A multi-objective optimization method for cylindrical gas seal based on SVR and NSGA-Ⅱ

Abstract

The application relates to a cylindrical gas film seal multi-objective optimization method based on SVR and NSGA- II, and belongs to the technical field of mechanical seal optimization design. The method comprises the following steps: constructing a cylindrical gas film seal structure parameter optimization model; obtaining initial sample points by adopting an orthogonal method design and performing finite element analysis to generate an input / output data set; establishing an SVR proxy model among structure parameters, buoyancy, leakage and friction; performing multi-objective optimization by adopting an NSGA- II algorithm, taking the SVR proxy model meeting the accuracy as a target function of the NSGA- II algorithm, obtaining a Pareto front optimal solution set, performing multi-scheme decision by adopting an approximation ideal solution sorting method, selecting a structure parameter combination with the optimal comprehensive performance and inputting the structure parameter combination into the cylindrical gas film seal structure parameter optimization model to obtain a multi-objective optimization result. The application aims to solve the technical problems that the prior art cannot simultaneously consider the three performance indexes of buoyancy, leakage and friction, the high-precision numerical simulation calculation cost is high, and the fitting accuracy of the proxy model is insufficient.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for cylindrical air film seals based on SVR and NSGA-Ⅱ, belonging to the field of mechanical seal optimization design technology. Background Technology

[0002] As aero-engines and high-pressure hydrogen turbines develop towards higher speeds, higher pressure ratios, and higher thrust-to-weight ratios, the sealing performance of the rotor system has become a key factor restricting overall engine efficiency and lifespan. Studies show that improving the sealing system can reduce engine fuel consumption by 1%–2% and increase thrust by approximately 9.7%. Among numerous non-contact sealing technologies, cylindrical gas film seals, due to their insensitivity to axial runout, high radial flexibility, and low power consumption, show broad application prospects in aero-engines and supercritical fluid machinery.

[0003] The performance of cylindrical gas film seals is primarily determined by the micro-gap flow field, and the microgroove structure created on the surface of the rotating ring or bushing is key to generating the hydrodynamic effect. Sealing performance is typically evaluated using three core indicators: buoyancy reflects the gas film's load-bearing capacity, directly determining whether the sealing surface can maintain a stable non-contact state; leakage rate characterizes the seal's leak-proof capability, affecting the medium loss in the sealing system; and friction reflects the energy loss and frictional wear characteristics during seal operation. However, these three performance parameters often exhibit mutual constraints: increasing buoyancy usually accompanies increased leakage, while pursuing low leakage may come at the cost of gas film stiffness; furthermore, friction has a complex coupling relationship with both.

[0004] Currently, scholars both domestically and internationally have conducted extensive research on the coordinated optimization of multiple performance indicators for cylindrical air film seals, but the following technical shortcomings still exist:

[0005] (1) Multi-objective optimization usually requires a large number of calls to high-precision numerical models. However, the computational cost of flow field solutions based on finite difference method or computational fluid dynamics is high and it is difficult to directly embed them into the iterative optimization process. To alleviate the computational burden, researchers often use surrogate models to replace the original numerical models. However, the commonly used polynomial response surface or radial basis function has limited fitting accuracy when dealing with the strong nonlinear relationship between groove parameters and sealing performance.

[0006] (2) Existing optimization objectives are mostly focused on the trade-off between buoyancy and leakage. Although some studies have incorporated frictional power consumption into the optimization framework, there is still a lack of systematic optimization research on buoyancy, leakage and friction. In particular, the complex trade-off relationship between the three objectives has not been effectively resolved.

[0007] Therefore, there is an urgent need to develop an automated grinding equipment equipped with a protective cover, capable of single-sided precision grinding, effectively controlling deformation, and capable of operating independently or being arranged in parallel to improve overall efficiency, depending on the condition of the sheet material. Summary of the Invention

[0008] The purpose of this invention is to provide a multi-objective optimization method for cylindrical air film seals based on SVR and NSGA-II, aiming to solve the technical problems in the existing technology of cylindrical air film seal optimization design that make it difficult to take into account the three performance indicators of buoyancy, leakage and friction, high cost of high-precision numerical simulation calculation, and insufficient fitting accuracy of surrogate models.

[0009] To achieve the above objectives, the technical solution of the present invention is: a multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II, comprising the following steps:

[0010] Step 1: Design variables and multi-objective functions to construct a parameter optimization model for the cylindrical air-film sealing structure;

[0011] Step 2: Use the orthogonal method to design and obtain initial sample points, and perform finite element analysis on the initial sample points to generate input / output datasets;

[0012] Step 3: Based on the input / output dataset, establish an SVR proxy model between structural parameters and buoyancy, leakage, and friction, and determine its accuracy.

[0013] Step 4: Use the NSGA-II algorithm for multi-objective optimization, and use the SVR surrogate model that meets the accuracy requirements as the objective function of the NSGA-II algorithm to obtain the optimal solution set of the Pareto front;

[0014] Step 5: Set the weights of each optimization objective, use the approximation of ideal solution ranking method to make multi-scheme decisions on the Pareto front optimal solution set, and select the structural parameter combination with the best overall performance;

[0015] Step 6: Input the optimal combination of structural parameters into the cylindrical air film sealing structure parameter optimization model to obtain the multi-objective optimization results.

[0016] Optionally, the design variables are specifically:

[0017] in, For the design variables, For the length of the groove, For the depth of the groove, This represents the average air film thickness. , respectively the length of the groove The upper and lower limits; , respectively, the depth of the trench The upper and lower limits; , Average air film thickness The upper and lower limits.

[0018] Optionally, the multi-objective function is expressed in minimization form, with the following expression:

[0019] in, It is a multi-objective function. For buoyancy, For leakage amount, This is friction.

[0020] Optionally, step 2 specifically includes:

[0021] The design includes three variables: trench length, trench depth, and average air film thickness. Each variable has four levels, resulting in a total of 16 test points.

[0022] Five different pressure differences were designed, resulting in an expanded 80 test points;

[0023] The obtained 80 test points were used in finite element analysis and computational fluid dynamics simulation to obtain the objective function response values ​​corresponding to the 80 test points. All test points and their corresponding function response values ​​constituted the input / output dataset.

[0024] Optionally, step 3 specifically includes:

[0025] Using the radial basis function kernel as the SVR surrogate model, the expression is:

[0026]

[0027] in, Represents sample points With sample points The kernel function values ​​between For kernel parameters;

[0028] The variables designed in the input / output dataset are used as the input to the SVR proxy model, and buoyancy, leakage, and friction are used as the output to establish three independent SVR proxy models.

[0029] Using the coefficient of determination R 2 The relative mean absolute error (MARE) is used to evaluate model accuracy when R... 2 When the accuracy is >0.95 and MARE <5%, the SVR proxy model is considered to meet the accuracy requirements.

[0030] Optionally, step 4 specifically includes:

[0031] Step 4.1: Combine the SVR surrogate model and the NSGA-II algorithm, and use the predicted value of the SVR surrogate model as the objective function value of the NSGA-II algorithm;

[0032] Step 4.2: Initialize the population;

[0033] Step 4.3: Perform fast non-dominated sorting to divide the individuals in the initial population into different Pareto front levels;

[0034] Step 4.4: Calculate the crowding distance between different individuals at the Pareto front in the initial population, and prioritize individuals with higher crowding. If the difference in crowding distance between two individuals is less than a preset threshold, then select the individual with the smaller objective function value in the Pareto front.

[0035] Step 4.5: Introduce an elite retention strategy to generate the parent population. Specifically, all individuals in the initial population are placed into population P from low to high according to their level, until it is impossible to place all individuals in a certain level into population P. Individuals in the current level are arranged from large to small according to their crowding distance and placed into population P in turn until population P is full. The full population P is the parent population.

[0036] Step 4.6: The parent population generates offspring populations through fitness selection, crossover, and mutation. The number of offspring populations is the same as that of the parent population. The parent population and the offspring populations it generates are merged, and a new offspring population is generated from the merged population. The number of new offspring populations is half that of the merged population.

[0037] Step 4.7: When the number of iterations reaches the maximum number of iterations, output the optimal solution set of the Pareto front.

[0038] Optionally, the step of using the approximation-ideal-solution sorting method to make multi-option decisions on the Pareto front optimal solution set specifically involves:

[0039] First, the objective function values ​​in the Pareto front optimal solution set are standardized to eliminate the influence of dimensions;

[0040] Then, calculate the Euclidean distance between each solution and the positive and negative ideal solutions;

[0041] Finally, the relative closeness of each solution is calculated, and the parameter combination with the highest relative closeness is selected as the optimal design variable scheme.

[0042] Optionally, the calculation of the relative closeness of each solution specifically involves:

[0043] in, Let represent the Euclidean distance between the i-th solution and the maximum value, and use it as the first distance; Let represent the Euclidean distance between the i-th solution and the minimum value, and use it as the second distance. r represents the relative proximity of the i-th solution. ijThe result is the standardized objective value of the i-th solution in the Pareto front optimal solution set; r j+ r represents the maximum value of the j-th index among all solutions; j - This represents the minimum value of the j-th index among all solutions. This indicates the number of objective functions.

[0044] The beneficial effects of this invention are:

[0045] 1. This invention replaces high-fidelity numerical simulation with an SVR proxy model, reducing the time for a single performance evaluation from minutes to milliseconds, significantly reducing the number of calls to the high-fidelity numerical model, and significantly reducing computational costs.

[0046] 2. This invention is the first to incorporate three mutually constraining performance indicators—buoyancy, leakage, and friction—into a unified optimization framework, achieving synergistic optimization of the three objectives and successfully breaking through the bottleneck of mutual constraint between buoyancy and leakage in traditional design.

[0047] 3. The SVR surrogate model of the present invention adopts a radial basis kernel function, which can effectively handle nonlinear mapping problems in small sample and high-dimensional parameter space, with a determination coefficient of over 0.95, and the surrogate model has high accuracy.

[0048] 4. The NSGA-II algorithm used in this invention employs fast non-dominated sorting, crowding distance calculation, and elite retention strategies to obtain a uniformly distributed Pareto front, demonstrating strong global optimization capabilities.

[0049] 5. The structural parameters optimized by this invention are located inside the constraint boundary, which facilitates actual processing and assembly. The entropy weight method-TOPSIS decision mechanism improves the scientific nature of engineering selection and has good engineering practicality. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the present invention;

[0052] Figure 2 This is a schematic diagram of the cylindrical air film sealing geometry of the present invention;

[0053] Figure 3 This is a grid division diagram of the cylindrical air film sealing of the present invention;

[0054] Figure 4 This is a schematic diagram of the Support Vector Regression (SVR) model of this invention;

[0055] Figure 5 This is a comparison chart of the predicted and actual buoyancy force values ​​of the SVR proxy model of this invention;

[0056] Figure 6 This is a comparison chart of the predicted and actual leakage values ​​of the SVR proxy model of this invention;

[0057] Figure 7 This is a comparison chart of the predicted and actual friction values ​​of the SVR proxy model of this invention;

[0058] Figure 8 This is a diagram showing the gas film pressure distribution before and after optimization under a rotational speed of 10000 rad / min.

[0059] Figure 9 This is a diagram showing the gas film pressure distribution before and after optimization under the condition of a rotation speed of 25000 rad / min.

[0060] Figure 10 This is a diagram showing the gas film pressure distribution before and after optimization under the operating condition of 40000 rad / min. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the described embodiments are merely some, not all, of the embodiments of this invention. Where there is no conflict, the embodiments and features in the embodiments of this invention can be combined with each other. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. To make the objectives, technical solutions, and beneficial effects of this application clearer, the preferred embodiments of this invention will be described in detail below in conjunction with the accompanying drawings to facilitate understanding by those skilled in the art.

[0062] Example 1: As Figure 1 As shown, a multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II includes the following steps:

[0063] Step 1: Design variables and multi-objective functions to construct a parameter optimization model for the cylindrical air-film sealing structure;

[0064] It should be noted that the schematic diagram of the cylindrical air film seal geometry is as follows: Figure 2 As shown, based on the characteristics of the cylindrical air film sealing structure, in this embodiment, for the convenience of modeling and numerical calculation, the numerical calculation model of its hysteresis characteristics is simplified and made the following assumptions:

[0065] (1) The lubricating medium is an ideal gas;

[0066] (2) Neglect the volume forces and inertial forces of the lubricating gas;

[0067] (3) The lubricating gas is in isothermal continuous flow;

[0068] (4) The lubricating gas is a viscous fluid, so it is assumed that there is no slippage during rotation;

[0069] (5) The sealing ring is considered a rigid body and will not deform.

[0070] Optionally, the design variables are specifically:

[0071] in, For the design variables, For the length of the groove, For the depth of the groove, The average air film thickness; , respectively the length of the groove The upper and lower limits; , respectively, the depth of the trench The upper and lower limits; , These are the average air film thicknesses. The upper and lower limits.

[0072] It should be noted that the variables designed in this embodiment are the main structural parameters affecting the performance of the cylindrical air film sealing. The groove length affects the generation area of ​​the dynamic pressure effect and the gas pumping effect: when the groove length is short, the gas shearing stroke is insufficient, the dynamic pressure effect is weak, and the buoyancy increase is limited; if the groove length is too long, high-pressure gas will leak prematurely along the axial direction, reducing sealing efficiency. The groove depth directly determines the depth of the dynamic pressure groove. A groove that is too shallow cannot form a sufficient air film pressure peak, while a groove that is too deep will exacerbate gas backflow, increase leakage, and increase frictional power consumption; there exists an optimal groove depth range that balances buoyancy and leakage. The average air film thickness is a characteristic dimension of the sealing gap, directly affecting the air film's load-bearing capacity and the cross-sectional area of ​​the leakage channel: a smaller average air film thickness can significantly reduce leakage, but a gap that is too small will increase friction and increase the risk of contact; a larger average air film thickness is beneficial for reducing friction, but it will weaken the dynamic pressure effect, leading to a decrease in buoyancy. Therefore, reasonably matching the groove length, groove depth, and average air film thickness is key to achieving synergistic optimization of buoyancy, leakage, and friction.

[0073] Optionally, the multi-objective function is expressed in minimization form, with the following expression:

[0074] in, It is a multi-objective function. For buoyancy, For leakage amount, This is friction.

[0075] Step 2: Use the orthogonal method to design and obtain initial sample points, and perform finite element analysis on the initial sample points to generate input / output datasets;

[0076] Optionally, the orthogonal method is designed by selecting an orthogonal table based on the number of design variables and the number of levels. Therefore, in this embodiment, the design includes three variables: tank length, tank depth, and average air film thickness. Each variable has four levels, resulting in a total of 16 test points, as shown in Table 1.

[0077] Table 1. Design Variable Level Table

[0078]

[0079] For each set of test points, the Reynolds equations were solved using the finite difference method. The computational domain mesh was uniformly divided into a circumferential area of ​​200 × an axial area of ​​40, as shown below. Figure 3 As shown. Boundary conditions: Inlet pressure is set based on pressure difference, outlet pressure is 0.1 MPa, and the boundary is circumferentially periodic. An over-relaxation iterative method (relaxation factor 1.2) is used, with the convergence criterion being that the relative pressure residual is less than 10. -6 .

[0080] Since the dependent variable is also affected by pressure difference, pressure difference is added as an influencing factor in this embodiment. Five pressure differences are designed to obtain 80 test points after expansion. In this embodiment, the five pressure differences are 0.1, 0.2, 0.3, 0.4, and 0.5 MPa, respectively.

[0081] The obtained 80 test points were used in finite element analysis and computational fluid dynamics simulation to obtain the objective function response values ​​corresponding to the 80 test points. All test points and their corresponding function response values ​​constituted the input / output dataset.

[0082] Step 3: Based on the input / output dataset, establish an SVR proxy model between structural parameters and buoyancy, leakage, and friction, and determine its accuracy.

[0083] Optionally, such as Figure 4 As shown, the radial basis function kernel is used as the SVR surrogate model, and its expression is:

[0084]

[0085] in, Represents sample points With sample points The kernel function values ​​between For kernel parameters;

[0086] The variables designed in the input / output dataset are used as the input of the SVR proxy model, and buoyancy, leakage, and friction are used as the output to establish three independent high-precision nonlinear mapping SVR proxy models.

[0087] Using the coefficient of determination R 2 The relative mean absolute error (MARE) is used to evaluate model accuracy when R... 2 When the accuracy is >0.95 and MARE <5%, the SVR proxy model is considered to meet the accuracy requirements.

[0088] Specifically, in this embodiment, the 80 sets of data are divided into a training set (56 sets) and a test set (24 sets) in a 7:3 ratio. Using the designed variables as inputs, and buoyancy, leakage, and friction as outputs, three independent SVR models are trained respectively.

[0089] Furthermore, accuracy was assessed: In this embodiment, a test set was used to evaluate the model's accuracy. The coefficients of determination for buoyancy, leakage, and friction were 0.982, 0.976, and 0.969, respectively, with relative average absolute errors of 2.16%, 3.42%, and 3.85%, all below 5%, meeting the accuracy requirements. Comparison between predicted and actual values ​​is shown below. Figures 5-7 As shown.

[0090] Step 4: Use the NSGA-II algorithm for multi-objective optimization, and use the SVR surrogate model that meets the accuracy requirements as the objective function of the NSGA-II algorithm to obtain the optimal solution set of the Pareto front;

[0091] Step 4.1: Combine the SVR surrogate model and the NSGA-II algorithm, and use the predicted value of the SVR surrogate model as the objective function value of the NSGA-II algorithm;

[0092] Step 4.2: Initialize the population by randomly selecting values ​​from the ranges of the three design variables. Specifically, for each design variable, a value is independently generated within its respective value range using a random function. The values ​​generated by the three design variables are then combined to form an individual. In this embodiment, the above process is repeated 200 times to obtain an initial population of 200.

[0093] Step 4.3: Perform fast non-dominated sorting to divide the individuals in the initial population into different Pareto front levels;

[0094] Step 4.4: Calculate the crowding distance between different individuals at the Pareto front in the initial population, and prioritize individuals with higher crowding. If the difference in crowding distance between two individuals is less than a preset threshold, then select the individual with the smaller objective function value in the Pareto front.

[0095] Step 4.5: Introduce an elite retention strategy to generate the parent population. Specifically, all individuals in the initial population are placed into population P from low to high according to their level, until it is impossible to place all individuals in a certain level into population P. Individuals in the current level are arranged from large to small according to their crowding distance and placed into population P in turn until population P is full. The full population P is the parent population.

[0096] Step 4.6: The parent population generates offspring populations through fitness selection, crossover, and mutation. The number of offspring populations is the same as that of the parent population. The parent population and the offspring populations it generates are merged, and a new offspring population is generated from the merged population. The number of new offspring populations is half that of the merged population.

[0097] Step 4.7: When the number of iterations reaches the maximum number of iterations, output the optimal solution set of the Pareto front.

[0098] Optionally, the specific parameters of the NSGA-II algorithm are: initial population size M = 100~300, maximum number of iterations Gmax = 80~200, and crossover probability p. c =0.8~0.95, mutation probability p m =0.05~0.15. In this embodiment, the initial population size is 200, the maximum number of iterations is 100, the crossover probability is 0.9, and the mutation probability is 0.08.

[0099] Step 5: Set the weights of each optimization objective, and use the Top-Optimal Solution Ranking Method (TOPSIS) to make multi-scheme decisions on the Pareto front optimal solution set, and select the combination of structural parameters with the best overall performance;

[0100] Optionally, the weights of each optimization objective can be set based on engineering experience and the designer's subjective preferences. In this embodiment, the weights of buoyancy, leakage, and friction are set to W respectively, according to the actual needs of the sealing system. F =0.4, W Q =0.4, W f =0.2, to highlight the dominant role of sealing performance (buoyancy and leakage) while taking into account system power consumption (friction).

[0101] Optionally, the step of using the approximation-to-ideal-solution ranking method to perform multi-scheme decision-making on the Pareto front optimal solution set involves calculating the comprehensive proximity of each solution, ranking them, and then selecting the optimal solution. Specifically:

[0102] First, the objective function values ​​in the Pareto front optimal solution set are standardized to eliminate the influence of dimensions;

[0103] Then, calculate the Euclidean distance between each solution and the positive and negative ideal solutions;

[0104] Finally, the relative closeness of each solution is calculated, and the parameter combination with the highest relative closeness is selected as the optimal design variable scheme.

[0105] Optionally, the calculation of the relative closeness of each solution specifically involves:

[0106] in, Let represent the Euclidean distance between the i-th solution and the maximum value, and use it as the first distance; Let represent the Euclidean distance between the i-th solution and the minimum value, and use it as the second distance. r represents the relative proximity of the i-th solution. ij The result is the standardized objective value of the i-th solution in the Pareto front optimal solution set; r j+ r represents the maximum value of the j-th index among all solutions; j - This represents the minimum value of the j-th index among all solutions. This indicates the number of objective functions.

[0107] Optionally, in this embodiment, the optimal combination of structural parameters for overall performance is: slot length =21.639mm, groove depth =10.407um, average air film thickness =10.422um.

[0108] Step 6: Input the optimal combination of structural parameters into the cylindrical air film sealing structure parameter optimization model to obtain the multi-objective optimization results.

[0109] Optionally, in this embodiment, the optimal combination of structural parameters is substituted into the cylindrical air film seal structure parameter optimization model for verification calculation. The changes in buoyancy, leakage and friction before and after optimization are compared to verify the effectiveness of the optimization method. The performance comparison before and after optimization is shown in Table 2.

[0110] Table 2 Performance Comparison Before and After Optimization

[0111]

[0112] As shown in Table 2, the optimized buoyancy increased by 87.425%, leakage decreased by 51.053%, and friction increased by 45.053%. The improvement in buoyancy and leakage far exceeded the increase in friction, indicating that the combination of structural parameters obtained based on the SVR-NSGA-Ⅱ optimization method not only significantly enhanced the dynamic pressure bearing capacity of the air film but also effectively suppressed leakage, achieving a comprehensive improvement in sealing performance.

[0113] Furthermore, to verify the applicability of the optimization method of the present invention under different operating conditions, three operating conditions were selected: rotational speeds of 10000 r / min, 25000 r / min, and 40000 r / min. The structural parameters before and after optimization were substituted into the numerical model for calculation to obtain the gas film pressure distribution at different rotational speeds, as shown below. Figures 8-10 As shown. From Figures 8-10 It can be seen that the pressure peak of the optimized structure at each rotational speed is significantly higher than that of the unoptimized structure, and the high-pressure zone is more evenly distributed and covers a wider range.

[0114] Understandably, this embodiment further investigated the influence of groove length, groove depth, and average air film thickness on buoyancy, leakage, and friction at different rotational speeds using the finite difference method and computational fluid dynamics. It was found that for the buoyancy of the cylindrical air film seal, at higher rotational speeds, increasing the groove length and groove depth significantly improves buoyancy, while the average air film thickness has an optimal range for its effect on buoyancy. For leakage, at higher rotational speeds, decreasing the average air film thickness and groove depth significantly reduces leakage, but the groove length has a relatively small impact on leakage. For friction, increasing the groove depth and average air film thickness both lead to an increase in friction, and the increase is more significant at higher rotational speeds, but the increase is still much smaller than the increase in buoyancy. Through the above analysis, it can be concluded that each structural parameter has varying degrees of influence on the buoyancy, leakage, and friction of the cylindrical air film seal. Therefore, this verifies the feasibility of optimizing the groove structure parameters of the cylindrical air film seal with the optimization objectives of maximizing buoyancy, minimizing leakage, and minimizing friction in this embodiment.

[0115] In summary, this invention significantly reduces the computational cost in the optimization process through the SVR proxy model, while achieving synergistic optimization of buoyancy, leakage, and friction, resulting in a significant improvement in overall performance. It can be widely applied to the refined design of cylindrical gas film seals for aero-engines and high-pressure hydrogen turbine machinery.

[0116] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II, characterized in that, The method includes the following steps: Step 1: Design variables and multi-objective functions to construct a parameter optimization model for the cylindrical air-film sealing structure; Step 2: Use the orthogonal method to design and obtain initial sample points, and perform finite element analysis on the initial sample points to generate input / output datasets; Step 3: Based on the input / output dataset, establish an SVR proxy model between structural parameters and buoyancy, leakage, and friction, and determine its accuracy. Step 4: Use the NSGA-II algorithm for multi-objective optimization, and use the SVR surrogate model that meets the accuracy requirements as the objective function of the NSGA-II algorithm to obtain the optimal solution set of the Pareto front; Step 5: Set the weights of each optimization objective, use the approximation of ideal solution ranking method to make multi-scheme decisions on the Pareto front optimal solution set, and select the structural parameter combination with the best overall performance; Step 6: Input the optimal combination of structural parameters into the cylindrical air film sealing structure parameter optimization model to obtain the multi-objective optimization results.

2. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 1, characterized in that, The design variables are specifically: ； in, For the design variables, For the length of the groove, For the depth of the groove, This represents the average air film thickness. , respectively the length of the groove The upper and lower limits; , respectively, the depth of the trench The upper and lower limits; , Average air film thickness The upper and lower limits.

3. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 2, characterized in that, The multi-objective function is expressed in minimization form, and its expression is: ; in, It is a multi-objective function. For buoyancy, For leakage amount, This is friction.

4. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 1, characterized in that, Step 2 specifically involves: The design includes three variables: trench length, trench depth, and average air film thickness. Each variable has four levels, resulting in a total of 16 test points. Five different pressure differences were designed, resulting in an expanded 80 test points; The obtained 80 test points were used in finite element analysis and computational fluid dynamics simulation to obtain the objective function response values ​​corresponding to the 80 test points. All test points and their corresponding function response values ​​constituted the input / output dataset.

5. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 1, characterized in that, Step 3 specifically involves: Using the radial basis function kernel as the SVR surrogate model, the expression is: ； in, Represents sample points With sample points The kernel function values ​​between For kernel parameters; The variables designed in the input / output dataset are used as the input to the SVR proxy model, and buoyancy, leakage, and friction are used as the output to establish three independent SVR proxy models. Using the coefficient of determination R 2 The relative mean absolute error (MARE) is used to evaluate model accuracy when R... 2 When the accuracy is >0.95 and MARE <5%, the SVR proxy model is considered to meet the accuracy requirements.

6. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Combine the SVR surrogate model and the NSGA-II algorithm, and use the predicted value of the SVR surrogate model as the objective function value of the NSGA-II algorithm; Step 4.2: Initialize the population; Step 4.3: Perform fast non-dominated sorting to divide the individuals in the initial population into different Pareto front levels; Step 4.4: Calculate the crowding distance between different individuals at the Pareto front in the initial population, and prioritize individuals with higher crowding. If the difference in crowding distance between two individuals is less than a preset threshold, then select the individual with the smaller objective function value in the Pareto front. Step 4.5: Introduce an elite retention strategy to generate the parent population. Specifically, all individuals in the initial population are placed into population P from low to high according to their level, until it is impossible to place all individuals in a certain level into population P. Individuals in the current level are arranged from large to small according to their crowding distance and placed into population P in turn until population P is full. The full population P is the parent population. Step 4.6: The parent population generates offspring populations through fitness selection, crossover, and mutation. The number of offspring populations is the same as that of the parent population. The parent population and the offspring populations it generates are merged, and a new offspring population is generated from the merged population. The number of new offspring populations is half that of the merged population. Step 4.7: When the number of iterations reaches the maximum number of iterations, output the optimal solution set of the Pareto front.

7. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 1, characterized in that, The specific steps of using the approximation ideal solution sorting method to perform multi-scheme decision-making on the Pareto front optimal solution set are as follows: First, the objective function values ​​in the Pareto front optimal solution set are standardized to eliminate the influence of dimensions; Then, calculate the Euclidean distance between each solution and the positive and negative ideal solutions; Finally, the relative closeness of each solution is calculated, and the parameter combination with the highest relative closeness is selected as the optimal design variable scheme.

8. The multi-objective optimization method for cylindrical air film sealing based on SVR and NSGA-II according to claim 7, characterized in that, The calculation of the relative similarity of each solution is specifically as follows: ； in, Let represent the Euclidean distance between the i-th solution and the maximum value, and use it as the first distance; Let represent the Euclidean distance between the i-th solution and the minimum value, and use it as the second distance. r represents the relative proximity of the i-th solution. ij The result is the standardized objective value of the i-th solution in the Pareto front optimal solution set; r j+ r represents the maximum value of the j-th index among all solutions; j - This represents the minimum value of the j-th index among all solutions. This indicates the number of objective functions.

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