Multi-objective optimization design method for labyrinth seal based on variable credibility proxy model and application

Abstract

The invention discloses a labyrinth seal multi-objective optimization design method based on a variable credibility proxy model and application, and the method comprises the steps: firstly defining a geometrical parameter of labyrinth seal as a design variable, and setting a minimum leakage rate and a total temperature rise as optimization objectives; secondly, generating an initial sample point set by adopting a sampling method, dividing the initial sample point set into high-fidelity samples and low-fidelity samples, respectively performing high-precision CFD simulation and low-precision CFD simulation, and constructing a multi-fidelity sample library; thirdly, an initial Kriging model is constructed based on the low-fidelity sample library, correction is carried out through the high-fidelity data, and a hierarchical Kriging proxy model fusing the multi-fidelity data is formed; and through model precision evaluation and variable credibility parallel expectation, a point adding strategy is improved, and sample supplementation and model optimization are realized. And finally, performing multi-target optimization by adopting an NSGA-II algorithm, obtaining a Pareto leading edge solution set, and finally screening an optimal structure parameter combination. The method is suitable for intelligent optimization design of the labyrinth seal structure under the condition of multiple working conditions and high-dimensional parameters, and has wide engineering application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimization design of aero-engine sealing structures, involving technologies such as multi-objective optimization, agent model construction, and sealing performance prediction. Specifically, it is a multi-objective optimization design method for grate seals based on a variable credibility agent model. This method can significantly reduce computational costs while ensuring prediction accuracy, thereby achieving efficient optimization and performance improvement of sealing structures under complex working conditions. Background Art

[0002] In aircraft engines, gaps inevitably form between rotating and stationary components. These gaps can lead to gas leakage, reducing engine efficiency and performance. Shrouded stator blades enhance blade stability, but the pressure differential creates a complex reverse cavity leakage flow between the inner stator shroud and the rotor, further exacerbating the leakage problem. To reduce leakage, grate seals, a non-contact seal, are widely used in aircraft engines. Research shows that for every 1% reduction in engine seal leakage, engine power increases by 1% and fuel consumption decreases by 0.1%. Therefore, improving the sealing performance of grate seals is crucial for extending component life and improving engine fuel efficiency.

[0003] A grate seal typically consists of multiple tooth elements arranged in sequence along the flow direction. Each tooth element is determined by parameters such as tooth height, tooth width, tooth spacing, and inclination angle. Its overall configuration can vary, including straight-through, staggered, and inverted. Through repeated expansion and compression between the teeth and the Reynolds turbulence effect, airflow energy is dissipated and pressure is reduced, achieving sealing. Compared to traditional labyrinth seals, grate seals offer significant advantages in terms of compactness, structural rigidity, and temperature adaptability. They are particularly well-suited for the complex structural layouts and high-temperature, high-pressure operating conditions found in the new generation of high-performance aircraft engines.

[0004] Traditional grate seal design methods often rely on theoretical analysis, empirical formulas, and experimental testing. Theoretical analysis is usually based on simplified flow models and is difficult to accurately capture the complex multi-physics field interactions that exist in actual engine environments. Empirical formulas are obtained by fitting experimental data under specific operating conditions and geometric parameters. Their applicability is limited and difficult to generalize to new design scenarios. Although experimental testing can provide relatively accurate performance evaluations, it is costly and time-consuming, making it difficult to meet the needs of rapid design iterations. In addition, traditional grate seal designs often use single-objective optimization methods, such as only considering minimizing leakage, while ignoring other important performance indicators such as temperature rise and vibration.

[0005] In recent years, CFD simulation-based grate seal design methods have gradually become mainstream. By establishing high-fidelity numerical models under typical operating conditions, more accurate leakage flow field distributions, temperature distributions, and fluid-structure interaction responses can be obtained. However, high-fidelity CFD simulations generally have high computational costs, making it difficult to generate large-scale sample data in a high-dimensional parameter space. Existing technologies, such as Chinese patents CN116011269A and CN109736720B, employ a single Kriging surrogate model but fail to address the challenges of high-fidelity data scarcity and low-fidelity prediction bias. While CN111625908A incorporates multi-constraint processing, its optimization efficiency is limited by a fixed point addition strategy. Consequently, the demand for more advanced optimization techniques is growing. However, optimizing labyrinth seals alone requires considering a wider range of geometric design variables, resulting in a high-dimensional design space. To efficiently explore optimal solutions within this complex design space, integrating advanced surrogate modeling techniques is imperative. A promising strategy for overcoming these challenges is the implementation of variable credibility surrogate models. These models integrate data from different fidelity levels to alleviate computational demands while maintaining accuracy.

[0006] In summary, the existing grate seal design methods have significant deficiencies in dealing with high-dimensional variables, multi-physical field coupling, multi-objective trade-offs, and adaptability to multiple working conditions. Therefore, how to achieve high-precision, high-efficiency, and high-robust multi-objective optimization design of grate seals with limited computing resources is a technical problem that needs to be urgently solved in the field of aero-engine sealing technology. Summary of the Invention

[0007] (1) Purpose of the invention This paper aims to propose a multi-objective optimization design method and application for grate seals based on a variable credibility proxy model. To address the large data requirements for high-dimensional variable optimization design of grate seals, a multi-objective optimization framework based on a hierarchical Kriging method and a variable credibility parallel expectation enhancement matrix addition strategy is established. This framework automatically allocates the number of additions for data of varying fidelity based on the proxy model's data requirements, reducing the computational resources required to build the proxy model. As the data increases, the constructed machine learning prediction model is continuously updated, improving model prediction accuracy. This method can be applied to different types of smooth grate seal optimization by varying the parameterization method.

[0008] (2) Technical solution In order to achieve the purpose of the invention and solve the technical problems, the present invention adopts the following technical solutions: The first object of the present invention is to provide a multi-objective optimization design method for a grate seal based on a variable credibility surrogate model, which is used to perform multi-objective optimization on the sealing performance and thermal performance of a grate seal structure for an aircraft engine in a high-dimensional design variable space while reducing computing resource consumption. The design method, when implemented, comprises at least the following steps: SS1. Design variables and optimization goal setting: The geometric parameters of the grate seal are defined as design variables. The multi-objective optimization objectives are set as minimizing leakage and minimizing total temperature rise. The upper and lower boundaries of each design variable and the structural manufacturability constraints are defined. SS2. Sample point generation and classification: Based on the sampling method, a uniformly distributed initial sample point set is generated in the high-dimensional constrained design space, and the sample point set is divided into high-fidelity samples and low-fidelity samples for high-precision and low-fidelity CFD simulations respectively. SS3. CFD simulation and multi-fidelity sample library construction: Perform corresponding CFD simulation calculations on high- and low-fidelity sample points respectively to obtain the corresponding leakage and total temperature rise response data, and build high- and low-fidelity sample libraries containing design variables and performance responses; SS4. Hierarchical Kriging surrogate model construction and training: First, an initial Kriging model is constructed based on a low-fidelity sample library. Then, the model is calibrated using the covariance matrix between the high-fidelity sample library data and the initial model prediction results to form a hierarchical Kriging proxy model that integrates multi-fidelity data. SS5. Surrogate model accuracy evaluation and iterative update: The prediction accuracy of the hierarchical Kriging surrogate model is evaluated. If the error of any objective function is higher than the set threshold, the convergence condition is not met, and the process proceeds to step SS6 to perform sample addition and model update until the prediction accuracy meets the convergence requirement, then proceeds to step SS7. SS6. Variable Credibility and Parallel Expectation Increase Point Strategy: Based on the predicted mean and variance of the current surrogate model, the variable credibility parallel expectation improvement matrix is used to batch increase high- and low-fidelity sample points in the optimization direction, and then return to execute steps SS3 to SS5; SS7. Multi-objective optimization and structural screening: Based on the hierarchical Kriging surrogate model, the NSGA-II algorithm is used to perform multi-objective optimization to obtain the Pareto frontier solution set, from which the optimal grate seal structure parameter combination is selected according to engineering application requirements. SS8. Optimized structure verification and iterative update: The selected optimal structure is verified by high-fidelity CFD simulation. If the error between the predicted value and the simulation result exceeds the set tolerance, the process returns to steps SS5 to SS8 and continues the optimization until convergence.

[0009] The second object of the present invention is to provide a grate seal, the structural design of which is based on the multi-objective optimization design method of the grate seal based on the variable credibility agent model of the present invention.

[0010] (3) Technical effects Compared with the prior art, the multi-objective optimization design method and application of the grate seal based on the variable credibility agent model of the present invention has the following beneficial and significant technical effects: 1. This paper employs a variable-credibility surrogate model, combining high-precision and low-precision CFD simulations to perform multi-objective optimization within a high-dimensional design space. By rationally allocating high- and low-fidelity sample points and implementing a desired point-adding strategy, this optimization framework can significantly save computing resources, reduce the cost of building surrogate models, and shorten the optimization design cycle while ensuring optimization accuracy. 2. This paper uses a hierarchical Kriging surrogate model, leveraging the correlation between high- and low-fidelity samples to perform error correction and model adjustments on the low-fidelity model's predictions, thereby improving the surrogate model's prediction accuracy. Furthermore, this paper employs cross-validation to evaluate the surrogate model's prediction accuracy and iterates based on the evaluation results to ensure the reliability of the optimization results.

[0011] 3. This method can simultaneously optimize the sealing and thermal performance of grate seals, meeting the multi-objective requirements of aircraft engine grate seal structures. Furthermore, by finding Pareto solutions for optimization problems under different operating conditions, this method can identify the optimal grate seal parameter combinations for each operating condition, thus improving the adaptability of the optimized grate seal structure. 4. This invention uses Latin hypercube sampling to generate the initial sample point set, ensuring representativeness across the entire design space. Furthermore, it employs a variable-credibility parallel expectation-raising matrix criterion to adaptively select high- and low-fidelity sample points, thereby enhancing the robustness and adaptability of the optimization algorithm. This method can be applied to various grate seal models by varying the parameterization method, broadening its applicability and promising future applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The accompanying drawings, which constitute part of the present invention, are provided to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are provided to explain the present invention and do not constitute undue limitations thereon. The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flow chart for the multi-objective optimization design of grate seals based on a variable credibility surrogate model; Figure 2 Schematic diagram of grate seal model construction and optimization parameters (design variables); Figure 3 Schematic diagram of a smooth staggered grate seal, where: (a) is the CFD model and boundary conditions, (b) is the high-fidelity model, (c) is the low-fidelity model, and (d) is the high-fidelity wall Y+.

[0013] Figure 4 Comparison diagram of the baseline structure and optimized structure of the grate seal.

[0014] Parameter description of the attached figure: h 1- tooth height of the first tooth, h 2- tooth height of the second tooth, h 3- tooth height of the third tooth, h 4- tooth height of the fourth tooth, h 5- tooth height of the fifth tooth, h 6- tooth height of the sixth tooth, p 1- the tooth spacing between the first and second teeth, p 2- the tooth spacing between the second and third teeth, p 3- the tooth spacing between the third and fourth teeth, p 4- the tooth spacing between the fourth and fifth teeth, p 5- tooth spacing between the fifth and sixth teeth, w 1-tooth width of the first tooth, w 2- the width of the second tooth, w 3- the width of the third tooth, w 4- the width of the fourth tooth, w 5-tooth width of the fifth tooth, w 6- the width of the sixth tooth, i 1- tooth rake angle of the first tooth, i 2- the back inclination angle of the first tooth, i 3- The inclination angle of the second tooth, i 4- the back inclination angle of the second tooth, i 5- The inclination angle of the third tooth, i 6- The back inclination angle of the third tooth, i 7- The inclination angle of the fourth tooth, i 8- The back inclination angle of the fourth tooth, i 9- tooth inclination angle of the fifth tooth, i 10 - the back inclination angle of the fifth tooth, i 11- tooth inclination angle of the sixth tooth, i 12 -The inclination angle of the sixth tooth. DETAILED DESCRIPTION

[0015] The present invention aims to propose a multi-objective optimization design method and application of a comb seal based on a variable credibility agent model. In order to make the purpose, technical solutions and advantages of the implementation of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are part of the embodiments of the present invention, not all of the embodiments, and the described embodiments are exemplary and do not limit the application of other comb seal structures and optimization methods. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0016] Figure 1 The optimization flow chart of the entire optimization framework of the multi-objective optimization design method for grate seals based on a variable credibility proxy model proposed in this invention is presented. The above optimization process can achieve multi-objective optimization of the grate seal as the optimization object. Specifically, the embodiment of the present invention includes the following main steps: SS1. Design variables and optimization goal setting: First, the structural parameters to be optimized for the smooth straight-through grate seal are clarified, such as Figure 2 As shown, the six tooth height parameters of the grate seal can be defined according to the optimization design requirements. h 1~ h 6. 5 tooth spacing parameters p 1~ p 5.6 tooth width parameters w 1~ w 6 and 12 tooth lead and back inclination parameters i 1~ i 12 , as a continuously adjustable design variable. And set up a dual-objective optimization problem, respectively with leakage Q Minimize the total temperature rise Δ T Minimization is the objective function. All design variables are set with constraints on manufacturability and structural rationality. For example, according to actual engineering requirements and structural manufacturability, the tooth height is limited. h ∈[0.8,1.5]mm, spacing between teeth p ∈[1.2,2.5]mm, each tooth width w ∈[0.3,0.8]mm, tooth front / back inclination angle i ∈[15°,45°], and finally a multi-objective optimization model with constraints is formed.

[0017] SS2. Sample point generation and classification: An initial set of sample points is generated based on an improved Latin hypercube sampling method. To address the inefficiency of the Latin hypercube sampling method under high-dimensional constraints, an embodiment of the present invention utilizes the formula for the uniformity of the distribution of data points within the exploration space in the Latin hypercube sampling method as the objective function. A genetic algorithm is then employed to optimize this objective within the high-dimensional constrained space, aiming to obtain a uniform set of points with good representativeness and global coverage within the constrained space for numerical calculations.

[0018] Afterward, based on a comprehensive consideration of model training and resource utilization efficiency, the samples were divided into high-fidelity and low-fidelity samples. The number of low-fidelity samples was set to be 2 to 5 times that of high-fidelity samples, used to construct high- and low-precision CFD simulation models, respectively. During the initial design phase, the number of high-fidelity sample points was set to be at least 3 times the number of design variables, and the number of low-fidelity sample points was set to be at least 10 times the number of design variables, to ensure the effectiveness and accuracy of subsequent surrogate model training.

[0019] SS3. CFD simulation and sample library construction: Corresponding CFD simulations are performed on high- and low-fidelity sample points, respectively, to obtain corresponding leakage and total temperature rise response data, and to construct high- and low-fidelity sample libraries containing design variables and performance responses. During parametric modeling and simulation calculations, the present invention utilizes Python program control to automatically execute the model, meshing, simulation calculations, and data collection. Simultaneously, data calculations of different fidelity levels are performed separately, and the calculation results are stored in different data sets.

[0020] Specifically, a geometric parameterized model is constructed based on the design variables of the grate seal to realize the automatic generation of the three-dimensional geometric model of the grate seal; the computational grid is automatically generated based on the preset meshing strategy; the solution parameters are automatically set and CFD calculations are performed based on the preset boundary conditions and calculation model; and the leakage and total temperature rise performance data are automatically extracted based on the preset post-processing method.

[0021] In addition, both types of simulations use the same boundary condition settings. High-precision CFD simulations use high-density structured grid division and use a turbulence model with an accuracy level not lower than the RANS model to improve the simulation accuracy of leakage and temperature rise. The number of grids is about 2 million, and the wall Y+≈1.0-2.4; low-precision CFD simulations use a method that reduces the grid density, simplifies the boundary processing, and / or reduces the turbulence model accuracy (for example, using k - eThe model was constructed using a grid of approximately 200,000 cells. The grid sizes for high- and low-fidelity CFD simulations differed by orders of magnitude to ensure a dynamic balance between modeling efficiency and accuracy. CFD simulations were performed on high- and low-fidelity sample points, respectively, to obtain corresponding leakage and total temperature rise response data. This allowed the construction of high- and low-fidelity sample libraries encompassing design variables and performance responses. Figure 3 A schematic diagram of a smooth staggered grate seal is shown. The mesh count between the high- and low-fidelity models differs by a factor of 10, saving computational resources during the grate seal optimization process.

[0022] SS4. Hierarchical Kriging surrogate model construction and training: First, an initial Kriging model is constructed based on a low-fidelity sample library. Then, the model is calibrated through the covariance matrix between the high-fidelity sample library data and the prediction results of the initial model to form a hierarchical Kriging proxy model that integrates multi-fidelity data.

[0023] Specifically, the embodiment of the present invention is implemented by calling the pykriging library in Python when constructing a hierarchical Kriging proxy model. First, a low-fidelity Kriging proxy model is constructed based on a low-fidelity sample library, and a Gaussian kernel function is used to describe the spatial correlation between sample points, and the parameters of the kernel function are determined by the maximum likelihood estimation method. Then, the covariance matrix of data with different fidelity is calculated to evaluate the accuracy of the low-fidelity data. Then, based on the low-fidelity Kriging model, high-fidelity data is used for correction to achieve an accuracy that meets the requirements for predicting high-fidelity data. Specifically, a recursive iterative algorithm is used to correct the low-fidelity model using high-fidelity sample data, and the covariance matrix between high- and low-fidelity data is calculated to construct a hierarchical Kriging model that fuses high- and low-fidelity data. Finally, the predicted mean and variance of the model are determined by Bayesian inference, thereby forming a variable credibility response surface model with multi-level data fusion capabilities and prediction confidence interval control capabilities, which is used for subsequent sample addition and optimization processes.

[0024] SS5. Surrogate model accuracy assessment and iterative judgment: The prediction accuracy of the hierarchical Kriging surrogate model is evaluated. If the error of any objective function is higher than the set threshold, the convergence condition is not met, and the process goes to step SS6 to perform sample addition and model update until the prediction accuracy meets the convergence requirements and then goes to step SS7.

[0025] As a preference, in the embodiment of the present invention, the prediction accuracy of the proxy model is evaluated by using k-fold cross validation and the coefficient of certainty R 2 The combined method is used to calculate the prediction accuracy for the two objective functions of leakage and total temperature rise.2 When both are greater than 0.95 and the average relative prediction error is less than 5%, the model accuracy is considered to meet the convergence requirements. When the verification error of any objective function exceeds the corresponding threshold, the model update process is triggered.

[0026] SS6. Variable Credibility and Parallel Expectation Increase Point Strategy: Based on the predicted mean and variance of the current surrogate model, the variable credibility parallel expectation improvement matrix is used to batch increase high and low fidelity sample points in the optimization direction, and then return to execute steps SS3 to SS5.

[0027] Specifically, an embodiment of the present invention adopts a variable credibility parallel expectation improvement matrix addition method. An effective filling strategy can improve the convergence speed and effectively manage high-dimensional optimization problems or complex response surfaces. The Kriging model not only provides a predicted value, but also quantifies the uncertainty of the prediction, laying the foundation for the application of the expectation improvement filling strategy. The expectation improvement matrix criterion is an effective multi-objective filling strategy based on the expectation improvement matrix. It significantly reduces the computational complexity by decomposing the traditional high-dimensional EI function integration problem into a summation problem of multiple one-dimensional EI integrals. In order to improve the efficiency of multi-objective optimization, a parallel expectation improvement matrix criterion is introduced. Instead of adding a single sample point at each stage, multiple sample points are iteratively selected.

[0028] More specifically, the implementation of the variable credibility parallel expectation improvement matrix method includes: first, constructing a multi-objective expectation improvement function based on the predicted mean and predicted variance of the current hierarchical Kriging surrogate model; then, decomposing the high-dimensional multi-objective expectation improvement function integral into a weighted sum of multiple one-dimensional expectation improvement integrals, and each weight coefficient is determined by the entropy weight method, and is calculated based on the prediction uncertainty information entropy of each objective in the sample space, thereby realizing adaptive information fusion between multiple objectives and reducing the computational complexity of sample supplementation; then, adopting a parallel computing strategy, multiple sample points with maximum information gain potential are simultaneously selected based on the multi-objective expectation improvement criterion in one point addition iterative process; the fidelity level of each sample point is dynamically allocated according to its uncertainty intensity in the prediction surface and the simulation resource allocation strategy, so as to maximize sample utilization and rapidly converge the global response surface, thereby improving the point addition efficiency and model update rate in the high-dimensional optimization space.

[0029] SS7. Multi-objective optimization and structural screening: After determining whether the surrogate model meets the accuracy requirements, the NSGA-Ⅱ algorithm is used to find the Pareto frontier solution of the grate seal. The leakage and total temperature rise predicted by the hierarchical Kriging model are used as target values. Combined with engineering application requirements, such as the weight coefficients for leakage and total temperature rise, or the preference for specific performance indicators, the optimal grate seal structural parameter combination is screened from the Pareto frontier solution set.

[0030] Preferably, an optimization algorithm is used in the embodiment of the present invention to find the optimal structural parameters. A machine learning prediction model for multi-working condition comb seals is constructed. After determining that the prediction accuracy of the proxy model is sufficient, NSGA-Ⅱ is used to find the Pareto front solution, and the optimal structure is selected according to the needs. Furthermore, when the NSGA-II algorithm is used for optimization: the population size is set to 10-20 times the number of design variables, the maximum evolutionary generations are set to 50-100 generations, the crossover probability is set to 0.8-0.9, the mutation probability is set to 0.1-0.2, and the convergence condition is that the change rate of the hypervolume index of the Pareto front is less than 0.5% for 5 consecutive generations. During the optimization process, the search direction is guided jointly by the crowding distance and the distance from the ideal point to improve the convergence of the Pareto front and the quality of the solution set distribution.

[0031] SS8. Optimized structure verification and closed-loop update: Compare the performance of the baseline structure and the optimal structure, and use CFD simulation to verify and analyze the reasons to ensure that the operation requirements of different working conditions are met. If the convergence conditions are not met, use the Python program to continue to increase the data in batches in the optimization direction to build a more accurate prediction model until the convergence conditions are met (for example, the relative error of leakage δQ ≤3%, relative error of total temperature rise δT ≤5%. When any indicator exceeds the limit, high-fidelity samples are added to the high-error area first, and incremental training is used to update the hierarchical Kriging proxy model). Figure 4 A comparison diagram of the baseline structure and the optimized structure is shown. By limiting the optimization range of structural parameters, the optimized structural parameters are guaranteed to be achievable.

[0032] The above embodiments fully and effectively achieve the objectives of the present invention. Those skilled in the art will appreciate that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the above specific embodiments. Although the present invention has been described with reference to the embodiments currently considered to be the most practical and preferred, it should be understood that the present invention is not limited to the disclosed embodiments, and any modifications that do not deviate from the functional and structural principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A multi-objective optimization design method for grate seal based on a variable credibility agent model, characterized in that: include: SS1. Define the geometric parameters of the grate seal as design variables, set the optimization objectives as minimizing leakage and minimizing total temperature rise, and define the upper and lower bounds of each design variable and structural manufacturability constraints. SS2. Generate a uniformly distributed initial sample point set within a high-dimensional constrained design space using a sampling method. This set of initial sample points is divided into high-fidelity and low-fidelity samples for high- and low-precision CFD simulations, respectively. SS3. Perform CFD simulations for each sample point to obtain corresponding leakage and total temperature rise response data, and construct a high- and low-fidelity sample library containing design variables and performance responses. SS4. First, an initial Kriging model is constructed based on the low-fidelity sample library. Then, the model is calibrated using the covariance matrix between the high-fidelity sample library data and the initial model predictions, forming a hierarchical Kriging proxy model that integrates multi-fidelity data. SS5. Evaluate the prediction accuracy of the hierarchical Kriging surrogate model. If the error of any objective function exceeds the set threshold, convergence conditions are not met. The process proceeds to step SS6 to perform sample addition and model update until the prediction accuracy meets the convergence requirements, at which point the process proceeds to step SS7. SS6. Based on the predicted mean and variance of the current surrogate model, use the variable credibility parallel expectation improvement matrix to batch increase high- and low-fidelity sample points in the optimization direction. Return to steps SS3-SS5. SS7. Based on a hierarchical Kriging surrogate model, the NSGA-II algorithm was used to perform multi-objective optimization, obtain the Pareto frontier solution set, and select the optimal grate seal structural parameter combination; SS8. Perform high-fidelity CFD simulations on the selected optimal structure. If the error between the predicted value and the simulation result exceeds the set tolerance, return to steps SS5-SS8 and continue optimization until convergence.

2. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS1, the geometric parameter design variables of the grate tooth seal include at least the tooth height, tooth spacing, tooth top width, tooth root width, tooth rake angle and tooth back rake angle of the grate teeth, and the constraints of each design variable are set in combination with actual engineering requirements and structural manufacturability.

3. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS2, the initial sample points are generated using the improved Latin hypercube sampling method, with the distribution uniformity function of Latin hypercube sampling in the design variable space as the objective function. The genetic algorithm is used to optimize the objective in the high-dimensional constrained space to generate an initial sample point set that meets the uniform distribution conditions and has good representativeness and global coverage capabilities.

4. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1 or 3, characterized in that: In the above step SS2, the ratio of the number of high-fidelity and low-fidelity samples is dynamically set based on computing resources and model complexity. The number of low-fidelity samples is 2-5 times the number of high-fidelity samples. In the initial design stage, the number of high-fidelity sample points is at least 3 times the number of design variables, and the number of low-fidelity sample points is at least 10 times the number of design variables.

5. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS3, the CFD simulation calculation is automatically executed under program control, including: constructing a geometric parameterized model based on the design variables of the grate seal to automatically generate the three-dimensional geometric model of the grate seal; automatically generating a calculation grid based on a preset grid division strategy; automatically setting solution parameters and executing CFD calculations based on preset boundary conditions and calculation models; and automatically extracting leakage and total temperature rise performance data based on a preset post-processing method.

6. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 5, characterized in that: In the above step SS3, the high-precision CFD simulation adopts high-density structured grid division, and the accuracy level of the turbulence model is not lower than that of the RANS model. The low-precision CFD simulation is constructed by reducing the grid density, simplifying the boundary processing and / or reducing the accuracy of the turbulence model. There is an order of magnitude difference in the grid scale between the high-precision and low-precision CFD simulations.

7. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS4, the construction of the hierarchical Kriging proxy model includes: first, constructing a low-fidelity Kriging model, using a Gaussian kernel function to describe the spatial correlation between sample points, and determining the parameters of the kernel function through the maximum likelihood estimation method; then, through a recursive iterative algorithm, using high-fidelity sample data to calibrate the low-fidelity model, calculating the covariance matrix between high- and low-fidelity data, and constructing a hierarchical Kriging model that fuses high- and low-fidelity data; finally, determining the predicted mean and variance of the model through Bayesian inference.

8. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS5, the prediction accuracy of the proxy model is evaluated by combining the k-fold cross validation and the deterministic coefficient R² method. The prediction accuracy is calculated for the two objective functions of leakage and total temperature rise respectively. When the deterministic coefficients R² of the two objective functions are equal, the prediction accuracy is calculated. 2 When both are greater than 0.95 and the average relative prediction errors are less than 5%, the model accuracy is considered to meet the convergence requirements; when the verification error of any objective function exceeds the corresponding threshold, the model update process is triggered.

9. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In the above step SS6, the implementation of the variable credibility parallel expectation improvement matrix method includes: first, constructing a multi-objective expectation improvement function based on the predicted mean and predicted variance of the current hierarchical Kriging proxy model; then, decomposing the high-dimensional multi-objective expectation improvement function integral into a weighted sum of multiple one-dimensional expectation improvement integrals, and each weight coefficient is determined by the entropy weight method; then, adopting a parallel computing strategy, in one point addition iterative process, multiple sample points with maximum information gain potential are simultaneously selected based on the multi-objective expectation improvement criterion; the fidelity level of each sample point is dynamically allocated according to its uncertainty intensity in the prediction surface and the simulation resource allocation strategy.

10. The multi-objective optimization design method for grate seals based on a variable credibility proxy model according to claim 1, characterized in that: In step SS7 above, when the NSGA-II algorithm is used for optimization: the population size is set to 10-20 times the number of design variables, the maximum number of evolution generations is set to 50-100 generations, the crossover probability is set to 0.8-0.9, the mutation probability is set to 0.1-0.2, and the convergence condition is that the hypervolume index of the Pareto front changes at a rate of less than 0.5% for five consecutive generations. In the optimization process, the crowding distance and the distance from the ideal point are jointly used to guide the search direction to improve the convergence of the Pareto front and the quality of the solution set distribution.

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