Large flexible wing static aeroelasticity analysis method based on physical information neural network

Abstract

The invention discloses a large flexible wing static aeroelasticity analysis method based on a physical information neural network, and belongs to the field of aircraft design. The method comprises the following steps: for the wing with the super-high aspect ratio, firstly, dispersing the wing into n spanwise sections based on a strip theory, and initializing a reference angle-of-attack parameter of each spanwise section; then, a physical information neural network (PINN) is built, unsteady flow field solving is carried out on each section, for the current ith iteration, the physical information neural network is used for sequentially traversing and extracting pressure distribution of the airfoil surface of each section, respective aerodynamic load distribution is calculated, and the generalized force of the airfoil is obtained; and solving a structural dynamics equation based on the generalized force and structural information of the wing, calculating the deformation of the large-deformation wing by using a modal rotation method, and finally, carrying out solving iterative circulation on aerodynamic force and structural deformation until the attack angle is converged, so as to obtain the actual lift force L of the wing. According to the method, the calculation precision and efficiency are remarkably improved, and different flight conditions and wing design can be adapted.

Description

Technical Field

[0001] The invention belongs to the field of aircraft design, and in particular is a static aeroelastic analysis method of a large flexible wing based on physical information neural network. Background Art

[0002] The static aeroelasticity of large flexible wings is a crucial research area in aircraft design. Large flexible wings experience significant bending deformation under aerodynamic loads, which in turn redistributes the aerodynamic loads, significantly altering the wing's aerodynamic characteristics and influencing parameters such as lift-to-drag ratio and moment coefficient. Therefore, studying the load redistribution and changes in the wing's aerodynamic characteristics under static aeroelastic deformation is crucial.

[0003] Existing methods for studying aircraft aeroelasticity include flight tests, wind tunnel tests, and numerical solutions. While flight tests can provide data under realistic flight conditions, their high cost and risks limit their application. Wind tunnel tests can be conducted in a relatively safe, controlled environment, but their results are still limited by the wind tunnel facilities and testing technology, and remain costly. Numerical solutions, by contrast, offer a relatively low-cost alternative, but in complex practical applications, they often face challenges balancing accuracy and computational efficiency. Each of these methods has its own advantages and limitations, making it difficult to achieve a perfect balance between cost, accuracy, and applicability. Therefore, researching and developing novel static aeroelastic analysis methods is crucial.

[0004] In traditional aeroelastic analysis, the acquisition of aerodynamic data typically relies on extensive wind tunnel testing and numerical calculations, which means a trade-off between cost and accuracy. In practical engineering applications, the aerodynamic data obtained at a fixed cost often only contains a small amount of high-precision data. In addition, the numerical solution of static aeroelastic analysis requires fluid-structure interaction technology to solve the steady-state response of the interaction between airflow and structure. However, the iterative process to the steady state often faces challenges such as difficult convergence, a large number of iterations, and high computational costs.

[0005] In order to overcome the above problems, in recent years, methods based on physical information neural network (PINN) and modal rotation methods have been widely used in the fields of fluid mechanics and structural mechanics.

[0006] By embedding physical equations into the neural network's loss function, PINN can effectively solve partial differential equations (PDEs) with high computational accuracy and efficiency. The modal rotation method, on the other hand, introduces modal coordinates and rotation tensors to describe the geometric nonlinear deformation of large flexible wings. By replacing displacement superposition with the linear superposition of local curvatures, it can reduce the complexity of structural calculations and improve computational speed to a certain extent. Summary of the Invention

[0007] The present invention provides a static aeroelastic analysis method for a large flexible wing based on a physical information neural network, which is used to solve the static aeroelastic deformation and aerodynamic load. It can analyze the load redistribution under static aeroelastic deformation and analyze the aerodynamic characteristics of the deformed configuration, thereby improving the analysis accuracy and efficiency.

[0008] The static aeroelastic analysis method of a large flexible wing based on physical information neural network has the following specific steps:

[0009] Step 1: Based on the strip theory, the large flexible wing is discretized into n spanwise sections, and the reference angle of attack parameter α of each spanwise section is initialized. 0,j and the initial angle of attack of the wing, α0;

[0010] α0 is an n×1 dimensional vector; j = 1, 2, 3, ... n;

[0011] Step 2: Build a physical information neural network and construct a loss function to optimize the network parameters;

[0012] The physical information neural network adopts a fully connected neural network with 7 hidden layers. Each hidden layer uses 128 neuron nodes. The Tanh activation function is used between hidden layers, and normalization technology is introduced to improve the stability of gradient propagation.

[0013] The loss function L is minimized by combining the back-propagation algorithm with the L-BFGS optimizer, and the network parameters are trained and optimized to predict the solution of the partial differential equation.

[0014] The loss function is

[0015] L=wL PDE +L BC

[0016] Among them, L PDE Represents the PDE equation loss function, L BC Represents the boundary condition loss function, and the weighting factor w represents the relative size of the two losses;

[0017] Step 3: For the current iteration i, the airfoil surface flow field coordinates, time and angle of attack [x, t, α i,j ] Input physical information neural network and output two velocity components and pressure [u, v, p];

[0018] i is the number of iterations, the initial value is 0, that is, i = 0, 1, 2, 3, ... m, m is the maximum number of iterations;

[0019] Specifically: the airfoil surface flow field coordinates, time and angle of attack [x sur ,t,α 0,j ] Input physical information neural network, output is speed and pressure [usur ,v sur ,p sur ];

[0020] x sur is the 2×200×1 dimensional vector of the airfoil surface coordinates, u sur ,v sur ,p sur Both are 200×1 dimensional vectors.

[0021] Step 4: Traverse j = 1, 2, 3, ... n, and extract the pressure distribution p of each airfoil surface of the current i-th iteration based on the physical information neural network. j,k , and the lift force L under the section is obtained j Resistance D j and moment M j ;

[0022] k represents the number of the airfoil surface point;

[0023] Lift coefficient calculation formula:

[0024]

[0025] Drag coefficient calculation formula:

[0026]

[0027] Torque coefficient calculation formula:

[0028]

[0029] Among them, θ k is the angle between the point normal of the airfoil surface and the horizontal direction, s k is the distance between two adjacent points on the airfoil surface, and b is the longitudinal distance from the surface point to the aerodynamic center.

[0030] Step 5: The lift L under the section j , resistance D j and moment M j Multiply them by the spanwise length c of the strip respectively to form the aerodynamic load distribution of each section of the wing in the i-th iteration, and then arrange them in the order of the spanwise sections to obtain the external force vector F of the wing i ;

[0031] External force vector F i The dimension is 3n×1;

[0032] Step 6: External force vector F based on the wing i , solve the structural statics equations and obtain the final generalized displacement q and displacement rotation matrix R according to the Runge-Kutta method;

[0033] The statics equation is Kq=F i ; where q is the generalized displacement and K is the stiffness matrix;

[0034] Using the obtained generalized displacement, the modal rotation method is used in combination with the displacement modal matrix of the wing to obtain the curvature modal matrix. Then the local curvature is obtained and linearly superimposed from the root of the wing. Finally, the iterative cycle converges to obtain the generalized displacement and displacement rotation matrix R of each section of the wing.

[0035] Step 7: Calculate the Euler angle in the span direction of each section through the displacement rotation matrix R, and then get the angle of attack α of the i+1th iteration i+1 ;

[0036] Step 8. Calculate two consecutive angles of attack α i and α i+1 Is the error less than the threshold? If so, output the actual α of the wing i+1 , through the corresponding external force vector F i Get the actual lift L of the wing. Otherwise, return to step 3 and iterate until the angle of attack converges;

[0037] The error is

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) The static aeroelastic analysis method of a large flexible wing based on a physical information neural network of the present invention adopts a physical information neural network (PINN) to calculate the flow field and accurately calculates the structural deformation through the modal rotation method, which significantly improves the calculation accuracy.

[0040] (2) The static aeroelastic analysis method for large flexible wings based on a physical information neural network can more accurately simulate low-Reynolds number flows through the NS equations and grid transformation technology. Furthermore, the present invention is adaptable to different flight conditions and wings, demonstrating improved generalization. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The present invention is a flow chart of a method for static aeroelastic analysis of a large flexible wing based on physical information neural network.

[0042] Figure 2 It is a specific structural diagram of the physical information neural network used in the present invention. DETAILED DESCRIPTION

[0043] In order to make the technical solution of the present invention clearer and easier to understand, the present invention is described in further detail below with reference to the accompanying drawings.

[0044] The present invention proposes a static aeroelastic analysis method of a large flexible wing based on physical information neural network. Figure 1 The specific steps are as follows:

[0045] Step 1: Based on the strip theory, the large flexible wing is discretized into n spanwise sections, and the reference angle of attack parameter α of each spanwise section is initialized. 0,j and the initial angle of attack of the wing, α0;

[0046] α0 is an n×1 dimensional vector; j = 1, 2, 3, ... n;

[0047] Step 2: Build a physical information neural network (PINN) and construct a loss function to optimize the network parameters;

[0048] The physical information neural network (PINN) is used to solve the unsteady flow field of each section's angle of attack and calculate the aerodynamic load of each section. The physical information neural network adopts a fully connected neural network with 7 hidden layers. Each hidden layer has 128 neuron nodes. The Tanh activation function is used between hidden layers, and normalization technology is introduced to improve the stability of gradient propagation.

[0049] The loss function L is minimized by combining the back-propagation algorithm with the L-BFGS optimizer, and the network parameters are trained and optimized to predict the solution of the partial differential equation.

[0050] The loss function is

[0051] L=wL PDE +L BC

[0052] Among them, L PDE Represents the PDE equation loss function, L BC Represents the boundary condition loss function, and the weighting factor w represents the relative size of the two losses to avoid optimization imbalance between the losses caused during training;

[0053] In order to improve the calculation accuracy of the flow field, grid transformation is used to transform the circular flow field domain into a square calculation domain, and the partial derivatives of u in the x and y directions are indirectly calculated. The Laplace equation is used as the transformation equation:

[0054]

[0055] Where (x, y) corresponds to the flow field coordinates obtained by the coordinate vector x, (ξ, η) corresponds to the coordinates of the computational space grid points, and δβγ is the iteration factor. The calculation method is given by the following formula:

[0056]

[0057] The first-order partial derivative of the computational domain with respect to the physical domain is obtained by automatic differentiation

[0058]

[0059] Step 3: For the current iteration i, the airfoil surface flow field coordinates, time and angle of attack [x, t, α i,j ] Input physical information neural network and output two velocity components and pressure [u, v, p];

[0060] i is the number of iterations, the initial value is 0, that is, i = 0, 1, 2, 3, ... m, m is the maximum number of iterations; x is a 2 × 200 × 1600 dimensional tensor, t is a 50 × 1 dimensional vector; u, v, p are all 200 × 1600 dimensional vectors;

[0061] Specifically: the airfoil surface flow field coordinates, time and angle of attack [x sur ,t,α 0,j ] Input physical information neural network, output is speed and pressure [u sur ,v sur ,p sur ];x sur is the 2×200×1 dimensional vector of the airfoil surface coordinates, u sur ,v sur ,p sur Both are 200×1 dimensional vectors.

[0062] Step 4: Traverse j = 1, 2, 3, ... n, and extract the pressure distribution p of each airfoil surface of the current i-th iteration based on the physical information neural network. j,k , and the lift force L under the section is obtained j Resistance D j and moment M j ;

[0063] k represents the number of the airfoil surface point; in this embodiment, k is selected to be 200;

[0064] Lift coefficient calculation formula:

[0065]

[0066] Drag coefficient calculation formula:

[0067]

[0068] Torque coefficient calculation formula:

[0069]

[0070] Among them, θ k is the angle between the point normal of the airfoil surface and the horizontal direction, s kis the distance between two adjacent points on the airfoil surface, and b is the longitudinal distance from the surface point to the aerodynamic center.

[0071] Step 5: The lift L under the section j , resistance D j and moment M j Multiply them by the spanwise length c of the strip respectively to form the aerodynamic load distribution of each section of the wing in the i-th iteration, and then arrange them in the order of the spanwise sections to obtain the external force vector F of the wing i ;

[0072] External force vector F i The dimension is 3n×1; the formula is as follows:

[0073]

[0074] Step 6: External force vector F based on the wing i , solve the structural statics equations and obtain the final generalized displacement q and displacement rotation matrix R according to the Runge-Kutta method;

[0075] After performing modal analysis on the undeformed structure using finite element software, the first four modes are extracted and the static equation is obtained as Kq=F i ; where q is the generalized displacement and K is the stiffness matrix;

[0076] Then, the generalized displacement q0 is obtained by iteration according to the Runge-Kutta method, and the curvature mode matrix [φ] is obtained by using the mode rotation method in combination with the displacement mode matrix [φ] of the wing. dθ ];

[0077] Then the local curvature is obtained and linearly superimposed from the root of the wing, and finally the iterative cycle converges to obtain the generalized displacement and displacement rotation matrix of each section of the wing [R j ](j=1,2,3,…n), which represents the rotation transformation of each segment local coordinate system relative to the global coordinate system.

[0078] In the 2D case, the rotation matrix of each node In the 3D case, the gradient rotation matrix [dR j ], and accumulate the rotation matrix of each segment [R j ]=[R j-1 ][dR j ].

[0079] According to the deformed geometry, the internal moment BM of each segment is calculated, and then the corrected generalized force is obtained:

[0080]

[0081] The modified generalized force F due to nonlinearityi+1 Re-enter the structural statics equation for iterative cycles, and after convergence, obtain the final generalized displacement q and the displacement rotation matrix of each segment [R j ], and then calculate the Euler angle in the span direction of each section, that is, the angle of attack α i+1 ;

[0082] Step 7: Calculate the Euler angle in the span direction of each section through the displacement rotation matrix R, and then get the angle of attack α of the i+1th iteration i+1 ;

[0083] Step 8. Calculate two consecutive angles of attack α i and α i+1 Is the error less than the threshold? If so, output the actual α of the wing i+1 , through the corresponding external force vector F i Get the actual lift L of the wing. Otherwise, return to step 3 and iterate until the angle of attack converges;

[0084] The error is

[0085] Example:

[0086] In this embodiment, step (1) first discretizes the wing and determines the number of sections, thereby obtaining the spanwise length c of the strips. The aerodynamic calculation of the section strips replaces the calculation of the aerodynamic characteristics of the entire wing.

[0087] Step (2) initializes the reference angle of attack parameters of each section of the wing in order to obtain the initial calculation of the aerodynamic load on the non-deformed wing and then load the load onto the structure.

[0088] Step (3) constructs an unsteady aerodynamic calculation model based on the physical information neural network, determines the calculation conditions, and trains the model.

[0089] like Figure 2 As shown, the physical information neural network consists of three parts: input, output and loss function;

[0090] The neural network input for training is the entire flow field coordinates, time and angle of attack [x, t, α i ], x is a 2×200×1600 dimensional vector, 200 is the number of points on the airfoil surface, 1600 is the number of points normal to the airfoil surface, t is a 50×1 dimensional vector, and since the unsteady period is about 2s, t = [0, 0.04, 0.08...2], and the output is the average velocity and pressure [u, v, p] of each flow field point with coordinates (x, y) for one cycle;

[0091] The loss function consists of two parts. First, the incompressible NS equation is given as the control equation, and the velocity inlet and pressure outlet are used as boundary conditions; the loss function L = wL NS +L BC

[0092] Among them, L NS Represents the NS equation loss function, L BC represents the boundary condition loss function, and the weighting factor w represents the relative size of the two losses to avoid optimization imbalance between the losses during training.

[0093] Boundary condition loss function L BC It consists of two parts: the residual of the velocity inlet and the pressure outlet at the flow field boundary:

[0094] L BC =L v +L p

[0095] NS equation loss function L NS It consists of two momentum equations and a continuity equation residual:

[0096] L NS =||L1||2+||L2||2+||L3||2

[0097] The residuals of the three equations are calculated as follows:

[0098] L1=u t +uu x +vu y +p x -Re -1 (u xx +u yy )

[0099] L2=v t +uv x +vv y +p y -Re -1 (v xx +v yy )

[0100] L3=u x +v y

[0101] Among them, u and v are the velocity components in the x and y directions respectively, u t and v t Represent the first-order partial derivatives of u and v with respect to time t, u x and u y Respectively represent the first-order partial derivatives of u in the x-direction and y-direction, u xx and uyy Represents the second-order partial derivative of u in the x-direction and y-direction, p x and p y Represent the partial derivatives of pressure p with respect to x and y, v x and v y Represents the first-order partial derivatives of v in the x and y directions, respectively. xx and v yy Represent the second-order partial derivatives of v with respect to the x-direction and the y-direction, and Re represents the Reynolds number.

[0102] A fully connected neural network is used to minimize the loss function L through the back-propagation algorithm combined with the L-BFGS optimizer, thereby optimizing the trainable parameters of the network. When the loss function L is less than a certain order of magnitude, the neural network training is completed and the solution of the partial differential equation is predicted.

[0103] The neural network input for prediction is the airfoil surface flow field coordinates, time and angle of attack [x sur ,t,α i ], since the airfoil surface has 200 points, x sur is the 2×200×1 dimensional vector of the airfoil surface coordinates, and the output is the velocity and pressure [u sur ,v sur ,p sur ],u sur ,v sur ,p sur By inputting the airfoil coordinates of each section, the pressure distribution p on the airfoil surface of each section is extracted. j,k , k represents the number of the airfoil surface point, and the lift L under the section can be obtained j Resistance D j and moment M j .

[0104] The lift force L j Resistance D j and moment M j Multiply by the spanwise length c of the strips and arrange them in the order from root to tip (j = 1, 2, 3, ... n) to get the external force vector F of the wing. i ;

[0105] Step (3) First initialize the modified generalized force F i , input the input structural information and the forces and moments acting on the structural nodes into the generalized structural statics equation Kq=F i , and then the generalized displacement is solved by the Runge-Kutta method.

[0106] The modal rotation method is used to calculate the node rotation matrix R from the root outward, and then the modified bending moment acting on the node is calculated. Whether the residual is less than the expected value is used to determine whether the modified bending moment acting on the node has converged. If it does not converge, the modified generalized force is calculated and re-substituted into the generalized structural statics equation for an iterative cycle; if it converges, the calculation ends. The Euler angle in the span direction of each section is calculated through the final displacement rotation matrix R. The Euler angle in the y direction is the angle of attack α i+1 .

[0107] Iterate steps 3 to 4 until the angle of attack α i Convergence is achieved, and then the structural changes of the wing are obtained, and the actual aerodynamic characteristics of the wing are calculated.

[0108] The present invention uses physical information neural network (PINN) to calculate flow field and modal rotation method to accurately calculate structural deformation, which significantly improves the calculation accuracy. The flow field calculation part uses grid transformation technology to quickly and accurately calculate low Reynolds number flow. The structural deformation calculation part uses modal rotation method to replace local deformation by local curvature, accurately calculate node deformation, and effectively deal with the geometric nonlinearity problem of large flexible wings.

[0109] In addition, the present invention has strong adaptability and can be applied to different flight conditions and wings. It also has good generalization and can perform accurate aeroelastic analysis under different flight conditions. It has demonstrated high precision and high efficiency in the static aeroelastic analysis of large flexible wings, providing important technical support for the design and optimization of aircraft.

Claims

1. A static aeroelastic analysis method for a large flexible wing based on a physical information neural network, characterized in that: The specific steps are as follows: Step 1: Based on the strip theory, the large flexible wing is discretized into n spanwise sections, and the reference angle of attack parameter α of each spanwise section is initialized. 0,j and the initial angle of attack of the wing, α0; α0 is an n×1 dimensional vector; 1 Step 2: Build a physical information neural network and construct a loss function to optimize the network parameters; The network parameters are trained and optimized by combining the back-propagation algorithm with the L-BFGS optimizer to minimize the loss function L, and then the solution of the partial differential equation is predicted; The loss function is L = wL PDE +L BC ; Among them, L PDE Represents the PDE equation loss function, L BC Represents the boundary condition loss function, and the weighting factor w represents the relative size of the two losses; Step 3: For the current iteration i, the airfoil surface flow field coordinates, time and angle of attack [x, t, α i,j ] Input physical information neural network and output two velocity components and pressure [u, v, p]; i is the number of iterations, the initial value is 0, that is, i=0,1,2,3,…m, m is the maximum number of iterations; 1j=1,2,3,…n; Step 4: Traverse j = 1, 2, 3, ... n, and extract the pressure distribution p of each airfoil surface of the current i-th iteration based on the physical information neural network. j,k , and the lift force L under the section is obtained j Resistance D j and moment M j ; k represents the number of the airfoil surface point; Step 5: The lift L under the section j , resistance D j and moment M j Multiply them by the spanwise length c of the strip respectively to form the aerodynamic load distribution of each section of the wing in the i-th iteration, and then arrange them in the order of the spanwise sections to obtain the external force vector F of the wing i ; External force vector F i The dimension is 3n×1; Step 6: External force vector F based on the wing i , solve the structural statics equations and obtain the final generalized displacement q and displacement rotation matrix R according to the Runge-Kutta method; Step 7: Calculate the Euler angle in the span direction of each section through the displacement rotation matrix R, and then get the angle of attack α of the i+1th iteration i+1 ; Step 8. Calculate two consecutive angles of attack α i and α i+1 Is the error less than the threshold? If so, output the actual α of the wing i+1 , through the corresponding external force vector F i Get the actual lift L of the wing; otherwise, return to step 3 and iterate until the angle of attack converges; The error is 2. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 1, characterized in that: In the step 2, the physical information neural network adopts a fully connected neural network, sets 7 hidden layers, each hidden layer adopts 128 neuron nodes, uses the Tanh activation function between hidden layers, and introduces normalization technology to improve the stability of gradient propagation.

3. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 2, characterized in that: In order to improve the calculation accuracy of the flow field, the physical information neural network uses grid transformation to transform the circular flow field into a square calculation domain, indirectly calculate the partial derivatives, and use the Laplace equation as the transformation equation: Where (x, y) corresponds to the flow field coordinates obtained by the coordinate vector x, (ξ, η) corresponds to the coordinates of the calculation space grid point, and δβγ is the iteration factor; 1 The first-order partial derivative of the computational domain with respect to the physical domain is obtained by automatic differentiation:

4. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 1, characterized in that: The step three is specifically as follows: the airfoil surface flow field coordinates, time and angle of attack [x sur ,t,α 0,j ] Input physical information neural network, output is speed and pressure [u sur ,v sur ,p sur ]; x sur is the 2×200×1 dimensional vector of the airfoil surface coordinates, u sur ,v sur ,p sur Both are 200×1 dimensional vectors.

5. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 1, characterized in that: The lift coefficient calculation formula is: Drag coefficient calculation formula: Torque coefficient calculation formula: Among them, 1θ k is the angle between the point normal of the airfoil surface and the horizontal direction, s k is the distance between two adjacent points on the airfoil surface, and b is the longitudinal distance from the surface point to the aerodynamic center.

6. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 1, characterized in that: In step 6, the statics equation is Kq=F i ; where q is the generalized displacement and K is the stiffness matrix; Using the obtained generalized displacement, the modal rotation method is used in combination with the displacement modal matrix of the wing to obtain the curvature modal matrix. Then the local curvature is obtained and linearly superimposed from the root of the wing. Finally, the iterative cycle converges to obtain the generalized displacement and displacement rotation matrix R of each section of the wing.

7. The static aeroelastic analysis method of a large flexible wing based on physical information neural network according to claim 1, characterized in that: The external force vector F in step 5 i The specific order is as follows:

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