Parameterization design method for wind turbine airfoil based on physical constraint data driving

Abstract

The invention relates to a wind turbine airfoil profile parameterization design method based on physical constraint data driving, which comprises the following steps: constructing a physical information neural network model based on a Bezier curve, inputting geometric parameters of an airfoil profile according to a design requirement, and generating an initial airfoil profile meeting a physical constraint requirement; converting the initial airfoil into coordinate point data, inputting the coordinate point data into an aerodynamic performance analysis module, and calculating an aerodynamic performance index; establishing a deep reinforcement learning model, and optimizing the initial airfoil profile by using a reward function and taking an aerodynamic performance index as an optimization target; and carrying out aerodynamic performance evaluation on the newly generated airfoil profile through iterative optimization until the aerodynamic performance index of the airfoil profile reaches an optimization target or converges, and obtaining a new airfoil profile which meets design requirements and is excellent in aerodynamic performance. According to the method, the airfoil design efficiency and quality are effectively improved, the dependence on the experience of a designer is reduced, and an efficient and reliable technical approach is provided for the airfoil design of the wind turbine.

Description

Technical Field

[0001] The present invention relates to the technical field of wind turbine blade design, and more specifically to a parametric design method for wind turbine airfoils based on physically constrained data-driven approach. Background Art

[0002] Wind power generation, as a clean and renewable energy source, has been widely applied globally. Wind turbine blades are the core components of wind turbines, and their aerodynamic performance directly affects the power generation efficiency and operation reliability of wind turbines. The design of wind turbine airfoils needs to consider multiple requirements such as aerodynamic performance, structural strength, and manufacturing process, which is difficult and complex. Especially in the design of large wind turbines, the geometric shape of the airfoil is directly related to power generation efficiency, load distribution, and structural reliability, and has a decisive impact on the overall performance of wind turbines. Different airfoils are required from the root to the tip of the wind turbine blade, and good geometric and aerodynamic compatibility needs to be maintained between these airfoils. Therefore, the design of the wind turbine airfoil family not only needs to consider the performance of a single airfoil but also ensure the smooth transition between various airfoils in the blade airfoils.

[0003] Currently, the design of wind turbine airfoils mainly adopts traditional empirical design methods and numerical optimization design methods. The traditional empirical design method mainly selects and modifies based on existing airfoil libraries (such as NACA series, FFA series, etc.). This method highly depends on the experience of designers, has low design efficiency, and it is difficult to ensure the optimization of design results. The numerical optimization design method combines computational fluid dynamics (CFD) with optimization algorithms. Although better design results can be obtained, it consumes a large amount of computing resources, has a long optimization cycle, and it is difficult to simultaneously meet multiple design objectives and constraint conditions.

[0004] The design of wind turbine airfoils faces severe technical challenges. In terms of performance requirements, a high lift-to-drag ratio is required to improve power generation efficiency, a large stall margin is required to ensure operation safety, and operation stability also needs to be guaranteed to reduce load fluctuations. In terms of geometric constraints, wind turbine airfoils usually require a relatively large relative thickness (usually 15%-35%) to meet the structural strength requirements, the position of the maximum thickness needs to be reasonably distributed to optimize the load distribution, and the leading-edge radius and trailing-edge thickness need to meet the requirements of the manufacturing process. In terms of the design space, the design of wind turbine airfoils involves complex nonlinear problems. There are strong coupling relationships between design variables, the relationship between performance indicators and geometric parameters is highly nonlinear, and the feasible solution space is restricted by multiple constraints. These characteristics make the design optimization of wind turbine airfoils a very challenging problem.

[0005] There are three main problems in the existing design methods. First, the design efficiency is low. The traditional method relies too much on manual experience, and the optimization process involves a large amount of calculation, resulting in a long design cycle. Second, it is difficult to handle constraints. It is difficult to satisfy multiple geometric constraint conditions simultaneously. The introduction of constraint conditions often significantly affects the optimization effect, and the constraints related to manufacturing processes are difficult to be fully considered in the design stage. Third, the performance optimization is insufficient. Although it is relatively easy to optimize a single performance index, it is difficult to achieve multi-objective optimization, and it is difficult to obtain the globally optimal solution. Summary of the Invention

[0006] Aiming at the deficiencies of the existing technology, the technical problem to be solved by the present invention is how to efficiently design a family of wind turbine airfoils that meet specific geometric constraints and have excellent aerodynamic performance. In this regard, the present invention provides a physically constrained data-driven parametric design method for wind turbine airfoils. This method combines a physics-informed neural network (PINN) and a deep reinforcement learning (DRL) algorithm, and uses physical constraint conditions and a data-driven model to realize the optimized design of airfoils.

[0007] To solve the above technical problems, the present invention provides the following technical solutions:

[0008] The present invention provides a physically constrained data-driven parametric design method for wind turbine airfoils, including the following steps:

[0009] (1) Construct a physics-informed neural network model based on Bezier curves, input the geometric parameters of the airfoil according to the design requirements, and generate an initial airfoil that meets the physical constraint requirements;

[0010] (2) Convert the generated initial airfoil into coordinate point data, input it into the aerodynamic performance analysis module, and calculate the aerodynamic performance index of the initial airfoil;

[0011] (3) Establish a deep reinforcement learning model, and use the reward function with the aerodynamic performance index as the optimization goal to optimize the initial airfoil;

[0012] (4) Through iterative optimization, conduct aerodynamic performance evaluation on the newly generated airfoil until the aerodynamic performance index of the airfoil reaches the optimization goal or converges.

[0013] Preferably, the specific method of step (1) is as follows:

[0014] (1-1) Establish a basic airfoil library as the training set and the validation set: collect the geometric parameters of the airfoil and the corresponding Bezier curve control points, uniformly distribute the coordinate point data of the airfoil to ensure that the input data scales are consistent; the geometric parameters include: the maximum thickness t of the airfoil max , the position of the maximum thickness of the airfoil the maximum camber c of the airfoil max , the position of the maximum camber of the airfoil Leading edge radius r of the airfoil le , trailing edge thickness g of the airfoil te ;

[0015] (1-2) Construct a physics-informed neural network model and establish a multi-layer perceptron structure model:

[0016] The input layer is the geometric parameter vector of the airfoil, denoted as vector where n is the number of geometric parameters; X is a vector containing n geometric parameters; is the set of real numbers;

[0017] The output layer generates the control points of the Bezier curve of the airfoil, with a total of m sampling points, each point having two coordinates x and y, flattened into a 2m-dimensional vector; is the coordinate of the control point of the airfoil Bezier curve finally predicted; is the vector space composed of m (x, y) points;

[0018] (1-3) Construct a physical constraint loss function, and the objective function is expressed as:

[0019]

[0020] where N is the number of training samples, is the output predicted by the model, is the true output data; ‖·‖ is the 2-norm of the vector;

[0021] The physical constraint loss function is composed as follows:

[0022]

[0023] where, is the curvature constraint loss function, is the thickness constraint loss function, is the leading edge constraint loss function, is the maximum camber constraint loss function, is the trailing edge constraint loss function;

[0024] N geo is the number of sampling points used to calculate physical constraints such as smoothness and thickness at the geometric level;

[0025] κ (i) represents the curvature value calculated at the i-th geometric sampling point;

[0026] is the target curvature, that is, the target curvature value at the i-th geometric sampling point;

[0027] T (i) represents the local thickness value of the airfoil at the \(i\)-th sampling point;

[0028] is the target thickness, i.e., the target thickness value at the \(i\)-th geometric sampling point;

[0029] T TE is the target trailing-edge thickness value;

[0030] x min is the minimum \(x\)-coordinate point of the airfoil; \(x\) max is the maximum \(x\)-coordinate point of the airfoil;

[0031] S LE is the translation distance in the leading-edge direction when there is a leading-edge constraint;

[0032] is the predicted maximum camber value; is the target maximum camber value;

[0033] y upper (x max ) is the upper surface \(y\)-coordinate value of the airfoil at \(x\) max ; \(y\) lower (x max ) represents the lower surface \(y\)-coordinate value of the airfoil at \(x\) max ;

[0034] The total loss function is:

[0035] where \(\lambda\) is the weight coefficient used to balance the data loss and the physical loss;

[0036] (1 - 4) Use the training set to train the physics-informed neural network model. By iteratively training the PINN model, learn the mapping relationship from geometric parameters to the airfoil shape, and obtain an airfoil that satisfies the initial geometric constraints; evaluate the performance of the physics-informed neural network model on the validation set to ensure that the trained physics-informed neural network model can accurately generate an airfoil that satisfies the physical constraints according to the given geometric parameters; during the training process, input the geometric feature parameters of the airfoil, the coordinate point data of the airfoil, and the Bezier curve control points, and output an airfoil that satisfies the geometric constraints. The model updates the neural network parameters by minimizing ;

[0037] (1 - 5) After the physics-informed neural network model is trained, use the trained physics-informed neural network model to construct a reinforcement learning environment. Input the given geometric parameters of the airfoil according to the design requirements, batch generate initial airfoils that satisfy the physical constraint requirements, and extract the initial airfoil coordinate data for performance analysis.

[0038] In the step (1-1), the method for solving the control points of the Bezier curve corresponding to the geometric parameters of the airfoil is as follows:

[0039] Parameterize the airfoil coordinate data points and calculate the parameter t j , and map the data points to the parameter domain;

[0040] Construct the Bernstein basis function matrix and calculate the Bernstein basis function values for each parameter t j to construct the matrix B;

[0041] Form a linear equation system, and convert the Bezier curve expression into a linear equation system BP = Q;

[0042] Apply the boundary conditions, fix the known leading-edge control point P0 and trailing-edge control point P n , separate the remaining unknown Bezier curve control points of the target quantity, and reconstruct the equation system;

[0043] Solve by least squares, use the normal equation and regularization term to solve the unknown Bezier curve control points;

[0044] Recombine the Bezier curve control points, combine the known and unknown Bezier curve control points to obtain a complete set of Bezier curve control points.

[0045] In the step (1-3), the physical constraint loss function includes a geometric constraint loss term (thickness constraint loss function, leading-edge constraint loss function, maximum camber constraint loss function, and trailing-edge constraint loss function) and a curvature regularization loss term (curvature constraint loss function); among them, the geometric constraint loss term ensures that the generated airfoil meets the specified geometric parameters, such as the monotonic change of the maximum thickness position of the airfoil geometric parameters; the curvature regularization loss term controls the smoothness of the airfoil curve and avoids excessive oscillation.

[0046] Preferably, in the step (1-2), the multi-layer perceptron structure model further includes a hidden layer, the hidden layer includes multiple fully connected layers, each layer has a specified number of neurons, uses Leaky ReLU as the activation function, introduces batch normalization and Dropout techniques, and adopts a residual block structure for residual connection.

[0047] In the step (1-4), the physical constraint requirements include: thickness constraint, curvature constraint, geometric constraint, and smoothness constraint.

[0048] Preferably, in the step (2), the aerodynamic performance analysis module is the aerodynamic performance solver Xfoil; the aerodynamic performance indicators include: lift coefficient C l , drag coefficient C d , moment coefficient C m , lift-to-drag ratio C l / C d 。

[0049] Preferably, in the step (3), the deep reinforcement learning model adopts the soft actor-critic algorithm, uses the geometric parameters and aerodynamic performance indexes of the airfoil as the state space, and uses the adjustment of the Bezier curve control points of the airfoil as the action space to construct a reward function;

[0050] Among them, the reward function includes: aerodynamic performance reward, geometric constraint penalty, and action penalty; under the condition of keeping the given geometric parameter requirements of the airfoil unchanged, the fine adjustment of the airfoil shape is realized; taking the aerodynamic performance index as the optimization goal, the airfoil shape is iteratively optimized.

[0051] Preferably, in the step (3), the state space of the deep reinforcement learning model: s = [P, A, G], where P represents the Bezier curve control points of the airfoil; A represents the aerodynamic performance indexes, including: lift coefficient C l , drag coefficient C d and moment coefficient C m ; G represents the geometric parameters corresponding to the initial airfoil obtained by the physics-informed neural network model;

[0052] Action space: a = ΔP = {(Δx i , Δy i )}, where Δx i , Δy i represent the horizontal and vertical coordinate adjustment amounts of the i-th control point;

[0053] Reward function: r(s, a) = R aero + R constraint + R action

[0054] Among them, R aero = w Cl ·C l - w Cd ·C d - w Cm ·|C m |

[0055]

[0056] R action = -β·‖a‖ 2

[0057] Among them, w Cl , w Cd , w Cm are the weight coefficients of C l , C d , C m respectively;

[0058] g k s≥0 represents the degree of violation of the k-th geometric constraint, λ is the penalty coefficient, β is the action penalty coefficient, and ‖a‖ 2 is the square of the two-norm of the action vector; R aero is the aerodynamic performance reward function, and R constraint is the geometric constraint reward function; R action is the action space reward function.

[0059] Preferably, in the step (4), through the alternating iteration of the physics-informed neural network model and the deep reinforcement learning model, the agent continuously interacts with the environment, adjusts the control points of the Bezier curve of the airfoil, and optimizes the aerodynamic performance of the airfoil; when the reward function converges and meets the design requirements, a new airfoil that meets the design requirements and has excellent aerodynamic performance is obtained. The agent optimizes the airfoil performance by adjusting the control points of the Bezier curve until the reward function is stable and meets the design requirements; finally, an optimized airfoil is generated and its geometric parameters and aerodynamic performance are calculated to ensure compliance with the design objectives.

[0060] Preferably, in the step (4), a double Q-network architecture is used, which includes two independent evaluation networks and and a policy network π φ (a|s), for iterative optimization. An experience replay buffer D is used to store the samples (s, a, r, s′) obtained from the interaction between the agent and the environment, and the control points are adjusted according to the reinforcement learning agent to optimize the generated initial wing; while maintaining geometric constraints, explore the design space to achieve the best aerodynamic performance;

[0061] Preferably, in the step (4), the network parameters are updated by minimizing the following loss function;

[0062] ①

[0063] where the calculation of the target y value is:

[0064]

[0065] ②

[0066] ③

[0067] where s is the state space; a is the action space; s′ is the new state that the environment transfers to after executing the action a in the next state; a′ is the next action, indicating the action taken in the next state s′; D is the experience replay buffer;

[0068] γ is the discount factor, 0 < γ < 1; α is the temperature parameter; r is the improvement degree of the aerodynamic performance index;

[0069] θ i is the current network parameter of the action value function Q; θj′ is the target network parameter of the action value function Q; φ is the parameter of the policy network; is the target entropy;

[0070] is the evaluation network loss function; is the policy network loss function; is the loss function of the temperature parameter; represents the expected operation;

[0071] represents the expected performance value adjusted by the action a in the state s;

[0072] r(s,a) represents the improvement degree of the aerodynamic performance index after executing the action a in the state s;

[0073] π φ (a|s) represents the probability distribution of selecting the action a in the state s.

[0074] The technical solution of the present invention has achieved the following beneficial technical effects:

[0075] The present invention provides a data-driven wind turbine airfoil parametric design method based on physical constraints, aiming to efficiently design a wind turbine airfoil family that meets specific geometric constraints and has excellent aerodynamic performance. This method combines a physics-informed neural network (PINN) and a deep reinforcement learning (DRL) algorithm, and uses physical constraint conditions and data-driven models to realize the optimal design of airfoils.

[0076] First, construct a physics-informed neural network model based on Bezier curves. Input the geometric feature parameters of the airfoil and the Bezier curve control points, and output the airfoil that meets the geometric constraints. The loss function includes a geometric constraint loss term (ensuring the monotonic change of parameters such as the maximum thickness position) and a curvature regularization loss term (controlling the smoothness of the airfoil curve). Secondly, convert the Bezier curve control points of the airfoil generated by PINN into coordinate point data and input it into the aerodynamic performance solver to calculate the aerodynamic performance indicators of the airfoil. Then, introduce a deep reinforcement learning optimization strategy and adopt the Soft Actor-Critic (SAC) algorithm. Take the geometric parameters and aerodynamic performance indicators of the airfoil as the state space, and the adjustment of the airfoil control points as the action space to construct a reward function, including aerodynamic performance rewards, geometric constraint penalties, and action penalties. On the premise of keeping the key geometric parameters unchanged, use performance indicators such as the lift-to-drag ratio as the optimization goal to iteratively optimize the airfoil shape. Finally, through the alternating iteration of PINN and DRL, the agent continuously interacts with the environment, adjusts the airfoil control points, and optimizes the aerodynamic performance of the airfoil. When the reward function converges and meets the design requirements, a new airfoil that meets the design requirements and has excellent aerodynamic performance is obtained. The present invention effectively improves the efficiency and quality of airfoil design, reduces the dependence on the experience of designers, and provides an efficient and reliable technical approach for the design of wind turbine airfoils.

[0077] Compared with the existing solutions, the present invention quickly generates an initial airfoil that meets geometric constraints through a physics neural network, combines the optimization strategy of deep reinforcement learning, realizes the automation and high efficiency of airfoil design, and effectively improves the design space of the airfoil. At the same time, directly integrate physical constraints into the deep learning model, avoiding the complex constraint handling problems in traditional optimization methods, and ensuring that the generated airfoil meets physical laws and engineering requirements. Introduce a deep reinforcement learning optimization strategy into the airfoil generation model to finely adjust the airfoil, fully explore the potential of airfoil shape optimization, and improve aerodynamic performance. Combining the advantages of physics-informed neural networks and deep reinforcement learning, the model has strong exploration and generalization capabilities in complex design spaces and can adapt to different design requirements. Brief Description of the Drawings

[0078] Figure 1 It is the overall flowchart of the airfoil design implementation method of the present invention.

[0079] Figure 2 It is the training architecture diagram of the physics-informed neural network in Embodiment 2 of the present invention.

[0080] Figure 3 It is the comparison diagram of airfoil generation using geometric parameters to control the physics-informed neural network in Embodiment 2 of the present invention.

[0081] Figure 4 It is the optimization design logic diagram of deep reinforcement learning in Embodiment 2 of the present invention.

[0082] Figure 5 This is the final airfoil comparison diagram in Embodiment 2 of the present invention;

[0083] Figure 6 This is the lift - to - drag ratio comparison diagram corresponding to the final airfoil in Embodiment 2 of the present invention. Detailed implementation manners

[0084] Embodiment 1

[0085] This embodiment provides a physics - constraint - based data - driven parametric design method for wind turbine airfoils, including the following steps:

[0086] (1) Generation of the initial geometric airfoil (based on PINN):

[0087] a. Data preparation: Collect the geometric parameters of the airfoil (maximum thickness, maximum thickness position, maximum camber, maximum camber position, leading - edge radius, trailing - edge thickness) and the corresponding Bezier curve control points, and construct a training data set.

[0088] b. PINN model construction: Construct a physics - informed neural network (PINN) model, taking the geometric constraint parameters of the airfoil as input and outputting the corresponding Bezier curve control points of the airfoil.

[0089] c. Incorporation of physical constraints: Add a geometric constraint loss term and a curve smoothness loss term to the loss function of the PINN model. The geometric constraint loss term ensures that the generated airfoil satisfies the specified geometric parameters, such as the monotonic change of the maximum thickness position. The curve smoothness loss term controls the smoothness of the airfoil curve and avoids excessive oscillation.

[0090] d. Model training: Through iterative training of the PINN model, learn the mapping relationship from geometric parameters to airfoil shape, and obtain an airfoil that satisfies the initial geometric constraints.

[0091] (2) Solution of the initial airfoil performance:

[0092] a. Airfoil data conversion: Convert the Bezier curve control points of the airfoil generated by PINN into airfoil coordinate point data, and use the aerodynamic performance solver Xfoil to calculate the airfoil performance.

[0093] b. Performance simulation calculation: Use the integrated two - dimensional airfoil aerodynamic calculation tool Xfoil to perform performance analysis on the generated initial airfoil, and obtain key performance indicators such as lift coefficient, drag coefficient, moment coefficient, and lift - to - drag ratio.

[0094] c. Result extraction: Generate a batch of airfoils that meet the conditions through the given geometric constraints, and extract the airfoil coordinate data for performance analysis.

[0095] (3) Introduction of Deep Reinforcement Learning (DRL) Optimization Strategy:

[0096] a. Deep reinforcement learning optimization strategy: To optimize the airfoil performance without changing the key geometric parameters, a deep reinforcement learning (DRL) strategy is introduced. Fine-tuning of the airfoil shape is achieved by keeping the given geometric parameters unchanged, and the performance of the airfoil is calculated using Xfoil.

[0097] b. Keeping geometric parameters unchanged: During the optimization process, the relative positions of the control points at the relevant geometric requirement parts are restricted to remain unchanged to ensure that the required geometric parameters of the airfoil do not change. In each iteration, the geometric parameters of the airfoil are recalculated to ensure that they meet the predefined constraint conditions.

[0098] c. Adjusting control points: By defining the optimization strategy, these control points are finely adjusted to change the local shape of the airfoil to improve the aerodynamic performance.

[0099] d. Reward function design: According to the performance analysis results of Xfoil, a reward function is designed. The reward function takes aerodynamic performance indicators such as the lift-to-drag ratio as the optimization goal to guide the model to adjust the control points in the direction of improving performance.

[0100] (4) Iterative optimization:

[0101] a. Initial generation: Use the airfoil generation model trained in step (1) to generate a batch of airfoils that meet the geometric requirements according to the specified geometric parameters. Use Xfoil to evaluate the aerodynamic performance of the initial airfoils, obtain key performance indicators such as the lift-to-drag ratio, and iteratively generate the airfoil with the best aerodynamic performance in the airfoil generation model.

[0102] c. Optimization design: Use the deep reinforcement learning model to adjust the positions of the control points in the airfoil according to the performance analysis results to maximize the reward function. During the adjustment process, the relative positions of the key control points are always kept unchanged to ensure the stability of the geometric parameters.

[0103] d. Repeated iteration: Regenerate the airfoil with the adjusted control points through reinforcement learning and perform performance analysis using the performance solver. Repeat the process of optimization and performance evaluation until the performance indicators of the airfoil reach the optimization goal or converge.

[0104] Embodiment 2

[0105] The present invention will be described in detail below with reference to the accompanying drawings.

[0106] Figure 1 It is the overall flowchart of a physics-constrained data-driven wind turbine airfoil parametric design method provided by the present invention.

[0107] This embodiment provides a data-driven parametric design method for wind turbine airfoils based on physical constraints, including the following steps:

[0108] (1) Train a neural network model based on physical constraints.

[0109] Input the geometric parameters of the airfoil, construct a physics-informed neural network model based on Bezier curves, with the output being the Bezier curve control points of the airfoil, and generate an initial airfoil that meets the physical constraint requirements;

[0110] Step (1-1), calculate the geometric parameters of the airfoil based on the airfoil library: maximum thickness t max 、maximum thickness position maximum camber c max 、maximum camber position leading edge radius r le , trailing edge thickness g te .

[0111] Step (1-2), solve for the airfoil Bezier control points:

[0112] Parametrize the airfoil coordinate data points, calculate the parameter t j , map the data points to the parameter domain. Construct a Bernstein basis function matrix, calculate the Bernstein basis function values for each parameter t j , and construct the matrix B. Form a system of linear equations, convert the Bezier curve expression into a system of linear equations BP = Q. Apply the boundary conditions, fix the known leading edge control point P0 and trailing edge control point P n , separate the remaining unknown control points of the target quantity, and reconstruct the system of equations. Solve using the least squares method, using the normal equation and regularization term, to solve for the unknown control points. Recombine the control points, combine the known and unknown control points, and obtain the complete set of control points.

[0113] Specifically, according to the curve equation:

[0114]

[0115] where, is the i-th Bernstein basis function, and P i represents the coordinates of the i-th control point (x i , y i );

[0116] is defined as:

[0117] where, is the combination number, representing the number of combinations of choosing i elements from n elements:

[0118]

[0119] Given a set of data points {Q j}, solve for the control points {P i} of the Bezier curve such that the curve B(t) coincides with the original data as much as possible. The objective function is:

[0120]

[0121] where t j is the parameter value corresponding to the data point Q j , m is the number of data points, and ‖·‖ represents the 2-norm of the vector.

[0122] To solve the above optimization problem, it is chosen to transform it into a system of linear equations and solve it by the least squares method.

[0123] To associate the data point Q j with the parameter t j , the data points are parameterized by using the method of cumulative arc length increment and normalized parameter.

[0124] Specifically, the actual distance (arc length) between data points is used as the parameter value, which reflects the distribution of data points on the curve.

[0125]

[0126] s j = s j-1 + Δs j-1 , j = 1, 2, …, m - 1

[0127]

[0128] where Δs j is the arc length increment between two adjacent data points, x j is the x-coordinate of the j-th data point, y j is the y-coordinate of the j-th data point, s j is the cumulative arc length from the starting point of the path to the j-th data point, s m is the total cumulative arc length from the first point to the last point, and t j is the normalized parameter value corresponding to the j-th data point, with a value range of [0, 1];

[0129] For each data point Q j , there is:

[0130]

[0131] Define the basis function matrix B:

[0132]

[0133] Control point matrix P:

[0134]

[0135] Data point matrix Q:

[0136]

[0137] Form a linear system:

[0138] BP = Q

[0139] Here, B is known, P is known, and Q needs to be solved. Since the number of data points m is usually greater than the number of control points n + 1, the system of equations is overdetermined and cannot be directly solved. By the least squares method, find P that minimizes the sum of the squares of the residuals.

[0140] Minimization objective:

[0141]

[0142] where ‖·‖ F represents the Frobenius norm.

[0143] Normal equations:

[0144] B T BP = B T Q

[0145] Solve for the control points:

[0146] P = (B T B) -1 B T Q

[0147] Specifically, to ensure that the control points are achieved as per the established requirements, define the starting and ending points of the curve to ensure precise matching of the curve with the data curve at the endpoints. The known conditions are as follows:

[0148] P0 = Q start

[0149] P n = Q end Modify the equations, removing P0 and P from the unknown P n Regarding them as known quantities, obtain the modified data point matrix:

[0150]

[0151] Obtain a new linear system:

[0152] B′P′ = Q′

[0153] Where P′ is the unknown intermediate control point.

[0154] To prevent overfitting and improve the stability of the solution, regularization terms are added to the minimization objective.

[0155] Regularized objective function:

[0156]

[0157] Among them, λ is the regularization parameter, which controls the weight of the regularization term.

[0158] Normal equations with regularization terms:

[0159] (B T B+λI)P=B T Q

[0160] Furthermore, in order to unify the number and distribution of data points, the upper / lower surfaces of the airfoil are interpolated and resampled. Generate equally spaced x coordinates, generate a unified x sequence in the interval [0,1]; calculate the corresponding y values: use the interpolation function to calculate the y coordinates of the upper / lower surface under the new x sequence. Get the unified coordinates of the upper / lower surface of the airfoil, which is convenient for using data for training.

[0161] like Figure 2 As shown in the figure, the training process of the physical neural network is as follows:

[0162] Steps (1-3) first construct a neural network structure model using a multi-layer perceptron (MLP) structure, including: an input layer that accepts shape parameters or design parameters as input. Hidden layers, multiple fully connected layers, each layer contains a given number of neurons, uses Leaky ReLU as an activation function, and adds batch normalization and Dropout technology to prevent overfitting. Residual connections use a residual block (ResNet) structure to make the network deeper and less prone to the gradient vanishing problem. The specific formula is expressed as in Represents a function that undergoes a series of linear and nonlinear transformations.

[0163] Specifically, the calculation method in step (1-2) is used to solve the Bezier curve control points of the airfoil, and the curve is reconstructed to obtain complete airfoil coordinate data;

[0164] The input is set as the geometric parameters of the airfoil, recorded as a vector Where n is the number of geometric parameters; X is a vector containing n geometric parameters; is the set of real numbers;

[0165] The output is the Bezier curve control points of the airfoil. There are a total of m sampling points, each with two coordinates x and y, which are flattened into a 2m-dimensional vector; They are the control point coordinates of the airfoil Bezier curve obtained by the final prediction; It is a vector space composed of m (x, y) points;

[0166] Among them, the geometric parameters include the maximum thickness t max , the position of the maximum thickness the maximum camber c max , the position of the maximum camber the leading edge radius r le , the trailing edge thickness g te .

[0167] In steps (1-4), a physical constraint loss function is constructed to measure the gap between the predicted airfoil coordinates and the true airfoil coordinates. Specifically, the function is expressed as:

[0168]

[0169] where N is the number of training samples, is the output predicted by the model, is the true output data, and ‖·‖ is the 2-norm of the vector.

[0170] Furthermore, the physical constraint loss function consists of:

[0171]

[0172]

[0173] where, is the curvature constraint loss function, is the thickness constraint loss function, is the leading edge constraint loss function, is the maximum camber constraint loss function, is the trailing edge constraint loss function;

[0174] N geo is the number of sampling points used to calculate physical constraints such as smoothness and thickness at the geometric level;

[0175] k (i) represents the curvature value calculated at the i-th geometric sampling point;

[0176] is the target curvature, that is, the target curvature value at the i-th geometric sampling point;

[0177] T (i) represents the local thickness value of the airfoil at the i-th sampling point;

[0178] is the target thickness, i.e., the target thickness at the i-th geometric sampling point;

[0179] x min is the minimum x-coordinate point of the airfoil; x max is the maximum x-coordinate point of the airfoil;

[0180] S LE is the translation distance in the leading-edge direction when there is a leading-edge constraint;

[0181] is the predicted maximum camber value; is the target maximum camber value;

[0182] y upper (x max ) is the y-coordinate value of the upper surface of the airfoil at x max ; y lower (x max ) represents the y-coordinate of the lower surface of the airfoil at x max ;

[0183] T TE is the target trailing-edge thickness value;

[0184] The total loss function is: During the training process, the model updates the neural network parameters by minimizing and evaluates the model performance on the validation set to ensure that it can accurately generate an initial airfoil that satisfies the physical constraints according to the given geometric parameters.

[0185] Among them, the physical constraint requirements include: thickness constraint, curvature constraint, geometric constraint, and smoothness constraint. The physical constraint loss function contains a geometric constraint loss term and a curvature regularization loss term; among them, the geometric constraint loss term is used to ensure the monotonic change of the airfoil geometric parameters; the curvature regularization loss term is used to control the smoothness of the airfoil curve.

[0186] As Figure 3 shown, it is a comparative verification diagram of generating an airfoil by using geometric parameters to control a physical neural network.

[0187] Figure 3 In

[0188] it, "original airfoil" represents the original airfoil surface data used for training, and "generated airfoil" represents the airfoil generated by inputting all the geometric parameters of the original airfoil using the above method.

[0189] (2) Convert the generated initial airfoil into coordinate point data and input it into the aerodynamic performance analysis module (aerodynamic performance solver Xfoil) to calculate the aerodynamic performance indicators of the initial airfoil (including: lift coefficient C l , drag coefficient C d , moment coefficient C m , lift-to-drag ratio C l / C d );

[0190] Specifically, generate an airfoil that meets certain geometric conditions according to the initial airfoil obtained from the physics neural network, and use the air performance solver Xfoil to solve the performance of the airfoil to obtain the best initial airfoil.

[0191] As Figure 4 shown, for the deep reinforcement learning optimization design process, the specific steps are as follows:

[0192] (3) Establish a deep reinforcement learning model, and use the reward function with the aerodynamic performance indicators as the optimization goal to optimize the initial airfoil;

[0193] Among them, the deep reinforcement learning model adopts the soft actor-critic algorithm, takes the geometric parameters and aerodynamic performance indicators of the airfoil as the state space, takes the adjustment of the B-spline curve control points of the airfoil as the action space, and constructs the reward function;

[0194] The reward function includes: aerodynamic performance reward, geometric constraint penalty, and action penalty; under the condition of keeping the given geometric parameter requirements of the airfoil unchanged, realize the fine adjustment of the airfoil shape; take the aerodynamic performance indicators as the optimization goal and iteratively optimize the airfoil shape.

[0195] Specifically, use deep reinforcement learning to refine and adjust the airfoil generated by the method in steps (1-3), that is, the B-spline curve basic control points of the airfoil obtained by using the calculation method in steps (1-2) (as the initial control point coordinates), and at the same time explore the design space under the condition of keeping the given geometric requirements to achieve the optimal design of the airfoil.

[0196] Use the B-spline curve control points P of the airfoil calculated by steps (1-2) as the basic state space, use the performance data calculated by Xfoil as the aerodynamic performance indicator A, and the geometric parameters G corresponding to the initial airfoil are obtained by using the calculation in step (1). Therefore, the initial state space s can be expressed as: s = [P, A, G], and the definition of the action space a = ΔP = {(Δx i , Δy i )},

[0197] where, Δx i , Δy i represents the adjustment amount of the horizontal and vertical coordinates of the i-th control point. Action is a continuous vector, indicating that the action vector a belongs to the real space of 2n dimensions, that is, each action consists of 2n continuous values; n is the number of control points of the Bezier curve of the airfoil, and each control point defines the geometry of the airfoil.

[0198] The reward function r(s,a) is designed by comprehensively considering the following factors according to the calculation results obtained from solving the aerodynamic performance, maximizing the lift coefficient C l and minimizing the drag coefficient C d and the moment coefficient C m . The specific function is expressed as: R aero = w Cl ·C l - w Cd ·C d - w Cm ·|C m |.

[0199] Among them, w Cl , w Cd , w Cm are the weight coefficients of C l , C d , C m respectively;

[0200] If the adjusted airfoil violates the geometric constraints (such as thickness and camber limitations), a penalty is given. Define the penalty function: R constraint = -λ·∑ k max(0, g k s), where g k s≥0 represents the degree of violation of the kth geometric constraint, and λ is the penalty coefficient.

[0201] To encourage smaller control point adjustments and prevent excessive modifications. Define the action penalty term R action = -β·‖a‖ 2 , where β is the action penalty coefficient, and ‖a‖ 2 is the square of the two-norm of the action vector.

[0202] Combining the above factors, the reward function is:

[0203] r(s,a) = R aero + R constraint + R action

[0204] (4) Through iterative optimization, the aerodynamic performance of the newly generated airfoil is evaluated until the aerodynamic performance index of the airfoil reaches the optimization goal or converges.

[0205] Among them, through the alternating iteration of the physical information neural network model and the deep reinforcement learning model, the control points of the Bezier curve of the airfoil are adjusted to optimize the aerodynamics of the airfoil; when the reward function converges and meets the design requirements, a new airfoil that meets the design requirements and has excellent aerodynamic performance is obtained.

[0206] The network architecture adopts a double Q-network architecture, including two independent evaluation (Critic) networks and and a policy (Actor) network π φ (a|s). The goal is to minimize the following loss function:

[0207] 1) Evaluation network loss function:

[0208] Among them, is the loss function of the Critic network, which is used to minimize the mean square error between the estimated action value and the target value;

[0209] is the expected operation, indicating that the sampling expectation of the state transition (s, a, r, s′) involves sampling different airfoil designs and their adjusted results from the experience replay pool;

[0210] is the expected performance value of the Critic network for the current airfoil design in the state s = [P, A, G] after adjustment through the action a = ΔP = {(Δx i , Δy i )};

[0211] y is the target value, which combines the immediate reward and the discounted future reward estimate to guide the update of the Critic network;

[0212] θ i is the current network parameter, the parameter of the current Critic network for estimating the action value function Q;

[0213] The calculation of the target y value is:

[0214]

[0215] In the formula, s is the state space, a is the action space; s′ is the new state that the environment transfers to after executing the action a in the next state; a′ is the next action, indicating the action taken in the next state s′;

[0216] r is the reward used to measure the performance feedback of the current airfoil design; r(s, a) represents the improvement degree of the immediate aerodynamic performance index obtained after executing the action a in the state s, such as, lift coefficient C l , drag coefficient C d, Moment coefficient C m Increase or decrease;

[0217] γ is the discount factor, used to weigh the importance of future rewards, with a value between 0 and 1;

[0218] θ j ′ is the target network parameter, that is, the delayed updated version of the Critic network parameter, used to stabilize training;

[0219] φ is the parameter of the actor network, used for the parameters of the policy π;

[0220] π φ π(a|s) is the probability distribution of the policy function to select action a in state s;

[0221] α is the temperature parameter, used to adjust the entropy of the policy, balancing exploration and exploitation;

[0222] is the expectation of sampling action a′ according to the policy π in the next state s′, representing the expected future performance under the adjusted new airfoil design s′; φ Sampling action a′, indicating the expected future performance under the adjusted new airfoil design s′;

[0223] is the minimum operation in double Q-learning, used to prevent overestimation of action values, used to stabilize the evaluation of different design adjustments, and avoid overly optimistic performance predictions;

[0224] α·logπ φ π(a′|s′) is the entropy regularization term, used to encourage the randomness of the policy, prevent the agent from converging to a deterministic policy prematurely, and thus maintain a wide exploration of the airfoil design space;

[0225] 2) Policy network loss function:

[0226] In the formula, D is the experience replay buffer;

[0227] is the loss function of the Actor network, aiming to maximize the expected return of the policy while considering the entropy of the policy;

[0228] is the expectation operation, sampling the state s from the experience replay pool D, manifested as the review and learning of historical airfoil designs and their performances;

[0229] α·logπ φ π(a|s) is the entropy term, encouraging the randomness of the policy to increase exploration and ensure that the agent can explore various possible design improvement directions when adjusting the control points;

[0230] To select the minimum Q value among the two Critic networks as the benchmark for policy improvement, which helps the agent choose design adjustments that can still improve performance in the worst-case scenario;

[0231] 3) Use the experience replay buffer D to store the samples (s, a, r, s′) obtained from the interaction between the agent and the environment. During training, randomly sample a small batch of samples from D for gradient update to reduce the correlation between samples and improve learning efficiency. The adaptive temperature parameter α controls the randomness of the policy. By minimizing the following loss function, the entropy of the policy is made close to the target entropy The specific function is:

[0232]

[0233] In the formula, is the target entropy, that is, the preset policy entropy target, which is used to ensure sufficient exploration;

[0234] is the loss function of the temperature parameter α, which is used to automatically adjust the value of α to match the target entropy

[0235] is the expected operation, which is the evaluation of different airfoil design adjustment schemes;

[0236] By minimizing this loss function, it is ensured that the exploration of the policy in airfoil design adjustment is both sufficient and not excessive.

[0237] Among them, when the policy entropy is higher than the target entropy, increase α to make the policy more deterministic. When the policy entropy is lower than the target entropy, decrease α to encourage the policy to explore.

[0238] From Figure 5 It can be seen that when the design goal is to achieve the maximum lift-to-drag ratio (L / D) at an angle of attack of 10°, by using a physics-informed neural network (PINN) model to generate the baseline airfoil and combining it with the deep reinforcement learning (DRL) method to optimize the airfoil, compared with the initial airfoil, the optimized airfoil has achieved a significant improvement in lift-to-drag ratio performance. Specifically, based on the experimental data analysis, compared with the initial airfoil, the overall lift-to-drag ratio has increased by about 6.28%, and the best airfoil has increased by about 23.8% at an angle of attack of 10°.

Claims

1. A parametric design method for wind turbine airfoils based on physically constrained data-driven, characterized in that, It includes the following steps: (1) Construct a physics-informed neural network model based on Bezier curves, input the geometric parameters of the airfoil according to the design requirements, and generate an initial airfoil that meets the physical constraint requirements; (2) Convert the generated initial airfoil into coordinate point data, input it into the aerodynamic performance analysis module, and calculate the aerodynamic performance indicators of the initial airfoil; (3) Establish a deep reinforcement learning model, and use the reward function with the aerodynamic performance indicators as the optimization goal to optimize the initial airfoil; (4) Through iterative optimization, conduct aerodynamic performance evaluation on the newly generated airfoil until the aerodynamic performance indicators of the airfoil reach the optimization goal or converge.

2. The method for parametric design of a wind turbine airfoil based on physically constrained data-driven according to claim 1, characterized in that The specific method of step (1) is as follows: (1-1) Establish a basic airfoil library as the training set and validation set: collect the geometric parameters of the airfoil and the corresponding Bezier curve control points, uniformly distribute the coordinate point data of the airfoil, and ensure that the input data scales are consistent; The geometric parameters include: the maximum thickness t of the airfoil max , the position of the maximum thickness the maximum camber c of the airfoil max , the position of the maximum camber of the airfoil the leading-edge radius r of the airfoil le , the trailing-edge thickness g of the airfoil te ; (1-2) Establish a multi-layer perceptron structure model: The input layer is a vector of the geometric parameters of the airfoil, denoted as vector where n is the number of geometric parameters; X is a vector containing n geometric parameters; is the set of real numbers; The output layer generates the control points of the Bezier curve of the airfoil. There are a total of m sampling points, each point has two coordinates x and y, and they are flattened into a 2m-dimensional vector. They are the coordinates of the control points of the airfoil Bezier curve obtained by the final prediction. It is a vector space composed of m (x, y) points. (1-3) Construct a physical constraint loss function, and the objective function is expressed as: where N is the number of training samples, is the output predicted by the model, is the true output data; ||·|| is the 2-norm of the vector; Physical constraint loss function is composed as follows: Among them, is the curvature constraint loss function, is the thickness constraint loss function, -edge is the leading edge constraint loss function, -max is the maximum camber constraint loss function, -edge is the trailing edge constraint loss function; N geo is the number of sampling points used to calculate physical constraints; κ (i) is the curvature at the i-th sampling point; is the target curvature at the i-th sampling point; T (i) is the local thickness at the i-th sampling point; is the target thickness at the i-th sampling point; T TE is the target trailing edge thickness value; S LE The distance translated in the leading edge direction when there is a leading edge constraint; is the predicted maximum camber value; is the target maximum camber value; x min is the minimum x - coordinate point of the airfoil; x max is the maximum x - coordinate point of the airfoil; y upper (x max ) is the y - coordinate value of the upper surface of the airfoil at x max ; y lower (x max ) represents the y - coordinate value of the lower surface of the airfoil at x max ; The total loss function is as follows: where λ is the weight coefficient; (1-4) Use the training set to train a physics-informed neural network model, and evaluate the performance of the physics-informed neural network model on the validation set; during the training process, input the geometric feature parameters of the airfoil, the coordinate point data of the airfoil, and the Bezier curve control points, and output an airfoil that satisfies the geometric constraints, and update the neural network parameters by minimizing Update the neural network parameters; (1-5) After the physics-informed neural network model is trained, input the geometric parameters of the airfoil according to the design requirements, and generate an initial airfoil that meets the physical constraint requirements.

3. The method for parametric design of a wind turbine airfoil based on physically constrained data-driven as claimed in claim 2, wherein In step (1-1), the solution method for the Bezier curve control points corresponding to the geometric parameters of the airfoil is as follows: Parametric airfoil coordinate data points, calculate parameter t j , map the data points to the parameter domain; Construct the Bernstein basis function matrix and calculate the Bernstein basis function values for each parameter t j to construct matrix B; Form a linear equation system, and convert the Bezier curve expression into a linear equation system BP = Q; Apply boundary conditions to fix the known leading-edge control point P0 and trailing-edge control point P n , separate the unknown Bessel curve control points of the remaining target quantity, and reconstruct the system of equations; Solve by least squares, use the normal equation and regularization term to solve the unknown Bezier curve control points; Recombine the Bezier curve control points, combine the known and unknown Bezier curve control points to obtain a complete set of Bezier curve control points.

4. The parametric design method of the wind turbine airfoil based on physical constraint data driving according to claim 2, characterized in that In step (1-2), the multi-layer perceptron structure model also includes a hidden layer, the hidden layer contains multiple fully connected layers, each layer has a specified number of neurons, uses Leaky ReLU as the activation function, introduces batch normalization and Dropout techniques, and adopts a residual block structure for residual connection.

5. The parametric design method of the wind turbine airfoil based on physical constraint data driving according to claim 1, characterized in that, In the step (2), the aerodynamic performance analysis module includes, but is not limited to, the aerodynamic performance solver Xfoil; the aerodynamic performance indicators include: lift coefficient C l , drag coefficient C d , moment coefficient C m , lift-to-drag ratio C l / C d .

6. The parametric design method of the wind turbine airfoil based on physical constraint data driving according to claim 1, characterized in that In step (3), the deep reinforcement learning model adopts the Soft Actor-Critic algorithm, takes the geometric parameters and aerodynamic performance indicators of the airfoil as the state space, takes the adjustment of the Bezier curve control points of the airfoil as the action space, and constructs a reward function; Among them, the reward function includes: aerodynamic performance reward, geometric constraint penalty, and action penalty; under the condition of keeping the given airfoil geometric parameter requirements unchanged, realize fine adjustment of the airfoil shape; take the aerodynamic performance indicators as the optimization goal and iteratively optimize the airfoil shape.

7. The parametric design method of the wind turbine airfoil based on physical constraint data driving according to claim 6, wherein In the step (3), the state space of the deep reinforcement learning model: s = [P, A, G], where P represents the Bezier curve control points of the airfoil; A represents the aerodynamic performance indicators, including: lift coefficient C l , drag coefficient C d , and moment coefficient C m ; G represents the geometric parameters corresponding to the initial airfoil obtained by the physics-informed neural network model; Action space: a = ΔP = {(Δx i , Δy i )}, where Δx i and Δy i represent the adjustment amounts of the horizontal and vertical coordinates of the i-th control point; Reward function: r(s,a) = R aero +R constraint +R action wherein, R aero = w Cl ·C l - w Cd ·C d - w Cm ·|C m | R action = -β·||a|| 2 where, w Cl , w Cd , w Cm are the weight coefficients of C l , C d , C m respectively; g k s ≥ 0 represents the violation degree of the k-th geometric constraint, λ is the penalty coefficient, β is the action penalty coefficient, ||a|| 2 is the square of the two-norm of the action vector; R aero is the aerodynamic performance reward function; R constraint is the geometric constraint reward function; R action is the action space reward function.

8. The method for parametric design of a wind turbine airfoil based on physically constrained data-driven as claimed in claim 1, wherein In step (4), through the alternating iteration of the physics-informed neural network model and the deep reinforcement learning model, the agent continuously interacts with the environment, adjusts the Bezier curve control points of the airfoil, and optimizes the aerodynamic performance of the airfoil; when the reward function converges and meets the design requirements, a new airfoil that meets the design requirements and has excellent aerodynamic performance is obtained.

9. The method for parametric design of a wind turbine airfoil based on physically constrained data-driven as claimed in claim 8, wherein In the step (4), a dual Q-network architecture is used, which includes two independent evaluation networks and and a policy network π φ (a|s), and iterative optimization is performed.

10. The method for parametric design of a wind turbine airfoil based on physically constrained data-driven as described in claim 9, wherein In step (4), update the network parameters by minimizing the following loss function; The calculation of the target y value is as follows: Among them, s is the state space; a is the action space; s′ is the new state that the environment transfers to after executing action a in the next state; a′ is the next action, indicating the action taken in the next state s′; D is the experience replay buffer; γ is the discount factor, where 0 < γ < 1; α is the temperature parameter; r is the improvement degree of the aerodynamic performance index; θ i is the current network parameter of the action value function Q; θj′ is the target network parameter of the action value function Q; φ is the parameter of the policy network; is the target entropy; For evaluating the network loss function; For the policy network loss function; For the loss function of the temperature parameter; Denotes the expected operation; Represents the expected performance value adjusted by action a in state s; r(s,a) represents the improvement degree of the aerodynamic performance index after performing action a in state s; π φ (a|s) represents the probability distribution of selecting action a in state s.

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