CN104866692B - A kind of aircraft Multipurpose Optimal Method based on Adaptive proxy model - Google Patents

Abstract

A kind of aircraft Multipurpose Optimal Method based on Adaptive proxy model disclosed by the invention, is related to a kind of Multipurpose Optimal Method for processing complex aircraft design, belongs to Flight Vehicle Design optimization field.The present invention constructs comprehensive preference function by physical layout method, realize the single-object problem that multi-objective optimization question is converted into reflection design preference, again to comprehensive preference function and constraints construction Adaptive proxy model, instead of high accuracy analysis model, solve the problems, such as that the calculating of optimization design is time-consuming big, restricted problem is finally converted into by unconstrained problem using augmented Lagrange multiplier method, and is solved with genetic algorithm.The solution procedure that the present invention will calculate time-consuming aircraft multi-objective optimization question simplifies, efficient, so that quick obtaining meets the Pareto noninferior solutions of user's request to shorten the design cycle of aircraft, reduces design cost.Additionally, highly versatile of the present invention, is easy to implement program development.

Description

Aircraft multi-objective optimization method based on adaptive agent model

Technical Field

The invention relates to a multi-objective optimization method for processing complex product designs, in particular to a multi-objective optimization method for processing complex aircraft designs, and belongs to the field of aircraft design optimization.

Background

In the aircraft engineering design, various performance indexes of an aircraft system are generally required to be comprehensively considered, the multi-objective optimization problem is balanced and processed, and in addition, a large amount of time is consumed when a high-precision subject analysis model is called for performance calculation, so that a set of feasible optimization design method is required for design guidance aiming at the problems that the weight is difficult to select and the time is high in the multi-objective optimization design of the aircraft.

In terms of processing the problem of multi-objective optimization, the commonly used methods include Pareto (Pareto) evolutionary algorithm, weighting coefficient method, physical programming method and the like. The Pareto evolutionary algorithm needs to calculate a large number of non-inferior solutions to obtain a non-inferior solution set, and then selects a scheme meeting requirements from the non-inferior solution set, so that the method has a serious problem of time consumption in calculation, and the design period of the aircraft is greatly prolonged. When the multi-objective optimization problem is solved by the weighting coefficient method, the weights need to be continuously modified to obtain a non-inferior solution meeting the user requirements, and the waste of computing resources is also caused. Moreover, if the non-inferior solution satisfying the preference is a non-convex non-inferior solution, no satisfactory result can be obtained regardless of how the weight is modified. Physical planning is an effective method for processing multi-objective optimization problems proposed by professor a. messac in the united states, and the method is suitable for a plurality of fields such as structural design, control and the like. The core idea is to introduce a preference function and convert different objective functions into satisfaction targets with the same magnitude. The method can directly solve the non-inferior solution meeting the requirements according to the user requirements, and does not need to spend a large amount of time to determine the optimal weighting coefficient like a weighting coefficient method, thereby greatly improving the calculation efficiency and the optimization result.

In order to improve the optimization efficiency of the aircraft system design, an approximate optimization strategy based on experimental design and a proxy model is an effective method. Through research in recent 20 years, various key technologies of an approximate optimization strategy are developed greatly and are widely applied to design optimization of an aircraft system. The method can be divided into a static agent model and an adaptive agent model according to different construction strategies of the agent model in the optimization process. The static proxy model is constructed by only once point sampling, and in order to ensure the approximate precision of the static proxy model, more sample points are often sampled in a design space, so that the number of times of calling the high-precision model is more, and the optimization efficiency is reduced. The self-adaptive proxy model initially takes fewer sample points, then the sample points are added in the optimization process according to the single-step optimization result, and the proxy model is updated. The construction strategy of the proxy model can effectively reduce the calling times of the high-precision model and improve the optimization searching efficiency.

In order to better explain the technical scheme of the invention, the following is a detailed description of the relevant basic methods that may be applied:

1 concept related to physical planning method

The preference function introduced in the physical planning method is a function which enables a user to determine 'how good the good is and how bad the bad is', the objective function value and the preference function value are in a one-to-one mapping relation, and the smaller the preference function is, the more satisfactory the objective function is. The preference function in physical planning can be divided into three types, i.e. Smaller Is Better (SIB), Larger Is Better (LIB) and more towards a certain value is better (Center is better, CIB). Each preference is further divided into soft and hard (S, H) types. For soft preferences, different objective function values correspond to different preference function values, whereas for hard preferences, the objective function value is only required to be within a given feasible region. In order to make the physical planning more convenient and flexible, the physical planning uses some boundary values to decompose the soft preference into a plurality of continuous intervals representing different satisfaction degrees: highly desirable, acceptable, undesirable, highly undesirable, and unacceptable.

The preference function curve is illustrated by taking as an example the smaller the better the type. The definition is very desirable to be 1 zone, desirable to be 2 zone, and so on, and very undesirable to be 5 zone, and the non-accepted area can be used as a constraint without defining a curve. 5 boundary values g for defining a preference function curve_iThe corresponding 5 preference function values are g_PiThe slope is S_iI is 1,2, …, 5. Wherein g is_iAnd g_P1Given by the user as a preference, the rest is calculated according to the relevant specifications of the physical plan. Specifying g as a function of the object, g_PIs a preference function value corresponding to the objective function value.

The preference function curve for region 1 is:

in the i (i-2, 3, …,5) th zone, let

The preference function curve of the i-th region in the 2-5 regions is

Wherein a, b, c and d are uniquely determined by function values and derivative values at boundary points.

For a multi-target problem containing m target functions, substituting the obtained preference function curve of each target function into the target function value to obtain a corresponding preference function value, and further obtaining a comprehensive preference function value g of the physical planning_PT。

In the formula n_scIs the number of soft preferences.

2 radial basis function proxy model introduction

The mathematical description of the aircraft optimization design problem using the surrogate model is as follows:

x^LB≤x≤x^UB

wherein,andthe proxy model approximation response values for the objective function and the constraints, respectively. For some problems, if the calculation of the constraint conditions is not time-consuming, the real constraint conditions can be directly used for optimization, and only the proxy model is constructed for the objective function.

The method comprehensively considers approximation precision and calculation efficiency, and adopts the radial basis function as a proxy model of the multi-objective optimization design method of the aircraft.

Radial functions are a class of functions that take the euclidean distance between an unknown point and a data point as an argument. Based on the Radial Function, a model constructed by linear superposition is a Radial Basis Function (RBF). The method converts a multi-dimensional problem into a one-dimensional problem through a radial function, thereby greatly simplifying the calculation cost of establishing the model and ensuring higher precision. The basic form of the radial basis function is as follows:

is a basis function;is a weight coefficient vector, β should satisfy the interpolation condition:

f_i＝y_i,i＝1,2,...n_s(7)

wherein, y_iTo an accurate value, f_iIs a predicted value. Thus, there are:

Aβ＝y (8)

β＝A^-1y (9)

in the formula:

φ_(r)for radial functions, commonly used radial functions include:

1) cubic function phi (r, c) ═ r + c³

2) Thin-plate spline function phi (r, c) r²ln(cr)

3) Gauss function phi (r, c) exp (-cr)²)

4) Inverse multiple quadratic function

5) Multiple quadratic function

Wherein c is a positive real constant.

Disclosure of Invention

The invention discloses an aircraft multi-objective optimization method based on a self-adaptive agent model, which aims to solve the technical problem that the solving process of the aircraft multi-objective optimization problem which is time-consuming in calculation is simplified and efficient, so that Pareto (Pareto) non-inferior solutions meeting the requirements of users are quickly obtained to shorten the design period of an aircraft and reduce the design cost.

The method constructs the comprehensive preference function through a physical programming method, realizes the conversion of a multi-objective optimization problem into a single-objective optimization problem reflecting design preference, constructs the self-adaptive agent model for the comprehensive preference function and the constraint condition to replace a high-precision analysis model, solves the problem of large calculation time consumption of optimization design, finally adopts an augmented Lagrange multiplier method to convert the constraint problem into an unconstrained problem, and uses a Genetic Algorithm (GA) to solve the unconstrained problem. The method has strong universality, is convenient for realizing program development, further improves the optimization design means of the complex aircraft system, improves the optimization design efficiency, reduces the design cost, and can meet the multi-objective optimization design requirement of the modern complex aircraft system.

The purpose of the invention is realized by the following technical scheme.

The invention discloses an aircraft multi-objective optimization method based on a self-adaptive agent model, which comprises the following steps:

step 1, establishing a high-precision analysis model in the multi-objective optimization design problem of the aircraft, and determining an initial design variable x₀And a design space A₀Setting the number of initial sample points N_initialAnd the number N of newly added sample points_addAnd let the iteration count parameter k equal to 1. The high-precision analysis model is used for solving an objective function and a constraint condition.

Number of initial sample points:

in the formula n_vTo design the variable dimensions.

Step 2, in the whole design space A₀In the method, N is generated by adopting an optimal Latin hyper-square design method_initialAnd storing the initial sample points and the response values thereof in a sample database.

And 3, calculating a real response value of the high-precision analysis model corresponding to the current sample point, and constructing a comprehensive preference function of the physical planning.

Step 3 the implementation method comprises steps 3.1, 3.2,

and 3.1, when k is equal to 1, calling an aircraft system high-precision analysis model, and calculating a model real response value corresponding to each initial sample point selected in the step 2, wherein the real response value comprises a constrained real response value and a designed target real response value. And when k is larger than or equal to 2, calling the high-precision analysis model of the aircraft system, and calculating the real response values of the model corresponding to the newly-added sample points in the step 8, wherein the real response values comprise the constrained real response value and the designed target real response value.

The proxy model is updated in real time through the newly added sample points, namely the adaptivity of the proxy model is realized, and the precision of the proxy model near the global optimal solution can be further improved.

Step 3.2, calculating the comprehensive preference function value g by adopting a physical planning method_PT。

For each objective function, respective preference type and preference function boundary value are given, then preference function curves of the functions are described by using the given preference type and boundary value, the preference function curves are substituted into the preference function curves according to the design objective real response value obtained in the step 3.1 to obtain corresponding preference function values, and further comprehensive preference function values g of the physical planning are obtained_PT。

Calculating by a physical programming method to obtain a comprehensive preference function value g_PTFor the comprehensive preference function value g_PTOptimization is carried out, so that a multi-objective optimization problem is converted into a single-objective optimization problem reflecting design preference, Pareto non-inferior solutions meeting user requirements can be rapidly obtained, the design period of the aircraft is shortened, and the design cost is reduced.

Step 3.3, the real response value of the constraint condition obtained in the steps 3.1 and 3.2 and the comprehensive preference function value g_PTAnd storing the data into a sample database.

And 4, extracting all sample points in the sample database and corresponding comprehensive preference function values and constraint condition real response values thereof to respectively construct a radial basis function proxy model of the target function and the constraint condition.

Because the radial basis function surrogate model is adopted to replace the high-precision analysis model, the solution process of the aircraft multi-objective optimization problem which is time-consuming in calculation is simplified and efficient. And updating the proxy model in real time by using the newly added sample points, namely realizing the adaptivity of the proxy model, and further improving the precision of the proxy model near the global optimal solution.

And step 5, constructing an augmented Lagrange function shown as a formula (12), converting the constraint problem into an unconstrained problem by using an augmented Lagrange multiplier method, calling the radial basis function proxy model in the step 4 by using a Genetic Algorithm (GA) to perform global optimization, and obtaining a possible optimal solution of the kth iterationAnd corresponding proxy model response values

In the formula, λ_j(j 1.. m) is a multiplier, σ_j(j ═ 1.. times, m) is a penalty factor, h_kIs an equality constraint, and_jthe following formula:

in the formula, g_j(x) Is the jth inequality constraint.

Step 6, substituting the current optimal solution of the kth time obtained in the step 5 into a high-precision analysis model, and calculating to obtain a real response value of the design targetAnd the real response value of the constraint condition, and storing the real response value into the sample database.

And 7, judging whether the real response value of the current optimal solution meets the constraint condition and the convergence condition.

When k is 1, the process proceeds directly to step 8. When k is>1, comparing the real response values of the current optimal solution of the k-1 th time and the k-th timeAndand (3) judging whether the convergence condition is met or not according to the convergence criterion given by the formula (14), simultaneously judging whether the constraint condition is met or not, if so, stopping circulation, wherein the current optimal solution obtained in the step 6 is the optimal solution of the aircraft multi-objective optimization design meeting the design preference, and finishing the optimization process. Otherwise, the procedure goes to step 8,

and 8, constructing a key sampling space according to the current possible optimal solution, and adding sample points in the key sampling space by adopting an optimal Latin hyper-square design method.

Step 8 comprises steps 8.1, 8.2,

step 8.1, determining the central point x of the key sampling space_cWhen k is 1, the best possible solution of the current proxy model is selectedAs the central point x of the new sampling space_c. When k is greater than or equal to 2, if f (x)_k)-f(x_k-1)<0, then the best possible solution for the current proxy modelAs the center point x of the updated sampling space_cOtherwise, selecting the central point of the original sampling space as the central point x of the updated sampling space_c。

And 8.2, determining the size of the key sampling space.

When k is equal to 1, the key sampling space is the initial design space a₀。

When k is more than or equal to 2, the key sampling space matrix B of the kth iteration_kThe upper and lower bounds are:

in the formula,the vector of the lower bound of the space is sampled for the emphasis of the kth iteration,the vector of the upper boundary of the space is sampled for the emphasis of the kth iteration,and is the best possible solution at the k-1 st time, a is the heavily sampled spatial coefficient,_Lfor the initial design of space A₀Is expressed as follows

If the space B is heavily sampled_kExceeds the design space A₀Then, the sampling space and the initial design space are emphasizedThe intersection of (a) and (b) serves as a new key sampling space.

Step 8.3, increasing N in the key sampling space by the optimal Latin hyper-square design method_addAnd adding the sample points and storing the added sample points into a sample database. Let the iteration count parameter k be k +1, go to step 2.

And 9, finishing the design task of the designated aircraft by using the optimal result obtained in the step 7, and indirectly having the advantages of shortening the overall design period of the aircraft, reducing the cost and the material consumption of the designated design task, further improving the comprehensive performance of the aircraft in the designated design task, and the like.

Has the advantages that:

1. compared with the traditional multi-objective optimization design method of the complex aircraft system, the method adopts the agent model technology to approximate the high-precision analysis model, utilizes the self-adaptive agent model construction strategy, improves the approximate precision of the agent model near the global optimal solution, optimizes the agent model by combining the optimization method with the global optimization capability, can improve the optimization efficiency and save the optimization design cost of the complex aircraft system.

2. The method adopts a physical programming method to process the multi-objective optimization problem, can quickly and effectively obtain the optimal solution meeting the design preference through the construction of the preference function, and solves the problems of high calculation cost and incapability of obtaining all non-convex and non-inferior solutions brought by the traditional multi-objective optimization method.

3. By utilizing the augmented Lagrange function, the method is suitable for processing the optimization design problem of the aircraft system with constraints.

4. The aircraft multi-objective optimization method based on the self-adaptive agent model can complete the design task of the designated aircraft, and indirectly has the advantages of shortening the overall design cycle of the aircraft, reducing the cost and the material consumption of the designated design task, further improving the comprehensive performance of the aircraft in the designated design task and the like.

Drawings

FIG. 1(a) is a graph of the satisfaction degree interval of the soft-like preference as the smaller the physical programming method is;

FIG. 1(b) is a graph of the satisfaction interval of the soft preference of the better class the larger the physical programming method is;

FIG. 1(c) is a graph of satisfaction intervals of soft-like preference as the physical programming approaches a certain value;

FIG. 2 is a process for optimizing the solution of a multi-objective problem by a physical programming method;

FIG. 3 is a flow chart of a multi-objective optimization design method for the efficient aircraft based on the adaptive agent model according to the invention;

FIG. 4(a) is an airfoil shape before and after airfoil optimization in a specific embodiment;

FIG. 4(b) is a pressure coefficient distribution before and after airfoil optimization in an embodiment;

fig. 4(c) shows the radar scattering cross section (RCS) distribution before and after the airfoil optimization in the embodiment.

Detailed Description

In order to better illustrate the purposes and advantages of the invention, the invention is further illustrated by a wing airfoil aerodynamic stealth multi-objective optimization design example in combination with a table and an attached drawing, and the comprehensive performance of the invention is verified and analyzed by comparing the results with the results of the traditional optimization method.

In order to verify the effectiveness of the method, the pneumatic stealth performance of the laminar flow airfoil NACA64A816 is optimized by respectively adopting the method, a static proxy model method (abbreviated as S-RBF) and a Genetic Algorithm (GA) for directly optimizing a real model. And in the aspect of processing the pneumatic stealth multi-objective optimization problem, the same objective function preference boundary is adopted. The number of sample points of the static proxy model remains the same as the final number of sampling points of the invention.

Example 1: and optimizing the wing airfoil design.

The optimization of aerodynamic and stealth design of wing airfoil profile has important significance for improving the overall aerodynamic and stealth performance of the aircraft. With the development of computer technology, Computational Fluid Dynamics (CFD) technology and computational electromagnetics (CME) technology are widely used in airfoil design optimization. The method is characterized in that NACA64A816 is used as a reference airfoil profile, a CST method is selected to describe coordinate points of the upper surface and the lower surface of the airfoil profile, and the design goal is that the lift-drag ratio is maximum and the radar scattering cross section (RCS) is minimum on the premise that the airfoil profile meets constraint conditions by modifying the curve shape of the airfoil profile. The constraints employed include: maximum thickness t of airfoil^* _maxNot less than the initial maximum airfoil thickness t_max0To ensure structural strength; lift coefficient Cl is not less than initial airfoil lift coefficient Cl₀To ensure that the wing profile provides sufficient lift to the aircraft. The problem is described mathematically as follows:

max f₁＝L/D

s.t.t_max≥t_max0,Cl≥Cl₀

solving a pneumatic and stealth subject high-precision analysis model: selecting commercial software Gambit to perform grid division, and then performing pneumatic analysis and calculation by using Fluent; commercial software FEKO is selected for carrying out stealth performance analysis and calculation. The specific implementation steps for optimizing the NACA64A816 airfoil profile by adopting the efficient aircraft multi-objective optimization design method based on the self-adaptive agent model are as follows:

step 1, calculating a lift-drag ratio and a radar scattering cross section (RCS) of a wing based on a pneumatic and stealth high-precision analysis model of a wing airfoil of NACA64A 816; the design variables are CST to describe the 12 shape function coefficients of the airfoil profile, i.e.X＝(Au₀,Au₁,Au₂,Au₃,Au₄,Au₅,Al₀,Al₁,Al₂,Al₃,Al₄,Al₅) Initial design variable X₀(0.2584,0.2587,0.4372,0.2901,0.4697,0.3648, -0.0992, -0.0815, -0.0631, -0.1601,0.1623, -0.0108); design space A₀The upper and lower boundary vectors of (a) are respectively: a. the_U0＝(0.3359,0.3363,0.5683,0.3771,0.6107,0.4742,-0.0694,-0.0570,-0.0442,-0.1120,0.2110,-0.0075)，A_L0(0.1809,0.1811,0.3060,0.2030,0.3288,0.2554, -0.1290, -0.1059, -0.0820, -0.2081,0.1136, -0.0140). Number of initial sample points N_initialWhen the sample point number is 91, newly adding the number N of the sample points_addLet iteration count parameter k be 1, 3.

Step 2, designing the space A₀In the method, the optimal Latin super-square is adopted to select the scale to be N_initialThe selected sample point is stored in the sample database.

And 3, calculating a lift-drag ratio and a radar scattering cross section (RCS) corresponding to each sample point selected in the step 2 by calling a pneumatic and stealth high-precision analysis model of the wing airfoil, and simultaneously obtaining the maximum thickness and lift coefficient of the airfoil.

Setting relevant parameters of a physical planning method: the larger the preferred type of the lift-to-drag ratio, the better the preferred type of the radar scattering cross section (RCS), and the preferred boundary values are shown in table 1.

TABLE 1 Objective function preference boundaries

According to the lift-drag ratio and the radar scattering cross section (RCS) obtained by calculation, the comprehensive preference function value g of the physical planning is obtained_PTAnd storing the comprehensive preference function, the maximum thickness of the airfoil profile and the lift coefficient into a sample database.

And 4, extracting all sample points in the sample database and corresponding comprehensive preference function values, maximum thickness of airfoil profiles and lift coefficients thereof, and constructing a radial basis agent model.

Step 5, converting the constraint problem into an unconstrained problem by using an augmented Lagrange multiplier method, and performing global optimization on the radial basis function surrogate model in the step 4 by using a Genetic Algorithm (GA) to obtain a possible optimal solution of the kth iterationAnd corresponding proxy model response values

Step 6, substituting the kth iterative possible optimal solution obtained in the step 5 into a high-precision analysis model, calculating to obtain the wing lift-drag ratio and the radar scattering cross section (RCS) of the current possible optimal solution, and further obtaining the real preference function value corresponding to the current possible optimal solutionAnd storing the real preference function value, the maximum thickness of the airfoil profile and the lift coefficient into a sample database.

In step 7, when k is equal to 1, the process proceeds directly to step 8. When k is more than or equal to 2, comparing the real preference function values of the possible optimal solutions of the k-1 th time and the k-th timeAndand (4) judging whether the convergence criterion is met or not by using the formula (18), and judging whether the maximum thickness and the lift coefficient of the airfoil meet the constraint condition or not according to the formula (19). If the wing airfoil aerodynamic stealth optimization design meets the requirements, the possible optimal solution obtained in the step 6 is the optimal solution of the wing airfoil aerodynamic stealth optimization design, and the optimization process is finished. If not, go to step 8.

t_k≥0.1599,Cl_k≥0.8214 (19)

Step 8, in the current possible optimal solutionAnd constructing a key sampling space nearby, and adding a new sample point.

Firstly, determining a central point x of a key sampling space_cWhen k is 1, the best possible solution of the current proxy model is selectedAs the central point x of the new sampling space_c. When k is greater than or equal to 2, if f (x)_k)-f(x_k-1)<0, then the best possible solution for the current proxy modelAs the center point x of the updated sampling space_cOtherwise, selecting the central point of the original sampling space as the central point x of the updated sampling space_c。

The size of the emphasized sampling space is then determined. When k is equal to 1, the key sampling space is the initial design space a₀. When k is more than or equal to 2, the upper and lower boundaries of the key sampling space are determined by equation (15), wherein a is 0.5.

And finally, adding 3 newly added sample points in the key sampling space through the optimal Latin super-square ESEA, and storing the newly added sample points into a sample database. Let the iteration count parameter k be k +1, go to step 2.

The matters not described in detail in the specification of the present invention are all the basic knowledge and the technology related to the field.

Table 2 shows the optimization results obtained by the present invention, fig. 4(a), (b), and (c) show the profile, pressure coefficient distribution, and radar cross-section (RCS) distribution before and after optimization, respectively, and table 3 shows the comparison of the optimization results of the present invention with S-RBF and Genetic Algorithm (GA).

TABLE 2 wing profile optimization results

TABLE 3 comparison of Performance of optimization design methods

As can be seen from the data in Table 2, under the constraint conditions of meeting the lift coefficient and the maximum thickness of the airfoil, the lift-drag ratio of the airfoil is improved by 25.84%, and the radar scattering cross section (RCS) is reduced by 27.12%. Comparing the data in table 6, it can be seen that, under the condition of the same number of sample points, the result obtained by the present invention is superior to the traditional optimization method based on the static proxy model, wherein the lift-drag ratio is improved by 7.74%, and the radar scattering cross section (RCS) is reduced by 9.9%. Compared with a genetic algorithm, the time spent on optimizing the method is only 10.5% of that of the genetic algorithm, and the optimization efficiency is obviously improved.

According to the analysis of the airfoil optimization design based on NACA64A816, the invention basically achieves the expected object, and the invention is helpful for improving the optimization design result and the design quality; on the other hand, the invention relates to the optimization design problem of the high-precision analysis model of the aircraft, and the invention can also greatly improve the optimization efficiency, reduce the optimization design cost and shorten the optimization design period.

The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. An aircraft multi-objective optimization method based on an adaptive agent model is characterized in that: the method comprises the following steps:

step 1, establishing a high-precision analysis model in the multi-objective optimization design problem of the aircraft, and determining an initial design variable x₀And a design space A₀Setting the number of initial sample points N_initialAnd the number N of newly added sample points_addAnd making the iteration counting parameter k equal to 1; the high-precision analysis model is used for solving an objective function and constraint conditions;

number of initial sample points:

$N_{initial}=\frac{(n_v+1)(n_v+2)}{2}---\left(1\right)$

in the formula n_vTo design the variable dimensions;

step 2, in the whole design space A₀In the method, N is generated by adopting an optimal Latin hyper-square design method_initialInitial sample points and storing the initial sample points and response values thereof in a sample database;

step 3, calculating a real response value of the high-precision analysis model corresponding to the current sample point, and constructing a comprehensive preference function of the physical planning;

step 4, extracting all sample points in the sample database and corresponding comprehensive preference function values and constraint condition real response values thereof to respectively construct a radial basis function proxy model of the target function and the constraint condition;

and 5, constructing an augmented Lagrange function shown as the formula (2), converting the constraint problem into an unconstrained problem by using an augmented Lagrange multiplier method, calling the radial basis function proxy model in the step 4 by using a Genetic Algorithm (GA) to perform global optimization, and obtaining a possible optimal solution of the kth iterationAnd corresponding proxy model response values

$A(x,\mathrm{\&lambda;},\mathrm{\&sigma;})=f\left(x\right)+\underset{j}{\overset{m}{\&Sigma;}}\&lsqb;{\mathrm{\&lambda;}}_j{\mathrm{\&psi;}}_j+{\mathrm{\&sigma;}}_j{{\mathrm{\&psi;}}_j}^2\&rsqb;+\underset{k=1}{\overset{l}{\&Sigma;}}\{{\mathrm{\&lambda;}}_{k+m}{h}_k\left(x\right)+{\mathrm{\&sigma;}}_j{\&lsqb;h_k\left(x\right)\&rsqb;}^2\}---\left(2\right)$

In the formula, A (x, lambda, sigma) represents an augmented Lagrange function, f (x) represents an initial function, and m represents the original problemConstrained at m inequalities, λ_jJ is 1, a, m is a multiplier, σ_jJ 1.. m is a penalty factor, l represents that l equality constraints exist in the original problem, and h_kIs an equality constraint, and_jthe following formula:

${\mathrm{\&psi;}}_j=max\&lsqb;g_j\left(x\right),\frac{-{\mathrm{\&lambda;}}_j}{2{\mathrm{\&sigma;}}_j}\&rsqb;---\left(3\right)$

in the formula, g_j(x) Is the jth inequality constraint;

step 6, substituting the current optimal solution of the kth time obtained in the step 5 into a high-precision analysis model, and calculating to obtain a real response value of the design targetAnd the real response value of the constraint condition, and storing the real response value into a sample database;

step 7, judging whether the real response value of the current optimal solution meets constraint conditions and convergence conditions;

when k is 1, directly carrying out step 8; when k is>1, comparing the real response values of the current optimal solution of the k-1 th time and the k-th timeAndjudging whether a convergence condition is met according to a convergence criterion given by the formula (4), wherein the convergence error represents a convergence error, and simultaneously judging whether a constraint condition is met, if so, stopping circulation, wherein the current optimal solution obtained in the step 6 is the optimal solution of the multi-objective optimization design of the aircraft meeting the design preference, and finishing the optimization process; otherwise, the procedure goes to step 8,

$\left|\frac{f\left({x^{*}}_k\right)-f\left({x^{*}}_{k-1}\right)}{f\left({x^{*}}_{k-1}\right)}\right|\&le;\mathrm{\&epsiv;}---\left(4\right)$

step 8, constructing a key sampling space according to the current possible optimal solution, and adding sample points in the key sampling space by adopting an optimal Latin hyper-square design method;

said step 8 comprises steps 8.1, 8.2,

step 8.1, determining the central point x of the key sampling space_cWhen k is 1, the best possible solution of the current proxy model is selectedAs the central point x of the new sampling space_c(ii) a When k is greater than or equal to 2, if f (x)_k)-f(x_k-1) If < 0, then the current agent model is best possible solutionAs the center point x of the updated sampling space_cOtherwise, selecting the central point of the original sampling space as the central point x of the updated sampling space_c；

Step 8.2, determining the size of a key sampling space;

when k is equal to 1, the key sampling space is the initial design space a₀；

When k is more than or equal to 2, the key sampling space matrix B of the kth iteration_kThe upper and lower bounds are:

$\begin{array}{c}{B}_k^L=x_{k-1}^{*}-aL\\ B_k^U=x_{k-1}^{*}+aL\end{array}---\left(5\right)$

in the formula,the vector of the lower bound of the space is sampled for the emphasis of the kth iteration,the vector of the upper boundary of the space is sampled for the emphasis of the kth iteration,for the k-1 th possible optimal solution, a is the key sampling space coefficient, and L is the initial design space A₀Is expressed as follows

$L=A_0^U-A_0^L---\left(6\right)$

Wherein,represents the upper bound of the design space,represents the lower bound of the design space;

if the space B is heavily sampled_kExceeds the design space A₀Taking the intersection of the key sampling space and the initial design space as a new key sampling space;

step 8.3, increasing N in the key sampling space by the optimal Latin hyper-square design method_addAdding new sample points, and storing the new sample points to the sample dataIn a library; let the iteration count parameter k be k +1, go to step 2.

2. The method of claim 1 for multi-objective optimization of an aircraft based on an adaptive proxy model, wherein: the step 3 implementation method comprises steps 3.1, 3.1 and 3.2,

step 3.1, when k is equal to 1, calling an aircraft system high-precision analysis model, and calculating a model real response value corresponding to each initial sample point selected in the step 2, wherein the real response value comprises a constrained real response value and a designed target real response value; when k is larger than or equal to 2, calling the high-precision analysis model of the aircraft system, and calculating the real response values of the model corresponding to the newly-added sample points in the step 8, wherein the real response values comprise the constrained real response value and the real response value of the design target;

step 3.2, calculating the comprehensive preference function value g by adopting a physical planning method_PT；

For each objective function, respective preference type and preference function boundary value are given, then preference function curves of the functions are described by using the given preference type and boundary value, the preference function curves are substituted into the preference function curves according to the design objective real response value obtained in the step 3.1 to obtain corresponding preference function values, and further comprehensive preference function values g of the physical planning are obtained_PT；

Step 3.3, the real response value of the constraint condition obtained in the steps 3.1 and 3.2 and the comprehensive preference function value g_PTAnd storing the data into a sample database.

3. The method for multi-objective optimization of an aircraft based on an adaptive proxy model according to claim 1 or 2, characterized in that: and 9, completing the design task of the specified aircraft by using the optimal result obtained in the step 7.

4. The method of claim 1 for multi-objective optimization of an aircraft based on an adaptive proxy model, wherein:

the specific implementation steps for optimizing the wing airfoil are as follows:

step 1, calculating a lift-drag ratio and a radar scattering cross section (RCS) of a wing based on a pneumatic and stealth high-precision analysis model of a wing airfoil of NACA64A 816; the design variable CST describes the 12 shape function coefficients of the airfoil, i.e. X ═ Au (Au)₀,Au₁,Au₂,Au₃,Au₄,Au₅,Al₀,Al₁,Al₂,Al₃,Al₄,Al₅) Initial design variable X₀(0.2584,0.2587,0.4372,0.2901,0.4697,0.3648, -0.0992, -0.0815, -0.0631, -0.1601,0.1623, -0.0108); design space A₀The upper and lower boundary vectors of (a) are respectively: a. the_U0＝(0.3359,0.3363,0.5683,0.3771,0.6107,0.4742,-0.0694,-0.0570,-0.0442,-0.1120,0.2110,-0.0075)，A_L0(0.1809,0.1811,0.3060,0.2030,0.3288,0.2554, -0.1290, -0.1059, -0.0820, -0.2081,0.1136, -0.0140); number of initial sample points N_initialWhen the sample point number is 91, newly adding the number N of the sample points_addSetting an iteration counting parameter k to be 1;

step 2, designing the space A₀In the method, the optimal Latin super-square is adopted to select the scale to be N_initialStoring the selected sample point in a sample database;

step 3, calculating a lift-drag ratio and a radar scattering cross section corresponding to each sample point selected in the step 2 by calling a pneumatic and stealth high-precision analysis model of the wing airfoil profile, and simultaneously obtaining the maximum thickness and lift coefficient of the airfoil profile;

setting relevant parameters of a physical planning method: the larger the preference type of the lift-drag ratio is, the better the preference type of the radar scattering cross section RCS is, and the preference boundary value is shown in Table 1;

TABLE 1 Objective function preference boundaries

According to the lift-drag ratio and the radar scattering cross section obtained by calculation, the comprehensive preference function value g of the physical planning is obtained_PTAnd integrating the preference function and the airfoil profileStoring the maximum thickness and the lift coefficient into a sample database;

step 4, extracting all sample points in a sample database and corresponding comprehensive preference function values, maximum thickness of airfoil profiles and lift coefficients thereof, and constructing a radial basis function proxy model;

step 5, converting the constraint problem into an unconstrained problem by using an augmented Lagrange multiplier method, and performing global optimization on the radial basis function surrogate model in the step 4 by using a Genetic Algorithm (GA) to obtain a possible optimal solution of the kth iterationAnd corresponding proxy model response values

Step 6, substituting the kth iteration possible optimal solution obtained in the step 5 into a high-precision analysis model, calculating to obtain the wing lift-drag ratio and the radar scattering cross section of the current possible optimal solution, and further obtaining the real preference function value corresponding to the current possible optimal solutionStoring the real preference function value, the maximum thickness of the airfoil profile and the lift coefficient into a sample database;

step 7, when k is equal to 1, directly switching to step 8; when k is more than or equal to 2, comparing the real preference function values of the possible optimal solutions of the k-1 th time and the k-th timeAndjudging whether the convergence criterion is met or not by using the formula (7), and judging whether the maximum thickness and the lift coefficient of the airfoil meet the constraint condition or not according to the formula (8); if the wing airfoil aerodynamic stealth optimization design meets the requirements, the possible optimal solution obtained in the step 6 is the optimal solution of the wing airfoil aerodynamic stealth optimization design, and the optimization process is finished; if not, then turn toStep 8 is entered;

$\left|\frac{f\left({x^{*}}_k\right)-f\left({x^{*}}_{k-1}\right)}{f\left({x^{*}}_{k-1}\right)}\right|\&le;0.01---\left(7\right)$

t_k≥0.1599,Cl_k≥0.8214 (8)

step 8, in the current possible optimal solutionConstructing a key sampling space nearby, and newly adding sample points;

firstly, determining a central point x of a key sampling space_cWhen k is 1, the best possible solution of the current proxy model is selectedAs the central point x of the new sampling space_c(ii) a When k is greater than or equal to 2, if f (x)_k)-f(x_k-1) If < 0, then the current agent model is best possible solutionAs the center point x of the updated sampling space_cOtherwise, selecting the central point of the original sampling space as the central point x of the updated sampling space_c；

Then determining the size of a key sampling space; when k is equal to 1, the key sampling space is the initial design space a₀(ii) a When k is more than or equal to 2, determining the upper and lower boundaries of the key sampling space by an equation (4), wherein a is 0.5;

finally, 3 newly added sample points are added in a key sampling space through an optimal Latin hyper-square based on an improved random evolution algorithm, and the newly added sample points are stored in a sample database; let the iteration count parameter k be k +1, go to step 2.