CN117648763B

CN117648763B - CST-EGO multi-parameter optimization design method of synergistic jet wing profile

Info

Publication number: CN117648763B
Application number: CN202410126947.0A
Authority: CN
Inventors: 王波; 应培; 张国鑫; 范景峰; 曹华振; 沈思颖; 袁起航; 王若尘
Original assignee: Institute of Engineering Thermophysics of CAS
Current assignee: Institute of Engineering Thermophysics of CAS
Priority date: 2024-01-30
Filing date: 2024-01-30
Publication date: 2024-03-29
Anticipated expiration: 2044-01-30
Also published as: CN117648763A

Abstract

The invention provides a CST-EGO multi-parameter optimization design method of a synergistic jet wing profile, which can realize the integral optimization of design parameters of the synergistic jet wing profile and improve the aerodynamic efficiency and the flight performance of the synergistic jet wing profile. The method adopts a CST parameterization method to parameterize and describe the middle sinking section curve, adopts an EGO global optimization method and combines a uniformly distributed Latin hypercube method, a Kriging agent model and combines with an EI point adding criterion and the like to obtain an optimized design variable combination, wherein the optimized design variable combination comprises an air jet position, an air suction port position, a middle sinking section curve shape, a jet momentum coefficient and the like. The method comprehensively considers the interaction among a plurality of design variables and the complex relationship between the design variables and the flow field characteristics, and can effectively solve the problem of local optimum or suboptimal in the existing single-parameter optimization method, thereby improving the aerodynamic efficiency and the flight performance of the synergistic jet wing profile.

Description

CST-EGO multi-parameter optimization design method of synergistic jet wing profile

Technical Field

The invention belongs to the technical field of aircraft fluid control and aerodynamic optimization design, relates to flow control and aerodynamic optimization of wings, and in particular relates to a CST-EGO multi-parameter optimization design method of a synergistic jet wing profile, which realizes overall optimization of design parameters of the synergistic jet wing profile through parameterized description and a global optimization algorithm and improves aerodynamic efficiency and flight performance of the synergistic jet wing profile.

Background

The aircraft mainly depends on the lift force generated by the wing, the wing profile is the key of the wing design, and the aerodynamic characteristics of the wing profile determine the parameters such as the lift force, the resistance, the pitching moment and the like of the wing, so that the performances such as the flying speed, the stability and the maneuverability of the aircraft are affected. Conventional wing designs focus on achieving optimal aerodynamic efficiency through static shapes, however this approach generally does not perform optimally under specific flight conditions. With the development of aviation technology, an active or passive flow control method is introduced into the design of the wing, so that the structure and the characteristics of a flow field on the wing are changed by influencing the flow field, the pneumatic efficiency of the wing is effectively improved, and the overall flight performance of an airplane is further improved. Active flow control refers to the control of a flow field by adding or extracting energy or momentum to the flow field, or changing the pressure or temperature in the flow field. Passive flow control refers to control of the flow field by changing the shape or roughness of the wing surface, or by providing additional devices on the wing surface.

The principle of the collaborative Jet wing type technology (Co-flow Jet air) is that a suction pump is placed in the wing type, surface airflow is sucked by the pump from an air suction port near the trailing edge, high-speed Jet flow with equal mass is tangentially ejected from an air Jet port near the leading edge through pressurization of the pump, zero net mass flow control is realized, and further effective control of a flow field around the wing type is realized. The synergistic jet wing type technology has the advantages that the active control of the lift force, the resistance and the pitching moment of the wing can be realized by adjusting the strength and the direction of jet flow under the condition of not increasing the weight and the complexity of the wing, and the aerodynamic efficiency and the flight performance of the wing are improved. The design of the synergistic jet wing profile comprises a plurality of design parameters including the relevant design of the air jet mouth, the relevant design of the air suction mouth, the jet momentum coefficient, the curve shape between the air jet mouth and the air suction mouth, and the like, and can influence the aerodynamic effect of the synergistic jet wing profile design. For example, the design of the jet directly affects the speed and direction of the jet, while the design of the suction port affects the suction efficiency of the airflow. The jet momentum coefficient is a key parameter for determining the interaction strength of jet and surrounding flow field, and the shape between the jet port and the air suction port directly influences the flow characteristic of fluid on the surface of the airfoil.

The current collaborative jet wing profile design mainly adopts a single parameter optimization method, namely, a certain design parameter is used as a control variable while other design parameters are controlled to be unchanged, a group of design parameter combinations are formed by the other design parameters, and the optimal design point in the design parameter change interval is determined, so that the selection of one design parameter is completed; after determining one design parameter, a second design parameter is selected until all design parameters are obtained. Although this approach simplifies the design process to some extent, it also has the following significant drawbacks and limitations: firstly, because a plurality of design parameters are associated with each other, a single-parameter optimization method cannot obtain a globally optimal design parameter combination, and only a locally optimal or suboptimal design parameter combination can be obtained, so that the aerodynamic effect of the synergistic jet wing profile cannot reach an optimal level; secondly, the single parameter optimization method needs to carry out design parameter selection for a plurality of times, each selection needs to carry out a large number of numerical simulation or experimental tests, consumes a large amount of time and resources, and has low efficiency; in addition, the single-parameter optimization method is difficult to consider the interaction between design parameters and the complex relationship between the design parameters and the flow field characteristics, so that the aerodynamic mechanism of the synergistic jet wing profile is difficult to deeply analyze and understand, and an effective improvement scheme is difficult to propose.

Therefore, how to realize comprehensive optimization of a plurality of key design parameters in the design of the synergistic jet wing profile, so that the mutual relevance and influence among a plurality of design parameters and the complex relation between the design parameters and the flow field characteristics can be comprehensively considered, and the overall optimization of the design parameters of the synergistic jet wing profile is realized, so that the aerodynamic efficiency and the flight performance of the synergistic jet wing profile are improved, and the technical problem to be solved is urgent.

Disclosure of Invention

Object of the invention

Aiming at the defects and shortcomings existing in the existing collaborative jet wing profile design, particularly the problem that the mutual influence and the integral optimization among a plurality of design parameters cannot be comprehensively considered in the existing single-parameter optimization method, the invention aims to provide a CST-EGO multi-parameter optimization design method of a collaborative jet wing profile, and the integral optimization of parameters is realized by adopting a CST parameterization method to parameterize an intermediate sinking section curve, adopting an EGO optimization method, a Kriging agent model, combining a Latin hypercube method with an EI point adding criterion and the like, and comprehensively considering the interaction of key design variables such as the position of an air nozzle, the position of an air suction port, the shape of the intermediate sinking section curve, the jet momentum coefficient and the like, so that the pneumatic efficiency and the flight performance of the collaborative jet wing profile are improved.

(II) technical scheme

In order to achieve the aim of the invention and solve the technical problems, the invention adopts the following technical scheme:

a CST-EGO multi-parameter optimization design method of a synergistic jet wing profile is characterized by at least comprising the following steps when in implementation:

SS1. Selecting an existing synergic jet wing profile as an initial wing profile to be optimized, wherein the initial wing profile comprises a jet orifice arranged near a front edge position, an air suction port arranged near a tail edge position and an intermediate sinking section curve positioned between the jet orifice and the air suction port on a suction surface of the initial wing profile, and selecting optimization design variables according to requirements according to the comprehensive aerodynamic performance of the target synergic jet wing profile under aerodynamic design conditions, wherein the optimization design variables at least comprise the jet orifice position, the jet orifice size, the air suction port position, the air suction port size, the intermediate sinking section curve and/or the jet momentum coefficientC _μ ；

SS2Determining an optimization objective and constraints, the optimization objective being determined based at least on the energy consumption and/or aerodynamic performance of the objective co-jet airfoil under aerodynamic design conditions, including the airfoil lift coefficientC _L Coefficient of resistanceC _D Lift-drag coefficient C _L /C _D Coefficient of power consumptionP _C And/or an equivalent lift-drag coefficient taking into account energy consumptionK _C The constraint condition is determined at least based on the shape and size limitation, the energy consumption limitation and/or the pneumatic working condition limitation of the target cooperative jet airfoil under the pneumatic design condition;

SS3 parametric description of the geometry of the intermediate sink section curve by CST (Class function/Shape function Transformation) parametric description, CST fitting of the intermediate sink section curve by means of linear combination of multiple BPO polynomials (Bernstein polynomial, BPO), description of the basic contour and detailed geometry of the intermediate sink section curve by Class and shape functions in the CST fitting, and use of each BPO polynomial in the CST fittingCorresponding weight parametersA _i Adjusting the shape of the middle sinking section curve through weight parametersA _i The curvature of the middle sinking section curve is controlled by the change rate of the middle sinking section curve, and the two ends of the middle sinking section curve are subjected to slope constraint so as to be tangent with the air jet and the air suction port, and any part of the middle sinking section curve is prevented from being in a concave state;

SS4, obtaining an optimized design variable combination by adopting a EGO (Efficient Global Optimization) global optimization method, randomly selecting initial sample points in a multi-dimensional design space formed by all the optimized design variables by using a Latin hypercube sampling method with uniform distribution, constructing an initial sample point set by using a CFD numerical simulation method based on the initial sample point set, an optimization target and constraint conditions, calculating a corresponding pneumatic performance function value of each sample point, constructing a Kriging proxy model to approximately reflect a real pneumatic performance function and give uncertainty of a predicted value, evaluating an improved expected value of each candidate sample point according to the predicted value and the uncertainty of the Kriging proxy model by using EI (Expected Improvement) addition rule, and calculating a corresponding objective function value and constraint condition value of the candidate sample point with the maximum improved expected value under the pneumatic design condition;

And SS5, after each round of global EGO optimization, evaluating whether an optimization target meets a preset termination condition, if the optimization target meets or exceeds the preset target and meets constraint conditions, finishing the optimization process, outputting an optimized design variable combination, and if the optimization target does not meet the target, returning to step SS4, adding a candidate sample point with the maximum improved expected value as a new sample point into a sample point set, updating a Kriging proxy model, and continuing the optimization process until the termination conditions are met.

(III) technical effects

Compared with the prior art, the CST-EGO multi-parameter optimization design method of the synergistic jet wing profile has the following beneficial and remarkable technical effects:

(1) The invention provides a CST-EGO multi-parameter optimization design method of a synergistic jet wing profile, which can effectively realize pneumatic optimization design of the synergistic jet wing profile and improve pneumatic efficiency and flight performance of the synergistic jet wing profile. The method comprehensively considers the aspects of the geometry, the flow control parameters, the aerodynamic performance indexes, the energy consumption and the like of the synergistic jet wing profile, adopts a parameterization method and a global optimization method, can fully utilize the information of initial sample points, and realizes the integral optimization of design parameters of the synergistic jet wing profile, thereby realizing the improvement of the aerodynamic efficiency and the flight performance of the synergistic jet wing profile.

(2) The invention adopts a CST parameterization method to parameterize the geometric shape of the synergic jet wing profile, and utilizes the CST weight coefficient and the jet momentum coefficient as the optimization design variables, so that the geometric characteristics of the synergic jet wing profile can be accurately described, the number of the optimization design variables is reduced, and the complexity of the optimization problem is simplified. The CST parameterization method is a parameterization method based on a BPO polynomial, can flexibly describe airfoils of any shape, and is particularly suitable for a collaborative jet airfoil with a middle sinking section curve.

(3) According to the invention, the pneumatic optimization design is carried out on the collaborative jet wing profile by adopting the EGO global optimization method based on the Kriging agent model and the EI point adding criterion, the real pneumatic performance function is approximately represented by utilizing the Kriging agent model, and the improved expected value is evaluated by utilizing the EI point adding criterion, so that the global optimal solution can be effectively searched, and the optimization efficiency and quality are improved. The Kriging agent model is a regression model based on a Gaussian process, can utilize the aerodynamic performance function value of an initial sample point to realize the approximate representation of a real aerodynamic performance function, and simultaneously gives uncertainty of a predicted value so as to facilitate the subsequent optimization search. The EI point adding criterion is a common criterion for selecting the next sampling point, and can utilize the predicted value and uncertainty of the Kriging proxy model to evaluate the probability and expectation of the improvement quantity, thereby realizing effective search of the global optimal solution.

(4) According to the invention, the equivalent lift-drag ratio and the power consumption coefficient are adopted as optimization targets and constraint conditions, and the aerodynamic performance and the flow control effect of the synergistic jet wing profile are comprehensively considered, so that the lift force and the lift-drag ratio of the synergistic jet wing profile can be effectively improved, the power consumption and the resistance of the synergistic jet wing profile are reduced, and the flight performance of the synergistic jet wing profile is improved. The equivalent lift-drag ratio is a pneumatic efficiency index considering energy consumption, and can reflect the pneumatic performance of the synergic jet wing profile under the flow control condition, and the maximization means that the lift force and the lift-drag ratio of the synergic jet wing profile are maximized at the same time, and the power consumption and the resistance are minimized at the same time. The power consumption coefficient is a constraint condition considering flow control energy, and can reflect the flow control effect of the co-jet airfoil, and the satisfaction of the constraint condition means that the flow control energy of the co-jet airfoil is within an acceptable range.

Drawings

FIG. 1 is a flow chart of a CST-EGO multiparameter optimization design of a synergistic jet airfoil of the present invention.

FIG. 2 is a schematic illustration of design parameters on a co-jet airfoil.

Reference numerals illustrate:

an air jet 1, an air suction port 2 and a middle sinking section curve 3.

Detailed Description

For a better understanding of the present invention, the following examples are set forth to illustrate the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the invention. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. The following describes the structure and technical scheme of the present invention in detail with reference to the accompanying drawings, and an embodiment of the present invention is given.

Example 1

As shown in FIG. 1, the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil of the invention at least comprises the following steps in implementation:

SS2. Determining optimization objectives and constraints, the optimization objectives being determined based at least on the energy consumption and/or aerodynamic performance of the target co-jet airfoil under aerodynamic design conditions, including the lift coefficient of the airfoilC _L Coefficient of resistanceC _D Lift-drag ratioCoefficients ofC _L /C _D Coefficient of power consumptionP _C And/or an equivalent lift-drag coefficient taking into account energy consumptionK _C The constraint condition is determined at least based on the shape and size limitation, the energy consumption limitation and/or the pneumatic working condition limitation of the target cooperative jet airfoil under the pneumatic design condition;

The embodiment 1 shows a CST-EGO multi-parameter optimization design method of a synergic jet wing profile, which is provided by the invention, wherein the method takes the existing synergic jet wing profile as an initial wing profile, selects optimization design variables such as an air jet, an air suction port, a middle sinking section curve and the like, determines an optimization target and constraint conditions, adopts the CST method to carry out parameterization description on the middle sinking section curve, adopts the EGO method to obtain an optimized design variable combination, evaluates whether the optimization target meets a termination condition, and outputs the optimized design variable combination. The method can effectively improve the aerodynamic performance and the energy efficiency of the synergistic jet wing profile.

Example 2

On the basis of the above embodiment 1, the present embodiment 2 focuses on the preferred examples of the steps SS1 and SS2 in the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil provided by the present invention.

As a preferred example of the present invention, in the above step SS1, the aerodynamic design conditions include at least Mach number Ma of the incoming gas and angle of attack of the gas flowαThe method comprises the steps of carrying out a first treatment on the surface of the The position of the air jet, the position of the air suction port, the curve of the middle sinking section between the air jet and the air suction port and the jet momentum coefficient are closely related to the aerodynamic performance and the energy consumption of the wing shape in the synergic jet wing shapeC _μ As an optimal design variable, the positions of the air jet ports are the coordinates of the air jet ports arranged on the suction surface of the airfoil in the X direction, namely the chord direction, and the coordinates of the air jet ports arranged on the suction surface of the airfoil in the Y direction, namely the vertical chord direction, the positions of the air suction ports are the coordinates of the air suction ports arranged on the suction surface of the airfoil in the X direction and the Y direction, and the curve of the middle sinking section is the air jetThe shape and length of the curve between the air inlet and the air suction inlet, the jet momentum coefficientC _μ For quantifying the momentum addition or reduction of jet flow to main flow, the ratio of the mass of air flow sprayed from the air nozzle to the mass of air flow sucked from the air suction port is expressed asIn which, in the process,ρ _j in order to achieve a jet density,V _j in order for the jet velocity to be the same,A _j is the area of the air nozzle,ρ _∞ for the density of the far-field incoming stream,U _∞ for the velocity of the far-field incoming stream,Sis the spanwise area of the synergistic jet airfoil.

As a preferred example of the present invention, in the above step SS2, the equivalent lift-to-drag ratio of the energy consumption will be considered K _C Takes the maximization of aerofoil power consumption coefficient which can be provided by an aircraft platform as an optimization targetP _C Constructing an optimization objective function for the selected optimization design variable as a constraintf(X)：

Wherein,Xin order to optimize the design variables of the design,K _C is equivalent to the lift-drag ratio, and the expression is，C _L 、C _D Respectively the lift coefficient and the resistance coefficient of the wing profile,P _C is the power consumption coefficient of the wing shape, and the expression is +.>，PIn order to cooperate with the power consumption of the jet airfoil,ρfor the density of the flow field,U _∞ for incoming flow speed, S is the span area of the wing of the cooperative jet flow, and the power consumption coefficientP _C Cannot exceed the maximum power consumption coefficient provided by the aircraft platformP _C,max . Equivalent literResistance ratioK _C Higher means better aerodynamic efficiency of the co-jet airfoil, thus equivalent lift-drag ratioK _C Maximization serves as an optimization objective. The energy consumed by the cooperative jet wing profile in operation cannot exceed the power consumption provided by the aircraft platform, so the power consumption coefficient is calculatedP _C As a constraint in the optimization of a co-jet airfoil.

Example 2 focuses on preferred examples concerning steps SS1, SS 2. Under the pneumatic design condition, the embodiment takes the air jet position, the air suction port position, the middle sinking section curve and the jet momentum coefficient as optimization design variables, takes the maximization of the equivalent lift-drag ratio as an optimization target, takes the power consumption coefficient as a constraint condition, constructs an optimization objective function, parameterizes the airfoil profile by using a CST method, and obtains the optimized design variable combination by using an EGO method. This example can effectively improve the aerodynamic efficiency and energy efficiency of the co-jet airfoil.

Example 3

On the basis of the above embodiment 1, the preferred example of the step SS3 in the CST-EGO multiparameter optimization design method of the present invention is mainly presented in this embodiment 3.

As a preferred example of the present invention, in the step SS3, when the CST parameterization method is used to parameterize the middle sink segment curve, the method at least includes the following sub-steps:

SS31 normalized by CST parameterization to adapt to the change of the length and position of the middle sinking section curve caused by the change of the positions of the air jet and the air suction port, determining the length and two end references of the middle sinking section curve according to the positions of the air jet and the air suction port, and recording the length of the air suction port in X direction relative to the air jet asζThe Y-direction height of the air inlet relative to the air nozzle is denoted as deltay _TE Actual coordinates of any given point on the intermediate dip curveNormalized representation is performed as follows:

in the method, in the process of the invention,x、yrespectively the X coordinate and the Y coordinate of the middle sinking section curve after normalization,、/>the actual coordinate positions of the air nozzles are respectively +.>Respectively the actual coordinate positions of the air inlets, and；

SS32, carrying out CST fitting on the middle sinking section curve by utilizing a mode of linear combination of a plurality of BPO polynomials, and expressing a CST fitting formula of the normalized middle sinking section curve as:

Wherein,y(x) Representing the curve of the middle sinking section at a given pointxThe height of the position is equal to the height of the position,xis an independent variable and has a value ranging from 0 to 1,nfor the order of the BPO polynomial,represent the firstiPersonal (S)nThe expression of the order BPO polynomial is thatWherein->Is the number of combinations representing the slavenFetching from different elementsiThe number of combinations of the individual elements,A _i representing BPO polynomial->Corresponding weight parameters for adjusting the respective BPO polynomials +.>Weights in forming the shape of the intermediate dip section curve,

and wherein the first and second heat sinks are disposed,fitting a class function in the formula for CST and for defining the basic shape of the middle dip curve, #>Fitting a shape function in a formula for CST and adjusting detail characteristics of the middle sinking section curve;

SS33 to ensure tangential ejection and tangential suction of the jet flow along the airfoil surface, the slope constraint is applied to the two ends of the normalized intermediate sink segment curve to make the two ends tangent to the jet port and the suction port and avoid concave surfaces, wherein the slope at any point on the normalized intermediate sink segment curvekThe expression is as follows:

the angles of the air jet and the air suction port are respectively recorded asθ ₁ Andθ ₂ the slopes of the normalized middle sinking section curves at the two ends of the air jet and the air suction port are respectively recorded as k ₁ Andk ₂ thenk ₁ Andk ₂ the respective expressions are as follows:

，

due to，ζAnd deltay _TE Is constant when given toWhen the positions of the air jet and the air suction port are determined, the weight parameters at two ends are limitedA ₀ AndA _n i.e. the range of (c) is such that the constraint on the slope of the two ends of the curve can be achieved.

Further, in the step SS3, to accurately describe the generation range of the curve shape of the middle dip segment, the CST weight parameter is setA _i Rate of change of (2)γ _i As an optimization design variable for controlling curve camber of the middle sinking section, wherein CST weight parametersA _i Rate of change of (2)γ _i The definition is as follows:

in the method, in the process of the invention,i=1,…,n+1，nthe order of the bernstein polynomial,A _i a CST weight parameter representing the change in each iteration,A _i0 and representing fitting CST weight parameters corresponding to the intermediate sinking section curve preliminarily generated when the positions of the air jet and the air suction port are changed in each iteration. In the optimization process, the positions of the air jet and the air suction port are changed within a certain interval range, and the length of the middle sinking section curve and the references at the two ends of the synergistic jet airfoil are also changed continuously, so that the CST weight parameter range for generating the middle sinking section curve is also controlled to be changed. In order to accurately describe the generation range of the shape of the middle sinking section curve, the change rate of the CST weight parameter is used as an optimal design variable for controlling the bending degree of the middle sinking section curve.

The above embodiment 3 focuses on introducing a preferred example of the relevant step SS3 in the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil, where the example adopts the CST parameterization method to parameterize the middle submerged segment curve, including sub-steps such as normalization processing, BPO polynomial linear combination fitting, two-end slope constraint, camber control, and the like, so as to adapt to the change of the positions of the air nozzle and the air suction port, ensure the tangential ejection and suction of the jet along the airfoil surface, and accurately describe the generation range of the shape of the middle submerged segment curve.

Example 4

On the basis of the above embodiment 1, the preferred example of steps SS4 and SS5 in the CST-EGO multi-parameter optimization design method of the present invention for a synergistic jet airfoil is presented in embodiment 4.

As a preferred example of the present invention, in the step SS4, when the EGO global optimization method based on the Kriging proxy model and the EI point criteria is used to search the design space for the global optimal solution, the implementation at least includes the following sub-steps:

SS41, constructing a multi-dimensional design space with numerical value boundaries based on the value ranges of all the optimal design variables, randomly selecting initial sample points which are not lower than a preset number threshold in the multi-dimensional design space by adopting a Latin hypercube sampling method with uniform distribution, and constructing an initial sample point set by adopting the initial sample points, wherein the number of the initial sample points covers the whole multi-dimensional design space to fully express the design space, each initial sample point corresponds to an optimal design variable combination consisting of a CST weight coefficient of an air nozzle position, an air suction port position and a middle sinking section curve, the change rate of the CST weight coefficient and the value of a jet momentum coefficient, and each optimal design variable combination corresponds to the geometric shape of a collaborative jet wing profile;

SS42, calculating the objective function value and the constraint condition value thereof corresponding to the aerodynamic design condition one by adopting a CFD numerical simulation method based on the geometric shape of the synergistic jet wing profile corresponding to each initial sample point and the optimization target and constraint condition, namely the equivalent lift-drag ratio and the power consumption coefficient value, taking the objective function value and the constraint condition value thereof corresponding to each initial sample point as response values, and constructing a training data set corresponding to the initial sample point set;

SS43, based on the training data set, adopting a Kriging model based on a Gaussian process as a proxy model and estimating parameters of the proxy model by using a maximum likelihood method, so that the proxy model can be maximally fitted with the aerodynamic performance function value of an initial sample point and can simultaneously give a predicted value and uncertainty, namely a predicted variance, of the aerodynamic performance function value of a cooperative jet wing profile corresponding to any sampling point in a multidimensional design space, thereby realizing approximate representation of a real aerodynamic performance function so as to facilitate subsequent optimized search;

and SS44, based on the predicted value and the predicted variance of the Kriging proxy model, calculating and evaluating the improved expected values of different candidate sample points in the multidimensional design space by adopting an EI (equivalent index) point adding rule, namely, the possibility and the improvement degree of the aerodynamic performance function value of the sample point are higher than those of the currently known optimal value, and for the candidate sample point with the maximum improved expected value, calculating the objective function value and the constraint condition value thereof corresponding to the candidate sample point under the aerodynamic design condition by using a CFD (computational fluid dynamics) numerical simulation method based on the geometric shape of the collaborative jet wing profile corresponding to the candidate sample point, thereby realizing the effective search of the global optimal solution.

As a further preferred example of the present invention, in the above sub-step SS41, the latin hypercube sampling method is implemented by uniformly dividing the multidimensional design space into M intervals along each dimension of the optimal design variable, so that the probability of each interval is the same, thereby forming m×n subspaces, where N is the number of the optimal design variables, then randomly selecting one sampling point in each subspace, so that only one sampling point in each interval in each dimension is ensured to ensure the uniform distribution and independence of the sampling points, then combining the sampling points in each subspace into M optimal design variable combinations according to an arbitrary order, each optimal design variable combination is composed of N sampling points, each sampling point corresponds to a value of the optimal design variable, and finally determining the geometric shape of the corresponding synergistic jet airfoil according to each optimal design variable combination, thereby constructing the initial sample point set. The Latin hypercube sampling method disclosed by the invention can effectively cover each area of a multidimensional design space, improve the sampling efficiency and quality and reduce the sampling quantity and time.

As a further preferred example of the present invention, in the above substep SS43, the Kriging model based on gaussian process is a non-parametric regression model, which in practice comprises at least the following substeps:

SS431 assuming a true aerodynamic performance function with a mean value of 0 and a covariance function ofRIs a random process of (1), i.eWhereinXIn order to optimize the combination of design variables,Yis a function value of aerodynamic performance->For obeying mean value 0, variance 0σ ² Is a gaussian white noise which is independent and distributed uniformly;

SS432 approximating the true aerodynamic performance function with an implementation of a Gaussian process, with a mean of a linear function and a covariance function ofRI.e.WhereinbThe coefficient vector being a linear function,F(X) The basis function vector which is a linear function,Z(X) For a mean value of 0 and a covariance function of 0RIs a gaussian random process of (a);

SS433 estimating parameters of the Gaussian process by maximum likelihood method, comprising coefficient vector b of the linear function and covariance functionRSuper parameter of (2)θI.e.WhereinYIs the vector of aerodynamic performance function values for the initial sample point,Xoptimally designing variable combination matrix for initial sample points, < >>For given purposesX、bAndθtime of dayYIs subjected to a multivariate gaussian distribution;

SS434. Calculate the predicted value and uncertainty of any sampling point using the mean and variance formulas of gaussian process, where the predicted value is the conditional expectation of gaussian process and the uncertainty is the conditional variance of gaussian process, namely:

Wherein the method comprises the steps ofr(X) For covariance vectors of any one sampling point and the initial sample point,Rfor the covariance matrix between the initial sample points,Fis a matrix of basis functions of the initial sample points.

The Kriging model disclosed by the invention can effectively utilize the information of the initial sample points to realize the approximate representation of the real pneumatic performance function so as to facilitate the subsequent optimized search.

As a further preferred example of the present invention, in the above substep SS44, the EI-point criterion comprises at least the following substeps when implemented:

SS441 defining the improvement amount as the currently known optimum valueY _min And any sampling point aerodynamic performance function valueY(X) The difference between, i.eI(X)=Y _min -Y(X)WhereinXOptimizing the combination of design variables;

SS442 assuming that the improvement obeys a Gaussian distribution with mean and variance ofAndwhereinY _min Predicted value, which is currently known as optimal value,/->And->The predicted value and the uncertainty of any sampling point are given by a Kriging proxy model;

SS443 calculating the probability that the improvement is greater than 0, i.eWherein Φ is a cumulative distribution function of a standard normal distribution;

SS444 calculating the desire for improvement, i.eWherein->Probability density function of standard normal distribution;

SS445 searching for a desired maximum of improvement in a multidimensional design space, i.e And takes this as an improvement expectation value, i.e. +.>；

SS446. Selecting the sampling point with the maximum improvement expectation value as the next addition point;

and SS447, calculating an objective function value and a constraint condition value corresponding to the cooperative jet airfoil under the pneumatic design condition by using a CFD numerical simulation method based on the geometric shape of the cooperative jet airfoil corresponding to the next adding point, thereby realizing the effective search of the global optimal solution.

As a further preferred example of the present invention, in the above step SS5, after each round of EGO global optimization, according to the objective function value and the constraint condition value corresponding to the candidate sample point with the largest improvement expected value obtained in step SS4, it is evaluated whether the optimization target meets the predetermined termination condition, if the optimization target meets or exceeds the preset target and meets the constraint condition, the optimization process is ended, and the optimized design variable combination, that is, the optimal jet position, the suction port position, the CST weight coefficient of the middle dip section curve, the change rate of the CST weight coefficient, and the jet momentum coefficient is output, and if the optimization target is not met, the step SS4 is returned, and the candidate sample point with the largest improvement expected value is added as a new sample point set and the Kriging proxy model is updated, and the optimization process is continued until the termination condition is met.

The above embodiment 4 focuses on the preferred examples of the relevant steps SS4 and SS5 in the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil, and the example adopts the EGO global optimization method based on the Kriging proxy model and the EI point adding criterion to search the global optimal solution in the multidimensional design space, which includes the substeps of constructing an initial sample point set, calculating the aerodynamic performance function value, establishing the Kriging proxy model, evaluating the improvement expected value, selecting the next adding point, and the like, so that the information of the initial sample point can be effectively utilized, and the approximate representation and the optimal search of the actual aerodynamic performance function can be realized. This example also prefers embodiments of Latin hypercube sampling methods, kriging models of Gaussian processes, and EI point-wise criteria, improving the efficiency and quality of sampling, and reducing the time and cost of computation. The example also sets an optimized termination condition, outputs an optimized design variable combination when a preset target is met or exceeded and a constraint condition is met, otherwise continues the optimization process until the termination condition is met.

Example 5

Based on the above embodiment 1, the embodiment 5 presents the implementation flow of the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil provided by the present invention in combination with the actual parameter panorama.

As shown in fig. 1 and 2, in this embodiment, the CST-EGO multi-parameter optimization design method of the synergistic jet airfoil at least includes the following steps:

SS1. The existing NACA6415 airfoil is selected as an initial airfoil, a jet orifice 1 is designed at a position 7.5 percent c away from the front edge and a suction port 2 is designed at a position 88.5 percent c away from the front edge on the upper airfoil, namely the suction surface of the airfoil, the size of the jet orifice is 0.65 percent c, the size of the suction port is 1.35 percent c, and c is the chord length of the airfoil.

And on the basis of the above-mentioned optimization design variable, the bending degree and jet momentum coefficient of the intermediate sinking section curve 3 between the air jet and air suction port can be selected according to the comprehensive aerodynamic performance of target cooperative jet airfoil under the aerodynamic design conditionC _μ And 4 design variables are taken as optimization design variables. Wherein, the jet position: 5.5% c is less than or equal to the position of the air nozzle and less than or equal to 11.5% c, and the position of the air suction port: 58.5% c.ltoreq.suction port position.ltoreq.88.5% c, jet momentum coefficient: 0.01-0.06. The aerodynamic design condition of the cooperative jet wing profile is set to be that the Mach number of the incoming gas is 0.18 and the attack angle of the gas flowαIs 2 degrees of working condition.

SS2. Determining optimization objectives and constraints: at Mach number 0.18, angle of attack of the airflow αUnder the pneumatic working condition of 2 degrees, the maximum equivalent lift-drag ratio considering energy consumption is taken as an optimization target; wing-shaped power consumption coefficient that can be provided by an aircraft platformP _C Constructing an optimized objective function as a constraint conditionf(X) The method comprises the following steps:

wherein,Xin order to optimize the design variables of the design,K _C is equivalent to the lift-drag ratio, and the expression is，C _L 、C _D Respectively the lift coefficient and the resistance coefficient of the wing profile,P _C is the power consumption coefficient of the wing shape, and the expression is +.>，PIn order to cooperate with the power consumption of the jet airfoil,ρfor the density of the flow field,U _∞ for incoming flow speed, S is the span area of the wing of the cooperative jet flow, and the power consumption coefficientP _C Cannot exceed the maximum power consumption coefficient provided by the aircraft platformP _C,max Finally, the power consumption coefficient is limited to be less than or equal to 0.0021 according to the actual situation.

And SS3, parameterizing and describing the middle sinking section curve 3 by adopting a CST parameterization method, performing CST fitting on the middle sinking section curve by adopting a mode of linear combination of a plurality of 4-order BPO polynomials, wherein a CST fitting formula for describing the middle sinking section curve is as follows:

in the method, in the process of the invention,x、yrespectively the X coordinate and the Y coordinate of the middle sinking section curve after normalization,y(x) Representing the middleAt a given point of the sinking section curvexThe height of the position is equal to the height of the position,xis an independent variable and has a value ranging from 0 to 1,nfor the order of the BPO, ζRepresenting a curve of the middle dip sectionXThe length in the direction of the vehicle is,Δy _TE the Y-direction height of the suction port relative to the air ejection port is shown.

In order to ensure that jet is ejected and sucked tangentially along the surface, slope constraint is carried out on two ends of the curve of the middle sinking section to ensure that the curve is tangential to the air jet and the air suction port, and the curve is not concave, and the slope at any point on the curve of the middle sinking section after normalizationkThe expression is as follows:

the angles of the air jet and the air suction port are respectively recorded asθ ₁ Andθ ₂ the slopes of the normalized middle sinking section curves at the two ends of the air jet and the air suction port are respectively recorded ask ₁ Andk ₂ thenk ₁ Andk ₂ the respective expressions are as follows:

，

because ofWhen the positions of the air jet and the air suction port are given,ζandΔy _TE is constant and can be obtained by defining two-end weight parametersA ₀ AndA _n the range of (3) implements a constraint on the slope of the two ends of the curve 3.

To accurately describe the generation range of the curve shape of the middle sinking section, CST weight parameters are used forA _i Rate of change of (2)γ _i As an optimization design variable for controlling curve camber of the middle sinking section, wherein CST weight parametersA _i Rate of change of (2)γ _i The definition is as follows:

in the method, in the process of the invention,i=1,…,n+1，nthe order of the bernstein polynomial,A _i a CST weight parameter representing the change in each iteration,A _i0 and representing fitting CST weight parameters corresponding to the intermediate sinking section curve preliminarily generated when the positions of the air jet and the air suction port are changed in each iteration. According to the definition of the change rate of CST weight coefficient, the setting is performed in the embodiment 。

In this embodiment, 600 sample points are randomly selected in the multidimensional design space by using a latin hypercube sampling method with uniform distribution to establish an initial sample point set, the number of the initial sample points should cover the whole multidimensional design space to fully express the design space, each initial sample point corresponds to an optimal design variable combination composed of a gas jet position, a gas suction port position, a CST weight coefficient of a middle sinking section curve, a change rate of the CST weight coefficient and a value of a jet momentum coefficient, and each optimal design variable combination corresponds to a geometric shape of a synergistic jet airfoil.

And then, calculating the objective function value and the constraint condition value thereof corresponding to the aerodynamic design condition by adopting a CFD numerical simulation method one by one based on the geometric shape of the synergic jet wing profile corresponding to each initial sample point in the initial sample point set and the optimization target and constraint condition, namely, the equivalent lift-drag ratio and the power consumption coefficient, taking the objective function value corresponding to each initial sample point and the constraint condition value thereof as response values, and constructing a training data set corresponding to the initial sample point set.

Then, a Kriging proxy model based on a Gaussian process is constructed based on the training data set, and parameters of the proxy model are estimated by using a maximum likelihood method, so that the proxy model can be fitted with the aerodynamic performance function value of an initial sample point to the maximum extent, and simultaneously, a predicted value and uncertainty, namely a predicted variance, of the aerodynamic performance function value of the collaborative jet wing profile corresponding to any one sampling point in a multidimensional design space can be given, thereby realizing approximate representation of a real aerodynamic performance function, and facilitating subsequent optimized searching.

On the basis, an optimized design variable combination is obtained through an EI point adding rule and an EGO algorithm, namely, the EI point adding rule is adopted to carry out calculation and evaluation on improved expected values of different candidate sample points in a multidimensional design space, namely, the aerodynamic performance function value of the sample point is more likely and more improved than the currently known optimal value, for the candidate sample point with the maximum improved expected value, the objective function value and constraint condition value corresponding to the candidate sample point under the aerodynamic design condition are calculated by utilizing a CFD numerical simulation method based on the geometric shape of the collaborative jet wing profile corresponding to the candidate sample point, so that the effective search of a global optimal solution is realized.

And SS5, judging whether an optimization target is met, after global optimization of each round of EGO, evaluating whether the optimization target meets a preset termination condition according to an objective function value and a constraint condition value corresponding to a candidate sample point with the maximum improvement expected value obtained in step SS4, if the optimization target meets or exceeds a preset target and meets the constraint condition, finishing the optimization process, outputting an optimized design variable combination, namely an optimal jet position, an air suction port position, a CST weight coefficient of a middle sinking section curve, a change rate of the CST weight coefficient and a jet momentum coefficient, and if the optimization target is not met, returning to step SS4, adding the candidate sample point with the maximum improvement expected value into a sample point set as a new sample point, updating a Kriging proxy model, and continuing the optimization process until the termination condition is met.

The final obtained optimized variable combinations and initial variable combinations pairs are shown in table 1. The equivalent lift-drag ratio of the synergistic jet wing profile under the initial combination is 118.5, and the equivalent lift-drag ratio of the synergistic jet wing profile under the optimized combination is 147.7, so that the synergistic jet wing profile obtained by adopting the CST-EGO multi-parameter optimization design method of the synergistic jet wing profile has better aerodynamic efficiency.

The object of the present invention is fully effectively achieved by the above-described embodiments. Those skilled in the art will appreciate that the present invention includes, but is not limited to, those illustrated in the drawings and described in the foregoing detailed description. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.

Claims

1. A CST-EGO multi-parameter optimization design method of a synergistic jet wing profile is characterized by at least comprising the following steps when in implementation:

SS1. Selecting an existing synergic jet wing profile as an initial wing profile to be optimized, wherein the initial wing profile comprises a jet orifice arranged near a front edge position, an air suction port arranged near a tail edge position and an intermediate sinking section curve positioned between the jet orifice and the air suction port on a suction surface of the initial wing profile, and selecting optimization design variables according to requirements according to the comprehensive aerodynamic performance of the target synergic jet wing profile under aerodynamic design conditions, wherein the optimization design variables at least comprise the jet orifice position, the jet orifice size, the air suction port position, the air suction port size, the intermediate sinking section curve and/or the jet momentum coefficient C _μ ；

SS2. Determining optimization objectives and constraints, the optimization objectives being determined based at least on the energy consumption and/or aerodynamic performance of the target co-jet airfoil under aerodynamic design conditions, including the lift coefficient of the airfoilC _L Coefficient of resistanceC _D Lift-drag coefficientC _L /C _D Coefficient of power consumptionP _C And/or an equivalent lift-drag coefficient taking into account energy consumptionK _C The constraint is based at least on shape and size constraints of the target co-jet airfoil under aerodynamic design conditionsDetermining an energy consumption limit and/or a pneumatic operating condition limit;

SS3 parametric description of the geometry of the middle sinking section curve by using a CST parametric method, CST fitting of the middle sinking section curve by using a linear combination mode of a plurality of BPO polynomials, description of the basic outline and detailed geometry characteristics of the middle sinking section curve by using class functions and shape functions in the CST fitting formula, and fitting of each BPO polynomial in the CST fitting formulaCorresponding weight parametersA _i Adjusting the shape of the middle sinking section curve through weight parametersA _i The curvature of the middle sinking section curve is controlled by the change rate of the middle sinking section curve, and the two ends of the middle sinking section curve are subjected to slope constraint so as to be tangent with the air jet and the air suction port, and any part of the middle sinking section curve is prevented from being in a concave state;

SS4, obtaining an optimized design variable combination by adopting an EGO global optimization method, randomly selecting initial sample points in a multi-dimensional design space formed by all the optimized design variables by using a Latin hypercube sampling method with uniform distribution, constructing an initial sample point set by using a CFD numerical simulation method based on the initial sample point set, an optimization target and constraint conditions, calculating a corresponding pneumatic performance function value of each sample point, constructing a Kriging proxy model to approximately reflect a real pneumatic performance function and give uncertainty of a predicted value, evaluating an improved expected value of each candidate sample point according to the predicted value and the uncertainty of the Kriging proxy model by using an EI adding point criterion, and calculating a corresponding objective function value and constraint condition value of the candidate sample point with the maximum improved expected value under the pneumatic design condition;

2. The method for optimizing the design of a co-jet airfoil CST-EGO parameters according to claim 1, wherein in said step SS1, said aerodynamic design conditions include at least Mach number Ma of incoming gas and angle of attack of the incoming gasαThe method comprises the steps of carrying out a first treatment on the surface of the The position of the air jet, the position of the air suction port, the curve of the middle sinking section between the air jet and the air suction port and the jet momentum coefficient are closely related to the aerodynamic performance and the energy consumption of the wing shape in the synergic jet wing shapeC _μ As an optimal design variable, the positions of the air jet ports are the coordinates of the air jet ports arranged on the suction surface of the airfoil in the X direction, namely the chord direction, and the coordinates of the air suction ports arranged on the suction surface of the airfoil in the Y direction, namely the vertical chord direction, the positions of the air suction ports are the coordinates of the air suction ports arranged on the suction surface of the airfoil in the X direction and the Y direction, the curve of the middle sinking section is the shape and the length of the curve between the air jet ports and the air suction ports, and the jet momentum coefficientC _μ For quantifying the momentum addition or reduction of jet flow to main flow, the ratio of the mass of air flow sprayed from the air nozzle to the mass of air flow sucked from the air suction port is expressed asIn which, in the process,ρ _j in order to achieve a jet density,V _j in order for the jet velocity to be the same,A _j is the area of the air nozzle,ρ _∞ for the density of the far-field incoming stream,U _∞ for the velocity of the far-field incoming stream, SIs the spanwise area of the synergistic jet airfoil.

3. The method for optimizing the design of a collaborative jet airfoil CST-EGO multi-parameter according to claim 1 or 2, wherein in the step SS2, the equivalent lift-drag ratio of energy consumption is consideredK _C Takes the maximization of aerofoil power consumption coefficient which can be provided by an aircraft platform as an optimization targetP _C Constructing, as constraints, variables for the selected optimal designIs an optimized objective function of (a)f(X)：

Wherein,Xin order to optimize the design variables of the design,K _C is equivalent to the lift-drag ratio, and the expression is C _L 、C _D Respectively the lift coefficient and the resistance coefficient of the wing profile,P _C is the power consumption coefficient of the wing shape, and the expression is +.>，PIn order to cooperate with the power consumption of the jet airfoil,ρfor the density of the flow field,U _∞ for incoming flow speed, S is the span area of the wing of the cooperative jet flow, and the power consumption coefficientP _C Cannot exceed the maximum power consumption coefficient provided by the aircraft platformP _C,max 。

4. The method for optimizing the design of the multiple parameters of the CST-EGO of the synergistic jet airfoil according to claim 1, wherein in the step SS3, when the parametric description of the middle sinking section curve is performed by adopting the CST parametric method, the method at least comprises the following sub-steps:

SS31 normalized by CST parameterization to adapt to the change of the length and position of the middle sinking section curve caused by the change of the positions of the air jet and the air suction port, determining the length and two end references of the middle sinking section curve according to the positions of the air jet and the air suction port, and recording the length of the air suction port in X direction relative to the air jet as ζThe Y-direction height of the air inlet relative to the air nozzle is denoted as deltay _TE Actual coordinates of any given point on the intermediate dip curveThe following steps are carried outA representation of:

，/>

in the method, in the process of the invention,x、yrespectively the X coordinate and the Y coordinate of the middle sinking section curve after normalization,、/>the actual coordinate positions of the air nozzles are respectively +.>、/>The actual coordinate positions of the air inlets are respectively +.>，；

the angles of the air jet and the air suction port are respectively recorded asθ ₁ Andθ ₂ the middle sinking section after normalization is curvedThe slopes of the line at both ends of the air jet and the air suction port are respectively recorded ask ₁ Andk ₂ thenk ₁ Andk ₂ the respective expressions are as follows:

，

as a result of the fact that,ζand deltay _TE At a constant value, when the positions of the air nozzle and the air suction port are given, the weight parameters at two ends are definedA ₀ AndA _n i.e. the range of (c) is such that the constraint on the slope of the two ends of the curve can be achieved.

5. The method for optimizing CST-EGO multi-parameter design of a synergistic jet airfoil as claimed in claim 4, wherein in said step SS3, CST weight parameters are used to accurately describe the generation range of the middle sink curve shapeA _i Rate of change of (2)γ _i As an optimization design variable for controlling curve camber of the middle sinking section, wherein CST weight parametersA _i Rate of change of (2)γ _i The definition is as follows:

in the method, in the process of the invention,i=1,…,n+1，nthe order of the bernstein polynomial,A _i a CST weight parameter representing the change in each iteration, A _i0 And representing fitting CST weight parameters corresponding to the intermediate sinking section curve preliminarily generated when the positions of the air jet and the air suction port are changed in each iteration.

6. The method for optimizing the design of the CST-EGO multi-parameter of the synergistic jet airfoil according to claim 1, wherein in the step SS4, when the global optimal solution is searched in the design space by adopting the EGO global optimization method based on the Kriging proxy model and the EI point adding rule, the method at least comprises the following sub-steps:

7. The method for optimizing the design of a co-jet airfoil CST-EGO parameters according to claim 6, wherein in said sub-step SS41, said latin hypercube sampling method is implemented by at least the following sub-steps:

SS411. By dividing the multidimensional design space into M intervals along each dimension of the optimal design variables uniformly, making the probability of each interval the same, thereby forming M x N subspaces, wherein N is the number of the optimal design variables;

SS412. Randomly selecting a sampling point in each subspace, so that only one sampling point exists in each interval in each dimension to ensure the uniform distribution and independence of the sampling points;

SS413, combining sampling points in each subspace into M optimal design variable combinations according to any sequence, wherein each optimal design variable combination consists of N sampling points, and each sampling point corresponds to the value of one optimal design variable;

SS414. Determining the geometry of the corresponding co-jet airfoil from each optimum design variable combination, thereby constructing an initial set of sample points.

8. The method for optimizing the design of a co-jet airfoil with multiple CST-EGO parameters according to claim 6, wherein in the substep SS43, the Kriging model based on the Gaussian process is a non-parametric regression model, which comprises at least the following substeps:

SS433 estimating parameters of the Gaussian process by maximum likelihood method, comprising coefficient vector b of the linear function and covariance functionRSuper parameter of (2)θI.e.WhereinYIs the vector of aerodynamic performance function values for the initial sample point,Xthe variable combination matrix is designed for optimization of the initial sample points,

for given purposesX、bAndθtime of dayYIs subjected to a multivariate gaussian distribution;

9. The method for optimizing the design of a co-jet airfoil CST-EGO parameters according to claim 6, wherein in said substep SS44, said EI-dotting criteria, when implemented, comprises at least the substeps of:

SS441 defining the improvement amount as the currently known optimum valueY _min And any sampling point aerodynamic performance function valueY(X) The difference between, i.eI(X)= Y _min -Y(X)WhereinXOptimizing the combination of design variables;

SS444 calculating the period of improvementInspection of the eyes, i.eWherein->Probability density function of standard normal distribution;

SS445 searching for a desired maximum of improvement in a multidimensional design space, i.eAnd takes this as an improvement expectation value, i.e. +. >；

10. The method according to claim 1, wherein in step SS5, after each round of EGO global optimization, according to the objective function value and the constraint condition value corresponding to the candidate sample point with the largest improvement expected value obtained in step SS4, whether the optimization target meets the predetermined termination condition is evaluated, if the optimization target meets or exceeds the preset target and the constraint condition is met, the optimization process is ended, and the optimized design variable combination, that is, the optimal jet position, the suction port position, the CST weight coefficient of the middle dip curve, the change rate of the CST weight coefficient, and the jet momentum coefficient is output, and if the optimization target is not met, the method returns to step SS4, and the candidate sample point with the largest improvement expected value is added as a new sample point to the sample point set and the Kriging proxy model is updated, and the optimization process is continued until the termination condition is met.