An Experimental Design Method for Shape Space Oriented to Aerodynamic Shape Optimization

Abstract

The present invention discloses a shape space experimental design method for aerodynamic shape optimization, which includes the following steps: Step 1, given the calculation conditions for experimental design, including the number of sampling points in each experimental design matrix, the dimension of design variables, geometric constraint conditions, and the shape parameterization method; Step 2, construct a multi-objective optimization model with the sample point set as the design variable and the number of feasible solutions and the spatial uniformity evaluation index as the objective function; Step 3, use the non-dominated sorting genetic algorithm to iteratively solve the multi-objective optimization model to obtain the optimal experimental design scheme. The method of the present invention considers the uniformity of the distribution of the aerodynamic geometric shapes generated by the sample point set in the shape space and the feasibility of geometric constraints, making the initial sample point set more reasonable, obtaining more comprehensive spatial information, and having a higher quality of the initial surrogate model, thereby improving the efficiency of optimization design and analysis. The present invention is applied to the field of aerodynamic optimization technology for aircraft design.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft design aerodynamic optimization, and particularly to a shape space experimental design method for aerodynamic shape optimization. Background Art

[0002] Experimental design is one of the key steps based on the sequential approximation optimization method. Its task is to find a set of simulation model evaluation points with as uniform a distribution as possible in the design space for constructing a surrogate model. The experimental design method directly affects the quality of the initial surrogate model. A reasonable experimental design method can obtain a better sampling scheme to obtain more spatial information. Currently, classical experimental design methods (such as Latin hypercube experimental design, optimized Latin hypercube experimental design, etc.) only evaluate the space filling property of the sampling point set in the design variable space. However, in the problem of aerodynamic shape optimization design, usually based on the experimental design sample points, parametric methods (CST parametric method, B-spline curve, etc.) are used to characterize the aerodynamic geometry. Therefore, for the sample points evenly distributed in the design space generated by the classical experimental design method, the distribution uniformity of the corresponding aerodynamic geometries in the shape space may be poor, which will lead to a poor quality of the initial surrogate model, and further affect the efficiency of sequential approximation optimization. In the prior art, the commonly used experimental design methods for aerodynamic shape optimization are as follows:

[0003] Latin hypercube experimental design: This method is simple and convenient, easy to implement, can achieve uniform sampling of design variables in any dimension, and does not require complex calculation processes. However, the design result of the Latin hypercube experimental design has strong randomness, and the space filling property and orthogonality cannot be guaranteed. In addition, this type of method only focuses on obtaining a better sample point set with space filling property in the design variable space, without considering the uniformity of the aerodynamic shapes generated by the point set in the shape space;

[0004] Optimized Latin hypercube experimental design: This method constructs an optimization problem with the space filling performance of the Latin hypercube experimental design as the objective function for solution, and can obtain a sampling point set with better space filling property and orthogonality. However, although it can generate a better sample point set with space filling property, this type of method also faces the problem of poor uniformity of the aerodynamic shapes generated by the design result in the shape space. Summary of the Invention

[0005] In view of the problem in the existing aerodynamic shape optimization design that the classical experimental design method only focuses on obtaining a sample point set with better space filling in the design variable space, while ignoring the filling of the corresponding aerodynamic shape in the shape space, the present invention provides a shape space experimental design method for aerodynamic shape optimization. By optimizing the filling evaluation index constructed in the shape space, the uniform distribution of the aerodynamic shapes generated by the sampling point set in the shape space is realized, thereby improving the efficiency of optimization design and analysis.

[0006] To achieve the above object, the present invention provides a shape space experimental design method for aerodynamic shape optimization, including the following steps:

[0007] Step 1, specifying the experimental design calculation conditions, including the number m of sampling points of each experimental design matrix, the design variable dimension n, the geometric constraint conditions, and the shape parameterization method;

[0008] Step 2, constructing a multi-objective optimization model with the sample point set as the design variable and the number of feasible solutions and the space uniformity evaluation index as the objective functions;

[0009] Step 3, using the non-dominated sorting genetic algorithm to iteratively solve the multi-objective optimization model to obtain the optimal experimental design scheme.

[0010] In one embodiment, in Step 2, the multi-objective optimization model is specifically:

[0011] Find:X

[0012]

[0013] s.t:S a >S 0 ,T a >T 0 ,a=1,2,…,m

[0014] Wherein, is the experimental design matrix; num(X) is the number of sample points in the experimental design matrix X that satisfy the geometric constraint conditions, and the geometric constraint conditions include the area constraint S i >S 0 , the thickness constraint T i >T 0 ; φ p is the uniformity evaluation index of the design variable in the shape space, S i represents the airfoil area corresponding to the a-th row in the experimental design matrix X, S 0 represents the area constraint value, T i represents the airfoil thickness corresponding to the a-th row in the experimental design matrix X, T 0 represents the thickness constraint value.

[0015] In one embodiment, step 3 specifically includes:

[0016] Step 3.1, randomly generate an initial population of 10m experimental design matrices with m rows and n columns as the parental population;

[0017] Step 3.2, generate an offspring population based on the parental population, that is, for each experimental design matrix in the parental population, generate a new experimental design matrix through random exchange between elements in a certain dimension;

[0018] Step 3.3, perform fitness evaluation on each experimental design matrix in the parental population and the offspring population to obtain the fitness evaluation results. Among them, the fitness evaluation results include the number of feasible solutions in the experimental design matrix and the uniformity evaluation index of the aerodynamic geometry shape generated by it in the shape space;

[0019] Step 3.4, after merging the parental population and the offspring population, perform a selection operation, and retain 10m experimental design matrices with more feasible solutions and higher space uniformity evaluation indexes according to the dominance relationship as the new generation population;

[0020] Step 3.5, if the number of iterations reaches the set threshold or the new generation population obtained continuously for K max times no longer updates, output the current population, otherwise use the current population as the parental population and return to step 3.2;

[0021] Step 3.6, based on the current population, select the design scheme closest to the 45° reference vector in the objective space of the multi-objective optimization model as the final experimental design result.

[0022] In one embodiment, in step 3.1, the Latin hypercube experimental design method is used to randomly generate an initial population of 10m experimental design matrices.

[0023] In one embodiment, in step 3.3, the uniformity evaluation index in the shape space is specifically:

[0024]

[0025] In the formula, d ij is the distance between the i-th and j-th design variables in the shape space, and its calculation method is as follows:

[0026]

[0027] In the formula, are the aerodynamic geometry curves formed by the i-th and j-th experimental design matrices respectively, and Ω is the change region of the aerodynamic set shape

[0028] A shape space experimental design method for aerodynamic shape optimization provided by the present invention takes into account the uniformity of the distribution of the aerodynamic geometric shapes generated by the sample point set in the shape space and the feasibility of geometric constraints, making the initial sample point set more reasonable, obtaining more comprehensive spatial information, and having a higher quality of the initial surrogate model, thereby improving the efficiency of optimization design and analysis. Description of the Drawings

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0030] Figure 1 It is the flowchart of the shape space experimental design method in the embodiment of the present invention;

[0031] Figure 2 It is the airfoil set generated by the present invention in the example;

[0032] Figure 3 It is the airfoil set generated by other experimental design methods in the example.

[0033] The realization, functional features, and advantages of the object of the present invention will be further described in conjunction with the embodiments with reference to the drawings. Detailed Embodiments

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0035] It should be noted that all directional indications (such as up, down, left, right, front, back...) in the embodiments of the present invention are only used to explain the relative position relationship and movement conditions between components in a specific posture (as shown in the drawings). If the specific posture changes, the directional indications will also change accordingly.

[0036] In addition, in the present invention, descriptions such as "first" and "second" are for descriptive purposes only, and should not be construed as indicating or implying their relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0037] In the present invention, unless otherwise clearly specified and defined, terms such as "connection" and "fixation" shall be understood in a broad sense. For example, "fixation" may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection, an electrical connection, a physical connection or a wireless communication connection; it may be directly connected, or indirectly connected through an intermediate medium, and may be the communication inside two elements or the interaction relationship between two elements, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0038] In addition, the technical solutions between various embodiments of the present invention can be combined with each other, but it must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0039] In view of the problem that in the optimization design of aerodynamic shape, the classical experimental design method can only ensure good space filling of the sample point set in the design variable space, while ignoring the filling problem of the corresponding aerodynamic geometric shape in the shape space, this embodiment proposes a shape space experimental design method for aerodynamic shape optimization. This method constructs a multi-objective optimization model with the experimental design sample point set as the design variable and the number of feasible solutions and the uniformity evaluation index of the generated aerodynamic geometric shape in the shape space as the objective function, and uses the optimal design variable corresponding to this optimization problem as the initial sampling point set. Compared with the existing implementation solutions, this embodiment considers the uniformity of the distribution of the aerodynamic geometric shape generated by the sample point set in the shape space and the feasibility of geometric constraints, making the initial sample point set more reasonable, obtaining more comprehensive spatial information, and having a higher quality of the initial surrogate model, thereby improving the efficiency of optimization design and analysis.

[0040] Reference Figure 1 , a shape space experimental design method for aerodynamic shape optimization in this embodiment specifically includes the following steps:

[0041] Step 1, given the calculation conditions for experimental design, including the number m of sampling points in each experimental design matrix, the dimension n of design variables, geometric constraint conditions, and the shape parameterization method, etc.;

[0042] Step 2: Construct a multi-objective optimization model with the sample point set as the design variable and the number of feasible solutions and the spatial uniformity evaluation index as the objective functions, specifically as follows:

[0043] Find: X

[0044]

[0045] s.t: S a > S 0 , T a > T 0 , a = 1, 2, …, m

[0046] In the formula, is the experimental design matrix; num(X) is the number of sample points in the experimental design matrix X that satisfy the geometric constraint conditions, and its geometric constraint conditions include the area constraint S i > S 0 , and the thickness constraint T i > T 0 ; φ p is the uniformity evaluation index of the design variable in the shape space, S i represents the airfoil area corresponding to the a-th row in the experimental design matrix X, S 0 represents the area constraint value, T i represents the airfoil thickness corresponding to the a-th row in the experimental design matrix X, T 0 represents the thickness constraint value;

[0047] Step 3: Use the non-dominated sorting genetic algorithm to iteratively solve the multi-objective optimization model to obtain the optimal experimental design scheme, specifically including:

[0048] Step 3.1: Randomly generate an initial population of experimental design matrices with 10m matrices of m rows and n columns using the Latin hypercube experimental design method as the parental population;

[0049] Step 3.2: Generate an offspring population based on the parental population, that is, for each experimental design matrix in the parental population, generate a new experimental design matrix by randomly exchanging elements between a certain dimension. Among them, the random exchange of elements between a certain dimension means randomly selecting two columns of the matrix for column exchange;

[0050] Step 3.3: Evaluate the fitness of each experimental design matrix in the parental population and the offspring population to obtain the fitness evaluation results. Among them, the fitness evaluation results include the number of feasible solutions in the experimental design matrix and the uniformity evaluation index of the generated aerodynamic geometric shape in the shape space;

[0051] The uniformity evaluation index in the shape space is specifically:

[0052]

[0053] In the formula, d ij is the distance between the i-th and j-th design variables in the shape space, and its calculation method is as follows:

[0054]

[0055] In the formula, are the aerodynamic geometric shape curves formed by the i-th and j-th experimental design matrices respectively, and Ω is the change region of the aerodynamic set shape.

[0056] Step 3.4: After merging the parent population and the offspring population, perform a selection operation. Retain 10m experimental design matrices with a larger number of feasible solutions and a higher spatial uniformity evaluation index according to the dominance relationship as the new generation population. Among them, the dominance relationship is a conventional method in multi-objective optimization problems and will not be elaborated in this embodiment;

[0057] Step 3.5: If the number of iterations reaches the set threshold or the new generation population obtained continuously for K max times no longer updates, output the current population; otherwise, use the current population as the parent population and return to Step 3.2;

[0058] Step 3.6: Based on the current population, select the design scheme closest to the 45° reference vector in the objective space of the multi-objective optimization model as the final experimental design result. The specific process is as follows:

[0059] Calculate num(X) and φ corresponding to all experimental design matrices in the current population p , with num(X) as the abscissa X and φ p as the ordinate Y. Place all the points (num(X), φ p ) corresponding to the experimental design matrices in a two-dimensional coordinate system, and screen out the experimental design matrix corresponding to the point closest to the line y = x as the final experimental design result.

[0060] The method of this embodiment will be further described below with specific examples.

[0061] Taking the experimental design of a certain airfoil profile as an example, the implementation case is given, and the specific steps are as follows:

[0062] Given the experimental design conditions, including the number m of sampling points of each experimental design matrix, the dimension n of the design variables, geometric constraint conditions, etc.;

[0063] Construct a multi-objective optimization model with the sample point set as the design variable, the number of feasible solutions and its filling index in the shape space as the objective function, and the airfoil thickness and area as the constraints;

[0064] An optimization algorithm is used to solve the multi-objective optimization model, and the optimization results are used as the initial sample point set for sequential approximation optimization.

[0065] The upper and lower surfaces of the airfoil given in the case are described by third-order CST parametric equations, each containing four design variables, that is, the dimension n of the experimental design variables is 8, and its upper and lower limits are respectively:

[0066] lb = [0.1, 0, 0, 0, 0.1, 0, 0, 0]

[0067] ub = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2]

[0068] In the formula, lb and ub are the upper limits of the design variables respectively.

[0069] In the case, the number of sampling points m of each experimental design matrix is 20, and the area constraint threshold S 0 = 0.06, and the thickness constraint threshold T 0 = 0.08. To illustrate the superiority of the present invention, the experimental design method in the present invention and the optimized Latin hypercube experiment method are simultaneously used to solve this case, and the convergence condition is set to the maximum fitness evaluation times of 1,000,000 for the experimental design matrix. The design results of the two methods are as Figures 2-3 shown, and the number of feasible solutions generated and the uniformity index of the airfoil in the shape space are shown in Table 1.

[0070] Table 1 Indexes of the airfoils generated by the sampling point set in the shape space

[0071]

[0072] It can be seen from the above results that the experimental design method proposed by the present invention obtains more feasible solutions under the same computing resources, and the airfoils generated by it are more evenly distributed in the aerodynamic geometry space, proving the superiority of the method of the present invention.

[0073] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structural transformation made under the inventive concept of the present invention by using the content of the specification and drawings of the present invention, or directly / indirectly applied in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A shape space experimental design method for aerodynamic shape optimization, characterized in that, used for airfoil profile experimental design, including the following steps: Step 1, given the calculation conditions of the experimental design, including the number m of sampling points of each experimental design matrix, the design variable dimension n, the geometric constraint conditions, and the shape parameterization method, where the geometric constraint conditions include the area constraint S of the airfoil i > S 0 , the thickness constraint T i > T 0 , S i represents the airfoil area corresponding to the a-th row in the experimental design matrix X, and S 0 represents the area constraint value, and T i represents the airfoil thickness corresponding to the a-th row in the experimental design matrix X, and T 0 represents the thickness constraint value; Step 2, construct a multi-objective optimization model with the sample point set as the design variable and the number of feasible solutions and the spatial uniformity evaluation index as the objective function, specifically: In the formula, is the experimental design matrix; num(X) is the number of sample points in the experimental design matrix where X satisfies the geometric constraint conditions, and φ p is the uniformity evaluation index of the design variables in the shape space; Step 3, use the non-dominated sorting genetic algorithm to iteratively solve the multi-objective optimization model to obtain the optimal experimental design scheme, specifically including: Step 3.1, randomly generate an initial population with 10m experimental design matrices of m rows and n columns as the parental population; Step 3.2, generate an offspring population based on the parental population, that is, for each experimental design matrix in the parental population, generate a new experimental design matrix by randomly exchanging elements in a certain dimension; Step 3.3, perform fitness evaluation on each experimental design matrix in the parental population and the offspring population to obtain the fitness evaluation results, where the fitness evaluation results include the number of feasible solutions in the experimental design matrix and the uniformity evaluation index of the generated aerodynamic geometry in the shape space, and the uniformity evaluation index in the shape space is specifically: where d ij is the distance between the i-th and j-th design variables in the shape space, and its calculation method is as follows: In the formula, are respectively the aerodynamic geometric shape curves formed by the i-th and j-th experimental design matrices, and Ω is the change region of the aerodynamic set shape; Step 3.4, after merging the parental population and the offspring population, perform a selection operation, and retain 10m experimental design matrices with more feasible solutions and higher spatial uniformity evaluation indexes according to the dominance relationship as the new generation population; Step 3.5, if the number of iterations reaches the set threshold or the new generation population obtained for K max consecutive times no longer updates, then output the current population, otherwise use the current population as the parental population and return to Step 3.2; Step 3.6, based on the current population, select the design scheme closest to the 45° reference vector in the objective space of the multi-objective optimization model as the final experimental design result.

2. The shape space experimental design method for aerodynamic shape optimization according to claim 1, characterized in that, in Step 3.1, the Latin hypercube experimental design method is used to randomly generate an initial population with 10m experimental design matrices.

Images