Aerodynamic configuration optimization design method based on adaptive FFD parameterization

Abstract

The invention discloses an aerodynamic configuration optimization design method based on adaptive FFD parameterization, and belongs to the technical field of aerodynamic configuration optimization design, and the method comprises the steps: generating control points based on an FFD parameterization method, taking optimization problem design variables as control point adaptive indicators, and adaptively adjusting parameter control point positions based on a spring comparison method; and the design variable solution is used as a basis for calculating the rigidity of the spring system to comprehensively reflect the influence of the gradient of the target function and the constraint function on the adaptive adjustment of the control points, so that the density of the control points is adjusted according to the difference of the component values of the design variable. According to the method, the aerodynamic configuration optimization design capability can be improved, and the robustness can be ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerodynamic shape optimization design, and more particularly to an aerodynamic shape optimization design method based on adaptive FFD parameterization. BACKGROUND

[0002] The aerodynamic shape optimization design is essentially a mathematical optimization problem, and its basic elements are an optimization objective function, design variables, constraint functions and variable boundaries. In engineering applications, for the aerodynamic shape optimization technology problem of an aircraft, the objective function values are generally aerodynamic parameter variables such as drag and lift-drag ratio, and they do not have exact analytical expressions. The function values need to be evaluated by means of numerical calculation on a computer, and this process needs to be performed repeatedly many times, which puts high requirements on the computing power.

[0003] For the calculation field of solving the objective function by using a numerical method, the generation of design variables is a process of parameterizing a large number of grid points into relatively fewer parameters. Free-Form Deformation (FFD) is a commonly used parameterization method, which is suitable for three-dimensional problems and has strong adaptability to optimized shapes, and is widely used in aerodynamic optimization design. The FFD method takes the displacement of control points as the design variables of the optimization problem, and correlates the displacement of the FFD control points with the change of the aerodynamic shape by establishing a mapping between the control points and the grid points. However, there is a contradictory problem in the aerodynamic shape optimization process. More control points (design variables) can produce better optimization results, but the amount of calculation increases. Fewer control points can improve the optimization convergence speed, but may not achieve the desired optimization effect. SUMMARY

[0004] The present application aims to overcome the shortcomings of the prior art and provide an aerodynamic shape optimization design method based on adaptive FFD parameterization, which can improve the aerodynamic shape optimization design capability and ensure robustness.

[0005] The purpose of the present application is achieved by the following scheme: An aerodynamic shape optimization design method based on adaptive FFD parameterization, comprising: Generating control points based on the FFD parameterization method, taking the design variables of the optimization problem as the adaptive indicators of the control points, and adaptively adjusting the positions of the parameter control points based on the spring analogy method; Taking the solution of the design variables as the basis for calculating the stiffness of the spring system, so as to comprehensively reflect the influence of the gradients of the objective function and the constraint function on the adaptive adjustment of the control points, and to adjust the density of the control points according to the difference between the component values of the design variables.

[0006] Further, the FFD parameterization method generates control points to optimize the design variable as an adaptive indicator of the control points, and adaptively adjusts the parameter control point position based on a spring analogy method; and then uses the design variable solution as a calculation basis for spring system stiffness to comprehensively reflect the influence of the gradient of the objective function and the constraint function on the adaptive adjustment of the control points, so as to adjust the density of the control points according to the difference between the design variable component values, and specifically includes the following sub-steps: S1: defining an optimization problem of a research object, parameterizing to form a design variable, and evaluating the objective function, the constraint function and the gradient thereof with respect to the design variable of the optimization problem; S2: judging the convergence of the optimization problem; S3: if the optimization converges, the optimization stops; otherwise, the design variable is updated by an optimizer, and the current updated design variable solution is input into a spring system to generate a new position control point through spring system solving, and after FFD parameterization and gradient mapping based on the current new position control point and the aerodynamic shape, a new optimization problem is solved to find an optimal value; S4: after starting the optimal value solving of the new optimization problem, when the adaptive condition of the control point is met, the current design variable is input to adaptively adjust the control point position by using a spring analogy method, and parameterization and gradient mapping are performed again; S5: based on the new mapping gradient information, a new design variable is solved according to the adaptive indicator, and the updated control point position is used to comprehensively reflect the influence of the gradient of the objective function and the constraint.

[0007] Further, in S1, the research object includes a transonic airfoil Rae2822.

[0008] Further, when the research object is the transonic airfoil Rae2822, the constraint conditions of the constraint function include the lift coefficient, the pitching moment coefficient and the cross-sectional airfoil area.

[0009] Further, the design variable is the z-direction displacement of all FFD control points distributed around the Rae2822 airfoil, and the displacements of the upper and lower control points of the leading and trailing edges of the Rae2822 airfoil are set to be opposite in sign in the design variable.

[0010] Further, in S2, the convergence is specifically judged based on the KKT condition.

[0011] Further, in step S3, the FFD parameterization is performed again based on the current new position control point and the aerodynamic shape, including the following sub-steps: The FFD control body is divided into a plurality of control points i , j , kThree directions are used to establish a parameter coordinate system, and the following deformation formula is used to express the mathematical relationship among the global coordinates of the design shape, the parameter coordinates of the design shape, and the global coordinates of the control body: ; for any point on the design shape, X represents the global coordinate vector of the point, u , v , w represents the parameter coordinate vector of the point, is the global coordinate vector of the control point, respectively, l , m and n are the Bernstein polynomials of the second order.

[0012] Further, in step S4, the spring analogy method is used to adaptively adjust the position of the control point, and specifically includes the following sub-steps: The FFD control point generated by the FFD parameterization method is regarded as a spring node, and the spring stiffness is used as the function of the updated design variable in the optimization process. The entire spring system forms a linear equation system, and the solution is the updated position of the FFD control point.

[0013] The beneficial effects of the present application include: The method of the present application is based on FFD parameterization, and uses the design variable of the optimization problem as the adaptive indicator of the control point. The position of the parameter control point is adaptively adjusted based on the spring analogy method, thereby reducing the dependence of the parameterization of the design variable of the aerodynamic shape optimization design problem on artificial experience. The method has a simple flow and is easy to implement by programming, and has strong engineering application. It is a simple and effective design method that can improve the effect of aerodynamic shape optimization design.

[0014] The present application proposes an adaptive FFD parameterization method based on the spring analogy method. The FFD control point is regarded as a spring node, and the spring stiffness is used as the function of the updated design variable in the optimization process. The entire spring system forms a three-diagonal linear equation system, and the solution is the updated position of the FFD control point. The solution of the design variable is used as the basis for calculating the stiffness of the spring system, and the influence of the gradients of the objective function and the constraint function on the adaptive adjustment of the control point is comprehensively reflected, thereby achieving the effect of automatically adjusting the density of the control point according to the difference in the component value of the design variable. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0016] Figure 1 FFD control point adaptive graph based on spring analogy method; Figure 2 Optimization framework graph based on adaptive FFD parameterization; Figure 3 Rae2822 airfoil optimization initial mesh graph; wherein (a) represents the overall mesh, (b) represents the leading edge mesh, and (c) represents the trailing edge mesh; Figure 4 FFD control point graph of the Rae2822 airfoil; Figure 5 Adaptive adjustment control point position graph; Figure 6 Design variable update graph; Figure 7 Drag convergence curve graph based on adaptive FFD parameterization; Figure 8 Mach number distribution graph before and after the optimization of the Rae2822 airfoil; wherein (a) represents the Mach number distribution before the optimization of the Rae2822 airfoil, and (b) represents the Mach number distribution after the optimization of the Rae2822 airfoil, and Mach represents the Mach number. DETAILED DESCRIPTION

[0017] All features disclosed in all examples in the specification, or all steps in the methods or processes impliedly disclosed, can be combined and / or extended, replaced, except for mutually exclusive features and / or steps, in any manner.

[0018] The specific implementation process of the present application is as follows: The flowchart of the design method of the present application is shown in Figure 2 Taking the aerodynamic shape optimization design of the Rae2822 airfoil as an example, the specific steps include the following: S1: Define the optimization problem, parameterize to form design variables, and evaluate the objective function, constraint function and its gradient with respect to the design variables of the optimization problem. In this embodiment, the optimization object studied is the transonic airfoil Rae2822, the incoming Mach number is 0.734, the Reynolds number is 6.5E6, and the grid is shown in Figure 3 The constraint conditions of the optimization problem include the lift coefficient, the pitching moment coefficient and the cross-sectional airfoil area. Figure 4 The FFD control point distribution surrounding the Rae2822 airfoil is taken as an example, and the design variable is the z-direction displacement of all control points. In order to prevent large curvature from occurring on the leading and trailing edges of the airfoil, the displacements of the upper and lower control points of the leading and trailing edges are set to be opposite to each other. The number of design variables is 18.

[0019] S2: Convergence is determined based on KKT conditions. KKT conditions are a set of important criteria used in mathematical optimization to determine the optimal solution to a constrained optimization problem. Specifically, the convergence criteria are based on a convergence accuracy of 10⁻¹⁸ for the flow field and adjoint equation residuals in each optimization sub-iteration, and a convergence accuracy of 10⁻¹⁸ for the KKT optimization conditions in SLSQP. The flow field solution is implemented using NNW-FlowStar software, which provides high-fidelity predictions of vehicle aerodynamic characteristics and multi-body separation properties.

[0020] S3: If convergence is achieved, the optimization stops; otherwise, the design variables are updated based on the SLSQP algorithm optimizer. The adaptive operation involves inputting the updated design variable solution into the spring system. New chord-wise position control points are generated through system solution. FFD parameterization is then performed again based on the new control points and the aerodynamic shape, and the optimal value solution for a new optimization problem begins. Specifically, generating parameterized control points involves the following process: FFD control body i 、 j 、 k A parametric coordinate system is established with the three directions as coordinate axes, and the following transformation formula is used to express the mathematical relationship between the global coordinates of the designed shape, the parametric coordinates of the designed shape, and the global coordinates of the control volume: For any point on the design shape, X represents its global coordinate vector, ( u , v , w ) represents its parameter coordinate vector, is the global coordinate vector of the control point, They are l 、 m and n Bernstein polynomial. For example, the Bernstein polynomial expression is: When any control point in the control volume is displaced , which can be substituted into the FFD deformation formula to calculate the global coordinate displacement Δ of any point X : . X and Δ X Superposition to obtain the deformed global coordinates X '= X +Δ X . Note that in the above formula, ( u , v , w ) remains unchanged during the deformation process. For a given initial shape and control volume, we can store ( u , v ,w ) and used repeatedly without repeating the calculation. The control body is along the i , j , k three directions respectively have l +1, m +1, n +1 control points, B i,p , B j,q , B k,r are p , q and r NURBS base functions. Taking B i,p as an example, the NURBS recursive form is defined as .

[0021] S4: When the control point adaptive condition is met, the current design variable is input, the control point position is adaptively adjusted by using the spring analogy method, as shown in Figure 5 , and the parameterization and gradient mapping are re-performed. Specifically, the adaptive process of the control point includes the following flow: To achieve the adaptation of the parameterized control point position, the parameterized control point is regarded as a spring node, and the nodes are connected by springs with different stiffness. Taking a one-dimensional spring system as an example (the spring node only moves in the x direction), when the system is in equilibrium, the elastic force between the i-1, i, and i+1 spring nodes forms a balance equation . Wherein, is the one-dimensional coordinate of the spring node, K i+1 / 2 is the spring stiffness between the i-th and i+1-th spring nodes, which is expressed as , wherein the parameter A is the ratio of the maximum and minimum node spacing in the spring system, which reflects the density of the parameterized control point after adaptation. , a i and a i-1 determine the relative size of the stiffness , for the aerodynamic shape optimization problem of the present application, they are the sensitivity of the objective function (or constraint) with respect to the design variable, a min and a max are the maximum and minimum values of the sensitivity of all design variables, after normalization processing, so that is between 0 and 1, so that is also between 0 and 1, let F(f) = f B , where B is a positive number. In this embodiment, take , so that the ratio of the maximum and minimum node spacing in the spring system depends only on parameter A. At the same time, this setting can also achieve the maximum node spacing ratio, and the adaptive adjustment range of the parameterized control point is larger. Similarly, for the one-dimensional problem, the unknown quantities of the node positions to be determined in the spring analogy method form a linear equation system. To solve this system, first calculate and store , and then solve for The tridiagonal linear equations for : ; Among them, x1 and x N are the two endpoints of the spring system, N is the number of spring nodes, and generally, these two points remain fixed.

[0022] S5: Based on the new gradient information, solve for the new design variables. Adaptive control point parameterization requires an indicator. In this embodiment, after the main iteration of the SLSQP optimizer, the indicator is selected as the updated design variable corresponding to each control point. Therefore, the updated control point position comprehensively reflects the influence of the objective function and the constraint gradient. The control point adaptation operation occurs after the main iteration step. The updated design variables are introduced into the spring system to calculate the new position of the control point, such as Figure 1 As shown in Figure 2. Since the position of the FFD control point has changed, it is necessary to reparameterize the surface mesh nodes and calculate the gradients of the objective function and constraints. According to the chain rule, the gradient of the objective function relative to the design variable is equal to the product of the gradient of the objective function relative to the mesh point and the gradient of the mesh node relative to the design variable, that is, ,and Independent of the parameterization method, no re-solution is required. In this embodiment, A=20 is taken, and the control points are adaptively clustered in two areas: the leading edge and about 80% of the chord length, so that the local minimum chord-wise normalized spacing is 0.061 and 0.055, as shown in the following example: Figure 6 As shown in the figure, from the optimization convergence process, the objective function of the adaptive example continues to decrease after the control point adjustment, and the objective function of the subsequent iteration steps is basically smaller than that of the uniform 24 design variable example. The convergence result of the objective function is better than that of the latter, as shown in the figure. Figure 7 shown. Figure 8 The Mach number distribution of the flow field before and after optimization is shown. The optimized airfoil eliminates the upper surface shock wave and reduces the airfoil drag. This demonstrates that the chordwise position adaptation method of the control point in this embodiment can maintain the objective function with a small number of design variables and achieve rapid descent, while also achieving a higher number of design variables and a lower convergence result for the objective function.

[0023] The units described in the embodiments of the present application can be implemented by software, or by hardware, or by a combination of software and hardware. The units described can also be implemented in a processor. In some cases, the names of the units do not constitute a limitation on the units themselves.

[0024] According to an aspect of the embodiments of the present application, a computer program product or computer program is provided, which includes computer instructions stored in a computer readable storage medium. A processor of a computer device reads the computer instructions from the computer readable storage medium, and the processor executes the computer instructions, so that the computer device performs the method provided in the various optional implementation manners.

[0025] As another aspect, the embodiments of the present application also provide a computer readable medium, which can be included in the electronic device described in the above embodiments, or can exist separately without being assembled into the electronic device. The computer readable medium carries one or more programs, which, when executed by the electronic device, enable the electronic device to implement the method described in the above embodiments.

Claims

1. A method for aerodynamic shape optimization design based on adaptive FFD parameterization, characterized in that, The method comprises the following steps: The control points are generated based on the FFD parameterization method, the design variables of the optimization problem are used as the adaptive indicators of the control points, and the positions of the control points are adaptively adjusted based on the spring analogy method. The solution of the design variables is used as the basis for calculating the stiffness of the spring system, so as to comprehensively reflect the influence of the gradients of the objective function and the constraint function on the adaptive adjustment of the control points, and to adjust the density of the control points according to the difference between the component values of the design variables.

2. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 1, wherein, The control points are generated based on the FFD parameterization method, the design variables of the optimization problem are used as the adaptive indicators of the control points, and the positions of the control points are adaptively adjusted based on the spring analogy method. The solution of the design variables is used as the basis for calculating the stiffness of the spring system, so as to comprehensively reflect the influence of the gradients of the objective function and the constraint function on the adaptive adjustment of the control points, and to adjust the density of the control points according to the difference between the component values of the design variables, and the method comprises the following sub-steps: S1: defining the optimization problem of the research object, parameterizing the design variables, and evaluating the objective function, the constraint function and the gradients thereof with respect to the design variables; S2: judging the convergence of the optimization problem; S3: if the optimization converges, the optimization stops; otherwise, the design variables are updated by the optimizer, and the current updated solution of the design variables is input into the spring system to generate new position control points, and after the FFD parameterization and the mapping of the gradients based on the current new position control points and the aerodynamic shape, the optimal value solving of a new optimization problem is started; S4: after starting the optimal value solving of the new optimization problem, when the adaptive control point condition is met, the current design variables are input, the positions of the control points are adaptively adjusted by using the spring analogy method, and the parameterization and the gradient mapping are re-performed; S5: based on the new mapping gradient information, the new design variables are solved according to the adaptive indicators, and the influence of the updated control point positions on the gradients of the objective function and the constraints is comprehensively reflected.

3. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, In S1, the research object includes the transonic airfoil Rae2822.

4. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, When the research object is the transonic airfoil Rae2822, the constraint conditions of the constraint function include the lift coefficient, the pitching moment coefficient and the cross-sectional airfoil area.

5. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, The design variables are the z-direction displacements of all FFD control points distributed around the Rae2822 airfoil, and the displacements of the upper and lower control points of the leading and trailing edges of the Rae2822 airfoil are set to be opposite in sign.

6. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, In S2, the convergence is judged based on the KKT condition.

7. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, In step S3, the FFD parameterization based on the current new position control points and the aerodynamic shape comprises the following sub-steps: FFD control body i 、 j 、 k A parametric coordinate system is established with the three directions as coordinate axes, and the following transformation formula is used to express the mathematical relationship between the global coordinates of the designed shape, the parametric coordinates of the designed shape, and the global coordinates of the control volume: ; For any point on the design shape, X represents its global coordinate vector, ( u , v , w ) represents its parameter coordinate vector, is the global coordinate vector of the control point, They are l 、 m and n degree Bernstein polynomial.

8. The aerodynamic shape optimization design method based on adaptive FFD parameterization of claim 2, wherein, In step S4, the positions of the control points are adaptively adjusted by using the spring analogy method, which comprises the following sub-steps: The FFD control points generated by the FFD parameterization method are regarded as spring nodes, the spring stiffness is used as the function of the updated design variables in the optimization process, the entire spring system forms a linear equation system, and the solution of the linear equation system is the updated positions of the FFD control points.

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