Wave rider shape approximate optimization method based on proxy model

Abstract

The invention discloses a wave rider shape approximate optimization method based on an agent model. According to the method, the parameterized shape of the waverider is established and passivated by adopting the CST method, the three-dimensional viscous effect and the front edge passivation effect of the shape of the waverider are considered, and the flight surface grid local parameters are generated by adopting the Jacobian conversion method, so that automatic updating of the waverider space grid in the optimization process is realized; then, the aerodynamic / thermal characteristics of the waverider are calculated based on a Reynolds average Navier-Stokes equation (RANS); the method comprises the following steps: constructing a waverider shape optimization problem by taking the maximum lift-drag ratio as an optimization target, solving the optimization problem by adopting an agent model assisted constraint optimization algorithm, and circularly selecting new sample points to update an agent model based on a certain point adding criterion in the solving process until approximate optimization convergence. According to the method, the optimization efficiency can be effectively improved, the design period is shortened, and optimization and modification of the wave rider shape scheme can be rapidly achieved in the overall design stage.

Description

Technical Field

[0001] This invention relates to the field of hypersonic aircraft and aerodynamic shape design technology, specifically to a waverider shape approximation optimization method based on a surrogate model. Background Technology

[0002] Hypersonic vehicles refer to aircraft with a maximum speed of Mach 5 or higher that maneuver within or across the atmosphere for extended periods. Their aerodynamic design directly determines their performance. Waverider configurations have attracted widespread attention due to their high lift-to-drag ratio at hypersonic speeds. Computational fluid dynamics (CFD)-based waverider shape design methods can fully consider three-dimensional viscous effects and leading-edge passivation effects. Combining these with numerical optimization algorithms can further improve the aerodynamic performance of the aircraft. However, CFD simulations are time-consuming, and traditional numerical optimization algorithms require extensive calls to computational models, posing a computational complexity challenge to CFD-based waverider shape optimization design.

[0003] Traditional waverider shape optimization techniques are typically based on low-precision models such as the element method, resulting in low reliability of the optimized design and a lack of consideration for three-dimensional viscous effects and leading-edge passivation. To further improve the aerodynamic performance of waverider aircraft, it is necessary to conduct waverider shape optimization based on CFD that considers viscosity and leading-edge passivation. Using surrogate model techniques can reduce computational complexity and the number of model calls, thereby improving the lift-to-drag ratio and reducing stagnation point heat flux density within limited design resources. However, existing surrogate model-based optimization algorithms lack customization for the waverider shape optimization problem and exhibit low optimization efficiency when handling black-box constraints. Summary of the Invention

[0004] In view of this, this invention provides an approximate optimization method for the shape of a waverider based on a surrogate model. It establishes a waverider shape with a blunted leading edge and an aerodynamic / thermal model based on the Reynolds-averaged Navier-Stokes equations (RANS). The waverider shape is parameterized using a three-dimensional function-like / shape function transformation (CST) method, and the aerodynamic / thermal model is parameterized using the Jacobi transformation method. The waverider shape optimization problem is solved using an optimization technique based on a surrogate model, resulting in low computational complexity and high optimization efficiency. A customized sampling strategy for the optimization process is further developed to improve optimization efficiency and effectively shorten the design cycle.

[0005] This invention discloses a method for approximate optimization of the shape of a waverider based on a surrogate model, comprising the following steps:

[0006] The waverider shape approximation optimization method based on a surrogate model of the present invention includes:

[0007] S1. The three-dimensional CST method is used to establish the geometric parameterization model of the waverider, namely the reference waverider. Then, the reference waverider is passivated and lofted to obtain the analytical expression of the waverider's shape.

[0008] S2, determine the length L′ of the aircraft, generate the initial shape based on the analytical expression of the waverider shape established in S1 and perform mesh generation to generate the initial spatial mesh; read the aircraft surface mesh in the initial spatial mesh and calculate the local parameters corresponding to the coordinate points of the aircraft surface mesh in the analytical expression of the aircraft shape;

[0009] S3, taking the geometric configuration parameters of the waverider, i.e. the design variables, as the optimization variables, and under the condition of satisfying the upper and lower bound constraints of the design variables, the optimization objective is to maximize the lift-to-drag ratio of the aircraft, and construct the waverider shape optimization problem;

[0010] S4, using a surrogate model-assisted constraint optimization algorithm to solve the optimization problem, including:

[0011] S41, Based on experimental design methods, generate N within the initial design space. init Initial geometric configuration parameter sample points;

[0012] In step S42, the geometric configuration parameter sample points are substituted into the analytical expression of the waverider's shape. Based on the local parameters calculated in S2, the positions of the surface mesh points are calculated, and the corresponding surface meshes are generated. A mesh deformation solver is used to deform the initial spatial mesh, generating a spatial mesh corresponding to the surface meshes corresponding to the geometric configuration parameter sample points. The aerodynamic / thermal characteristics of the waverider corresponding to the geometric configuration parameter sample points are obtained based on CFD calculations. A sample library is constructed based on the geometric configuration parameter sample points and their corresponding aerodynamic / thermal characteristics of the waverider.

[0013] S43, Construct a proxy model for the optimization problem based on the current sample library;

[0014] S44. The sequential quadratic programming algorithm is used to optimize the current agent model and obtain a pseudo-optimal solution. With the pseudo-optimal solution To add new geometric configuration parameter sample points, and obtain them according to the S42 method. Update the sample database with the corresponding waverider aerodynamic / thermal characteristics;

[0015] S45. Based on the objective function response values ​​of the newly added sample points in the current iteration step and the objective function response values ​​of the newly added sample points in the previous iteration step, determine whether the optimization algorithm has converged. If it has converged, end the optimization and determine the current pseudo-optimal solution. This is the optimal geometric configuration parameter for the waverider; otherwise, execute S46.

[0016] S46. The optimal experimental sample is selected using a filter-based interest sampling or dynamic coordinate search strategy. With the aforementioned optimal test sample As new sample points for geometric configuration parameters;

[0017] S47, obtained in the same way as S42 The corresponding aerodynamic / thermal characteristics of the waverider are used to update the sample library and return to S43.

[0018] In a preferred waverider geometric parameterization model, the geometric control parameters include: overall control parameters length L′, width W′, and thickness H′. U and H′ L The shape control parameters include the leading edge curve control parameter T′ and the body axis section control parameter N′. U and N L Spanning section control parameter M′ U and M L ′, bending control parameters G′, F′ and I′, H′.

[0019] A better approach is to use elliptic passivation, which involves superimposing a passivation deformation function onto the reference waverider to achieve passivation of the waverider.

[0020] The passivation method for the upper surface of the reference waverider is as follows:

[0021] The passivation deformation function y is superimposed on the edge curve of the reference waverider in the XOY plane. blt (x):

[0022]

[0023] Where R′ is the passivation parameter;

[0024] The passivation deformation function z is superimposed on the centerline of the upper surface of the reference waverider in the XOZ plane. blt (x):

[0025]

[0026] The passivation deformation function z is superimposed on each section of the upper surface of the reference waverider in the YOZ plane. blt :

[0027]

[0028] in, The y-axis coordinates of the edge x = R′ after passivation:

[0029]

[0030] The passivation method of the lower surface of the reference waverider is the same as that of the upper surface, only the lifting direction is opposite.

[0031] Preferably, in S2, Jacobi iteration is used to calculate the local parameters corresponding to the grid coordinates of the aircraft surface in the analytical expression of the aircraft shape.

[0032] Preferably, in S3, the constraints also include: lift coefficient, stagnation heat flux density and / or volume fraction.

[0033] Preferably, in S41, the initial sample points are generated in the initial design space using the Latin hypersquare experimental design method based on Maximin.

[0034] Preferably, in S42, when performing CFD calculations, the open-source aerodynamic simulation software SU2 is used to solve the flow field, the governing equation is RANS, the Spalart-Allmaras turbulence model is used, the flux solution uses the AUSM scheme, the spatial discretization method is first-order, the time discretization uses the implicit Euler scheme, and the adaptive Coulomb number is used; the aircraft surface is set as a no-slip isothermal wall, the outer boundary of the flow field is the pressure far field, and the incoming gas parameters are selected according to the calculation conditions.

[0035] Preferably, the surrogate model adopts a radial basis function (RBF) surrogate model or a Kriging surrogate model.

[0036] Preferably, in step S45, the convergence of the optimization algorithm is determined according to equation (21):

[0037]

[0038] in, Add the objective function response value of the new sample point for the current iteration step. The objective function response value of the newly added sample points in the previous iteration step is ε, which is a set threshold.

[0039] Preferably, in step S46, an improved filter-based interest sampling method is used to select the optimal test sample. Specifically:

[0040] Based on the objective function values ​​and constraint function values ​​of the sample points in the current sample database, a filter is constructed according to the dominance criterion; the sample center x of the sample points in the current sample database belonging to the current filter is calculated. FC Based on the current pseudo-optimal solution With the current sample center x FC The distance between them is used to construct the interest sampling step size I. s Based on I s right Apply random perturbation to generate multiple test sample point sets X trial For the experimental sample point set X trialAn evaluation was conducted, and the experimental sample with the best evaluation results was selected. As new sample points for geometric configuration parameters.

[0041] Beneficial effects:

[0042] This invention employs a three-dimensional morphological transformation (CST) method to establish a parameterized shape of a waverider considering three-dimensional viscous effects and leading-edge passivation effects. It considers the three-dimensional viscous effects and leading-edge passivation effects of the waverider shape and uses the Jacobi transformation method to generate a surface mesh for the new shape. Combined with mesh deformation technology, it achieves automatic updating of the waverider model during the optimization process. Furthermore, it establishes a waverider aerodynamic / thermal parameterized model considering leading-edge passivation based on the Reynolds-averaged Navier-Stokes (RANS) equations. A surrogate model is used to approximate the waverider shape optimization problem, and a local exploration strategy is employed to dynamically update the surrogate model. This minimizes the surrogate model prediction value addition criterion and the interest sampling addition criterion, while improving the feasibility and optimality of the sample database. The optimal solution is approximated through sequential approximate sampling, thus completing the waverider shape optimization design. This effectively improves optimization efficiency, shortens the design cycle, and enables rapid optimization and modification of the waverider shape scheme during the overall design phase. Attached Figure Description

[0043] Figure 1 The meaning of the shape parameters of the waverider aircraft is shown below; (a) is the side view of the initial shape; (b) is the front view of the initial shape; (c) is the top view of the initial shape; and (d) is a schematic diagram of the bending parameters.

[0044] Figure 2 This is a schematic diagram of the passivation of the upper surface of the waverider; where (a) is the passivation of the ZOX plane edge; and (b) is the passivation of the upper surface edge.

[0045] Figure 3 The structured mesh model is generated based on ICEM; where (a) is the surface mesh of the waverider; and (b) is the spatial mesh of the waverider.

[0046] Figure 4 The calculation process for parameterized aerodynamic / thermal models of waveriders.

[0047] Figure 5 Enhance the constraint optimization algorithm flow for interest-based surrogate models.

[0048] Figure 6 A comparison of the shape of the waverider before and after optimization; where (a) is a top view and (b) is a front view.

[0049] Figure 7 To compare the flow field before and after optimization of the pressure coefficient; where (a) is the flow field of the initial shape; (b) is the flow field of the optimized shape. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0051] This invention provides a method for approximate optimization of the shape of a waverider based on a surrogate model, comprising the following steps:

[0052] Step 1: Establish the parametric shape of the waverider considering leading-edge passivation using the 3D CST method, specifying the length L′, width W′, and thickness H′. U and H′ L Leading edge curve control parameter T′, body axis section control parameter N′ U and N L Spanning section control parameter M′ U and M L The bending control parameters G′, F′ and I′, H′ and the passivation parameter R′ generate the shape of the waverider and realize the analytical representation of the aircraft surface.

[0053] Step 1.1: Establish the geometric parameterization model of the waverider using the 3D CST method. The expression is as follows:

[0054]

[0055] In the formula, u and v are surface parameters, and Δz(u,v) is a deviation term used to control the distortion of the surface described by the CST method. For the normalized category function:

[0056]

[0057] In the formula, C N for The maximum value in the interval [0,1] is obtained by dividing by C. N ,Will The values ​​are controlled within [0,1]. S(u,v) is a three-dimensional shape function. To reduce optimization variables, a plane is used as the shape function. The control parameters of the waverider geometric parameterization model include length L′, width W′, and thickness H′. U and H′ L The shape control parameters include the leading edge curve control parameter T′ and the body axis section control parameter N′. U and N L Spanning section control parameter M′ U and M L ′, bending control parameters G′, F′ and I′, H′, such as Figure 1 As shown. The surface equations for the parametric surfaces of the upper and lower surfaces of the semi-molded shape are:

[0058]

[0059] where \(v'=(1 + v) / 2\), and the deviation term expression is:

[0060]

[0061] A reference waverider is obtained.

[0062] Step 1.2: Introduce the passivation functions \(y blt (x)\) and \(z blt (x)\). Superimpose the passivation deformation function on the reference waverider to achieve the passivation of the waverider edge. The passivation function should meet the following requirements: ① It has an analytical expression; ② The leading edge curvature radius of the passivated shape is approximately equal to the passivation parameter (passivation radius) \(R'\); ③ The volume or surface area should not change too much after passivation. Taking the upper surface passivation process as an example, the calculation formula for the coordinates of the passivated points is:

[0063]

[0064] The definition process of the passivation deformation function is as follows: Define the passivation parameter \(R'\), and the elliptical passivation operation symbol is:

[0065]

[0066] First, perform the passivation deformation on the edge curve of the reference waverider in the XOY plane. The passivation deformation function is:

[0067]

[0068] Superimpose the passivation deformation function on the initial edge profile of the reference waverider to obtain the passivated edge as shown in Figure 2 (a):

[0069] On this basis, perform the deformation passivation on the upper surface. First, consider the shape of the centerline of the upper surface of the reference waverider in the XOZ plane. The same passivation deformation function is used:

[0070]

[0071] Superimpose the above passivation deformation function on the initial centerline of the upper surface of the reference waverider to obtain the passivated centerline of the upper surface. Subsequently, consider the passivation of each cross-section of the upper surface of the reference waverider in the YOZ plane. Since the edge after passivation is not a circular arc at the head, the passivation of the cross-section edge is completed using an ellipse. Take \(x = R'\) as the demarcation point to process the passivation of the upper surface cross-section respectively. When \(x < R'\), the expression of the cross-section passivation deformation function is:

[0072]

[0073] where is the y-axis coordinate of the passivated edge. Let be the y-axis coordinate of the passivated edge when \(x = R'\):

[0074]

[0075] When x≥R′, the expression for the cross-sectional passivation deformation function is:

[0076]

[0077] By superimposing the passivation deformation functions of each section onto the reference waverider section, the final passivated waverider can be obtained, such as... Figure 2 As shown in (b), the passivation method of the lower surface of the reference waverider is the same as that of the upper surface, only the lifting direction is opposite.

[0078] Step 1.3: Based on the analytical description of the back plane of the waverider after passivation of the upper and lower surfaces, it is obtained by lofting the trailing edge curves of the upper and lower surfaces. The expression is:

[0079]

[0080] To control the centering of the waverider's body axis, H′ is set. U =H L ′ and G′=-I′.

[0081] Step 2: Generate the initial shape based on the parameterized geometric model of the passivated waverider and perform mesh generation to create the initial spatial mesh. In this embodiment, ICEM is used to generate the initial spatial mesh using structured mesh generation. The surface mesh of the aircraft is read from the initial spatial mesh, and the local parameters u and v corresponding to the coordinates of the surface mesh points in the analytical expression of the aircraft shape are calculated. Specifically:

[0082] Step 2.1: Determine the aircraft length L′, generate the initial shape based on the parameterized geometric model of the passivated waverider, and generate the initial spatial mesh using ICEM (Integrated Electron Mesh Model). The specific parameters of the initial waverider in this embodiment are shown in Table 1, and the mesh is as follows: Figure 3 As shown, the number of grids is 2.56 million.

[0083] Table 1 Initial waverider shape and geometric parameters

[0084]

[0085] Step 2.2: Read the aircraft surface mesh from the initial spatial mesh, and use the Jacobi iteration to calculate the local parameters u and v corresponding to the surface mesh coordinate points in the analytical expression of the aircraft shape. The Jacobi projection iteration expression is:

[0086]

[0087] In the formula, the Jacobian matrix is ​​expressed as:

[0088]

[0089] In the formula, S u S v δu and δv are the derivatives of the parametric surface coordinates x and y with respect to parameters u and v, respectively, and D is the position coordinate difference dx and dy between the grid coordinate point and the projection point. By continuously updating the parameters u and v of the projection point through δu and δv, the local parameters u and v of the grid coordinate point on the aircraft surface are finally obtained.

[0090] Step 3: Construct a waverider shape optimization problem based on actual needs. Using the waverider's geometric configuration parameters as optimization variables, and satisfying the upper and lower bound constraints of the design variables, the optimization objective is to maximize the aircraft's lift-to-drag ratio. In this embodiment, lift coefficient, stagnation heat flux density, and volume fraction are also selected as constraints. The optimization problem is described as follows:

[0091]

[0092] In the formula, W′,H′ U ,T′,N′ U N L ′,M′ U ,M′ L G′, F′, H′, R′ are the waverider geometric parameters from step one, which are the design variables x in the optimization problem; x LB With x UB These represent the upper and lower bounds of the design variable, respectively. The values ​​for these bounds in this embodiment are shown in Table 3. L / D For the lift-to-drag ratio, C L Q is the lift coefficient. S The stagnation point heat flux density is calculated using a parameterized aerodynamic / thermal model of the waverider; η V The formula for calculating the volume ratio of an aircraft is as follows:

[0093]

[0094] Where V is the volume of the aircraft and S is the surface area of ​​the aircraft.

[0095] Table 3. Optimization range of waverider shape parameters

[0096]

[0097] Step four: The waverider shape optimization problem is a time-consuming black-box constrained optimization problem. A surrogate model-assisted constrained optimization algorithm is used to solve the waverider shape optimization problem in Step three. Initial sampling is performed using a design-of-experiments method to obtain a database of the objective function and constraint functions for the waverider shape optimization problem. A surrogate model is constructed to approximate the objective function and constraint functions. Based on a certain "addition criterion," new sample points are iteratively selected to update the surrogate model until approximate optimization convergence occurs. The addition criterion can be a minimum predicted value addition criterion, an improved expected value addition criterion, a confidence lower bound addition criterion, a dynamic coordinate search addition criterion, etc.

[0098] This embodiment employs a minimum predicted value addition criterion based on a sequential quadratic programming algorithm and an interest sampling addition criterion based on filters and clustering to improve the convergence performance of the optimization algorithm. The process is as follows: Figure 5 As shown.

[0099] Step 4.1: Determine the design space x for the design variable x. LB x UB Objective function f, constraint function g, and maximum number of model calls N FE Algorithm parameter N init N trial I min I max The Latin hypersquare experimental design method based on Maximin is used to generate N in the initial design space. init Initial design variable sample points x.

[0100] In this embodiment, the maximum number of model calls is set to 200, and the initial number of points added is N. init =60, Number of test points N trial =500, generate N within the initial design space. init =60 initial design variable sample points.

[0101] Step 4.2: Based on the local parameters u and v generated in Step 2, calculate the surface mesh coordinates corresponding to each design variable sample point. Use the mesh deformation solver of the open-source software SU2 to deform the initial spatial mesh, generating a spatial mesh corresponding to the surface mesh of the design variable sample point. Based on the spatial mesh, use the CFD solver of the open-source software SU2 to solve the Reynolds-Averaged Navier-Stokes (RANS) equations to obtain the spatial flow field, and thus obtain the waverider aerodynamic / thermal characteristics at the design variable sample point. The specific process is as follows... Figure 4 As shown, it includes the following sub-steps:

[0102] Step 4.2.1: Based on the local parameters u and v of the surface mesh points and the design variable sample points, calculate the positions of the surface mesh points using the surface geometric analytical expression from Step 1, and generate the corresponding surface mesh.

[0103] Step 4.2.2: Use the mesh deformation solver of the open-source software SU2 to deform the initial spatial mesh and generate a spatial mesh corresponding to the surface mesh. The element stiffness adopts the wall inverse distance mode to improve the robustness of mesh generation.

[0104] Step 4.2.3: The flow field is solved using the open-source aerodynamic simulation software SU2. The governing equations are RANS, and the Spalart-Allmaras (SA) turbulence model is used. The flux solution uses the AUSM scheme, with a first-order spatial discretization method and an implicit Euler scheme for time discretization. An adaptive Courant number is used, and a reasonable variation range is set. The aircraft surface is set as a no-slip isothermal wall, and the wall temperature is set. The outer boundary of the flow field is the pressure far field. The incoming gas parameters are selected according to the calculation conditions. Combining the spatial mesh generated in Step 4.2.2, the waverider aerodynamic / thermal characteristics corresponding to the sample points of this design variable are calculated and obtained.

[0105] Step 4.2.4: Based on the definition of the waverider body shape optimization problem in Step 3, and combined with the aerodynamic / thermal characteristics of the waverider body, obtain the objective function and constraint function response values ​​of the sample points, and add them to the sample database D.

[0106] In this embodiment, the flight altitude is selected as H = 40 km, and the incoming Mach number is M. ∞ =8.0, and the incoming gas parameters are shown in Table 2.

[0107] Table 2 Incoming gas parameters under design conditions

[0108]

[0109] Step 4.3: Construct / update surrogate models for the objective function and each constraint function of the optimization problem. Either a radial basis function (RBF) surrogate model or a Kriging surrogate model can be used. This embodiment uses the Kriging surrogate model.

[0110] Step 4.4: Select new sample points using the point addition criterion based on the sequential quadratic programming algorithm:

[0111] For the current proxy model, a local optimization model based on the sequential quadratic programming algorithm is constructed, as shown in equation (20). Taking the optimal sample point in the sample database as the starting point, the sequential quadratic programming algorithm is used to solve the local optimization of equation (20) to obtain the pseudo-optimal solution.

[0112]

[0113] Step 4.5: Using a pseudo-optimal solution As a new sample point, the corresponding aerodynamic / thermal properties are obtained by referring to the process in step 4.2. The objective function and constraint function response values ​​of the new sample point are obtained and added to the sample database D.

[0114] Step 4.6: Determine whether the algorithm has converged according to equation (21):

[0115]

[0116] In the formula, Add the objective function response value (i.e., lift-to-drag ratio) for the new sample point in the current iteration step. The objective function response value of the new sample point is added to the previous iteration step; ε is a manually set threshold, and optimization terminates when the value is less than this value, which can usually be set to 1e-5.

[0117] If the algorithm does not converge, proceed to step 4.7; if the algorithm converges, the optimization is completed, and the optimal sample point in the sample database is used as the final optimized shape of the waverider.

[0118] Step 4.7: Select new sample points using the interest sampling and addition criteria based on filters and clustering. The specific process is as follows:

[0119] Step 4.7.1: Based on the objective function values ​​and constraint function values ​​of the existing sample points in the current sample database, construct the current filter F based on the dominance criterion. The dominance criterion between samples is defined as follows:

[0120] 1) Feasible samples dominate infeasible samples.

[0121] 2) When both are infeasible samples, the one with a smaller constraint violation dominates the one with a larger constraint violation.

[0122] 3) When both are feasible solutions, the one with the smaller objective function value dominates the one with the larger objective function value.

[0123] Based on whether a sample belongs to the current filter F, the samples in the sample database are divided into two categories, as shown in equation (22):

[0124]

[0125] Step 4.7.2: Use the K-means clustering algorithm to obtain the sample centers x belonging to the current filter F. FC Based on the sample center x FC Optimal sample points Constructing the interest sampling step size I s As shown in equation (23):

[0126]

[0127] Based on I s right Apply random perturbation to generate N trial A set of experimental sample points X triall As shown in equation (24):

[0128]

[0129] In the formula, the perturbation step size z follows a Gaussian distribution z: GP(0, I) s ).

[0130] Step 4.7.3: Evaluate the test sample point set X according to the CEI sampling criterion, CMSE sampling criterion, or CLCB sampling criterion. trial Taking the CEI sampling criterion as an example, the formula is as follows:

[0131]

[0132] The experimental sample with the highest CEI value was selected as the new sample point.

[0133] Step 4.8: with As a new sample point, refer to step 4.2 to obtain the corresponding aerodynamic / thermal properties, obtain the objective function and constraint function response values ​​of the new sample point, and add them to the sample database D; return to step 4.3.

[0134] In this embodiment, a comparison of the waverider's shape before and after optimization is shown below. Figure 6 , Figure 6 (a) is a top view. Figure 6 (b) is a front view, showing a comparison of the lower surface pressure coefficient before and after optimization. Figure 7 As shown, where Figure 7 (a) shows the initial shape. Figure 7 (b) To optimize the shape. The comparison of the shape parameters of the waverider before and after optimization is shown in Table 4, and the optimization of the performance indicators is shown in Table 5.

[0135] Table 4 Results of Waverider Parameter Optimization

[0136]

[0137]

[0138] Table 5 Performance index optimization results

[0139]

[0140] The above optimization design results show that the present invention can obtain a set of waverider shape parameters that can meet the constraints of lift coefficient, stagnation point heat flux density and volume ratio with a small computational cost, thus achieving the expected purpose of the invention and verifying the rationality, effectiveness and engineering applicability of the present invention.

[0141] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for approximate optimization of waverider shape based on a surrogate model, characterized in that, include: S1. Establish the geometric parameterization model of the waverider and passivate it to obtain the analytical expression of its shape. S2, Generate the initial shape and initial spatial mesh, and calculate the local parameters corresponding to the mesh coordinate points on the shape surface based on the analytical expression; S3, using the geometric parameters in the analytical expression as optimization variables and the maximum lift-to-drag ratio as the optimization objective, construct the waverider shape optimization problem; S4, Solve the optimization problem: S41, Generate initial geometric parameter samples; S42, Substitute the geometric parameter samples into the analytical expression, and calculate the positions of the mesh points on the outer surface based on the local parameters; The initial spatial mesh is deformed based on the positions of the surface mesh points; The aerodynamic / thermal characteristics corresponding to the geometric parameter sample are obtained based on CFD calculations. Build a sample library; S43, Construct a proxy model for the optimization problem based on the current sample library; S44. The SQP algorithm is used to optimize the current agent model, resulting in a pseudo-optimal solution. by For new samples, obtain them according to method S42. Update the sample database with the corresponding aerodynamic / thermal features; S45, determine if the optimization has converged. If it has converged, then... If the optimal geometric parameters are found, then proceed to step S46. S46. Select samples using an interest sampling strategy or a dynamic coordinate strategy. by To add new geometric parameter samples, and obtain them according to method S42. The corresponding aerodynamic / thermal features are used to update the sample library, and the result is returned to S43.

2. The method as described in claim 1, characterized in that, Geometric control parameters include: overall control parameters length L′, width W′, and thickness H′. U and H′ L The shape control parameters include the leading edge curve control parameter T′ and the body axis section control parameter N′. U and N L Spanning section control parameter M′ U and M L ′, bending control parameters G′, F′ and I′, H′.

3. The method as described in claim 1 or 2, characterized in that, Elliptical passivation is adopted, and passivation deformation functions are superimposed on the established geometric parameterized model of the waverider, i.e. the reference waverider, to achieve passivation; The passivation method for the upper surface of the reference waverider is as follows: The passivation deformation function y is superimposed on the edge curve of the reference waverider in the XOY plane. blt (x): Where R′ is the passivation parameter; The passivation deformation function z is superimposed on the centerline of the upper surface of the reference waverider in the XOZ plane. blt (x): The passivation deformation function z is superimposed on each section of the upper surface of the reference waverider in the YOZ plane. blt : in, The y-axis coordinates of the edge x = R′ after passivation: The passivation method of the lower surface of the reference waverider is the same as that of the upper surface, only the lifting direction is opposite.

4. The method as described in claim 1, characterized in that, In S2, Jacobi iteration is used to calculate the local parameters corresponding to the grid coordinates of the aircraft surface in the analytical expression of the aircraft shape.

5. The method as described in claim 1, characterized in that, In S3, the constraints include: lift coefficient, stagnation heat flux density and / or volume fraction.

6. The method as described in claim 1, characterized in that, In step S41, the Latin hypersquare experimental design method based on Maximin is used to generate initial geometric configuration parameter sample points in the initial design space.

7. The method as described in claim 1, characterized in that, In S42, when performing CFD calculations, the open-source aerodynamic simulation software SU2 is used to solve the flow field. The governing equation is RANS, the Spalart-Allmaras turbulence model is used, the flux solution uses the AUSM scheme, the spatial discretization method is first-order, the time discretization uses the implicit Euler scheme, and the adaptive Coulomb number is used. The aircraft surface is set as a no-slip isothermal wall, the outer boundary of the flow field is the pressure far field, and the incoming gas parameters are selected according to the calculation conditions.

8. The method as described in claim 1, characterized in that, The proxy model used is either the RBF proxy model or the Kriging proxy model.

9. The method as described in claim 1, characterized in that, In S45, the convergence of the optimization algorithm is determined according to equation (21): in, Add the objective function response value of the new sample point for the current iteration step. The objective function response value of the newly added sample points in the previous iteration step is ε, which is a set threshold.

10. The method as described in claim 1, characterized in that, In step S46, an improved filter-based interest sampling method is used to select the optimal test sample. Specifically: Based on the objective function values ​​and constraint function values ​​of the sample points in the current sample database, a filter is constructed according to the dominance criterion; the sample center x of the sample points in the current sample database belonging to the current filter is calculated. FC Based on the current pseudo-optimal solution With current sample center x FC The distance between them is used to construct the interest sampling step size I. s Based on I s right Apply random perturbation to generate multiple test sample point sets X trial For the experimental sample point set X trial An evaluation was conducted, and the experimental sample with the best evaluation results was selected. As new sample points for geometric configuration parameters.

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