Gradient enhanced sampling method for aircraft proxy optimization design

Abstract

The invention relates to a gradient enhanced sampling method for aircraft proxy optimization design, and belongs to the technical field of aircraft profile proxy optimization. The method comprises the following steps: determining a design space of a hypercube; calculating the gradient of the target variable relative to the design variable at the center design point of the design space; determining a gradient descent sub-design space according to the gradient information; latin hypercube sampling is carried out in the hypercube design space; calculating the conversion probability of each sampling point; the sampling points in the design space are converted into a gradient descent subspace according to the conversion probability; the gradient enhanced sampling method provided by the invention is suitable for random sampling of design points under an aircraft proxy optimization framework, and can improve the sampling probability of the region of interest on the premise of ensuring the filling effect of the whole design space, so that a high-precision pneumatic proxy model can be constructed by using fewer sampling points in the proxy optimization process, and the method is simple and convenient to operate. And a method basis is provided for processing complex aircraft shape optimization design by a proxy optimization design method.

Description

Technical Field

[0001] The present invention relates to a sampling method combining prior gradient information in an aircraft proxy optimization framework, and in particular to a gradient enhancement sampling method for aircraft proxy optimization design, belonging to the technical field of aircraft shape proxy optimization. Background Art

[0002] Aircraft optimization design can be described as an optimization problem constrained by partial differential equations. Due to the complex shape of the aircraft and the expensive computational overhead of aerodynamic targets (such as lift and drag coefficients), the aircraft optimization design problem belongs to the optimization problem of high-dimensional nonlinear black box functions, and its numerical solution is very difficult.

[0003] For the optimization design of aircraft shape, surrogate optimization is a common global optimization algorithm. It estimates the target value of a limited number of sample points in the design space to establish a surrogate model of the target with respect to the design variables, and finally uses the surrogate model to complete the optimization process. In the surrogate optimization algorithm, sampling of the design space is a crucial link. Since it is expensive to obtain the target response value at each sample point (often requiring the help of computational fluid dynamics and other means), the sampling method needs to use as few sample points as possible to fill the entire design space as much as possible.

[0004] For sampling high-dimensional design spaces, Latin Hypercube Design (LHD) is one of the most commonly used sampling methods. This method has excellent space filling capabilities even when the number of sample points is small. However, for extremely high-dimensional design spaces in surrogate optimization problems, due to the lack of prior information, LHD-based sampling methods also face challenges. When the number of sampling points is small, it is often difficult to explore the target drop area, resulting in insufficient accuracy of the surrogate model near the minimum point, which in turn leads to inefficiency or even non-convergence of the surrogate optimization algorithm.

[0005] Therefore, the use of prior information (especially gradient information) can help guide the sampling method to increase the sampling probability of the area of ​​interest, which helps to greatly improve the sampling effect. For example, in the proxy optimization problem, the area of ​​interest is the target descent area or near the minimum value, so more sample points can be arranged along the negative gradient direction or area of ​​the target. How to incorporate prior information such as gradients into the design of the sampling method and maintain the spatial filling effect of the sampling as much as possible is the key to improving the sampling effect in the aircraft proxy optimization algorithm. Summary of the invention

[0006] The technical problem solved by the present invention is: in order to sample more efficiently in the design space, a gradient enhancement sampling method for aircraft proxy optimization design is designed. Within the framework of the proxy optimization algorithm, this method can use a very small number of sampling points to achieve a better space filling effect, and can effectively explore the gradient descent area in the design space, thereby improving the accuracy of the proxy model near the target descent or minimum point, and ultimately improving the performance of the optimization results generated by the aircraft proxy optimization algorithm.

[0007] The technical solution of the present invention is as follows:

[0008] A gradient enhancement sampling method for aircraft proxy optimization design, comprising:

[0009] According to the number of design variables d and each design variable D of the aircraft shape or working condition optimization problem i The range of i ,u i ], design space Initialization of

[0010] Calculate the design space The geometric center point D (0) , Among them, d i represents the midpoint of the variation range of the i-th design variable, and

[0011] Calculate the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D

[0012] Using the gradient information g J Define the design space The aerodynamic target descent subspace

[0013] According to the Latin hypercube sampling method, in the design space Collect N random design points in k represents the kth design point;

[0014] Calculate D for each design point (k) The conversion probability

[0015] Set the confidence radius to determine the D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in If possible, the conversion is performed; otherwise, no conversion is performed.

[0016] In the above-mentioned gradient enhancement sampling method for aircraft agent optimization design, the initialization design space is in the form of:

[0017]

[0018] In the above-mentioned gradient enhancement sampling method for aircraft proxy optimization design, the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D The approximate calculation formula is as follows:

[0019]

[0020] Where, ΔD i =(0,…,ΔD i ,…,0), the element at its i-th position is the perturbation ΔD i , and the rest of the positions are 0.

[0021] In the above-mentioned gradient enhancement sampling method for aircraft proxy optimization design, the disturbance ΔD i Satisfies normal distribution Take σ=0.01.

[0022] In the above-mentioned gradient enhancement sampling method for aircraft proxy optimization design, the aircraft aerodynamic performance target J includes an aerodynamic drag coefficient or a lift coefficient.

[0023] In the above-mentioned gradient enhancement sampling method for aircraft proxy optimization design, the gradient information g is used J Define the design space The aerodynamic target descent subspace The form is as follows:

[0024]

[0025] Among them, t i Representation subspace The relative coordinate of the i-th dimension.

[0026] In the above-mentioned gradient enhancement sampling method for aircraft proxy optimization design, each design point D is calculated (k) The conversion probability methods, including:

[0027]

[0028]

[0029] Among them, ‖·‖ represents the 2-norm of a vector, and <·,·> represents the angle between two vectors.

[0030] In the above gradient-enhanced sampling method for the surrogate optimization design of an aircraft, a confidence radius is set, and each design point D is judged (k) whether it can be converted to a point in the aerodynamic objective descent subspace The method includes: Set the confidence radius r, and take r = 0.1×max

[0031] {u i≤d -l i} i ;

[0032] If then let Generate a random number ω according to the uniform distribution between (0, 1). If the random number ω < s, then convert the design point D to a point in the aerodynamic objective descent subspace (k) The method includes: Otherwise, no conversion is performed. In the above gradient-enhanced sampling method for the surrogate optimization design of an aircraft, if a conversion is performed, the design point D

[0033] is converted to a point in the aerodynamic objective descent subspace (k) The method includes: Calculate the relative coordinate t of the kth sample point D in the design space

[0034] (k) (k) ,

[0035]

[0036]

[0037] (k) in the subspace The actual physical coordinates are:

[0038]

[0039]

[0040] A gradient-enhanced sampling system for the surrogate optimization design of an aircraft includes:

[0040] An initialization module, which initializes the design space according to the number of design variables d of the aircraft shape or operating condition optimization problem and the range [l i , u i of each design variable D i ; Initialization;

[0041] The center point calculation module calculates the design space The geometric center point D (0) , D (0) =(d1,d2…d i …,d d ), where d i represents the midpoint of the variation range of the i-th design variable, and

[0042] Gradient calculation module, calculates the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D

[0043] Subspace design module, using the gradient information g J Define the design space The aerodynamic target descent subspace

[0044] The sample collection module uses the Latin hypercube sampling method to collect samples in the design space Collect N random design points in k represents the kth design point;

[0045] Probability calculation module, calculates each design point D (k) The conversion probability

[0046] Conversion module, set the confidence radius, judge each design D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in If possible, the conversion is performed; otherwise, no conversion is performed.

[0047] Compared with the prior art, the present invention has at least the following beneficial effects:

[0048] (1) The gradient enhancement sampling method included in the embodiment of the present invention, when used in the proxy optimization algorithm, can effectively increase the sampling probability of the region of interest (target descent area and near the minimum point) and improve the sampling effect. Compared with the classic LHD, the aerodynamic performance of the aircraft optimization design result can be stably and significantly improved under the same number of sample points.

[0049] (2) The gradient enhancement sampling method designed in the embodiment of the present invention, combined with the RBFs proxy optimization framework, can better balance the contradiction between mining the design space and high design efficiency. Under the premise of fully mining the potential area in the design space, the design points evaluated by CFD are reduced from the O(d) level to the O(1) level (where d represents the dimension of the design space), which effectively alleviates the dimensionality curse problem and provides a methodological basis for the proxy optimization design method to handle the optimization design of complex aircraft shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 An algorithm flow chart of a gradient enhancement sampling method for aircraft agent optimization design according to an embodiment of the present invention;

[0051] Figure 2 The two-dimensional design space of the embodiment of the present invention ,Schematic diagram of sample point conversion;

[0052] Figure 3 Schematic diagram of the initial airfoil performance results of the drag reduction optimization verification example of the two-dimensional NACA-0012 airfoil according to the embodiment of the present invention, wherein Figure 3 (a) is the initial airfoil shape and computational mesh. Figure 3 (b) is a schematic diagram of the transonic flow field (density) around the initial airfoil;

[0053] Figure 4 Schematic diagram of the transonic flow field (density) of the final shape generated by different sampling methods in the drag reduction optimization verification example of the two-dimensional NACA-0012 airfoil in the embodiment of the present invention, wherein Figure 4 (a)-(c) are the results of three sampling experiments based on the LHD sampling method. Figure 4 (d)-(f) are the results of three sampling experiments based on the gradient enhanced sampling method of the present invention;

[0054] Figure 5 The pressure distribution (C) of the final shape generated by different sampling methods in the drag reduction optimization verification example of the two-dimensional NACA-0012 airfoil in the embodiment of the present invention is p ) result diagram, where Figure 5 (a)-(c) are the results of three sampling experiments based on the LHD sampling method. Figure 5 (d)-(f) are the results of three sampling experiments based on the gradient enhanced sampling method of the present invention;

[0055] Figure 6It is an optimization convergence curve diagram of different sampling methods in the drag reduction optimization verification example of the two-dimensional NACA-0012 airfoil according to an embodiment of the present invention, wherein the horizontal axis nEval represents the number of CFD evaluation sample points, and the vertical axis Cd represents the value of the optimized target drag coefficient. DETAILED DESCRIPTION

[0056] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0057] like Figure 1 As shown, the gradient enhancement sampling method for aircraft proxy optimization design provided by the embodiment of the present invention includes the following steps:

[0058] S1. According to the number of design variables d and each design variable D of the aircraft shape or working condition optimization problem i The range of i ,u i ], design space Initialization.

[0059] In an optional embodiment, the form of initializing the design space is as follows:

[0060]

[0061] S2. Calculate the design space The geometric center point D (0) , D (0) =(d1,d2…d i …,d d ), where d i represents the midpoint of the variation range of the i-th design variable, and i represents the i-th dimension of the design space.

[0062] S3. Calculate the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D

[0063] In an optional embodiment, the gradient of the optimization objective J with respect to the design variable D is The approximate calculation formula is as follows:

[0064]

[0065] Where, ΔD i =(0,…,ΔD i ,…,0), only the element at its i-th position is the perturbation ΔD i , and the rest of the positions are 0. Disturbance ΔD i Satisfies normal distribution Take σ=0.01.

[0066] In an optional embodiment, the aircraft aerodynamic performance target J includes an aerodynamic drag coefficient or a lift coefficient.

[0067] S4. Using gradient information g J =(g1,g2,…,g d ) Define the original design space Gradient descent subspace

[0068] In an optional embodiment, the design space The aerodynamic target descent subspace The form is as follows:

[0069]

[0070] Among them, t i Representation subspace The relative coordinate of the i-th dimension.

[0071] S5. According to the classic Latin hypercube sampling method, in the design space Collect N random design points in k represents the kth design point.

[0072] S6. Calculate each design point D (k) The conversion probability

[0073] In an optional embodiment, the calculation method is as follows:

[0074]

[0075] Among them, ‖·‖ represents the 2-norm of a vector, and <·,·> represents the angle between two vectors.

[0076] S7. Set the confidence radius to determine the D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in If possible, the conversion is performed; otherwise, no conversion is performed.

[0077] In an optional embodiment, the method for determining whether to convert includes:

[0078] Set the confidence radius r, take r = 0.1 × max i≤d {u i -l i};

[0079] if Then Generate a random number between (0,1) That is, according to the uniform distribution between (0, 1) Generate a random number ω. If the random number ω < s, then convert the design point D (k) into a point in the aerodynamic target descent subspace Otherwise, no conversion is performed. Here represents the uniform distribution between (0, 1).

[0080] In an alternative embodiment, if conversion is performed, then the design point is converted into a point in the aerodynamic target descent subspace The method includes:

[0081] First, calculate the relative coordinate t of the k-th sample point D (k) in the design space (k) ,

[0082]

[0083] Secondly, calculate the actual physical coordinate of the relative coordinate t (k) in the subspace :

[0084]

[0085] For example Figure 2 shows the conversion schematic diagram of sample points in the 2D design space in the embodiment of the present invention In the figure, the arrow represents the negative gradient direction -g J , and the shaded area is the target descent subspace D (1) , D (2) are two sample points generated by the Latin hypercube sampling method is the sample point after conversion. It can be seen from Figure 2 that the relative positions of D (1) , D (2) in the original design space are the same as those of in the subspace , that is, the relative coordinates are the same.

[0086] On the other hand, the present invention provides a radial basis function (RBFs) surrogate optimization framework for implementing the sampling method designed in the first aspect, which is used to test the effect of the sampling method in the present invention.

[0087] Combined with the other aspect, its main steps are as follows:

[0088] ​​​S1. Experimental design, design sampling method to collect a certain number of sample points in the design space Where N is the number of generated sample points;

[0089] S2. Evaluate the target response value of the sample point, use the computational fluid dynamics (CFD) method to simulate the flow field distribution of the corresponding shape of the sample point with different designs, and then calculate the target response value

[0090] S3. Establish a proxy model and use data sample points and its corresponding value The proxy model function relationship between the target and the data sample is obtained by radial basis function (RBFs) interpolation J = π θ (D), where θ represents the unknown parameters in the surrogate model;

[0091] S4. Point addition criteria, using the proxy model J = π θ (D) Implement the optimization algorithm and add new sample points according to specific point addition criteria during the optimization process This continuously improves the accuracy of the proxy model and assists in the optimization process.

[0092] Example

[0093] like Figure 1 The embodiment of the present invention includes the following steps: initializing the design space according to the actual optimization problem Calculate the geometric center point D of the design space (0) ; Calculate the gradient g of the objective with respect to the design variable at the geometric center point J ; Use gradient information to define the target descent subspace Use the classic Latin hypercube sampling method to collect N random sample points in the design space Calculate the conversion probability of each sample point Convert each original sample point to the subspace according to the conversion probability Points in

[0094] The drag reduction optimization verification example of a two-dimensional NACA-0012 airfoil is used to illustrate the implementation process and details of the gradient enhancement sampling method for proxy optimization of this embodiment.

[0095] The drag reduction optimization problem of the two-dimensional NACA-0012 airfoil can be described as the following optimization problem:

[0096]

[0097] (1) D represents the design variable, which in this problem is the control vertex of the free form deformation frame (FFD) that controls the airfoil shape. U represents the flow field state variable, which is solved by the differential equation constraint R(U,D)=0.

[0098] (2) The differential equation constraint R(U,D)=0 is a two-dimensional compressible Euler equation system in this problem. The specific initial boundary value problem is:

[0099]

[0100] Among them, U is the flow field state variable, x, t are space and time variables respectively, F(U) is the inviscid flux matrix, U0(x) is the initial value condition, and B(x, t) is the boundary condition at the computational boundary Γ. The specific forms of U and F(U) are as follows:

[0101]

[0102] Where ρ, p, and E represent the density, pressure, and total energy per unit volume of the fluid, respectively, and v = (v1, v2) T represents the fluid velocity, v i is its velocity component in each spatial dimension, δ ij is the Kronecker symbol.

[0103] (3) J(U,D) is the optimization target, which is the aerodynamic drag coefficient C in this problem. d , its specific form is:

[0104]

[0105] Among them, Γ w represents the solid wall boundary of the outer surface, is the far-field free energy, l is the shape reference length, p is the flow field pressure, and n is the boundary Γ w is the unit external normal vector of , and α represents the flight angle of attack.

[0106] (4)c I (U,D)≤0 is an algebraic inequality constraint, which means that the lift and area of ​​the airfoil do not decrease in this problem, and is specifically expressed as:

[0107]

[0108] Where A represents the area of ​​the airfoil, A0 represents the area of ​​the reference airfoil; C l is the lift coefficient, C l0 Denotes the lift coefficient of the reference airfoil. Lift coefficient C l The specific form is as follows:

[0109]

[0110] The parameters are consistent with those in the resistance coefficient.

[0111] (5) The RBFs proxy optimization algorithm is selected as the optimization algorithm for solving the optimization problem. The LHD sampling method and the gradient enhancement sampling method proposed in the present invention are respectively adopted in the experimental design. The discontinuous Galerkin methods (DGMs) are selected as the CFD solver to numerically solve the fluid control equations. The RBFs interpolation function is selected as the proxy model, and the hybrid criterion is adopted as the point addition criterion.

[0112] (6) Set the design variable dimension to 16, the initial number of sample points to N = 20, and the maximum number of sample points to N max = 40. Since the sampling in the experimental design stage is random, three independent sampling experiments were conducted for each different sampling method in this verification example.

[0113] Figure 3 The figure shows the flow field results around the initial NACA-0012 airfoil. Figure 4 It can be seen that the airfoil shapes produced by the two sampling methods can weaken the shock wave intensity on the upper surface of the airfoil, achieving the effect of reducing resistance. Figure 4 The optimized flow field produced by the gradient enhanced sampling method (present) of the embodiment of the present invention shown in (d)-(f) has a more obvious effect of weakening the shock wave intensity than the optimized flow field produced by the classical LHD sampling method shown in 4(a)-(c).

[0114] from Figure 5 It can be seen more clearly that the airfoil shapes produced by the two methods can weaken the shock wave intensity on the upper surface of the airfoil (C p The jump amplitude of the curve), and Figure 5 The pressure distribution produced by the gradient enhanced sampling method of the present invention shown in (d)-(f) is significantly higher than the pressure distribution produced by the classical LHD sampling method shown in (a)-(c). p The jump amplitude of the curve is significantly weakened, which means that the sampling method designed by the present invention has a stronger shock wave weakening effect when used in the proxy optimization framework compared with the LHD sampling method.

[0115] from Figure 6It can be seen that the gradient enhanced sampling method (present) designed by the present invention can stably detect design sample points with better performance (smaller target value) in the experimental design stage, resulting in the subsequent optimization convergence curves of present-1 / 2 / 3 being compared with the optimization convergence curves of LHD-1 / 2 / 3, and finally obtaining design sample points with smaller target values.

[0116] Table 1 below is a performance comparison table of the final optimization results produced by different sampling methods in the drag reduction optimization verification example of the two-dimensional NACA-0012 airfoil.

[0117] Table 1

[0118]

[0119] It can be concluded from Table 1 that the performance improvement effect (average drag reduction of 58.2%) of the final optimization result obtained by three independent sampling experiments of the gradient enhanced sampling method (present) designed in the embodiment of the present invention is significantly better than the performance improvement effect (average drag reduction of 38.2%) of the final optimization result obtained by three independent sampling experiments of the LHD sampling method.

[0120] The above results verify that in the RBFs proxy optimization framework, the gradient enhancement sampling method designed by the present invention can more stably explore the target drop area in the design space, which helps to enable the proxy optimization algorithm to produce better final optimization results under the premise of a small number of the same number of samples.

[0121] The above description is only the best specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0122] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A gradient enhancement sampling method for aircraft proxy optimization design, characterized in that: include: According to the number of design variables d and each design variable D of the aircraft shape or working condition optimization problem i The range of i ,u i ], design space Initialization of Calculate the design space The geometric center point D (0) , D (0) =(d1,d2…d i …,d d ), where d i represents the midpoint of the variation range of the i-th design variable, and Calculate the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D Using the gradient information g J Define the design space The aerodynamic target descent subspace According to the Latin hypercube sampling method, in the design space Collect N random design points in k represents the kth design point; Calculate D for each design point (k) The conversion probability Set the confidence radius to determine the D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in If possible, the conversion is performed; otherwise, no conversion is performed.

2. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: The initialization design space is in the following form:

3. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: The geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D The approximate calculation formula is as follows: Where, ΔD i =(0,…,ΔD i ,…,0), the element at its i-th position is the perturbation ΔD i , and the rest of the positions are 0.

4. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 3 is characterized in that: The disturbance ΔD i Satisfies normal distribution Take σ=0.

01.

5. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: The aircraft aerodynamic performance target J includes an aerodynamic drag coefficient or a lift coefficient.

6. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: Using the gradient information g J Define the design space The aerodynamic target descent subspace The form is as follows: Among them, t i Representation subspace The relative coordinate of the i-th dimension.

7. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: Calculate D for each design point (k) The conversion probability methods, including: Among them, ‖·‖ represents the 2-norm of a vector, and <·,·> represents the angle between two vectors.

8. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1, characterized in that: Set the confidence radius to determine the value of each design point D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in methods, including: Set the confidence radius r, take r = 0.1 × max i≤d {u i -l i }; If then let Generate a random number ω according to the uniform distribution between (0, 1). If the random number ω < s, then convert the design point D to a point in the pneumatic target descent subspace (k) Otherwise, no conversion is performed. ​​ 9. The gradient enhancement sampling method for aircraft proxy optimization design according to claim 1 or 8, characterized in that: If the conversion is performed, the design point D (k) According to the conversion to aerodynamic target descent subspace Points in methods, including: Calculate the kth sample point D (k) In the design space The relative coordinates in t (k) , Calculate the relative coordinate t (k) In subspace The actual physical coordinates in:

10. A gradient enhancement sampling system for aircraft proxy optimization design, characterized in that: include: Initialization module, according to the number of design variables d of the aircraft shape or working condition optimization problem and each design variable D i The range of i ,u i ], design space Initialization of The center point calculation module calculates the design space The geometric center point D (0) , D (0) =(d1,d2…d i …,d d ), where d i represents the midpoint of the variation range of the i-th design variable, and Gradient calculation module, calculates the geometric center point D (0) The gradient of the aerodynamic performance target J of the aircraft with respect to the design variable D Subspace design module, using the gradient information g J Define the design space The aerodynamic target descent subspace The sample collection module uses the Latin hypercube sampling method to collect samples in the design space Collect N random design points in k represents the kth design point; Probability calculation module, calculates each design point D (k) The conversion probability Conversion module, set the confidence radius, judge each design D (k) Whether it is possible to switch to the aerodynamic target descent subspace Points in If possible, the conversion is performed; otherwise, no conversion is performed.

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