Airfoil profile multi-objective optimization method and system based on reinforcement learning and Pareto

Abstract

The invention discloses an airfoil profile multi-objective optimization method and system based on reinforcement learning and Pareto, and relates to the technical field of mechanical optimization design. Comprising the steps of building an airfoil profile parameterization design platform based on a convolutional neural network and a generative adversarial network, evaluating the airfoil profile performance by adopting Neuralfoil based on a physical neural network, and building an airfoil profile multi-objective optimization model based on reinforcement learning and Pareto optimization. According to the method, through combination of the convolutional neural network and the generative adversarial network, airfoil profile parameter dimension reduction is realized, and airfoil profile malformation in a design space is avoided; the problem that traditional Xfoil is not converged in the calculation process is solved through Neuralfoil, the method is particularly suitable for processing airfoils with the shapes frequently adjusted in the reinforcement learning process, and more stable and faster aerodynamic characteristic calculation is provided; through combination of reinforcement learning and Pareto, application exploration of reinforcement learning in the aspect of airfoil profile multi-objective optimization is realized, and a new thought for airfoil profile optimization is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical optimization design, and in particular to a multi-objective optimization method and system for airfoil based on reinforcement learning and Pareto. Background Art

[0002] The optimal design of airfoils is of great significance to improving the operating performance of high-end fluid equipment such as aircraft, underwater propulsion systems, and nuclear power plant main pumps. Under actual working conditions, airfoil optimization is often multi-objective, and these objectives often constrain each other. Traditional single-objective optimization methods are difficult to effectively handle these complex constraints and trade-offs. The concept of Pareto front provides a solution to this problem. By finding a set of non-dominated solutions in multi-objective optimization, it can effectively deal with situations where multiple design objectives conflict with each other, providing a more comprehensive and effective means for engineering design.

[0003] In traditional airfoil optimization design methods, weighted methods are usually used to carry out multi-objective optimization, and multi-objective optimization methods based on Pareto frontiers are usually combined with evolutionary algorithms, genetic algorithms, etc. for solution. However, with the development of deep learning and reinforcement learning technologies, their application in multi-objective optimization can more efficiently handle large-scale design spaces and multi-dimensional parameter problems. Through the exploration ability of reinforcement learning and the feature extraction ability of deep learning, the Pareto multi-objective optimization method can more efficiently explore the design space and find the optimal solution set in complex airfoil design problems. At the same time, deep learning can model historical data, accelerate the optimization process, and further improve the optimization accuracy through the feedback mechanism of reinforcement learning. At the same time, deep learning methods can increase the possibility of future method migration.

[0004] In addition, in the parametric design of airfoils, traditional methods usually rely on a large number of design parameters to define the airfoil shape, which not only increases the complexity of the design, but also requires the designer to have rich domain knowledge to generate a reasonable airfoil. However, with the development of Generative Adversarial Network (GAN), the parametric problem of airfoil design has been effectively solved. The generator of GAN can learn the characteristic distribution of complex airfoils through training, so as to quickly generate airfoils with excellent aerodynamic performance. This method not only reduces the workload of designers, but also improves the flexibility of design and provides more possibilities for airfoil optimization. At the same time, in the calculation process based on traditional Xfoil, especially in the process of optimization design, Xfoil is prone to non-convergence, especially when the airfoil shape is constantly changing, which will greatly affect the efficiency of optimization and the accuracy of the results. To solve this problem, Neuralfoil based on Physics-Informed Neural Networks (PINN) provides a more stable calculation tool. Compared with Xfoil, Neuralfoil can better cope with the dynamic changes of airfoil shapes. During the reinforcement learning process, it can calculate the aerodynamic characteristics of different airfoils more efficiently and accurately, avoiding the convergence problem of Xfoil. It is especially suitable for optimization processes that require frequent adjustments to airfoil shapes.

[0005] Therefore, the present invention proposes a multi-objective optimization design method for airfoils based on reinforcement learning and Pareto optimality. Through the application of convolutional neural networks and generative adversarial networks, this method can reduce the dimension of airfoil parameters, and can quickly generate reasonable airfoil shapes from random numbers, which greatly simplifies the parametric design process of the airfoil and reduces the design complexity. At the same time, the PINN-based Neuralfoil replaces the traditional Xfoil, providing a more stable and efficient aerodynamic performance calculation tool, which is particularly suitable for processing dynamically adjusted airfoil shapes during reinforcement learning. In addition, the Pareto concept is integrated into reinforcement learning to achieve multi-objective optimization of airfoils. This method can find the optimal balance between multiple design objectives, explore the application of reinforcement learning in the field of multi-objective optimization of airfoils, and achieve efficient and more practical airfoil optimization design. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention is proposed.

[0007] The problems to be solved by the present invention are: 1. How to solve the problems of huge design space, high calculation cost and difficult algorithm search caused by excessive parameter dimension in traditional airfoil design, as well as the problem of a large number of airfoil deformities in the airfoil design space after parameter dimensionality reduction; 2. How to solve the problem of non-convergence that easily occurs in Xfoil during complex optimization processes, resulting in unstable calculation and slow speed; 3. The problem of how to apply reinforcement learning in multi-objective optimization of airfoils.

[0008] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0009] In a first aspect, an embodiment of the present invention provides a multi-objective optimization method for an airfoil based on reinforcement learning and Pareto, which includes building an airfoil parameterization design platform based on a convolutional neural network and a generative adversarial network, based on which a basic airfoil can be parameterized and dimensionally reduced, and a reasonable design space similar to an airfoil database can be formed;

[0010] Neuralfoil, a physical neural network-based method, is used to evaluate airfoil performance, improving the non-convergence and slow calculation problems of the commonly used xfoil method during the calling process.

[0011] A multi-objective optimization model for the airfoil was built based on reinforcement learning and Pareto optimality, and the Pareto solution set consisting of the optimized airfoil performance parameters and its geometric coordinates were output.

[0012] As a preferred solution of the multi-objective optimization method of airfoil based on reinforcement learning and Pareto of the present invention, the specific implementation logic of the airfoil parameterized design platform based on convolutional neural network and adversarial generative network is:

[0013] A convolutional neural network-based airfoil parameter dimensionality reduction model is constructed, including an encoder and a decoder; the encoder reduces the dimensionality of the airfoil image data into several parameters, and the decoder reconstructs the airfoil from the parameters into the airfoil image data; the airfoil parameter dimensionality reduction model is trained by a public airfoil database to ensure a one-to-one correspondence between the dimensionality reduction parameters and the airfoil;

[0014] An airfoil design model based on a generative adversarial network is constructed, including a generator and a discriminator; the input of the generator is the noise randomly sampled in the airfoil parameter space; the output of the generator is restored to the coordinate points of the airfoil through the airfoil decoder and used as the input of the discriminator, and the input form is the point coordinates representing the airfoil shape; at the same time, the discriminator also receives the point coordinates of the normal airfoil in the airfoil data set, which is used to train the discriminator to distinguish between true airfoils and false airfoils.

[0015] As a preferred solution of the multi-objective optimization method of airfoil based on reinforcement learning and Pareto of the present invention, wherein: Neuralfoil is constructed by a physics-based neural network and trained using the calculation data of Xfoil; the input of Neuralfoil is the coordinates and flow condition parameters of the basic airfoil, the flow condition parameters include the airfoil angle of attack and the Reynolds number, and the output is the lift-to-drag ratio of the airfoil and the minimum surface pressure coefficient.

[0016] As a preferred solution of the airfoil multi-objective optimization method based on reinforcement learning and Pareto of the present invention, the airfoil multi-objective optimization model specifically includes the following logic:

[0017] The state of reinforcement learning is Z i =[P i , C Li , C Di , C pmi ], where P is the fitting parameter of the first airfoil, which is a 6-dimensional vector, namely: P = [P 0 , P 1 ,……,P 5 ], C L , C D They represent the lift coefficient and drag coefficient of the first airfoil under the corresponding fitting parameters, Cp m The minimum surface pressure coefficient of the first airfoil under the corresponding fitting parameters; the action is a vector A with the same shape as the airfoil fitting parameters i =[a 0 、a 1 ,……,a 5 ], representing the impact of this action on each parameter;

[0018] The airfoil optimization model is based on the Proximal Policy Optimization (PPO) reinforcement learning framework, in which the intelligent agent is constructed through a convolutional neural network and is responsible for decision-making in multi-objective optimization tasks.

[0019] As a preferred solution of the airfoil multi-objective optimization method based on reinforcement learning and Pareto of the present invention, the specific application logic of the airfoil performance prediction model is:

[0020] Neuralfoil, a physics-based neural network, is used to evaluate the airfoil performance. Neuralfoil is a physics-based neural network model. The evaluation data of various airfoils are trained through Xfoil, covering multiple Reynolds numbers, multiple Mach numbers and other working conditions, and physical mechanisms are added.

[0021] As a preferred solution of the multi-objective optimization method of airfoil based on reinforcement learning and Pareto of the present invention, the reward value is mainly determined by the optimization objective and the Pareto frontier, specifically:

[0022] The reward value is set as:

[0023] Reward 1 =2+α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m ))

[0024] Reward 2 = -2 + α (I (k) + I (Cp m ))+(1-α)(D(k)+D(Cp m ))

[0025] Reward 3 =α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m ))

[0026] k=C l / C d

[0027]

[0028] Where k is the lift-to-drag ratio C corresponding to the current airfoil l / C d , Cp m is the current minimum surface lift coefficient; k front is the lift-to-drag ratio of the solution that is closest to the current Pareto front and the current airfoil; CP mfront k is the minimum surface pressure coefficient of the solution closest to the previous Pareto front and the current airfoil; object is the target lift-to-drag ratio initially set; Cp mobject is the target minimum surface pressure coefficient; I represents the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the current Pareto front improvement; D represents the distance reduction value of the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the target; α is the weight coefficient in the value range (0,1).

[0029] As a preferred solution of the multi-objective optimization method of airfoil based on reinforcement learning and Pareto, when the current solution is the dominant solution, the reward is Reward 1 , when the current solution is the dominated solution, the reward is Reward 2 , when the current solution is neither the dominant solution nor the dominated solution, the reward is Reward 3 ;

[0030] After the reward of the current solution is calculated, the current solution is added to the Pareto front, and the relationship between all Pareto front solutions is updated to remove the dominated solutions.

[0031] In a second aspect, an embodiment of the present invention provides an airfoil multi-objective optimization system based on reinforcement learning and Pareto, which includes an airfoil parameterized design module for building an airfoil parameterized design platform based on a convolutional neural network and a generative adversarial network to form a design space similar to an airfoil database;

[0032] Airfoil performance evaluation module, used to evaluate airfoil performance using Neuralfoil based on physical neural network;

[0033] The multi-objective optimization module is used to build a multi-objective optimization model for airfoils based on reinforcement learning and Pareto optimality, and output the Pareto solution set composed of the optimized airfoil performance parameters and its geometric coordinates.

[0034] In a third aspect, an embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, the steps of the multi-objective optimization method of an airfoil based on reinforcement learning and Pareto are implemented as in the first aspect of the present invention.

[0035] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, the steps of the multi-objective optimization method for airfoils based on reinforcement learning and Pareto are implemented as in the first aspect of the present invention.

[0036] The beneficial effects of the present invention are as follows: the present invention provides a new idea in airfoil optimization design by combining reinforcement learning with Pareto multi-objective optimization. The convolutional neural network reduces airfoil design parameters, reduces design complexity, and improves design efficiency. In addition, the GAN avoids the situation of deformed airfoils in the airfoil design space, and can quickly generate reasonable airfoils. Neuralfoil based on PINN overcomes the problem of non-convergence of traditional Xfoil during the calculation process, improves calculation efficiency, and is particularly suitable for processing airfoils whose shapes are frequently adjusted during reinforcement learning. By combining the exploration ability of reinforcement learning with multi-objective optimization, the present invention can effectively search and find the optimal design solution set in a broad design space, achieving an efficient trade-off between design goals. The present invention significantly reduces computing costs, improves optimization efficiency, and expands the application potential of reinforcement learning technology in the field of airfoil optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0038] Figure 1 The flowchart of the multi-objective optimization method of airfoil based on reinforcement learning and Pareto;

[0039] Figure 2 A schematic diagram of network training for the multi-objective optimization method of airfoil based on reinforcement learning and Pareto;

[0040] Figure 3 The initial general airfoil diagram for the multi-objective optimization method of airfoil based on reinforcement learning and Pareto;

[0041] Figure 4 , Figure 5 Optimization process diagram of the optimization objectives of the multi-objective optimization method for airfoil based on reinforcement learning and Pareto;

[0042] Figure 6 Training Pareto front graphs for networks based on reinforcement learning and Pareto’s approach for multi-objective optimization of airfoils.

[0043] Figure 7 Comparison diagram of the airfoil before and after optimization based on reinforcement learning and Pareto's airfoil multi-objective optimization method. DETAILED DESCRIPTION

[0044] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0045] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0046] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0047] Example 1

[0048] Reference Figure 1 to Figure 7, which is the first embodiment of the present invention, and provides a multi-objective optimization method for airfoil based on reinforcement learning and Pareto, comprising:

[0049] Build an airfoil parameterization design platform based on convolutional neural networks and generative adversarial networks. Based on this platform, the basic airfoil can be parameterized and dimensionally reduced, and a design space similar to the airfoil database can be formed.

[0050] The specific implementation logic of the airfoil parametric design platform based on convolutional neural networks and adversarial generative networks is as follows:

[0051] A convolutional neural network-based airfoil parameter dimensionality reduction model is constructed, including an encoder and a decoder; the encoder reduces the dimensionality of the airfoil image data into several parameters, and the decoder reconstructs the airfoil from the parameters into the airfoil image data; the airfoil parameter dimensionality reduction model is trained by a public airfoil database to ensure a one-to-one correspondence between the dimensionality reduction parameters and the airfoil;

[0052] The model is trained using a public airfoil database. The airfoil image data in the public airfoil database can be converted into 6 fitting parameters through the airfoil parameter dimension reduction model, and the airfoil parameter space is obtained.

[0053] An airfoil design model based on a generative adversarial network is constructed, including a generator and a discriminator; the input of the generator is the noise randomly sampled in the airfoil parameter space; the output of the generator is restored to the coordinate points of the airfoil through the airfoil decoder and used as the input of the discriminator, and the input form is the point coordinates representing the airfoil shape; at the same time, the discriminator also receives the point coordinates of the normal airfoil in the airfoil data set, which is used to train the discriminator to distinguish between true airfoils and false airfoils.

[0054] At the same time, the discriminator also accepts normal airfoil data in the public airfoil database as input, which is used to train the discriminator to distinguish true and false airfoils; after training the airfoil design model, the generator can generate an airfoil design space with similar airfoil shapes to the public airfoil database.

[0055] Preferably, the public airfoil database should be explained as follows: the public airfoil database refers to the airfoil database published by the University of Illinois at Urbana-Champaign. The number of fitting parameters is preferably 6.

[0056] Neuralfoil based on PINN physical neural network is used to evaluate the airfoil performance to improve the non-convergence and slow calculation problems of the commonly used xfoil method during the calling process.

[0057] The specific application logic of the airfoil performance prediction model is:

[0058] Neuralfoil, which is based on a physical neural network, is used to evaluate the airfoil performance. Neuralfoil is trained with Xfoil data, covering multiple airfoils, multiple Reynolds numbers, multiple Mach numbers and other working conditions. It also adds physical mechanisms to achieve the same calculation accuracy as xfoil, while improving the non-convergence and slow calculation problems that occur during the calling process of xfoil.

[0059] The optimization variables are random vectors similar to the dimension reduction parameters in the airfoil parametric design platform; the optimization objectives consider the maximization of lift-to-drag ratio and the optimization of cavitation performance. The cavitation performance is determined by the minimum value of the surface pressure coefficient, that is, the optimization objectives are the maximum lift-to-drag ratio and the minimum surface pressure coefficient.

[0060] Neuralfoil is built with a physics-based neural network and trained using Xfoil's computational data. Neuralfoil's input is the coordinates of the basic airfoil and flow parameters, including the airfoil angle of attack and Reynolds number. The output is the airfoil's lift-to-drag ratio and the minimum surface pressure coefficient.

[0061] A multi-objective optimization model for the airfoil was built based on reinforcement learning and Pareto optimality, and the Pareto solution set consisting of the optimized airfoil performance parameters and its geometric coordinates were output.

[0062] Furthermore, the airfoil multi-objective optimization model specifically includes the following logic:

[0063] The state of reinforcement learning is Z i =[P i , C Li , C Di , C pmi ], where P is the fitting parameter of the first airfoil, which is a 6-dimensional vector, namely: P = [P 0 , P 1 ,……,P 5 ], C L , C D They represent the lift coefficient and drag coefficient of the first airfoil under the corresponding fitting parameters, Cp m The minimum surface pressure coefficient of the first airfoil under the corresponding fitting parameters; the action is a vector A with the same shape as the airfoil fitting parameters i =[a 0 、a 1 ,……,a 5 ], representing the impact of this action on each parameter;

[0064] The airfoil optimization model is based on the proximal policy optimization (PPO) reinforcement learning framework, in which the agent is constructed through a convolutional neural network and is responsible for making decisions in multi-objective optimization tasks. Specifically, in each round, the agent makes a decision based on the current airfoil optimization state Z. i =[P i , C Li , C Di , C pmi ]Select Action A i This action is used to adjust the six parameters of the airfoil and obtain the updated parameter set P i+1 =P i +A i .

[0065] The action of the intelligent agent is generated by the decision network, and the updated airfoil is evaluated by the Neuralfoil airfoil performance prediction model to obtain new performance indicators, including the lift-to-drag ratio of the airfoil, the minimum surface pressure coefficient, etc. The new airfoil optimization state is Z i+1 =[P i+1 , C Li+1 , C Di+1 , C pmi+1 ], and then fed back to the intelligent agent, forming a complete state-action-reward closed loop.

[0066] During this process, the reward function is used to measure the effect of each action, taking into account the lift-to-drag ratio and surface pressure coefficient of the airfoil. Through multiple rounds of interaction with the Neuralfoil model, the agent continuously collects "state-action-reward" samples, which are used to optimize the hyperparameters of the neural network to estimate the reward value more accurately. As the training progresses, the decision-making ability of the agent gradually improves, and the final set of fitting parameters can improve the performance of the airfoil while meeting the optimization goal.

[0067] Furthermore, the reward value is mainly determined by the optimization objective and the Pareto frontier, specifically:

[0068] The reward value is set as:

[0069] Reward 1 =2+α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m ))

[0070] Reward 2 = -2 + α (I (k) + I (Cp m ))+(1-α)(D(k)+D(Cp m ))

[0071] Reward 3 =α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m ))

[0072] k=C l / C d

[0073]

[0074] Where k is the lift-to-drag ratio C corresponding to the current airfoil l / C d , Cp m is the current minimum surface lift coefficient; k front is the lift-to-drag ratio of the solution that is closest to the current Pareto front and the current airfoil; CP mfront k is the minimum surface pressure coefficient of the solution closest to the previous Pareto front and the current airfoil; object is the target lift-to-drag ratio initially set; Cp mobject is the target minimum surface pressure coefficient; I represents the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the current Pareto front improvement; D represents the distance reduction value of the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the target; α is the weight coefficient in the value range (0,1).

[0075] The reward value is not limited to two target values, and constraints can also be taken into account.

[0076] Furthermore, when the current solution is the dominant solution, the reward is Reward 1 , when the current solution is the dominated solution, the reward is Reward 2 , when the current solution is neither the dominant solution nor the dominated solution, the reward is Reward 3 .

[0077] Exemplarily, α is selected as 0.5, and this value and specific reward value items can be changed according to the application scenario, optimization objectives and constraints of the airfoil to be optimized.

[0078] A large number of airfoil geometry parameter-action-reward value samples are obtained through the airfoil optimization design model, and the airfoil parameters are continuously adjusted to obtain a new airfoil lift-to-drag ratio, minimum surface pressure coefficient and reward value. These experience samples are accumulated and used to train the reinforcement learning network to evaluate the difference between the actual reward and the estimated reward. The network weights are continuously updated during the training process to improve the accuracy of the reward estimation.

[0079] The model training is carried out in two rounds. A fixed number of steps is preset in each round. After the fixed number of steps is reached, the airfoil to be optimized is updated to the optimal airfoil and its dimension reduction parameters in the previous training process, and the next round of optimization and model training is continued from this starting point.

[0080] Furthermore, after the reward of the current solution is calculated, the current solution is added to the Pareto front, and the relationship between all Pareto front solutions is updated to remove the dominated solution.

[0081] Furthermore, the present embodiment also provides an airfoil multi-objective optimization system based on reinforcement learning and Pareto, including an airfoil parameterized design module for building an airfoil parameterized design platform based on a convolutional neural network and a generative adversarial network to form a design space similar to an airfoil database;

[0082] Airfoil performance evaluation module, used to evaluate airfoil performance using Neuralfoil based on physical neural network;

[0083] The multi-objective optimization module is used to build a multi-objective optimization model for airfoils based on reinforcement learning and Pareto optimality, and output the Pareto solution set composed of the optimized airfoil performance parameters and its geometric coordinates.

[0084] This embodiment also provides a computer device, which is suitable for the case of a multi-objective optimization method for airfoils based on reinforcement learning and Pareto, including a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute computer-executable instructions to implement the multi-objective optimization method for airfoils based on reinforcement learning and Pareto as proposed in the above embodiment.

[0085] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.

[0086] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the multi-objective optimization method for an airfoil based on reinforcement learning and Pareto is implemented as proposed in the above embodiment.

[0087] In summary, the present invention provides a new idea in airfoil optimization design by combining reinforcement learning with Pareto multi-objective optimization. The convolutional neural network reduces the airfoil design parameters, reduces the design complexity, and improves the design efficiency. In addition, the GAN avoids the situation of deformed airfoils in the airfoil design space, and can quickly generate reasonable airfoils. The PINN-based Neuralfoil overcomes the problem of non-convergence of traditional Xfoil during the calculation process, improves the calculation efficiency, and is particularly suitable for processing airfoils whose shapes are frequently adjusted during the reinforcement learning process. By combining the exploration ability of reinforcement learning with multi-objective optimization, the present invention can effectively search and find the optimal design solution set in a wide design space, achieving an efficient trade-off between design goals. The present invention significantly reduces the computational cost, improves the optimization efficiency, and expands the application potential of reinforcement learning technology in the field of airfoil optimization design.

[0088] Example 2

[0089] This is the second embodiment of the present invention, which provides a multi-objective optimization method for airfoil based on reinforcement learning and Pareto. In order to verify the beneficial effects of the present invention, a scientific demonstration is carried out through simulation experiments.

[0090] In order to verify the effectiveness of the method of the present invention, this example selects the airfoil to be optimized through the airfoil parameterized design platform based on convolutional neural network and adversarial generative network, and its six fitting parameters are:

[0091] [-0.319,-0.513,-0.421,-0.139,-0.274,-0.247], the airfoil image is as follows Figure 3 shown.

[0092] Firstly, a parametric design platform for airfoils based on convolutional neural network (CNN) and generative adversarial network (GAN) was constructed. 1550 airfoils in the UIUC airfoil database were used as the training set. The hidden layer dimension of the generator was 256, with a total of 3 layers, and finally 69 coordinate points were output through the fully connected layer; the discriminator had a similar structure to the generator, with a hidden layer dimension of 128 and a total of 3 layers, and finally Sigmoid was used to output the probability. During training, the initial learning rate of the generator and the discriminator was 0.00005. The generator was trained once after every 5 training of the discriminator. The activation function used by the generator and the discriminator was LeakyReLU. The Adam optimizer was used to update the network parameters, the batch size was 16, and the total number of training rounds was 1000. The loss function of WGAN was used to train the model.

[0093] Next, Neuralfoil, a physical neural network, was used to evaluate the airfoil performance. 200 airfoil coordinate points were obtained by re-panelization through Xfoil. As the input of Neuralfoil, the airfoil angle of attack was selected as 4 degrees, the Reynolds number was 2e5, and the Mach number was 0.2. The output was the lift and drag coefficient and pressure coefficient of the airfoil under this condition.

[0094] Finally, a multi-objective optimization model for airfoils is built based on reinforcement learning and Pareto optimality. The reinforcement learning agent adopts the PPO algorithm. Both the policy network and the value network are 4-layer fully connected networks with 64 neurons in each layer. The reward function is designed according to the formula in claim 6, where α is taken as 0.5. The optimization goal is to maximize the lift-to-drag ratio and minimize the absolute value of the minimum surface pressure coefficient. Under the conditions of Reynolds number 2×10^5 and Mach number 0.2, the airfoil to be optimized is optimized at an angle of attack of 4°. This optimization design iterated a total of 1000 rounds, with a maximum number of steps of 1000 in each round. The results are as follows: Figure 4-Figure 7 As shown. Figure 4 , Figure 5 The changes of lift-to-drag ratio and minimum surface pressure coefficient in some rounds during the iteration process are shown respectively. Figure 6 , Figure 7 The images of the Pareto front solution set when the final optimization is completed and the images of a certain front solution after restoration by the airfoil parameterization platform are respectively shown. The lift-to-drag ratio of the common airfoil at the initial Reynolds number of 2e5 and the angle of attack is 73.0090, and the minimum surface pressure coefficient is -1.3411. After optimization, the Pareto front solution set is selected, and the lift-to-drag ratio and the minimum surface pressure coefficient are better than all the solutions in the initial state. The average lift-to-drag ratio is 82.8249, an increase of 13.445%, and the average minimum surface pressure coefficient is -1.9514, a decrease of -45.504%.

[0095] In summary, the multi-objective optimization method of airfoil based on reinforcement learning and Pareto proposed in the present invention can solve the problems of huge design space, high computational cost and difficult algorithm search caused by excessive parameter dimensions in traditional airfoil design, and also avoid the situation of designing deformed airfoil through GAN. At the same time, the introduction of Neuralfoil effectively solves the non-convergence problem that traditional Xfoil is prone to in the complex optimization process, and is particularly suitable for scenarios where the airfoil shape is frequently adjusted during reinforcement learning. Moreover, by integrating the concepts of reinforcement learning and Pareto optimality, the two objectives of lift-to-drag ratio and surface pressure coefficient are considered at the same time, and a better balance is found between the two. This method not only realizes the effective optimization of the airfoil, but also the reinforcement learning method is transferable, and will have great application value in the future.

[0096] Finally, this invention provides a new idea for the application of reinforcement learning in airfoil design, and is expected to produce important application value in the fields of aviation, underwater propulsion, etc.

[0097] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A multi-objective optimization method for airfoil based on reinforcement learning and Pareto, characterized by: include, Build an airfoil parameterization design platform based on convolutional neural networks and generative adversarial networks. Based on this platform, the basic airfoil can be parameterized and dimensionally reduced, and a design space similar to the airfoil database can be formed. Neuralfoil, a physical neural network-based method, is used to evaluate airfoil performance, improving the non-convergence and slow calculation problems of the commonly used xfoil method during the calling process. A multi-objective optimization model for the airfoil was built based on reinforcement learning and Pareto optimality, and the Pareto solution set consisting of the optimized airfoil performance parameters and its geometric coordinates were output.

2. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 1, characterized in that: The specific implementation logic of the airfoil parameterized design platform based on convolutional neural network and generative adversarial network is as follows: Building an airfoil parameter dimension reduction model based on a convolutional neural network, including an encoder and a decoder; the encoder reduces the dimension of the airfoil image data into several parameters, and the decoder reconstructs the airfoil from the parameters into the airfoil image data; The airfoil parameter dimension reduction model is trained by a public airfoil database to ensure a one-to-one correspondence between the dimension reduction parameters and the airfoil; An airfoil design model based on a generative adversarial network is constructed, including a generator and a discriminator; the input of the generator is the noise randomly sampled in the airfoil parameter space; the output of the generator is restored to the coordinate points of the airfoil through the airfoil decoder and used as the input of the discriminator, and the input form is the point coordinates representing the airfoil shape; at the same time, the discriminator also receives the point coordinates of the normal airfoil in the airfoil data set, which is used to train the discriminator to distinguish between true airfoils and false airfoils.

3. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 2, characterized in that: The Neuralfoil is constructed by a physics-based neural network and trained using Xfoil's computational data; the Neuralfoil's input is the coordinates of the basic airfoil and flow condition parameters, the flow condition parameters include the airfoil's angle of attack and Reynolds number, and the output is the airfoil's lift-to-drag ratio and the minimum surface pressure coefficient.

4. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 3, characterized in that: The airfoil multi-objective optimization model specifically includes the following logic: The state of the reinforcement learning is Z i =[P i , C Li , C Di , C pmi ], where P is the fitting parameter of the first airfoil, which is a 6-dimensional vector, namely: P = [P0, P1, ..., P5], C L , C D They represent the lift coefficient and drag coefficient of the first airfoil under the corresponding fitting parameters, Cp m The minimum surface pressure coefficient of the first airfoil under the corresponding fitting parameters; The action is a vector A with the same shape as the airfoil fitting parameters i =[a0, a1, ..., a5], representing the impact of this action on each parameter; The airfoil optimization model is based on the Proximal Policy Optimization (PPO) reinforcement learning framework, in which the intelligent agent is constructed through a convolutional neural network and is responsible for decision-making in multi-objective optimization tasks.

5. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 4, characterized in that: The specific application logic of the airfoil performance prediction model is: Neuralfoil, a physics-based neural network, is used to evaluate the airfoil performance. Neuralfoil is a physics-based neural network model. The evaluation data of various airfoils are trained through Xfoil, covering multiple Reynolds numbers, multiple Mach numbers and other working conditions, and physical mechanisms are added.

6. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 5, characterized in that: The reward value is mainly determined by the optimization objective and the Pareto frontier, specifically: The reward value is set as follows: Reward1=2+α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m )) Reward2=-2+α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m )) Reward3=α(I(k)+I(Cp m ))+(1-α)(D(k)+D(Cp m )) k=C l / C d Where k is the lift-to-drag ratio C corresponding to the current airfoil l / C d , Cp m is the current minimum surface lift coefficient; k front is the lift-to-drag ratio of the solution that is closest to the current Pareto front and the current airfoil; CP mfront k is the minimum surface pressure coefficient of the solution closest to the previous Pareto front and the current airfoil; object The target lift-to-drag ratio was initially set; Cp mobject is the target minimum surface pressure coefficient; I represents the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the current Pareto front improvement; D represents the distance reduction value of the lift-to-drag ratio and minimum surface pressure coefficient of the current airfoil relative to the target; α is the weight coefficient in the value range (0,1).

7. The airfoil multi-objective optimization method based on reinforcement learning and Pareto as claimed in claim 6, characterized in that: When the current solution is a dominant solution, the reward is Reward1; when the current solution is a dominated solution, the reward is Reward2; when the current solution is neither a dominant solution nor a dominated solution, the reward is Reward3; After the reward of the current solution is calculated, the current solution is added to the Pareto front, and the relationship between all Pareto front solutions is updated to remove the dominated solution.

8. A multi-objective optimization system for airfoils based on reinforcement learning and Pareto, based on the multi-objective optimization method for airfoils based on reinforcement learning and Pareto according to any one of claims 1 to 7, characterized in that: Also includes, The airfoil parametric design module is used to build an airfoil parametric design platform based on convolutional neural networks and generative adversarial networks to form a design space similar to the airfoil database; Airfoil performance evaluation module, used to evaluate airfoil performance using Neuralfoil based on physical neural network; The multi-objective optimization module is used to build a multi-objective optimization model for airfoils based on reinforcement learning and Pareto optimality, and output the Pareto solution set composed of the optimized airfoil performance parameters and its geometric coordinates.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the airfoil multi-objective optimization method based on reinforcement learning and Pareto are implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the airfoil multi-objective optimization method based on reinforcement learning and Pareto are implemented as described in any one of claims 1 to 7.

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