CN112329140B - Method for optimizing aerodynamics of variant aircraft based on expected improvement degree of improved position vector - Google Patents

Method for optimizing aerodynamics of variant aircraft based on expected improvement degree of improved position vector Download PDF

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CN112329140B
CN112329140B CN202011200643.2A CN202011200643A CN112329140B CN 112329140 B CN112329140 B CN 112329140B CN 202011200643 A CN202011200643 A CN 202011200643A CN 112329140 B CN112329140 B CN 112329140B
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龙腾
刘震宇
武宇飞
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a method for optimizing the aerodynamics of a variant aircraft with improved position vector expectation improvement degree, belonging to the technical field of overall optimization of aircraft. Selecting an initial reference airfoil profile and a relevant shape coefficient, and determining a design working condition; establishing an optimization model considering structural consistency constraint to solve the shape coefficient of the deformed airfoil profile, and establishing a high-precision pneumatic analysis model to solve the lift coefficient and the drag coefficient of the airfoil profile; establishing a Kriging agent model of the high-precision pneumatic analysis model, optimizing the Kriging agent model to obtain a pseudo-non-dominated solution, and judging whether the prediction variance of the Kriging agent model is larger than a threshold value or not; and if the prediction variance is not less than the threshold value, acquiring newly added sample points by adopting a position vector expected improvement degree criterion for updating the Kriging proxy model, and otherwise, screening the newly added sample points from the pseudo-non-dominant solution for updating the Kriging proxy model. The accuracy of the Kriging agent model at the front edge of Pareto is improved by screening newly added sample points, the optimality and the distributivity of the optimized non-dominated solution are improved, the optimization efficiency is improved, and the cost is saved.

Description

Method for optimizing aerodynamics of variant aircraft based on improved position vector expectation improvement degree
Technical Field
The invention relates to a method for optimizing the aerodynamics of a variant aircraft based on the improvement degree expected by an improved position vector, belonging to the technical field of overall optimization of aircraft.
Background
The traditional aircraft generally adopts a fixed aerodynamic layout, can achieve the optimal aerodynamic performance only under specific flight conditions, and has limited multitasking execution capacity. The variant aircraft can automatically change the aerodynamic shape according to different flight environments and combat missions, so that the aerodynamic performance is improved. The variable-wing aircraft in the variable-wing aircraft can adjust lift-drag ratio to adapt to different flight conditions by changing the camber or thickness of the wing profile, or the wing profile obtains different front and rear edge camber by means of the deformation of the front and rear edges of the wing profile, and the variable-wing aircraft replaces a traditional control surface to control the aircraft. An accurate and efficient wing type geometric parameterization method is a key step for developing wing type pneumatic design optimization and improving the performance of an aircraft. Considering the limitations of the internal wing support structure and the driving device on the deformation capability, the airfoil geometry parameterization method considering the structural consistency constraint needs to be customized. The Class Shape Transformation (CST) is an airfoil geometry parameterization method that describes the profile of an airfoil by using an analytic expression, generates different airfoil profiles by adjusting Shape coefficients, and can describe the structural consistency constraint by the analytic expression.
The calculation of the high-precision pneumatic analysis model of the variable-wing aircraft is extremely time-consuming, thousands of times of simulation calls are required to be carried out on the traditional multi-objective optimization algorithm to evaluate the optimization objective, and the application of the traditional multi-objective optimization algorithm in the calculation of the complex aerodynamic shape optimization design of the aircraft is limited to a great extent. The agent model constructs a prediction model through a small amount of sample point information, so that the calculation cost can be greatly reduced, and the agent model is widely applied. The Kriging agent model is an unbiased optimal estimation interpolation model with the minimum estimation variance, and the multi-objective optimization algorithm based on the Kriging agent model utilizes the predicted variance information of the Kriging agent model to effectively balance the non-dominant solution distribution and the optimality of the optimization algorithm. The method is characterized in that sequence sampling is guided by an Expected improved degree (EAPLI) criterion of a position vector, so that a Kriging agent model of an objective function is continuously updated, the distribution and the optimality of a non-dominated solution set can be balanced, the optimization process is remarkably accelerated, and the problem that the non-dominated solution is difficult to converge to a Pareto front edge when the prediction accuracy of part of the Kriging agent model of the objective function is high still exists.
In order to better explain the technical scheme of the invention, a certain introduction is made to the related mathematical basis.
Desired degree of improvement of position vector:
in multi-objective optimization, the quality of the sample points is usually considered in terms of both optimality and distribution. The optimality of a sample point can be described directly by the length of the position vector: the shorter the length of the position vector, the better the optimality of the sample points, and the distribution of the sample points can be described by the angle θ between the position vector and its closest reference vector (a series of vectors uniformly distributed in the target space): smaller angle θ indicates closer distance between the sample point and the reference vector, indicating better distribution of the sample point. An Angle-Penalized Length (APL) is defined by adopting a penalty function idea, the optimality and the distributivity of sample points can be considered, and the APL expression is as follows:
Figure BDA0002751117980000021
z in the formula (1)*Is a reference vector starting point; α is a penalty coefficient; θ represents an angle between the position vector and the reference vector V; gamma rayvIs an angle θ normalization parameter; | f (x) | is the length of the position vector. Target vector f (x) and reference vector V if non-dominated solution xjThe angle between the reference vectors is the smallest among all the reference vectors, and the non-dominant solution x and the reference vector V can be calledjAssociating, whereby the minimum value of the APL values corresponding to the non-dominant solution of the association of each reference vector can be taken as the APLrefThe expression of the Angle-constrained Length Improvement (APLI) of the reference vector V is as follows:
APLI(F,f,V,Z*,γv)＝max(APLref(F,V,Z*,γv)-APL(F,V,Z*,γv),0) (2)
in the formula (2), the reaction mixture is,
Figure BDA0002751117980000022
representing non-dominant solutions associated with reference vectors
Figure BDA0002751117980000023
The objective function value of (2).
The Kriging agent model is an unbiased optimal estimation interpolation model with minimum estimation variance, and can effectively provide the predicted value f (x) and the prediction variance s of any point2(x) .1. the The expected improvement degree of the position vector length of the sample point considering the angle constraint can be calculated, and the expression is as follows:
Figure BDA0002751117980000024
candidate points can be screened out by maximizing the EAPLI value of each sample point and serve as filling points to be used for updating the Kriging agent model.
CST method:
the CST method is an airfoil profile parameterization method for describing coordinate points of the upper surface and the lower surface of an airfoil profile, and the parameterization expression of the CST method is as follows:
Figure BDA0002751117980000025
in the formula (4), psi is an airfoil normalized x coordinate; ζ represents a unitUAnd ζLNormalized y-coordinates of the airfoil upper surface and the airfoil lower surface, respectively; ζ is Δ ζU(ψ)-ζL(ψ)，
Figure BDA0002751117980000026
And
Figure BDA0002751117980000027
the shape coefficients of the upper and lower airfoil surfaces, Ki,nN! L (i! (n-i!)), n is the polynomial order.
Disclosure of Invention
Aiming at the problems of insufficient restriction consideration of an internal structure on deformability and complex calculation of an optimization process in the aerodynamic multi-objective optimization design of a variable-wing aircraft, the invention discloses a method for the aerodynamic optimization of the variable-wing aircraft based on the expected improvement degree of an improved position vector, which aims to solve the technical problems that: the method is characterized in that the limitation of an internal wing supporting structure and a driving device on the deformation capacity of the variable wing type aircraft is described by customizing a wing type geometric parameterization method considering structural consistency constraint, the distributivity and the optimality of a non-dominated solution are balanced by a multi-objective optimization method based on the improved position vector expectation improvement degree, the efficient optimization of the variable wing type aircraft is realized, the problem of high time consumption in the optimization process of the variable wing type aircraft is solved by improving the optimization capacity and the optimization efficiency, the multi-task execution capacity of the variable wing type aircraft is improved by improving the pneumatic performance of the variable wing type aircraft under different flight conditions, the variable wing type aircraft has wide practicability and universality, and the research and development cost is further reduced.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for optimizing the aerodynamics of a variant aircraft based on the improvement degree of an improved position vector expectation, which comprises the steps of selecting an initial reference wing section and a related shape coefficient according to design requirements, and determining the design working condition; and establishing an optimization model considering structural consistency constraint so as to solve the shape coefficient of the deformed airfoil profile, and establishing a high-precision aerodynamic analysis model of the airfoil profile to solve the lift coefficient and the resistance coefficient of the airfoil profile. Establishing a Kriging agent model of the high-precision pneumatic analysis model of the wing section, optimizing the Kriging agent model to obtain a pseudo-non-dominated solution, and judging whether the prediction variance of the Kriging agent model is larger than a set threshold value or not. And if the prediction variance is not less than the threshold value, acquiring newly added sample points by adopting a position vector expected improvement degree criterion for updating the Kriging surrogate model, otherwise, screening the newly added sample points from the pseudo-non-dominated solution to update the Kriging surrogate model. The accuracy of the Kriging agent model on the Pareto frontier is improved by screening newly added sample points, the optimality and the distributivity of the optimized non-dominated solution are improved, the optimization efficiency is improved, and the calculation cost is saved. The design scheme that uses non-domination solution set as becoming wing section aircraft improves the flight performance of becoming wing section aircraft under multiple flight operating mode for become wing section aircraft has extensive practicality and commonality, reduces the design cost of aircraft.
The invention discloses a method for optimizing the aerodynamics of a variant aircraft based on the expected improvement degree of an improved position vector, which comprises the following steps:
step 1: according to the aerodynamic design requirements of the variable-wing aircraft, selecting initial reference wing profiles and structural parameters in the wing profiles, and determining the flight working conditions of the variable-wing aircraft.
The flight working conditions of the variable-wing aircraft comprise Mach number and attack angle.
Step 2: and establishing an airfoil geometric parameterization method considering structural consistency constraint to describe the limit of the internal supporting structure of the airfoil and a driving device on the deformation capacity of the variable-airfoil aircraft, solving the skin length through linear integration, solving an included angle through cosine theorem, and defining and solving the radius of a front edge through a shape coefficient to obtain an analytic expression mode of the structural consistency constraint. Based on the parameter model of the variable wing type aircraft, the aerodynamic parameters of the variable wing type aircraft are solved by using a high-precision computational fluid mechanics calculation method, so that the flight performance of the variable wing type aircraft under different flight conditions is described.
Step 2.1: determining the design variables of the optimization problem, and establishing an airfoil profile parameterization model considering the structural consistency constraint.
The wing section of the wing-type-variable aircraft is uniformly provided with n wing spars with vertical chords, and the wing spars divide skins on the upper surface and the lower surface of the wing section into (n +1) sections. In order to realize the change of the wing profile, drivers are installed on the upper surface or the lower surface by selecting adjacent partial skin sections to realize the change of the length of the skin, the skin section where the drivers are installed is called an active deformation section, and the rest skin sections are called passive deformation sections. The surface of the skin where the active deformation section is located is called an active deformation surface, and the skin where the passive deformation section is located is called a passive deformation surface. Taking into account the internal structural features of the aircraft, the structural conformance constraints during deformation include: the beam is not deformed, the included angle between the beam and the passive deformation surface is fixed, and the radius of the front edge is fixed. The method solves the skin length through line integral, solves the included angle through cosine theorem, and solves the radius of the front edge through Shape coefficient definition, so that an analytical expression mode of structural consistency constraint is obtained on the basis of a Shape Class Transformation (CST) method, and an analytical expression of the profile Shape is solved according to the Shape coefficient of a passive deformation surface, namely the variable camber profile parameterized geometric modeling considering the structural consistency constraint is realized.
The physical significance of the shape coefficient describing the airfoil is not clear enough and is difficult to be suitable for engineering practice, so that the deformation-driven variable camber airfoil parametric geometric modeling is further provided. The core of the deflection airfoil parametric geometric modeling driven by the deflection is that the shape coefficient of the passive deformation surface of the deformed airfoil is optimized, so that the difference between the deflection of the active deformation surface and the expected deflection is minimized on the premise that the deformed airfoil meets the structural consistency constraint, and the optimization model is shown as the formula (1). And solving the optimization problem in the formula (1) by adopting an optimization method to obtain the airfoil shape coefficient under the given active deformation section length.
Figure BDA0002751117980000041
In the formula (1), P represents a shape coefficient of an airfoil; the superscript p represents the airfoil before deformation, and c represents the airfoil after deformation; subscript P represents the airfoil passive deformation surface, a represents the airfoil active deformation surface; m is the number of the deformation sections of the active deformation surface,
Figure BDA0002751117980000042
and
Figure BDA0002751117980000043
desired and actual deformation, c, of the k-th deformation segment, respectivelypIs the chord length of the front wing of the deformation, LPIn order to be the length of the passive deformation surface,
Figure BDA0002751117980000044
and
Figure BDA0002751117980000045
normalized spar height, beta, of the pre-deformation and post-deformation airfoils, respectivelyjIs the included angle between the wing profile passive deformation surface and the wing beam.
Step 2.2: and (3) establishing a high-precision pneumatic analysis model of the wing profile based on the parameterized model of the wing profile obtained in the step (2.1), and solving the pneumatic parameters of the wing-variable profile aircraft to describe the pneumatic performance of the wing-variable profile aircraft.
Describing the profile of the airfoil profile by using a CST method based on the shape coefficient; a structured dynamic grid of airfoils is generated. In order to ensure sufficient calculation accuracy, the grid density is increased near the airfoil and at the front and rear edges, and the orthogonality and the aspect ratio of the grid are ensured. And (3) adopting a Computational Fluid Dynamics (CFD) solver to complete the aerodynamic analysis of the airfoil, and solving the lift coefficient and the drag coefficient of the airfoil to describe the aerodynamic performance of the variable airfoil type aircraft.
And 3, step 3: generating a sample point set Y in a design space by using a test design method, wherein the number of sample points in the sample point set Y and an optimization design variable dimension nvAnd (4) correlating. And generating a series of uniformly distributed reference vectors in a target space by using a simplex lattice point design method, wherein the number of the reference vectors is related to the number of the target functions.
Preferably, the number of initial sample point sets Y is 11nv-1。
And 4, step 4: calling the high-precision pneumatic analysis model of the airfoil profile in the step 2, obtaining a model response value at the sample point in the step 3, representing the model response value at the sample point x by using an objective function f (x), and storing sample point information.
And 5: and constructing or updating a Kriging agent model in the design space based on the sample point information of the step 4. The response value of the Kriging agent model at the sample point x is represented by the predicted objective function value f (x) of the Kriging agent model, and s is used2(x) Representing the prediction variance at sample point x.
And 6: a multi-objective optimization method is used for exploring a pseudo non-dominated solution of the current proxy model. And calculating an ideal point according to the pseudo non-dominated solution, wherein the ideal point is the starting point of the reference vector in the step 3. And screening out a non-dominant solution set according to the dominant relationship of the model response values of the sample point set Y.
And 7: the termination condition is checked. When the iteration times k reach the maximum iteration times, terminating the iteration, and obtaining and outputting a pneumatic optimization scheme of the variable-wing aircraft; otherwise step 8 is performed.
And 8: judging the predicted variance s of the Kriging agent model2(x) When the predicted variance s of any Kriging agent model2(x) When the value is not less than the preset threshold value, executing step 9; otherwise step 10 is performed.
And step 9: the sample points are filtered using the position vector expected improvement criterion to update the proxy model, and then step 4 is performed.
The specific implementation method of the step 9 is as follows:
step 9.1: calculating the Angle constraint Length (APL) value of each non-dominated solution obtained in the step 6, wherein the expression is as follows:
Figure BDA0002751117980000051
in the formula Z*Is a reference vector starting point; α is a penalty factor, taken as 0.05 in this study; θ represents an angle between the position vector and the reference vector V; gamma rayvIs an angle θ normalization parameter; | f (x) | is the length of the position vector. Target vector f (x) and reference vector V if non-dominated solution xjThe angle between the reference vectors is the smallest among all the reference vectors, and the non-dominant solution x and the reference vector V can be calledjAssociating, whereby the minimum value of the APL values corresponding to the non-dominant solution of the association of each reference vector can be taken as the APLrefThe expression of the Angle-constrained Length Improvement (APLI) of the reference vector V is as follows:
APLI(F,f,V,Z*,γv)＝max(APLref(F,V,Z*,γv)-APL(F,V,Z*,γv),0) (3)
in the formula (I), the compound is shown in the specification,
Figure BDA0002751117980000052
representing non-dominant solutions associated with reference vectors
Figure BDA0002751117980000053
The objective function value of (1). Calculating the expected improvement degree of the position vector length of the sample point considering the angle constraint, wherein the expression is as follows:
Figure BDA0002751117980000054
the Particle Swarm Optimization (PSO) is adopted to maximize the EAPLI value of each reference vector to screen out N candidate points.
Step 9.2: calculating a goodness base (nc) of each candidate point so as to calculate the fitness (fitness) of each candidate point, wherein the fitness calculation formula is as follows:
Figure BDA0002751117980000061
in the formula
Figure BDA0002751117980000062
Is a reference vector ViNumber of associated non-dominant solutions, θi,jRepresents a reference vector ViAnd a reference vector VjAngle between them, thetaj,minRepresenting all non-zero thetai,jMinimum value of (1). Dividing N candidate points into N by using a k-means methodaddAnd (5) classifying, selecting the candidate point with the maximum fitness from each class of candidate points as a newly added sample point, and executing the update agent model in the step (4) based on the newly added sample point.
Step 10: and screening sample points from the pseudo non-dominant solution to update a Kriging agent model, and balancing the distribution and the optimality of the non-dominant solution to improve the optimizing capability of the position vector expectation improvement criterion. Step 4 is performed.
The specific implementation of step 10 is as follows:
calculating the APL value of each non-dominant solution obtained in the step 6 according to the formula (2), and calculating the APL of each reference vector according to the incidence relation between the non-dominant solution and the reference vectorrefThe value is obtained. Calculating APLI values for each pseudo-non-dominated solution according to equation (3), maximizing each reference vectorAnd screening N candidate points from the pseudo-non-dominated solution. And (5) calculating the advantage base number of each candidate point according to the formula (5), thereby calculating the pseudo fitness of the candidate points as shown in the formula (6).
Figure BDA0002751117980000063
Dividing N candidate points into N according to a k-means methodaddAnd class, screening out the candidate point with the maximum pseudo-fitness from each class of candidate points as a newly added sample point, and executing the update agent model in the step 4 based on the newly added sample point.
Step 11: and (4) outputting the deformation schemes of the variable-wing aircraft under different flight working conditions by utilizing the step (7), improving the pneumatic performance of the variable-wing aircraft under different flight conditions, and improving the multi-task execution capacity of the variable-wing aircraft, so that the variable-wing aircraft has practicability and universality, and further, the research and development cost is reduced.
Has the beneficial effects that:
1. the invention discloses a pneumatic optimization method of a morphing aircraft based on an improved position vector expectation improvement degree, which is based on a CST method, establishes a morphing profile model considering structural consistency constraint, uses an optimization method to realize the corresponding relation between the length of an active morphing surface of a profile and the shape coefficient of the profile, and further meets the requirement of engineering realization. The aerodynamic performance of the wing-variable type aircraft under different flight conditions is improved, the multi-task execution capacity of the aircraft is improved, and the research and development cost is further reduced.
2. The invention discloses a variant aircraft pneumatic optimization method based on improved position vector expectation improvement degree, which overcomes the defect that a non-dominated solution is difficult to converge to a Pareto front edge when the Kriging agent model prediction variance is small by improving the position vector expectation improvement degree criterion, shortens the optimization period, improves the optimality and the distributivity of the non-dominated solution set by introducing a pseudo non-dominated solution to update the agent model, improves the optimization capability of the position vector expectation improvement degree criterion, solves the problem of high time consumption in the optimization process of a variable wing aircraft, and realizes the efficient optimization of the variable wing aircraft.
3. According to the method for optimizing the aerodynamic performance of the variant aircraft based on the improved position vector expectation improvement degree, the adopted position vector expectation improvement degree criterion can effectively explore a target space, balance the distribution and the optimality of a non-dominant solution, and screen out a plurality of newly added sample points in one-time iterative calculation, so that the iteration times can be obviously reduced, and the optimization process is accelerated.
Drawings
FIG. 1 is a flow chart of a method for aerodynamic optimization of a variable-wing aircraft based on an expected improvement degree of an improved position vector.
FIG. 2 is a schematic diagram of parametric modeling of an airfoil before and after deformation in consideration of structural consistency.
Detailed Description
In order to better illustrate the technical solutions and advantages of the present invention, the present invention is further described below by using a specific aerodynamic multi-objective optimization design example of a variable wing aircraft with a desired improvement degree of an improved position vector and by combining a table, and the specific embodiments are as follows.
As shown in fig. 1, the embodiment of the method for designing a multi-objective aerodynamic optimization of a variable-airfoil aircraft with an improved position vector expectation improvement degree disclosed in the present embodiment divides the optimization into two stages, and specifically includes the following implementation steps:
the first stage is as follows: optimizing the shape coefficient of the airfoil profile to ensure that the drag coefficient of the airfoil profile is minimum and the lift coefficient is maximum.
Step 1: the laminar flow airfoil NACA64A816 is selected as a reference initial airfoil, the design working condition is a low-speed cruise working condition, namely the flight Mach number Ma is 0.64, and the attack angle alpha is 2 degrees.
Step 2: and establishing an airfoil optimization model according to the requirements.
Step 2.1: establishing a parameterized model of the airfoil profile by taking the shape coefficient of the airfoil profile as a design variable
Using shape factor of airfoil as design variable, i.e. nvEqual to 12, the mathematical model of the optimization problem is as follows:
Figure BDA0002751117980000071
in the formula, AiAnd PiIs the shape factor, x, of the airfoil0Is an initial value of the airfoil shape coefficient, x0Is shown in Table 1, Dlow-cruiseThe resistance coefficient of the airfoil profile under the working condition of low-speed cruising, Llow-cruiseThe lift coefficient is under the working condition of low-speed cruising.
TABLE 1 NACA64A816 airfoil shape factor
Figure BDA0002751117980000072
Step 2.2: and establishing a high-precision pneumatic analysis model of the wing profile based on the parameterized model of the wing profile.
And generating the C-H type structured pneumatic grid by using Gambit. In order to ensure enough calculation accuracy, the grid density is increased near the airfoil and at the front edge and the rear edge, the orthogonality and the aspect ratio of the grids are ensured, and 50000 grids are formed. And (3) adopting Fluent software as a CFD solver to complete aerodynamic analysis of the airfoil profile, selecting an N-S equation as a main control equation for flow field numerical calculation, and setting 300 times of iterative calculation to solve the lift coefficient and the resistance coefficient of the airfoil profile.
And step 3: a set of sample points Y, the number of which is 131, is generated within the design space using a trial design method. A simplex lattice point design method is used for generating a series of uniformly distributed reference vectors in a target space, the number of the reference vectors is related to the number of target functions, the number of the target functions is 2, and the number of the reference vectors is 100.
And 4, step 4: calling the high-precision pneumatic analysis model of the airfoil profile in the step 2, obtaining a model response value of the sample point in the step 3, expressing the model response value of the sample point x by f (x), and storing sample point information.
And 5: and constructing or updating a Kriging agent model in the design space based on the sample point information of the step 4. Denote the Kriging surrogate model response value at sample point x by f (x), s2(x) Representing the prediction variance at sample point x.
And 6: the pseudo-non-dominated solution of the current proxy model was explored using the NSGA-II optimization algorithm, with population size and evolution generations of 500 and 100 for NSGA-II, respectively, cross probability and parameters set to 0.9 and 20, respectively, and mutation probability and parameters set to 1/12 and 20, respectively. And calculating an ideal point according to the pseudo non-dominated solution, wherein the ideal point is the starting point of the reference vector in the step 3. And screening out a non-dominant solution set according to the dominant relationship of the model response values of the sample point set Y.
And 7: the algorithm termination condition is checked. When the iteration number k reaches the maximum iteration number 40, the algorithm is terminated; otherwise, step 8 is executed.
And 8: judging the predicted variance s of the Kriging agent model2(x) When the predicted variance s of any Kriging agent model2(x) When the value is not less than the preset threshold value of 0.0001, executing the step 9; otherwise step 10 is performed.
And step 9: calculating the APL value of each non-dominant solution obtained in the step 6, and calculating the APL of each reference vector according to the incidence relation between the non-dominant solution and the reference vectorrefThe value is obtained. And screening 100 candidate points by adopting the EAPLI value of each PSO maximized reference vector, and respectively setting the population scale and the maximum algebra of the PSO algorithm to be 150 and 100. Calculating the fitness of each candidate point, dividing 100 candidate points into 5 classes by using a k-means method, selecting the candidate point with the maximum fitness from each class of candidate points as a newly added sample point, and re-executing the update agent model in the step 4 based on the newly added sample point.
Step 10: calculating the APL value of each non-dominant solution obtained in the step 6, and calculating the APL of each reference vector according to the incidence relation between the non-dominant solution and the reference vectorrefThe value is obtained. And calculating an APLI value of each pseudo-non-dominated solution, maximizing the APLI value of each reference vector, and screening N candidate points from the pseudo-non-dominated solution. And calculating the pseudo-fitness of the candidate points. And (4) dividing 100 candidate points into 5 classes by using a k-means method, screening the candidate point with the maximum pseudo-fitness from each class of candidate points to serve as a newly added sample point, and re-executing the update agent model in the step 4 based on the newly added sample point.
And (3) optimizing in the second stage: the length of the active deformation surface of the wing profile is optimized, and the optimal lift-drag ratio of the deformed wing profile under different working conditions is obtained.
Step 1: the optimized wing profile in the first stage is selected as a reference initial wing profile, and the design working conditions are a cruise working condition (Ma is 0.4, alpha is 4 degrees) and a high-speed cruise working condition (Ma is 0.8, alpha is 1 degree).
Step 2: and establishing an airfoil optimization model according to the requirements.
Step 2.1: establishing a parameterized model of the airfoil profile by taking the length of the active deformation surface of the airfoil profile as a design variable
And (3) taking the optimized airfoil profile in the first stage as a reference, arranging beams vertical to the chord length at 20%, 30%, 50%, 70% and 90% of the chord length, and dividing the upper surface skin and the lower surface skin of the airfoil profile into 6 sections respectively. The airfoil lower surface is the initiative face that warp, and the upper surface is the passive face that warp to arrange the actuator at the 3 rd, 4 th and 5 th section covers of initiative face that warp and realize initiative and warp, the mathematical model of optimization problem is as follows:
Figure BDA0002751117980000091
in the formula, psi is the length of the actuator after deformation under different working conditions, and a variable n is designedvEqual to 6; (L/D)loiterFor the airfoil lift-drag ratio under the working condition of flying patrol, (L/D)high-cruiseIs lift-drag ratio psi under high-speed cruising condition(ref)The actuator length being an undeformed airfoil.
Step 2.2: and establishing a high-precision pneumatic analysis model of the wing profile based on the parameterized model of the wing profile.
And generating the C-H type structured pneumatic grid by using Gambit. In order to ensure enough calculation accuracy, the grid density is increased near the airfoil and at the front edge and the rear edge, the orthogonality and the aspect ratio of the grids are ensured, and 50000 grids are formed. And (3) adopting Fluent software as a CFD solver to complete aerodynamic analysis of the airfoil profile, selecting an N-S equation as a main control equation for flow field numerical calculation, and setting 300 times of iterative calculation to solve the lift coefficient and the drag coefficient of the airfoil profile.
And step 3: a set of sample points Y is generated in the design space using a trial design method, the number of sample points being 65. A simplex lattice point design method is used for generating a series of uniformly distributed reference vectors in a target space, the number of the reference vectors is related to the number of target functions, the number of the target functions is 2, and the number of the reference vectors is 100.
And 4, step 4: calling the high-precision pneumatic analysis model of the airfoil profile in the step 2, obtaining a model response value of the sample point in the step 3, expressing the model response value of the sample point x by f (x), and storing sample point information.
And 5: and constructing or updating a Kriging agent model in the design space based on the sample point information of the step 4. The Kriging surrogate model response value at sample point x is represented by f (x), and s2(x) Representing the prediction variance at sample point x.
And 6: the pseudo-non-dominant solution of the current proxy model was explored using the NSGA-II optimization algorithm, with population size and evolution algebra of 500 and 100 for NSGA-II, respectively, cross probability and parameters set to 0.9 and 20, respectively, and mutation probability and parameters set to 1/12 and 20, respectively. And calculating an ideal point according to the pseudo non-dominated solution, wherein the ideal point is the starting point of the reference vector in the step 3. And screening out a non-dominant solution set according to the dominant relationship of the model response values of the sample point set Y.
And 7: the algorithm termination condition is checked. When the iteration number k reaches the maximum iteration number 40, the algorithm is terminated; otherwise step 8 is performed.
And step 8: judging the prediction variance s of the Kriging agent model2(x) When the predicted variance s of any Kriging agent model2(x) When the value is not less than the preset threshold value of 0.0001, executing the step 9; otherwise step 10 is performed.
And step 9: calculating the APL value of each non-dominated solution obtained in the step 6, and calculating the APL of each reference vector according to the incidence relation between the non-dominated solution and the reference vectorrefThe value is obtained. And screening 100 candidate points by adopting the EAPLI value of each PSO maximized reference vector, and respectively setting the population scale and the maximum algebra of the PSO algorithm to be 150 and 100. Calculating the fitness of each candidate point, dividing 100 candidate points into 5 classes by using a k-means method, selecting the candidate point with the maximum fitness from each class of candidate points as a newly added sample point, and selecting the candidate point with the maximum fitness based on the newly added sample pointThe sample point re-executes the update proxy model in step 4.
Step 10: calculating the APL value of each non-dominant solution obtained in the step 6, and calculating the APL of each reference vector according to the incidence relation between the non-dominant solution and the reference vectorrefThe value is obtained. And calculating an APLI value of each pseudo-non-dominated solution, maximizing the APLI value of each reference vector, and screening N candidate points from the pseudo-non-dominated solution. And calculating the pseudo-fitness of the candidate points. And (4) dividing 100 candidate points into 5 classes by using a k-means method, screening the candidate point with the maximum pseudo-fitness from each class of candidate points to serve as a newly added sample point, and re-executing the update agent model in the step (4) based on the newly added sample point.
The optimization results in the first stage are shown in table 2, and the optimization results in the second stage are shown in table 3.
TABLE 2 airfoil parameters before and after first stage optimization
Figure BDA0002751117980000101
The airfoil with the minimum resistance coefficient has the maximum lift-drag ratio, the airfoil with the minimum resistance coefficient is selected as the optimized airfoil in the first stage, the lift coefficient of the airfoil under the working condition of low-speed cruising is 1.0483, the resistance coefficient is 0.0169, and the lift-drag ratio is 62.0296; compared with the optimized front wing type, the lift coefficient is improved by 18.56%, the resistance coefficient is reduced by 44.59%, and the lift-drag ratio is improved by 113%.
TABLE 3 second stage optimization of fore and aft airfoil parameters
Figure BDA0002751117980000102
The lift-drag ratio of the optimal deformed airfoil profile under the cruise working condition is improved by 10.11 percent, and the lift-drag ratio of the optimal deformed airfoil profile under the high-speed cruise working condition is improved by 75.75 percent. The wing profile with the lift-to-drag ratio closest to the average value of the obtained non-dominant solution under the two working conditions is selected as the deformed wing profile, the lift-to-drag ratio of the deformed wing profile under the cruise working conditions is improved by 9.95% compared with that of the deformed wing profile under the deformation working conditions, and the lift-to-drag ratio of the deformed wing profile under the high-speed cruise working conditions is improved by 67.20% compared with that of the deformed wing profile under the deformation working conditions.
In order to better illustrate the advantage of the desired degree of improvement criterion for improving the position vector, 7 numerical test problems are further selected for optimization. Numerical test problems include LZ 08-F1-LZ 08-F4 and ZDT1-ZDT 3. For the above 7 test problems, the algorithm efficiency was measured by comparing the size of the near-optimal solution obtained at the end of the iteration. To eliminate the influence of accidental factors, each algorithm is continuously optimized for each test problem for 10 times. The mathematical model of each test example is shown in table 4.
Table 4 test examples
Figure BDA0002751117980000111
Figure BDA0002751117980000121
The optimality and diversity of a non-dominated solution is described using the Inverse Generational Distance (IGD) of the non-dominated solution, the expression of IGD is:
Figure BDA0002751117980000122
in the formula, P is a preset theoretical Pareto non-inferior solution set and is uniformly distributed on a Pareto front edge; p is a non-dominant solution set, and d (P, P) represents the minimum value of the euclidean distance from the point P to any point in P.
In the optimization process, the number of initial sample points is set to 65(11 n)v-1) adding a new number n of filling points per iteration add5, the maximum number of filling points is 200; the population scale and the evolution algebra of the NSGA-II are respectively 500 and 100, the cross probability and the parameter are respectively set to be 0.9 and 20, and the mutation probability and the parameter are respectively set to be 1/n and 20; the population size and maximum algebra of the PSO algorithm are set to 150 and 100, respectively. The optimization results are shown in table 5.
As shown in Table 5, for test problems LZ08-F1, LZ08-F3, and LZ08-F4, the improved EAPLI criterion is comparable to the result obtained by the EAPLI criterion, with IGD values that differ by no more than an order of magnitude. For the test problem LZ08-F2, under the condition of the current given maximum model calling times, the non-dominant solution of the EAPLI criterion and the non-dominant solution of the improved EAPLI criterion do not converge to a theoretical Pareto frontier, which shows that the convergence of the multi-objective optimization method based on the EAPLI criterion is to be further improved. For the test problems ZDT1-ZDT3, as can be seen from Table 5, the optimality and the distributivity of the non-dominated solution obtained by improving the EAPLI criterion are obviously better than those of the EAPLI criterion, because the Kriging agent model has high prediction precision on the target functions of the test problems ZDT1-ZDT3, and the improvement strategy fully utilizes the model information provided by the Kriging agent model.
TABLE 5 optimization results of standard test examples
Figure BDA0002751117980000123
Note: the bold represents that the index result is optimal
As can be seen from the comparison, the improvement of the EAPLI criterion can improve the optimality and the distribution of the non-dominant solution as a whole without increasing the calculation amount compared with the EAPLI criterion. The invention establishes a variable wing profile model considering structural consistency constraint based on a CST method, realizes the corresponding relation between the length of the active deformation surface of the wing profile and the shape coefficient of the wing profile by using an optimization idea, and further meets the requirement of engineering realization.
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 and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. The method for optimizing the aerodynamics of the wing-variable type aircraft by improving the expected improvement degree of the position vector is characterized in that: comprises the following steps of (a) preparing a solution,
step 1: according to the aerodynamic design requirements of the variable-wing aircraft, selecting initial reference wing profiles and structural parameters in the wing profiles, and determining the flight working conditions of the variable-wing aircraft;
the flight working conditions of the variable-wing aircraft comprise Mach number and an attack angle;
and 2, step: establishing an airfoil geometric parameterization method considering structural consistency constraint to describe the limitation of an internal wing supporting structure and a driving device on the deformation capacity of the variable-airfoil aircraft, solving the skin length through linear integration, solving an included angle through cosine theorem, and solving a leading edge radius through shape coefficient definition to obtain an analytic expression mode of the structural consistency constraint; based on a parameter model of the variable wing type aircraft, solving aerodynamic parameters of the variable wing type aircraft by using a high-precision computational fluid mechanics calculation method, thereby describing the flight performance of the variable wing type aircraft under different flight conditions;
and 3, step 3: generating a sample point set Y in a design space by using a test design method, wherein the number of sample points in the sample point set Y and an optimization design variable dimension nvCorrelation; generating a series of uniformly distributed reference vectors in a target space by using a simplex lattice point design method, wherein the number of the reference vectors is related to the number of target functions;
and 4, step 4: calling the high-precision pneumatic analysis model of the airfoil profile in the step 2, obtaining a model response value at the sample point in the step 3, representing the model response value at the sample point x by using a target function f (x), and storing sample point information;
and 5: constructing or updating a Kriging agent model in a design space based on the sample point information in the step 4; predicting objective function values using Kriging surrogate model
Figure FDA0003581582550000012
Representing the Kriging surrogate model response value at sample point x, in s2(x) Represents the predicted variance at sample point x;
and 6: exploring a pseudo non-dominated solution of the current agent model by using a multi-objective optimization method; calculating an ideal point according to the pseudo non-dominated solution, wherein the ideal point is the starting point of the reference vector in the step 3; screening out a non-dominant solution set according to the dominant relationship of the model response value of the sample point set Y;
and 7: checking a termination condition; when the iteration times k reach the maximum iteration times, terminating the iteration, and obtaining and outputting a variable wing type aircraft pneumatic optimization scheme; otherwise, executing step 8;
and step 8: judging the prediction variance s of the Kriging agent model2(x) When the predicted variance s of any Kriging agent model2(x) When the value is not less than the preset threshold value, executing the step 9; otherwise, executing step 10;
and step 9: screening sample points by using a position vector expected improvement degree criterion to update the proxy model, and then executing a step 4;
the specific implementation method of step 9 is as follows,
step 9.1: calculating the Angle constraint Length (APL) value of each non-dominated solution obtained in the step 6, and expressing the value as follows:
Figure FDA0003581582550000011
in the formula Z*Is the reference vector starting point; α is a penalty coefficient; θ represents an angle between the position vector and the reference vector V; gamma rayvIs an angle θ normalization parameter; | f (x) | is the length of the position vector; target vector f (x) and reference vector V if non-dominated solution xjThe angle between the reference vectors is the smallest among all the reference vectors, and the non-dominant solution x and the reference vector V can be calledjCorrelating, whereby the minimum value of APL values corresponding to the non-dominated solution of the correlation for each reference vector is taken as APLrefThe expression of the Angle-constrained position vector length improvement (APLI) of the reference vector V is as follows:
APLI(F,f,V,Z*,γv)＝max(APLref(F,V,Z*,γv)-APL(F,V,Z*,γv),0) (3)
in the formula (I), the compound is shown in the specification,
Figure FDA0003581582550000021
representing non-dominant solutions associated with reference vectors
Figure FDA0003581582550000022
The objective function value of (a); calculating the expected improvement degree of the position vector length of the sample point considering the angle constraint, wherein the expression is as follows:
Figure FDA0003581582550000023
screening N candidate points by maximizing EAPLI values of all reference vectors by adopting a Particle Swarm Optimization (PSO);
step 9.2: calculating a goodness base (nc) of each candidate point so as to calculate the fitness (fitness) of each candidate point, wherein the fitness calculation formula is as follows:
Figure FDA0003581582550000024
in the formula
Figure FDA0003581582550000025
Is a reference vector ViNumber of associated non-dominant solutions, θi,jRepresenting a reference vector ViAnd a reference vector VjAngle between them, thetaj,minRepresenting all non-zero thetai,jMinimum value of (1); dividing N candidate points into N by using a k-means methodaddSelecting a candidate point with the maximum fitness from each type of candidate points as a newly added sample point, and executing the update agent model in the step 4 based on the newly added sample point;
step 10: screening sample points from the pseudo non-dominant solution to update a Kriging agent model, and balancing the distribution and the optimality of the non-dominant solution to improve the optimizing capability of a position vector expectation improvement degree criterion; executing the step 4;
the method of implementing step 10 is as follows,
calculating the result of step 6 according to formula (2)The APL value of each non-dominant solution is calculated, and the APL of each reference vector is calculated according to the incidence relation between the non-dominant solution and the reference vectorrefA value; calculating an APLI value of each pseudo-non-dominated solution according to the formula (3), maximizing the APLI value of each reference vector, and screening N candidate points from the pseudo-non-dominated solution; calculating the profit base number of each candidate point according to the formula (5), thereby calculating the pseudo fitness of the candidate points, wherein the pseudo fitness is shown as the formula;
Figure FDA0003581582550000026
dividing N candidate points into N according to a k-means methodaddAnd class, screening out the candidate point with the maximum pseudo-fitness from each class of candidate points as a newly added sample point, and executing the update agent model in the step 4 based on the newly added sample point.
2. The method of aerodynamic optimization of a variable airfoil aircraft for improving the degree of improvement desired in a position vector as claimed in claim 1, wherein: the method also comprises a step 11 of outputting the deformation schemes of the variable wing type aircraft in the step 7 under different flight conditions, improving the pneumatic performance of the variable wing type aircraft under different flight conditions, and improving the multi-task execution capacity of the variable wing type aircraft, so that the variable wing type aircraft has practicability and universality, and further the research and development cost is reduced.
3. The method for aerodynamic optimization of a wing-shaped aircraft for the improvement of the desired degree of improvement of a position vector according to claim 1 or 2, characterized in that: the implementation method of the step 2 is that,
step 2.1: determining design variables of an optimization problem, and establishing an airfoil profile parameterization model considering structural consistency constraint;
n wing spars with vertical chords are uniformly arranged in the wing profile of the variable wing profile aircraft, and the wing spars divide skins on the upper surface and the lower surface of the wing profile into (n +1) sections; in order to realize the change of the wing profile, adjacent partial skin sections are selected on the upper surface or the lower surface to be provided with drivers so as to realize the change of the length of the skin, the skin section provided with the drivers is called an active deformation section, and the rest skin sections are called passive deformation sections; the surface of the skin where the active deformation section is located is called an active deformation surface, and the skin where the passive deformation section is located is called a passive deformation surface; considering the aircraft interior structural features, the structural conformance constraints during deformation include: the beam is not deformed, the included angle between the beam and the passive deformation surface is fixed, and the radius of the front edge is fixed; solving the skin length through linear integration, solving the included angle through cosine theorem and solving the radius of the front edge through shape coefficient definition, thereby obtaining an analytic expression mode of structural consistency constraint on the basis of a shape classification conversion method CST, solving an analytic expression of the airfoil shape according to the shape coefficient of the passive deformation surface, and realizing variable camber airfoil parametric geometric modeling considering the structural consistency constraint;
because the physical meaning of describing the shape coefficient of the airfoil is not clear enough and is difficult to be applied to engineering practice, the variable camber airfoil parametric geometric modeling driven by the deformation is further provided; the core of the deflection airfoil parametric geometric modeling driven by the deflection is that the shape coefficient of a passive deformation surface of a deformed airfoil is optimized, so that the difference between the deflection of an active deformation surface and the expected deflection is minimized on the premise that the deformed airfoil meets the structural consistency constraint;
step 2.2: establishing a high-precision pneumatic analysis model of the wing profile based on the parameterized model of the wing profile obtained in the step 2.1, and solving the pneumatic parameters of the wing-variable profile aircraft to describe the pneumatic performance of the wing-variable profile aircraft;
describing the profile of the airfoil profile by using a CST method based on the shape coefficient; generating a structural dynamic grid of the airfoil profile; in order to ensure enough calculation accuracy, the grid density is increased near the wing profile and at the front edge and the rear edge, and the orthogonality and the length-width ratio of the grid are ensured; and (3) adopting a Computational Fluid Dynamics (CFD) solver to complete aerodynamic analysis of the wing profile, and solving a lift coefficient and a drag coefficient of the wing profile to describe the aerodynamic performance of the wing-variable aircraft.
4. The method of aerodynamic optimization of a wing-shaped aircraft for the improvement of the desired degree of improvement of a position vector according to claim 1, characterized in that: the number of initial sample point sets Y is 11nv-1。
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