A variable-geometry propeller design and optimization method for water-air cross-medium vehicles

Abstract

The application discloses a variable airfoil propeller design and optimization method of a water-air cross-medium vehicle, and belongs to the field of artificial intelligence. The method comprises the following steps: coupling CST parameterized variables and a GAN generator to obtain a CST-GAN airfoil generation model; defining a chord length and a pitch angle distribution function and an airfoil transformation position, and generating a three-dimensional propeller geometric model; calculating aerodynamic force and hydrodynamic characteristics by using different resolution grids, and constructing a multi-precision data set; establishing a multi-precision neural network, and training a surrogate model by using a transfer learning method; and taking water-air propulsion efficiency as a multi-objective optimization function, and searching for a Pareto optimal solution by using a multi-objective optimization algorithm. The application expands the design space by using the CST-GAN, and effectively solves the cross-medium performance balance problem while reducing the calculation cost by combining a multi-precision transfer learning strategy, so that the efficient design and optimization of the propeller are realized.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence, and particularly relates to the application of deep learning in the field of fluid mechanics, and especially to a method for designing and optimizing a variable-wing propeller for a water-air transmedia vehicle. Background Technology

[0002] Aqua-air cross-medium vehicles are a new type of unmanned aerial vehicle (UAV) that combines the aerial flight capabilities of drones with the underwater navigation capabilities of unmanned underwater vehicles (UUVs), enabling them to operate in both water and air. Because they expand the exploration range of single media, can cope with more complex environments, and complete cross-medium tasks, they hold significant application prospects in multi-party collaboration and have therefore received extensive research in recent years. Among them, multi-rotor aqua-air cross-medium vehicles, with their vertical takeoff and landing (VTOL) and hovering capabilities, as well as high thrust-to-weight ratio, have attracted widespread attention. Multiple research teams both domestically and internationally have conducted research on multi-rotor aqua-air cross-medium vehicles in various directions, such as cross-medium process response speed, underwater thrust vector control, underwater drag reduction, and gearbox structure.

[0003] However, current prototypes of amphibious vehicles all directly use air-based propellers. Their thrust and propulsion efficiency underwater are significantly reduced due to the vast differences in the properties of water and air, making stable and rapid underwater navigation impossible. Furthermore, current amphibious propeller design methods primarily consider single-airfoil propellers, meaning the propeller geometry uses the same airfoil at different cross-sections. This not only fails to meet structural and strength requirements (due to the small airfoil thickness at the blade root) but also sacrifices optimization potential (due to significant differences in inflow conditions at different cross-sections). Therefore, there is an urgent need to propose a variable airfoil propeller design and optimization method capable of designing and optimizing propellers with excellent performance in both media. Summary of the Invention

[0004] The purpose of this invention is to provide a design and optimization method for a variable-blade propeller for a water-air cross-medium vehicle, in order to solve the problems of low underwater propulsion efficiency and lack of design methods for variable-blade water-air propellers in existing water-air cross-medium vehicles.

[0005] To address the aforementioned problems, this invention provides a method for designing and optimizing a variable-wing propeller for a water-to-air cross-medium vehicle, with the specific steps as follows:

[0006] Step 1: Couple the parameterized variables of the Categorical Shape Transformation (CST) method with the generator of the Generative Adversarial Network (GAN) to obtain the CST-GAN airfoil generation model. This model takes latent encoding and noise as input and outputs smooth airfoil coordinates and corresponding CST design variables.

[0007] Step 2: Define the distribution functions of chord length and pitch angle along the propeller radial direction, and define the radial position of airfoil transformation; using the CST-GAN airfoil generation model described in Step 1, generate different airfoils in different intervals divided by the radial position, and combine the parameters of blade number, radius and hub radius to generate a three-dimensional propeller geometric model.

[0008] Step 3: Based on the three-dimensional propeller geometric model, the same numerical simulation method is used to perform calculations using both low-resolution and high-resolution meshes to obtain the aerodynamic and hydrodynamic characteristics of the propeller in air and water media; the calculation results of the low-resolution mesh are used as low-precision samples, and the calculation results of the high-resolution mesh are used as high-precision samples to construct a multi-precision dataset.

[0009] Step 4: Establish a multi-precision neural network containing a pre-trained model and a high-precision model, with both models having the same network structure; first, train the pre-trained model on the low-precision samples, and then use the transfer learning method to fix the parameters of the first layer of the pre-trained model and fine-tune the parameters of the second layer using the high-precision samples to obtain the trained multi-precision neural network surrogate model.

[0010] Step 5: Using the propulsion efficiency of the propeller in water and air as the multi-objective optimization function, and the thrust coefficient and torque coefficient as constraints, a multi-objective optimization algorithm is used to search for the Pareto optimal solution in the state space to obtain the blade geometric parameters.

[0011] Furthermore, in step 1, the training process of the CST-GAN airfoil generation model includes:

[0012] The CST parameterization method is used to fit airfoils in the real airfoil database to obtain CST design variables as training labels;

[0013] Connect the CST design variables to the discriminator of the GAN, and configure the airfoil coordinates output by the generator to satisfy the true distribution and correspond to the CST parameters.

[0014] This training process, by combining the generative capabilities of GANs with the smoothness constraints of CSTs, can generate novel airfoil shapes that cannot be expressed by traditional parameterization, while ensuring geometric smoothness, significantly expanding the design space and avoiding the generation of deformed airfoils.

[0015] Furthermore, in step 2, the radial position of the airfoil transformation divides the propeller blade into K intervals along the radial direction, and each interval independently calls the CST-GAN airfoil generation model to generate a specific airfoil cross section.

[0016] This design process achieves true "variable airfoil" design. Compared to the traditional propeller design that only changes the angle of attack or chord length in the radial direction while keeping the airfoil unchanged, this step can match the optimal airfoil for the Reynolds number difference at different radii, thereby simultaneously improving the local aerodynamic / hydrodynamic performance in both water and air media.

[0017] Furthermore, the low-resolution mesh and the high-resolution mesh use the same turbulence model and boundary condition settings.

[0018] This design uses the same solver and only changes the mesh density, ensuring the consistency of the physical field control equations and eliminating the systematic errors caused by physical simplification (such as ignoring three-dimensional effects) in low-precision models. This makes feature extraction in the transfer learning process more accurate and the surrogate model prediction accuracy higher.

[0019] Furthermore, the multi-precision dataset is allocated in a 6:3:1 ratio for training, validation, and test sets. This ratio ensures sufficient model training while providing ample validation sets to prevent overfitting, making it particularly suitable for scenarios where high-precision samples are scarce, as described in this patent, and ensuring that the surrogate model still has good generalization ability on unseen geometric configurations.

[0020] Furthermore, the input variables of the multi-precision neural network include blade geometric parameters and reference Reynolds number, and the output variables include propeller thrust coefficient and torque coefficient; during the transfer learning process, the parameters of the previous layer network are fixed, and the parameters of the subsequent layer network are fine-tuned.

[0021] In this process, fixing the parameters of the first layer preserves the general flow field characteristics learned from a large amount of low-precision data, while fine-tuning the parameters of the second layer uses a small amount of high-precision data to correct numerical errors. Compared with training a high-precision model from scratch, this step achieves prediction accuracy close to that of high-precision simulation while significantly reducing computational costs (reducing the number of high-precision simulations).

[0022] Furthermore, the multi-objective optimization algorithm is the non-dominated sorting genetic algorithm NSGA-II;

[0023] The decision variables in the state space include:

[0024] Latent encoding and noise variables of airfoil generation model;

[0025] The maximum chord length, distribution coefficient, and location of the maximum chord length in the chord length distribution function;

[0026] The maximum pitch angle, distribution coefficient, and location of the maximum pitch angle in the pitch angle distribution function;

[0027] Airfoil transformation position variables.

[0028] This step utilizes NSGA-II, which can better handle multi-objective optimization problems where water-air efficiency conflicts, and obtains a uniformly distributed Pareto front. At the same time, the decision variables cover all parameters from the micro-shape of the airfoil to its macro-distribution, achieving more comprehensive synergistic optimization.

[0029] Furthermore, the optimization problem described in step 5 is to find suitable geometric parameters c1~c P z1~z P c max θ max β c β θ m c m θ loc1~loc K， P represents the dimension of latent coding and noise, and K represents the number of airfoil transformation positions. The goal is to maximize air and underwater efficiency while satisfying performance and geometric constraints, specifically expressed as follows: , In the formula, These are potential encoding variables for the airfoil generation model. For noise variables; The maximum chord length is the chord length distribution function. The maximum pitch angle is the pitch angle distribution function. The position of maximum chord length. This is the position of maximum pitch angle; The chord length distribution coefficient, The pitch angle distribution coefficient; For airfoil transformation position variables; For aerial propulsion efficiency, For underwater propulsion efficiency; This is the propeller thrust coefficient. This is the preset minimum thrust coefficient reference value; This is the propeller torque coefficient. The preset maximum torque coefficient reference value; Let be the radial coordinate of the i-th airfoil transformation position. Let be the radial coordinate of the (i-1)th airfoil transformation position; i is the index of the airfoil transformation position, and K is the total number of airfoil transformation positions; Number of cross sections; Let be the airfoil thickness at the j-th section, where j is the section index; Let be the minimum allowable airfoil thickness for the j-th section. is the maximum permissible airfoil thickness for the j-th cross section.

[0030] This step, by explicitly constraining the airfoil thickness, ensures that the optimized propeller has sufficient structural strength, avoiding the problem of the airfoil being too thin to manufacture that may occur with pure aerodynamic / hydrodynamic optimization, thus enhancing engineering practicality.

[0031] Furthermore, the method also includes a verification step: the blade geometric parameters obtained in step 5 are re-imported into the numerical simulation software, and verification calculations are performed using a high-resolution mesh. If the relative error between the surrogate model prediction value and the verification value is less than a preset threshold, the geometric parameters are output.

[0032] Another aspect of the present invention provides a variable-blade propeller for a water-air cross-medium vehicle, which is designed using the aforementioned variable-blade propeller design and optimization method for water-air cross-medium vehicles.

[0033] Beneficial effects:

[0034] The propeller design and optimization method for a water-air cross-medium vehicle of the present invention has the following advantages:

[0035] This paper proposes a solution to the problems of low underwater thrust and efficiency of propellers in existing trans-medium water-to-air vehicles. This solution can efficiently generate large datasets and quickly design propeller geometries that meet specific operating conditions, reducing computational costs and facilitating engineering implementation. Furthermore, it addresses the lack of design methods for variable airfoil water-to-air propellers, proposing a solution that allows for the design and optimization of propellers with various airfoils. This fully expands the optimization space, resulting in propeller geometries with superior performance. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. The drawings are for illustrative purposes only and are not intended to limit the present invention. In the drawings:

[0037] Appendix Figure 1 A schematic flowchart illustrating a method for designing and optimizing a propeller for a water-air cross-medium vehicle, provided in an embodiment of the present invention;

[0038] Appendix Figure 2 This is a schematic diagram of the airfoil generation model provided in an embodiment of the present invention;

[0039] Appendix Figure 3 This is a schematic diagram illustrating the low-precision and high-precision dataset acquisition method provided in an embodiment of the present invention;

[0040] Appendix Figure 4 This is a schematic diagram of a multi-precision neural network provided in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0042] As shown in Figures 1-4, this invention provides a method for designing and optimizing a variable-blade propeller for a water-to-air cross-medium vehicle. The specific steps are as follows:

[0043] Step 1, Establish the airfoil generation model: As shown in Figure 2, a CST-GAN airfoil generation model is established based on the CST method and GAN network, using a small number of airfoil design variables (including latent encoding). With noise Generate a smooth airfoil. Refit the airfoil from the real airfoil database using the CST parameterization method, using this as the training dataset. The upper and lower surfaces of the airfoil... There are points, with dimensionless coordinates as follows: The calculation formula is:

[0044]

[0045] In the formula, Indicates the first coordinate points, This represents the total number of coordinate points on a single surface. The CST parameterization method is coupled with the generator in the GAN, enabling the model to output a smooth airfoil and the corresponding CST design variables.

[0046] Step 2, establish a three-dimensional geometric database for the propeller: Divide the propeller blades radially into several equal sections, and determine the dimensionless radial position of each section. Values ​​in Within the range. Define the radial distribution function of chord length and pitch angle, with the specific expression as follows:

[0047]

[0048] In the formula, and These are the dimensionless radial positions. chord length and pitch angle at the point, and These are the maximum chord length and the maximum pitch angle, respectively. and These are the distribution coefficients for chord length and pitch angle, respectively. and These are the radial dimensionless positions where the maximum chord length and maximum pitch angle are located, respectively.

[0049] Define the airfoil transformation position ,in This indicates the dimensionless radial position at the end of the first airfoil. Indicates the second to the third The dimensionless radial position starting from the airfoil This represents the total number of airfoil transformation positions. The blade geometry is described by these blade geometric parameters, with values ​​ranging as shown in Table 1.

[0050] Table 1. Range of blade geometric parameters

[0051] Given the number of propeller blades, blade radius, and hub radius, the coordinates of the airfoil at each cross-section are calculated based on the chord length and pitch angle. This allows us to obtain the three-dimensional coordinates of all geometric points of the propeller and save them to a file.

[0052] Step 3, establish low-precision and high-precision datasets: As shown in Figure 2, generate geometric files based on the 3D coordinates of the propeller geometric points obtained in Step 2, draw low-resolution and high-resolution meshes respectively, perform numerical simulations, and calculate the aerodynamic and hydrodynamic characteristics (thrust coefficient and torque coefficient) of the propeller under given operating conditions using the following formulas:

[0053]

[0054] In the formula, For thrust coefficient, The torque coefficient, Thrust (unit: N). Torque (unit: N·m) The density of the medium is taken as 1.225 kg / m³ for air and 1025 kg / m³ for water. The propeller speed (unit: r / s). The diameter of the propeller (unit: m).

[0055] propeller propulsion efficiency The calculation formula is:

[0056]

[0057] In the formula, This is the advance coefficient. , The incoming flow velocity is expressed in m / s.

[0058] This method generates a large number of low-precision and high-precision performance parameter samples for underwater and aerial operating conditions, which are then used to form low-precision and high-precision datasets for aerodynamic and hydrodynamic characteristics, respectively. These datasets are allocated to the training set, validation set, and test set in a 6:3:1 ratio and finally saved to a file.

[0059] Step 4, Establish a multi-precision neural network: As shown in Figure 4, a multi-precision neural network is established using transfer learning. This includes a pre-trained model trained on a low-precision dataset and a high-precision model trained on top of it using a high-precision dataset (MFNN-TL model). The network structures of both models are consistent. The inputs to both models are airfoil and blade geometry parameters and a reference Reynolds number, and the outputs are the propeller thrust and torque coefficients.

[0060] This multiprecision neural network uses fully connected layers, and its forward propagation expression is:

[0061]

[0062] In the formula, For the first The output vector of the layer, For the input vector, For the first The weight matrix of the layer, For the first The layer's bias vector, The activation function is (in this embodiment, the ReLU function is used). The total number of network layers. This is the network output vector.

[0063] The number of hidden layers ranges from 2, 3, and 4, and the number of neurons per layer ranges from 64, 128, and 256. The learning rate of the pre-trained low-precision model is... The learning rate of the high-precision model is The batch size is set to 128. The Adam optimizer is used. The mean squared error (MSE) loss function is used, with the following expression:

[0064]

[0065] In the formula, For the sample size, Indicates the first The true value of each sample Indicates the first The predicted value for each sample.

[0066] Finally, by using the loss functions of the training and validation sets for different network structures, the number of layers in the N0 sub-network was determined to be 3, and the number of layers in the N1 and N2 sub-networks was 2. The number of neurons per layer in the N0 sub-network was 128, and the number of neurons per layer in the N1 and N2 sub-networks was 512. The network structure is shown in Figure 4.

[0067] Step 5, Train the surrogate model: First, train a low-precision pre-trained model on the low-precision dataset obtained in Step 3. Then, use transfer learning to keep the parameters of the first few N0 sub-network layers unchanged, and then fine-tune the later layers (fine-tuning the N1 sub-network parameters to obtain the N2 sub-network parameters), completing the training of the MFNN-TL model. The coefficient of determination is used. The model is evaluated using the following formula:

[0068]

[0069] In the formula, The average of the true values. The closer to 1, the higher the model's prediction accuracy.

[0070] A key indicator affecting the prediction accuracy of multi-precision neural networks is the ratio of low-precision to high-precision sample sizes. Too few low-precision samples result in insufficient overall training data, easily leading to overfitting; conversely, too many low-precision samples may cause the model to overfit the error distribution of the low-precision data, thus affecting its prediction accuracy for high-precision conditions. Ultimately, the surrogate model's prediction time for a single instance is 2 ms, while the numerical simulation requires 30 minutes. Therefore, the surrogate model has a significant advantage in reducing computational costs.

[0071] Step 6, Define the objective function: Based on the thrust coefficient and torque coefficient obtained from the surrogate model in both water and air, the propulsion efficiency of the propeller in both media is obtained using the efficiency formula in Step 3, and this is used as the objective function of the multi-objective optimization algorithm.

[0072] Step 7, Optimize propeller blade geometry: The NSGA-II multi-objective optimization algorithm is used, treating the geometry parameters as solutions in a population, with their value range forming the state space. After random initialization of the population, the Pareto front is sought under given constraints, using propulsion efficiency in both media as the objective function. The optimization problem is described as finding suitable airfoil geometry parameters. , ( (for the dimensions of latent coding and noise) and blade geometry parameters , , , , , , ( (The number of airfoil transformation positions) is used to maximize efficiency in the air and underwater under performance parameter and geometric constraints.

[0073] The mathematical programming expression for the optimization problem is:

[0074] Objective function:

[0075]

[0076] Constraints:

[0077]

[0078] In the formula, For aerial propulsion efficiency, For underwater propulsion efficiency; The preset minimum thrust coefficient reference value, The preset maximum torque coefficient reference value; This is the minimum allowable interval between adjacent airfoil transformation positions (0.1 in this embodiment); For the first The maximum thickness of the generated airfoil, of which This indicates the maximum thickness of the first generated airfoil (Airfoil 1). This indicates the maximum thickness of the second type of generated airfoil (Airfoil 2); and These are the upper and lower limits for thickness constraints.

[0079] Performance constraints are set to ensure that the optimized propeller has a higher thrust coefficient in both media and a lower torque coefficient underwater compared to the baseline propeller. Geometric constraints include airfoil thickness constraints and airfoil transformation position constraints. For each airfoil, the thickness is constrained individually; here, thickness refers to the maximum thickness of the airfoil along the chord direction. For airfoil transformation positions, at least one transition section is ensured between the two airfoils to guarantee blade surface smoothness.

[0080] Based on the same technical concept, another embodiment of the present invention also provides a variable-blade propeller for a water-air transmedia vehicle, which is designed using a variable-blade propeller design and optimization method for water-air transmedia vehicles.

[0081] Example 1

[0082] Design a small, dual-purpose, variable-air airfoil propeller with 3 blades, a blade radius of 0.12 m, a hub radius of 0.012 m, and two different airfoils.

[0083] Based on step 1, the CST parametric method is used to refit the real airfoil library, with 101 points on each of the upper and lower surfaces, and dimensionless coordinates are set as follows. , The latent encoding and noise dimensions are both set to 6, and the airfoil generation model is trained.

[0084] According to step 2, the propeller blade is divided into 10 equal sections along the radial direction, and the dimensionless radial position of the sections is... Values The geometric parameters of the reference propeller (a specific airfoil propeller, using the ClarkY airfoil) are set as follows: , , , , , .

[0085] Following step 3, the PythonOCC library was used to generate STL geometry files from the 3D coordinates. These files were then imported into Star-CCM+, and low-resolution and high-resolution meshes were drawn for numerical simulation. A total of 3000 low-precision samples for aerial and underwater conditions, and 200 high-precision samples for aerial and underwater conditions were generated.

[0086] According to step 4, the low-precision network maintains the same structure as the high-precision network, that is, the N0 sub-network has 3 hidden layers with 128 neurons per layer, and the N1 and N2 sub-networks have 2 hidden layers with 512 neurons per layer.

[0087] According to step 5, set the learning rate of the low-precision model to be... The learning rate of the high-precision model is The batch size was set to 128. The Adam optimizer was used. The mean squared error function was used as the loss function. The program was trained with different low-precision sample sizes (ratios of 2, 4, 6, 8, and 10) to compare the results. A suitable low-precision sample size was selected. The results are shown in Table 2. The model performed best when the low-precision sample size was 6 times that of the high-precision sample size.

[0088] Table 2. Accuracy of Models with Different Low-Precision Sample Sizes

[0089] According to step 6, the objective function is defined as the propulsion efficiency of the propeller in both media, i.e. and .

[0090] According to step 7, the optimization problem is shown in Table 3. Thrust constraints are set to ensure the optimized propeller has a higher thrust coefficient in both media, while the torque coefficient in underwater operation is constrained to avoid generating geometry with excessive torque. Constraints are also added regarding the relative positions of the maximum pitch angle and maximum chord length. For the airfoil, its thickness is constrained, where thickness refers to the maximum airfoil thickness. Furthermore, constraints are placed on the transition positions between the two airfoils, ensuring that at least one section uses Airfoil 1, and that there is at least one transition section between the two airfoils. The solution space of this algorithm includes 12 latent codes and 12 noises controlling the generation of the two airfoils, 6 blade design variables controlling the chord length and pitch angle distribution functions, and two airfoil transition positions. The NSGA-II optimization method parameters are set as follows: maximum number of iterations 200 generations, population size 200, and crossover probability 0.8.

[0091] Table 3. Description of the optimization problem

[0092] In the table, The maximum thickness of the baseline Clark Y airfoil, The maximum thickness of the first type of generated airfoil. This represents the maximum thickness of the second type of generated airfoil.

[0093] The optimization results are shown in Table 4. The results show that the optimized propeller geometry has better performance than the reference propeller in both media.

[0094] Table 4 Comparison of Propeller Performance

[0095] It is worth noting that existing technologies, limited by traditional parametric methods (such as Hicks-Henne) and single-precision models, struggle to account for the significant differences in physical properties between water and air media (density ratio approximately 800:1, Reynolds numbers spanning orders of magnitude), often falling into the performance trade-off of "increasing underwater efficiency at the expense of decreasing airborne efficiency." This application expands the geometric design space through a CST-GAN coupled model, exploring airfoil configurations unreachable by traditional methods. Simultaneously, it employs a multi-precision transfer learning strategy based on grid resolution differences. While ensuring the consistency of the physical field control equations, it utilizes low-precision samples to construct a global mapping and high-precision samples to correct boundary layer errors, significantly improving prediction accuracy under dual-media conditions. Experiments show that this application achieves a simultaneous improvement in airborne efficiency (17.08% to 17.18%) while significantly increasing underwater efficiency (63.25% to 70.89%), overcoming the "one-sided" shortcomings of existing technologies. This collaborative mechanism of "geometric constraints + multi-precision migration" achieves Pareto optimality of performance in both water and air modes within an acceptable cost, solving the technical bottleneck of balancing performance and computational efficiency in cross-medium design.

[0096] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for designing and optimizing a variable-blade propeller for a water-air cross-medium vehicle, characterized in that, include: Step 1: Couple the parameterized variables of the Categorical Shape Transformation Method (CST) with the generator of the Generative Adversarial Network (GAN) to obtain the CST-GAN airfoil generation model. This model takes latent encoding and noise as input and outputs airfoil coordinates and corresponding CST design variables. Step 2: Define the distribution functions of chord length and pitch angle along the propeller radial direction, and define the radial position of airfoil transformation; using the CST-GAN airfoil generation model, generate different airfoils in different intervals divided by the radial position, and combine the parameters of blade number, radius and hub radius to generate a three-dimensional propeller geometric model. Step 3: Based on the three-dimensional propeller geometric model, the same numerical simulation method is used to perform calculations using both low-resolution and high-resolution meshes to obtain the aerodynamic and hydrodynamic characteristics of the propeller in air and water media; the calculation results of the low-resolution mesh are used as low-precision samples, and the calculation results of the high-resolution mesh are used as high-precision samples to construct a multi-precision dataset. Step 4: Establish a multi-precision neural network containing a pre-trained model and a high-precision model, with both models having the same network structure; first, train the pre-trained model on the low-precision samples, and then use the transfer learning method to fix the parameters of the first layer of the pre-trained model and fine-tune the parameters of the second layer using the high-precision samples to obtain the trained multi-precision neural network surrogate model. Step 5: Utilize the multi-precision neural network surrogate model to predict the propulsion efficiency, thrust coefficient, and torque coefficient of the candidate geometric parameters. Using the propulsion efficiency of the propeller in water and air media as the multi-objective optimization function and the thrust coefficient and torque coefficient as constraints, a multi-objective optimization algorithm is used to search for the Pareto optimal solution in the state space to obtain the blade geometric parameters.

2. The method according to claim 1, characterized in that, In step 1, the training process of the CST-GAN airfoil generation model includes: The CST parameterization method is used to fit airfoils in the real airfoil database to obtain CST design variables as training labels; Connect the CST design variables to the discriminator of the GAN, and configure the output airfoil coordinates to satisfy the true distribution and correspond to the CST parameters.

3. The method according to claim 1, characterized in that, In step 2, the radial position of the airfoil transformation divides the propeller blade into K intervals along the radial direction, and the CST-GAN airfoil generation model is independently called to generate the airfoil section within each interval.

4. The method according to claim 1, characterized in that, In step 3, the low-resolution mesh and the high-resolution mesh use the same turbulence model and boundary condition settings.

5. The method according to claim 1, characterized in that, In step 3, the multi-precision dataset is allocated according to a ratio of 6:3:1 for the training set, validation set, and test set.

6. The method according to claim 1, characterized in that, In step 4, the input variables of the multi-precision neural network include blade geometric parameters and reference Reynolds number, and the output variables include propeller thrust coefficient and torque coefficient; during the transfer learning process, the parameters of the front layer network are fixed, and the parameters of the back layer network are fine-tuned.

7. The method according to claim 1, characterized in that, In step 5, the multi-objective optimization algorithm is the non-dominated sorting genetic algorithm NSGA-II; The decision variables in the state space include: Latent encoding and noise variables of airfoil generation model; The maximum chord length, distribution coefficient, and location of the maximum chord length in the chord length distribution function; The maximum pitch angle, distribution coefficient, and location of the maximum pitch angle in the pitch angle distribution function; Airfoil transformation position variables.

8. The method according to claim 7, characterized in that, The optimization problem described in step 5 is to find suitable geometric parameters c1~c P z1~z P c max θ max β c β θ m c m θ loc1~loc K， P represents the dimension of latent coding and noise, and K represents the number of airfoil transformation positions. The goal is to maximize air and underwater efficiency while satisfying performance and geometric constraints, specifically expressed as follows: ， In the formula, These are potential encoding variables for the airfoil generation model. For noise variables; The maximum chord length is the chord length distribution function. The maximum pitch angle is the pitch angle distribution function. The position of maximum chord length. This is the position of maximum pitch angle; The chord length distribution coefficient, The pitch angle distribution coefficient; For airfoil transformation position variables; For aerial propulsion efficiency, For underwater propulsion efficiency; This is the propeller thrust coefficient. This is the preset minimum thrust coefficient reference value; This is the propeller torque coefficient. The preset maximum torque coefficient reference value; Let be the radial coordinate of the i-th airfoil transformation position. Let be the radial coordinate of the (i-1)th airfoil transformation position; i is the index of the airfoil transformation position, and K is the total number of airfoil transformation positions; Number of cross sections; Let be the airfoil thickness at the j-th section, where j is the section index; Let be the minimum allowable airfoil thickness for the j-th section. is the maximum permissible airfoil thickness for the j-th cross section.

9. The method according to claim 1, characterized in that, It also includes a verification step, specifically: The blade geometry parameters obtained in step 5 are re-imported into the numerical simulation software, and a high-resolution mesh is used for verification calculation. If the relative error between the surrogate model prediction value and the verification value is less than a preset threshold, the geometry parameter is output.

10. A variable-blade propeller for a water-air transmedium vehicle, characterized in that, It is designed using the method described in any one of claims 1 to 9.

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