surrogate model prediction, uncertainty propagation analysis, and the non-dominated sorting genetic algorithm (NSGA-II) to achieve comprehensive performance evaluation and robust optimization of geometric design parameters under various operating conditions and machining errors.
[0061] During the optimization process, each individual in the population represents a set of geometric design parameters. In each iteration, corresponding perturbation samples are first generated based on the geometric variables of the individual, including operating condition fluctuation samples and geometric error samples. For each perturbation point, this embodiment utilizes the global surrogate model to quickly predict the blade's temperature response, thereby significantly reducing the computational overhead of the original CFD model during the iterative calculation phase.
[0062] like Figure 2 As shown, to characterize the statistical properties of the target quantity under uncertain input, this embodiment uses the PCE method to perform uncertainty propagation analysis on the predicted response. Let the average blade surface temperature response predicted by the surrogate model be... It can be expanded using PCE as follows:
[0063]
[0064] Where x is a deterministic geometric design parameter; Represents random variables arising from fluctuations in operating conditions and processing errors; These are orthogonal polynomial basis functions. The expansion coefficients are undetermined and obtained by regression or projection. For the index of the polynomial chaotic expansion term, The truncation order is the order of the highest polynomial used in the expansion.
[0065] This allows us to directly obtain the expected average surface temperature of the blade at multiple disturbance points corresponding to the same body. With variance As a multi-objective optimization evaluation index:
[0066]
[0067]
[0068] The mean temperature is used to measure the cooling performance level, while the variance reflects the sensitivity of the design to uncertainty and is a core indicator for robust optimization.
[0069] Based on the above statistics, this embodiment constructs a bi-objective fitness function:
[0070]
[0071]
[0072] This means that while ensuring overall cooling capacity, performance fluctuations are suppressed to the greatest extent possible, thereby optimizing stability.
[0073] The NSGA-II algorithm performs a global iterative search of four geometric parameters within the design space through non-dominated sorting, crowding distance calculation, and an elitist strategy. In each generation, the fitness of an individual is determined by the aforementioned uncertainty statistics (expectation and variance), followed by selection, crossover, and mutation operations to generate the next generation population. Thanks to the rapid response and predictive capabilities of the surrogate model, this embodiment can complete the evaluation and iteration of a large number of design points within an acceptable computational time, avoiding the massive computational burden caused by the reliance on CFD simulation in traditional methods during iterative optimization.
[0074] After multiple generations of evolution, a non-dominated solution set reflecting the trade-off between performance and robustness can be formed, i.e., the Pareto front. The Pareto front between performance and stability obtained in this embodiment is as follows: Figure 6 As shown, designers can select the geometric design scheme with the best overall performance in terms of cooling performance and stability from the Pareto front, based on specific engineering requirements.
[0075] The optimization results of this embodiment are as follows: Figure 7 As shown. From Figure 7 As can be seen, compared with the original scheme, the robust optimal design obtained in this embodiment can significantly reduce the mean blade temperature and significantly reduce the temperature variance, thus maintaining higher cooling performance stability under the combined effects of operating condition fluctuations and geometric errors. This embodiment verifies the effectiveness and engineering applicability of the robust optimization method proposed in this invention, providing an efficient and reliable technical path for the design optimization of turbine blade cooling structures.
[0076] This embodiment establishes an efficient, accurate, and robust turbine blade cooling optimization framework by integrating a Kriging surrogate model, uncertainty quantification, and a multi-objective genetic algorithm. This method significantly reduces sensitivity to geometric tolerances and operating condition fluctuations while ensuring cooling performance, providing a new technical path and theoretical support for the reliability design of complex hot-end components, and demonstrating outstanding engineering application prospects.
Claims
1. A turbine cooling blade optimization method based on surrogate model and uncertainty quantification, characterized in that: include: Sampling intervals were established for the key geometric parameters and operating condition parameters of the turbine cooling blades; Sampling is performed on each sampling interval to form a dataset containing multiple samples; For each sample, a corresponding blade geometry model was established, and computational fluid dynamics simulation was performed to obtain the key thermal response quantities of different samples. A global proxy model for predicting key thermal response quantities based on key geometric parameters and operating condition parameters was established and trained using a dataset. The key geometric parameters of the turbine cooling blades are iteratively optimized using a multi-objective genetic algorithm. The fitness of an individual is obtained by generating corresponding disturbance points based on the probability distribution of the machining error and operating condition fluctuations of the key geometric parameters of each individual. The key thermal response quantity corresponding to each disturbance point is predicted by a global surrogate model. The expected value and / or variance of the key thermal response at each perturbation point are used as the fitness of the corresponding individual.
2. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The multi-objective genetic algorithm uses a bi-objective fitness function based on minimizing the expectation and variance of key thermal response quantities; the optimization results of key geometric parameters of turbine cooling blades are selected from the Pareto front solution set obtained by iterative optimization.
3. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The global surrogate model adopts a kriging model based on Gaussian process regression, and the hyperparameters are optimized by maximum likelihood estimation or cross-validation. The key geometric parameters of each sample in the dataset are normalized before training the global surrogate model.
4. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: Before computational fluid dynamics simulation, a three-dimensional computational domain is constructed for the blade geometric model and an unstructured mesh is generated. During the unstructured mesh generation process, the local mesh is refined at the leading edge, trailing edge, and around the film cooling holes of the blade, and the minimum element size is refined in the high gradient region including the film cooling hole outlet and the hole wall.
5. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The key geometric parameters include the diameter of the air film pore, the expansion angle, the angle between the pore axis and the Z-axis, and the width of the impact pore.
6. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The operating conditions include the total temperature and total pressure at the front air inlet.
7. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The key thermal response quantity is the average surface temperature of the blade.
8. The turbine cooling blade optimization method based on surrogate model and uncertainty quantification according to claim 1, characterized in that: The Latin hypercube sampling method was used to obtain samples that were evenly distributed in each sampling interval.
9. A turbine cooling blade optimization system, characterized in that: The system is used to execute the turbine cooling blade optimization method as described in claim 1; the turbine cooling blade optimization system includes a sampling module, a modeling module, a simulation module, a surrogate prediction module, and a robust optimization module; The sampling module is used to establish multiple samples containing key geometric parameters and operating condition parameters, as well as to establish the probability distribution of key geometric parameters under the influence of machining errors and the probability distribution of operating condition parameters under operating condition fluctuations. The modeling module is used to establish blade geometric models with different key geometric parameters and to perform unstructured mesh generation; The simulation module is used to perform computational fluid dynamics simulation on each sample to obtain the corresponding key thermal response quantities. The proxy prediction module is used to establish a global proxy model based on the key geometric parameters, operating condition parameters and corresponding key thermal response quantities of different samples, and to use the global proxy model to predict the key thermal response quantities of different disturbance points. The robustness optimization module is used to iteratively optimize key geometric parameters using the expectation and / or variance of key thermal response quantities at different disturbance points as fitness.
10. A computer device, comprising a memory and a processor; wherein the memory stores a computer program executable on the processor; characterized in that: When the processor executes the computer program stored in the memory, it implements the turbine cooling blade optimization method as described in any one of claims 1-8.