Airfoil multi-objective constraint optimization method and system

Abstract

The application discloses a kind of airfoil multi-objective constraint optimization method and system, it is related to fluid mechanics artificial intelligence optimization field, including, airfoil generation method based on conditional diffusion model, key geometric condition is injected diffusion model network, controllable airfoil generation is realized;The aerodynamic performance of the airfoil generated is evaluated using a physical information neural network, the lift-drag ratio and minimum pressure coefficient are obtained;Combining PPO algorithm and pareto frontier, iterative optimization is driven by reinforcement learning in the geometric condition state space, the pareto frontier is maintained based on multi-component reward function, and automatic optimization and decision of airfoil under multi-objective constraint optimization are realized.Airfoil automatic design and decision under aerodynamic performance constraint are realized by conditional diffusion model combined with reinforcement learning driven pareto optimization.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence optimization in fluid mechanics, and in particular to a method and system for multi-objective constraint optimization of airfoils. Background Technology

[0002] In aerospace, underwater propulsion, hydropower, and many other fields, airfoils are key components of fluid machinery, and their aerodynamic performance directly determines energy conversion efficiency, operational stability, and reliability. Current mainstream optimization methods employ CST parametric modeling combined with intelligent algorithms, which improves efficiency. However, CST generation lacks diversity, and population algorithms are prone to getting trapped in local optima under multi-objective and multi-constraint scenarios, making it difficult to balance aerodynamic efficiency, structural strength, and manufacturing feasibility.

[0003] The rise of generative artificial intelligence has opened up new avenues for airfoil design: conditional diffusion models can directly generate diverse airfoil geometries that conform to physical laws; the PPO algorithm excels at searching complex constraint spaces. However, the PPO algorithm has limitations in modeling high-dimensional airfoil variables and lacks a systematic reward design under multi-objective constraints.

[0004] Furthermore, in scenarios with multiple objectives and constraints, there is still a lack of systematic methods for constructing reward functions, and a unified design framework is required. Summary of the Invention

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a multi-objective constraint optimization method for airfoils, which solves the problems of difficult multi-objective trade-offs, low constraint satisfaction efficiency, and insufficient automation in traditional airfoil design.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a multi-objective constraint optimization method for airfoils, which includes an airfoil generation method based on a conditional diffusion model, wherein key geometric conditions are injected into a diffusion model network to achieve controllable airfoil generation; The aerodynamic performance of the generated airfoil is evaluated using a physical information neural network to obtain the lift-to-drag ratio and minimum pressure coefficient. By combining the PPO algorithm and the Pareto front, iterative optimization is driven by reinforcement learning in the geometric condition state space. The Pareto front is maintained based on a multi-component reward function, thereby realizing automatic airfoil optimization and decision-making under multi-objective constraint optimization.

[0008] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, the airfoil generation method adopts a conditional one-dimensional U-Net network structure; The geometric conditions of maximum thickness, maximum thickness location, maximum curvature, and maximum curvature location are fused with the diffusion time step, and a condition vector is generated through the embedding layer. This condition vector is then injected into the downsampling stage, residual module, and upsampling stage of the network.

[0009] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, the parameters of the conditional one-dimensional U-Net network structure include: 1 input channel, 6 initial feature channels, and 4 conditional vector dimensions. The training dataset for the conditional one-dimensional U-Net network is an airfoil latent variable dataset constructed based on the UIUC dataset.

[0010] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, each sample of the airfoil latent variable dataset includes airfoil latent variables and a condition vector consisting of maximum thickness, maximum thickness location, maximum camber, and maximum camber location. The airfoil latent variables are obtained by dimensionality reduction of the UIUC dataset using a fully connected autoencoder model, which includes an encoder and a decoder. The encoder compresses the 20-dimensional input feature vector of each airfoil into 6-dimensional latent variables, and the decoder reconstructs the 6-dimensional latent variables into 20-dimensional input feature vectors. The 20-dimensional input feature vector includes 14-dimensional CST parameters, leading edge radius, trailing edge thickness, maximum thickness, maximum thickness position, maximum curvature, and maximum curvature position.

[0011] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, the multi-objective constraint optimization includes a reinforcement learning environment based on the PPO algorithm, an agent, and a Pareto front maintenance unit. The state is a 4-dimensional geometric condition vector consisting of the maximum thickness, the location of the maximum thickness, the maximum curvature, and the location of the maximum curvature; The action space is a set of discrete actions, and each action corresponds to the negative adjustment, positive adjustment, and stagnation of each dimension in the 4-dimensional geometric condition vector; The intelligent agent consists of a policy network and a value network. The policy network adopts a five-layer fully connected structure, with each hidden layer neuron having a dimension of 64 and an output layer dimension of 4. The value network adopts a five-layer fully connected structure, with the hidden layer neurons having dimensions of 16, 64, 64, and 32 respectively, and outputting a single scalar value. The reinforcement learning environment is configured to receive the current state in each interaction step, input the conditional diffusion model to generate 6-dimensional latent variables, decode and reconstruct them into airfoil geometric coordinates through an autoencoder, input physical information neural network to calculate lift-to-drag ratio and minimum pressure coefficient, calculate the reward according to the multi-component reward function and feed it back to the agent; The Pareto front maintenance unit is configured to temporarily store the candidate airfoils generated in each round in a temporary Pareto solution set, perform non-dominated discrimination with the global Pareto solution set, remove dominated solutions, and update the global Pareto solution set.

[0012] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, the reward function includes a Pareto reward term and a constraint penalty term; The Pareto reward items include sub-items of performance improvement, sub-items of proximity to the target, and non-dominant reward items; Among them, the performance improvement sub-item is calculated based on the improvement of the lift-to-drag ratio and minimum pressure coefficient relative to the benchmark value; the proximity to the target sub-item is calculated based on the proximity of the lift-to-drag ratio and minimum pressure coefficient to the preset target value; and the non-dominated reward sub-item is calculated based on the dominance relationship between the current candidate solution and the Pareto solution set. The constraint penalty terms include geometric violation penalty terms and performance degradation penalty terms; Among them, the geometric violation penalty sub-item is calculated based on the degree of violation of key geometric features relative to the preset constraint boundary; the performance degradation penalty sub-item is calculated based on the degree of decline of aerodynamic performance relative to the initial solution.

[0013] As a preferred embodiment of the multi-objective constraint optimization method for airfoils described in this invention, wherein: the geometric violation penalty sub-item adopts differentiated constraints on the variation range of the 4-dimensional geometric condition vector; The maximum camber is constrained by an absolute deviation relative to the maximum camber of the reference airfoil. The maximum thickness, maximum thickness location, and maximum camber location are constrained by a relative percentage relative to the reference airfoil reference value.

[0014] Secondly, the present invention provides a multi-objective constraint optimization framework system for airfoils, including a generation unit and an airfoil generation method based on a conditional diffusion model, wherein key geometric conditions are injected into the diffusion model network to achieve controllable airfoil generation; The evaluation unit uses a physical information neural network to evaluate the aerodynamic performance of the generated airfoil and obtain the lift-to-drag ratio and minimum pressure coefficient. The optimization unit combines the PPO algorithm and the Pareto front to drive iterative optimization in the geometric condition state space through reinforcement learning. It maintains the Pareto front based on a multi-component reward function, thereby realizing automatic airfoil optimization and decision-making under multi-objective constraints.

[0015] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, wherein when the computer program is executed by the processor, it implements any step of the airfoil multi-objective constraint optimization method as described in the first aspect of the present invention.

[0016] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the airfoil multi-objective constraint optimization method as described in the first aspect of the present invention.

[0017] The beneficial effects of this invention are as follows: This invention proposes a multi-objective constraint optimization framework for airfoils based on a combination of a conditional diffusion model and the PPO algorithm. This framework achieves interpretable airfoil geometry generation based on the conditional diffusion model, completing the modeling from geometric constraints to geometric shape. Furthermore, it introduces reinforcement learning methods to construct a reward function for multi-objective, multi-constraint optimization problems, enabling real-time online optimization of the airfoil. This joint framework not only provides a systematic solution path for airfoil optimization problems under complex constraints but also combines interpretable generation with real-time decision-making. It represents an innovative exploration in the field of artificial intelligence optimization in fluid mechanics, providing new ideas and methods for research and applications in related fields. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of a multi-objective constraint optimization method for airfoils.

[0020] Figure 2 This is a diagram illustrating the implementation process of the algorithm in the multi-objective constraint optimization method for airfoils.

[0021] Figure 3 This is a geometric comparison diagram of the baseline airfoil and the generated airfoil in the multi-objective constraint optimization method for airfoils.

[0022] Figure 4 This paper presents an optimized Pareto front plot based on the NACA4412 airfoil, within a multi-objective constrained optimization method for airfoils.

[0023] Figure 5 A comparison of random Pareto front airfoil samples and a reference airfoil in a multi-objective constrained optimization method for airfoils.

[0024] Figure 6 The training effect of the network for the multi-objective constraint optimization method for airfoils is shown in the figure.

[0025] Figure 7 This is a computer equipment diagram for the multi-objective constraint optimization method for airfoils. Detailed Implementation

[0026] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0027] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0028] 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 phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0029] Reference Figures 1 to 7 As an embodiment of the present invention, this embodiment provides a multi-objective constraint optimization method for airfoils, comprising the following steps: S1: An airfoil generation method based on a conditional diffusion model injects key geometric conditions into the diffusion model network to achieve controllable airfoil generation.

[0030] Approximately 1600 airfoils were selected from the UIUC coordinate database and fitted using the CST parameterization method. The upper and lower surfaces were fitted with 6th-order Bernstein polynomials (i.e., 7 control points), resulting in 14-dimensional CST parameters for each airfoil. Geometric parameters such as leading-edge radius, trailing-edge thickness, maximum thickness, maximum thickness location, maximum camber, and maximum camber location were calculated using coordinates. These 14-dimensional CST parameters, along with the leading-edge radius, trailing-edge thickness, maximum thickness, maximum thickness location, maximum camber, and maximum camber location, were combined to form a 20-dimensional feature vector, creating a 20-dimensional feature vector database based on the UIUC dataset.

[0031] A fully connected autoencoder model for airfoil dimensionality reduction is constructed, comprising an encoder and a decoder. The encoder compresses a 20-dimensional feature vector into 6-dimensional latent variables to represent the main shape information of the airfoil. The decoder reconstructs the 6-dimensional latent variables into a 20-dimensional feature vector. The autoencoder model is trained based on the resulting 20-dimensional feature vector database.

[0032] An airfoil generation model based on a conditional diffusion model is constructed using a conditional one-dimensional U-Net network structure. The conditional one-dimensional U-Net network structure has one input channel, six initial feature channels, and a conditional vector dimension of four. The four-dimensional geometric conditions of the airfoil (maximum thickness, maximum thickness location, maximum camber, and maximum camber location) are fused with the diffusion time step, and a conditional vector is generated through an embedding layer. This conditional vector is then injected into the network's downsampling stage, residual module, and upsampling stage.

[0033] The conditional diffusion model employs the Denoising Diffusion Probabilistic Model (DDPM) framework, is trained in the airfoil latent space, and is used to predict noise and generate airfoil latent variable representations that satisfy geometric conditions.

[0034] The training dataset for the conditional diffusion model is an airfoil latent variable dataset constructed based on the UIUC dataset. Each sample includes a 6-dimensional airfoil latent variable obtained through the autoencoder and a corresponding 4-dimensional conditional vector. The dataset is divided into a training set and a validation set in an 8:2 ratio, and the data is randomly shuffled in each round of training to improve the model's generalization ability.

[0035] Training parameters include: 1000 training epochs, 1000 diffusion time steps, and a cosine noise scheduler (noise range 1×10⁻⁶). -4 Up to 2×10 -2 Using the AdamW optimizer (learning rate 5×10), -5 The loss function is the mean squared error.

[0036] The generation process includes: inputting a 4-dimensional conditional vector of the target, generating 6-dimensional latent variables from noise through a DDIM sampler, reconstructing them into a 20-dimensional feature vector through a decoder, and finally restoring them to airfoil coordinates through the CST method to achieve controllable airfoil generation.

[0037] A reference airfoil (such as NACA4412) is selected, and its 14-dimensional CST parameters are obtained based on the CST method. The corresponding 4-dimensional geometric conditions are then calculated. These 4-dimensional geometric conditions are used as input conditions to the conditional diffusion model to generate a new airfoil latent variable representation. After reconstruction using a decoder and the CST method, the reconstruction accuracy is evaluated. like Figure 3 As shown, the generated airfoil closely matches the reference airfoil in terms of geometric profile, verifying the ability of the conditional diffusion model to accurately generate the target airfoil according to specified geometric constraints.

[0038] If the accuracy requirements are met, the generated airfoil will be input into the subsequent optimization module.

[0039] S2: Use a physical information neural network to evaluate the aerodynamic performance of the generated airfoil and obtain the lift-to-drag ratio and minimum pressure coefficient.

[0040] A conditional diffusion model generates 6-dimensional latent variables in the latent space, which are then reconstructed into CST parameter vectors by an autoencoder decoder and further converted into a complete set of airfoil geometric coordinates. These airfoil geometric coordinates, along with preset operating parameters, are then input into a pre-trained NeuralFoil physical information neural network model.

[0041] The NeuralFoil model employs a neural network architecture embedded with physical information, enabling efficient and accurate prediction of airfoil aerodynamic characteristics without the need for traditional, costly computational fluid dynamics simulations. The NeuralFoil model directly outputs key aerodynamic performance indicators, primarily including lift-to-drag ratio (CL). L / C D ) and minimum pressure coefficient (Cp) min Among them, the lift-to-drag ratio is used to characterize the overall aerodynamic efficiency of the airfoil, and the larger the value, the better the aerodynamic performance; the minimum pressure coefficient is usually a negative value, and the smaller the absolute value, the more moderate the pressure peak on the airfoil surface, which is beneficial to reduce shock wave intensity or delay stall.

[0042] In each interaction between the agent and the environment, every time a new candidate airfoil is generated, the NeuralFoil model is called in real time for performance evaluation. The obtained aerodynamic performance indicators will be directly used for subsequent reward function calculation, constraint judgment and Pareto front update, thereby providing reliable performance feedback for multi-objective multi-constraint optimization and ensuring that the entire optimization process forms a closed loop iteration.

[0043] S3: Combining the PPO algorithm and Pareto front, it drives iterative optimization in the geometric condition state space through reinforcement learning, maintains the Pareto front based on the multi-component reward function, and realizes automatic airfoil optimization and decision-making under multi-objective constraint optimization.

[0044] The multi-objective constrained optimization includes a reinforcement learning environment based on the PPO algorithm, an agent, and a Pareto front maintenance unit.

[0045] The intelligent agent consists of a policy network and a value network. The policy network adopts a five-layer fully connected structure, with each hidden layer neuron having a dimension of 64 and an output layer dimension of 4. The value network adopts a five-layer fully connected structure, with the hidden layer neurons having dimensions of 16, 64, 64 and 32 respectively, and outputting a single scalar value.

[0046] Actions are encoded as 4-bit binary vectors, corresponding to the four geometric dimensions of the latent variables. Each bit (0 or 1) represents a positive or negative adjustment in that dimension. To enhance exploratory power, the agent introduces a 10% random stagnation probability in action selection for each dimension to ensure sufficient coverage of the search space.

[0047] The reward value is determined by the Pareto reward term R. pareto and constraint penalty item R penalty Together, the Pareto reward term characterizes the degree of non-dominance of the current candidate solution in the Pareto solution set, and the constraint penalty term applies a negative penalty to solutions that violate the constraints. The two are fused according to a preset method, and their illustrative expression can be represented as follows: in, R represents the total reward at the current time step. pareto R represents the Pareto reward; penalty This indicates a constraint or penalty.

[0048] The Pareto reward item R pareto This is used to characterize the degree of non-dominance of the current candidate solution in the global Pareto solution set. The Pareto reward term R pareto It includes at least the following three sub-items: Performance Improvement Reward Sub-item I, which characterizes the performance improvement of the candidate solution relative to the benchmark solution; Proximity to Target Reward Sub-item D, which characterizes the closeness of the candidate solution to the preset target; and Non-Dominated Solution Reward Sub-item C, which provides additional positive rewards to candidate solutions in a non-dominated state. These sub-items are fused according to preset weights to form a Pareto reward term, the illustrative expression of which can be represented as: Where α represents the weighting coefficient, which can be adjusted according to the actual working conditions; The sub-item representing the degree of performance improvement; D represents the sub-item representing the degree of proximity to the target; C represents the sub-item representing the non-dominated solution.

[0049] When the current candidate solution S new Strictly govern the existing solution S existing (denoted as S) new ≻S existing When the current candidate solution S is found to be S, an additional positive reward should be given; when the current candidate solution S is found to be S, an additional positive reward should be given. new Strictly governed by existing solutions (denoted as S) new ≺S existing When the current candidate solution S is in a certain condition, an additional penalty should be imposed; new With existing solution S existing When there is no strict dominance relationship, there is no need to consider additional rewards or punishments.

[0050] The performance improvement reward item I is used to characterize the performance improvement of the candidate solution relative to the benchmark solution. The performance improvement reward item I includes at least two items: the lift-to-drag ratio improvement reward item I and the minimum pressure coefficient improvement reward item I. Its illustrative expression can be represented as: in, Sub-items indicating the degree of performance improvement in reward items; This represents the weighting coefficient for the lift-to-drag ratio enhancement sub-item; This represents the weighting coefficient of the sub-item that increases the minimum pressure coefficient; Indicates the lift-to-drag ratio; This indicates a reward item for the degree of improvement in lift-to-drag ratio; Indicates the minimum pressure coefficient; This indicates the reward sub-item for increasing the minimum pressure coefficient.

[0051] The lift-to-drag ratio improvement reward item I is used to characterize the improvement of the lift-to-drag ratio of the current candidate solution compared to the average lift-to-drag ratio of the current temporary Pareto solution set. Its schematic expression can be represented as follows: in, This indicates a reward item for the degree of improvement in lift-to-drag ratio; Indicates the lift-to-drag ratio; This represents the average lift-to-drag ratio of all non-dominated solutions in the current temporary Pareto solution set.

[0052] The minimum pressure coefficient improvement reward item I is used to characterize the improvement of the minimum pressure coefficient of the current candidate solution compared to the average minimum pressure coefficient of the current temporary Pareto solution set. Its illustrative expression can be represented as: in, This indicates the reward sub-item representing the degree of increase in the minimum pressure coefficient; Indicates the minimum pressure coefficient; It represents the average minimum pressure coefficient of all non-dominated solutions in the current temporary Pareto solution set.

[0053] The proximity-to-target reward sub-item D characterizes the degree of proximity of the candidate solution to the preset target; the proximity-to-target reward sub-item D includes at least the following two sub-items: lift-to-drag ratio proximity-to-target reward sub-item D and minimum pressure coefficient proximity-to-target reward sub-item D. Its illustrative expression can be represented as: Where D represents the reward sub-item for approaching the target; Indicates the lift-to-drag ratio; This indicates a reward item based on how close the lift-to-drag ratio is to the target. Indicates the minimum pressure coefficient; This indicates the reward item based on how close the minimum pressure coefficient is to the target. This indicates the weighting coefficient for the lift-to-drag ratio to be close to the target sub-item; This indicates the weighting coefficient of the target sub-item that is closest to the minimum pressure coefficient.

[0054] The lift-to-drag ratio proximity reward item D is used to characterize how close the lift-to-drag ratio of the current candidate solution is to the target value of the set lift-to-drag ratio. Its illustrative expression can be represented as follows: in, This indicates a reward item based on how close the lift-to-drag ratio is to the target. Indicates the lift-to-drag ratio; This indicates the lift-to-drag ratio of the initial airfoil; This represents the target value for the lift-to-drag ratio.

[0055] The lift-to-drag ratio proximity reward item D is used to characterize the degree of proximity of the current candidate solution's minimum pressure coefficient to the target value of the set minimum pressure coefficient. Its illustrative expression can be represented as follows: in, This indicates the reward item based on how close the minimum pressure coefficient is to the target. Indicates the minimum pressure coefficient; The lift-to-drag ratio of the initial airfoil; This is the target value for the lift-to-drag ratio.

[0056] The constraint penalty item R penalty This is used to characterize the degree to which the current candidate solution violates the constraints. The constraint penalty term R penalty It should include at least the following two sub-items: the geometric violation penalty R of the current candidate solution. geom The performance degradation penalty R of the current candidate solution performance Its illustrative expression can be represented as: in, Indicates a constraint or penalty item; This represents the geometric violation penalty for the current candidate solution; This represents the performance degradation penalty for the current candidate solution.

[0057] The geometric violation penalty R penalty This is used to characterize the degree of violation of the key geometric features of the current candidate solution relative to the preset constraint range. Its schematic expression can be represented as: in, Represents the constraint penalty term; Pi represents the single penalty value of the i-th geometric parameter; Si represents the actual value of the i-th geometric parameter of the candidate airfoil; L i and U i This represents the soft constraint boundary for the i-th geometric parameter; a violation of this boundary will result in an imposition of a constraint. The punishment; L i 'and U i ' represents the sub-soft constraint sub-boundary of the i-th geometric parameter; a violation of this constraint will result in an imposition of a constraint. The penalty, and the solution is not allowed to be included in the Pareto frontier; L T i and U T i This represents the hard constraint boundary of the i-th geometric parameter.

[0058] If a violation occurs, a large penalty value M (M>m>0) is imposed, the current trajectory is immediately truncated, and the solution is marked as invalid and will not participate in subsequent policy gradient updates or Pareto front construction.

[0059] The geometric violation penalty R performance This is used to characterize the degree of decline in aerodynamic performance of the current candidate solution compared to the initial solution. Its schematic expression can be represented as: in, The value represents the performance degradation penalty for the current candidate solution; M represents the large penalty constant. Indicates the lift-to-drag ratio; This represents the threshold coefficient for rise-to-drag ratio degradation. This represents the minimum pressure coefficient degradation threshold coefficient; Indicates the minimum pressure coefficient; This represents the lift-to-drag ratio of the initial airfoil.

[0060] The intelligent agent interacts continuously with the environment, repeating this process multiple times. For example... Figure 6 As shown, the moving average of the agent's reward during training shows a stable upward trend with the increase of training rounds, indicating that the designed PPO algorithm and multi-component reward function can effectively guide the agent to learn in the geometric condition state space and gradually improve the strategy to find a better airfoil design scheme.

[0061] After each interaction step, it is determined whether the optimized airfoil satisfies the soft constraints. If so, the candidate solutions generated in each round are temporarily stored in a temporary Pareto solution set. Then, the temporary Pareto solution set is compared with the current global Pareto solution set for non-dominated relationship determination. Dominated solutions are eliminated, and the global Pareto solution set is updated to obtain the final Pareto optimal solution set. If not, it is further determined whether the hard constraints are satisfied. If satisfied, the interaction continues; if not satisfied, the solution is eliminated, and the round terminates.

[0062] The constraints include: constraints on the initial generation of the airfoil using conditional information in the conditional diffusion model; and strict variation range given by setting the reward value to the 4D geometric information of the airfoil, so as to effectively control the degree of geometric variation in the airfoil optimization process, ensure that the optimization result maintains a recognizable morphological association with the initial airfoil, and ensure that the characteristics of the original airfoil and other strength requirements are fully preserved.

[0063] The constraint range of the geometric information includes: adopting a differentiated constraint strategy: considering that the maximum camber is extremely sensitive to changes in airfoil shape and has a small absolute value, it is constrained by the absolute value deviation of the maximum camber of the reference airfoil; the other three parameters (maximum thickness, maximum thickness position, and maximum camber position) are not sensitive to changes in airfoil shape because the data is large, so they are constrained by the relative percentage fluctuation range based on the reference airfoil's baseline value.

[0064] Finally, determine if the maximum number of exploration steps has been reached; if so, output the optimized airfoil. At this point, you can... Figure 4 In the Pareto front shown, the final optimized airfoil is selected based on actual engineering preferences.

[0065] By combining the conditional diffusion model and the PPO algorithm, a multi-objective constraint optimization method for airfoils is developed, achieving a closed-loop integration of generation, controllability, evaluation, and optimization. This method has the advantages of high efficiency, differentiability, and no need for costly CFD simulation, making it suitable for multi-objective constraint optimization design of airfoils in practical engineering.

[0066] This embodiment also provides an airfoil multi-objective constraint optimization framework system, including: The generation unit, based on the conditional diffusion model, injects key geometric conditions into the diffusion model network to achieve controllable airfoil generation.

[0067] The evaluation unit uses a physical information neural network to evaluate the aerodynamic performance of the generated airfoil and obtain the lift-to-drag ratio and minimum pressure coefficient.

[0068] The optimization unit combines the PPO algorithm and the Pareto front to drive iterative optimization in the geometric condition state space through reinforcement learning. It maintains the Pareto front based on a multi-component reward function, thereby realizing automatic airfoil optimization and decision-making under multi-objective constraints.

[0069] This embodiment also provides a computer device applicable to the airfoil multi-objective constraint optimization method, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the airfoil multi-objective constraint optimization method proposed in the above embodiment.

[0070] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0071] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the airfoil multi-objective constraint optimization method proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0072] In summary, this invention employs an innovative multi-objective constrained optimization framework for airfoils. It achieves controllable airfoil generation under geometric conditions through a conditional diffusion model, combines a NeuralFoil physical information-enhanced neural network for efficient aerodynamic performance evaluation, and introduces a PPO reinforcement learning algorithm to drive iterative adjustments in the geometric condition state space. By dynamically maintaining the Pareto front using a multi-component reward function, a fully closed-loop automated process of generation, evaluation, and optimization is formed. Ultimately, it outputs a set of Pareto-optimal airfoils, providing diverse and high-performance decision-making solutions for engineering design, demonstrating significant practicality and forward-looking potential.

[0073] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective constraint optimization method for airfoils, characterized in that: This includes an airfoil generation method based on a conditional diffusion model, which injects key geometric conditions into the diffusion model network to achieve controllable airfoil generation; The aerodynamic performance of the generated airfoil is evaluated using a physical information neural network to obtain the lift-to-drag ratio and minimum pressure coefficient. By combining the PPO algorithm and the Pareto front, iterative optimization is driven by reinforcement learning in the geometric condition state space. The Pareto front is maintained based on a multi-component reward function, thereby realizing automatic airfoil optimization and decision-making under multi-objective constraint optimization.

2. The airfoil multi-objective constraint optimization method as described in claim 1, characterized in that: The airfoil generation method employs a conditional one-dimensional U-Net network structure; The geometric conditions of maximum thickness, maximum thickness location, maximum curvature, and maximum curvature location are fused with the diffusion time step, and a condition vector is generated through the embedding layer. This condition vector is then injected into the downsampling stage, residual module, and upsampling stage of the network.

3. The airfoil multi-objective constraint optimization method as described in claim 2, characterized in that: The parameters of the conditional one-dimensional U-Net network structure include: 1 input channel, 6 initial feature channels, and 4 conditional vector dimensions. The training dataset for the conditional one-dimensional U-Net network is an airfoil latent variable dataset constructed based on the UIUC dataset.

4. The airfoil multi-objective constraint optimization method as described in claim 3, characterized in that: Each sample in the airfoil latent variable dataset includes airfoil latent variables and a condition vector consisting of maximum thickness, maximum thickness location, maximum camber, and maximum camber location; The airfoil latent variables are obtained by dimensionality reduction of the UIUC dataset using a fully connected autoencoder model, which includes an encoder and a decoder. The encoder compresses the 20-dimensional input feature vector of each airfoil into 6-dimensional latent variables, and the decoder reconstructs the 6-dimensional latent variables into 20-dimensional input feature vectors. The 20-dimensional input feature vector includes 14-dimensional CST parameters, leading edge radius, trailing edge thickness, maximum thickness, maximum thickness position, maximum curvature, and maximum curvature position.

5. The airfoil multi-objective constraint optimization method as described in claim 4, characterized in that: The multi-objective constrained optimization includes a reinforcement learning environment, an agent, and a Pareto front maintenance unit based on the PPO algorithm. The state is a 4-dimensional geometric condition vector consisting of the maximum thickness, the location of the maximum thickness, the maximum curvature, and the location of the maximum curvature; The action space is a set of discrete actions, and each action corresponds to the negative adjustment, positive adjustment, and stagnation of each dimension in the 4-dimensional geometric condition vector; The intelligent agent consists of a policy network and a value network. The policy network adopts a five-layer fully connected structure, with each hidden layer neuron having a dimension of 64 and an output layer dimension of 4. The value network adopts a five-layer fully connected structure, with the hidden layer neurons having dimensions of 16, 64, 64, and 32 respectively, and outputting a single scalar value. The reinforcement learning environment is configured to receive the current state in each interaction step, input the conditional diffusion model to generate 6-dimensional latent variables, decode and reconstruct them into airfoil geometric coordinates through an autoencoder, input physical information neural network to calculate lift-to-drag ratio and minimum pressure coefficient, calculate the reward according to the multi-component reward function and feed it back to the agent; The Pareto front maintenance unit is configured to temporarily store the candidate airfoils generated in each round in a temporary Pareto solution set, perform non-dominated discrimination with the global Pareto solution set, remove dominated solutions, and update the global Pareto solution set.

6. The airfoil multi-objective constraint optimization method as described in claim 5, characterized in that: The reward function includes a Pareto reward term and a constraint penalty term; The Pareto reward items include sub-items of performance improvement, sub-items of proximity to the target, and non-dominant reward items; Among them, the performance improvement sub-item is calculated based on the improvement of the lift-to-drag ratio and minimum pressure coefficient relative to the benchmark value; the proximity to the target sub-item is calculated based on the proximity of the lift-to-drag ratio and minimum pressure coefficient to the preset target value; and the non-dominated reward sub-item is calculated based on the dominance relationship between the current candidate solution and the Pareto solution set. The constraint penalty terms include geometric violation penalty terms and performance degradation penalty terms; Among them, the geometric violation penalty sub-item is calculated based on the degree of violation of key geometric features relative to the preset constraint boundary; the performance degradation penalty sub-item is calculated based on the degree of decline of aerodynamic performance relative to the initial solution.

7. The airfoil multi-objective constraint optimization method as described in claim 6, characterized in that: The geometric violation penalty sub-item adopts differentiated constraints on the range of variation of the 4-dimensional geometric condition vector; The maximum camber is constrained by an absolute deviation relative to the maximum camber of the reference airfoil. The maximum thickness, maximum thickness location, and maximum camber location are constrained by a relative percentage relative to the reference airfoil reference value.

8. A multi-objective constraint optimization framework system for airfoils, based on the multi-objective constraint optimization method for airfoils according to any one of claims 1 to 7, characterized in that: This includes a generation unit, an airfoil generation method based on a conditional diffusion model, which injects key geometric conditions into the diffusion model network to achieve controllable airfoil generation; The evaluation unit uses a physical information neural network to evaluate the aerodynamic performance of the generated airfoil and obtain the lift-to-drag ratio and minimum pressure coefficient. The optimization unit combines the PPO algorithm and the Pareto front to drive iterative optimization in the geometric condition state space through reinforcement learning. It maintains the Pareto front based on a multi-component reward function, thereby realizing automatic airfoil optimization and decision-making under multi-objective constraints.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the airfoil multi-objective constraint optimization method according to 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 the processor, it implements the steps of the airfoil multi-objective constraint optimization method according to any one of claims 1 to 7.

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