CN113657029A - Efficient approximate optimization method for aircraft driven by heterogeneous data - Google Patents

Efficient approximate optimization method for aircraft driven by heterogeneous data Download PDF

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CN113657029A
CN113657029A CN202110912712.0A CN202110912712A CN113657029A CN 113657029 A CN113657029 A CN 113657029A CN 202110912712 A CN202110912712 A CN 202110912712A CN 113657029 A CN113657029 A CN 113657029A
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龙腾
毛能峰
史人赫
武宇飞
王若冰
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a high-efficiency approximate optimization method of an aircraft driven by heterogeneous data, belonging to the technical field of aircraft engineering optimization. The method adopts a fuzzy clustering point selection strategy based on distance identification to select high-quality local high/low precision sample points with better feasibility and optimality from an alternative sample point set, and guides the optimization process to quickly converge towards a globally feasible optimal point; a Co-kriging agent model of an aircraft system analysis model is constructed through selected high/low precision sample points, multi-source simulation analysis models with different precisions in a project are fully utilized, precision-preserving quick response prediction of a complex aircraft engineering system is achieved, solving efficiency and robustness of aircraft system optimization problems related to high-time-consuming analysis models are improved, and performance of the complex aircraft system is improved. The method is suitable for the field of aircraft complex engineering system optimization including high-precision analysis models, and solves the corresponding relevant engineering problems.

Description

Efficient approximate optimization method for aircraft driven by heterogeneous data
Technical Field
The invention relates to a high-efficiency approximate optimization method for an aircraft driven by heterogeneous data, and belongs to the technical field of aircraft engineering optimization.
Background
With the development of discipline modeling technology, numerical computation technology and computer software and hardware, high-precision Analysis models are increasingly applied to engineering practice of aircraft optimization, such as Computational Fluid Dynamics (CFD) models of the pneumatic discipline, Finite Element Analysis (FEA) models of the structural discipline, and the like. The application of the high-precision analysis model can improve the reliability of results and the quality of the aircraft, but also increases the calculation cost. In addition, the high-precision analysis model is repeatedly called to find the optimal scheme in the optimization process of the aircraft, so that the calculation complexity is further increased. In order to alleviate the above problems, an Optimization method (metal-based Design and Optimization, MBDO) based on a proxy model is studied in depth, aiming at guiding the Optimization process to quickly converge to an optimal solution by constructing a reasonable approximate model, thereby reducing the calculation cost and shortening the Design period. The optimization method based on the dynamic proxy model (also called adaptive MBDO method) can effectively improve the optimization efficiency and the global convergence, and becomes a current research hotspot.
The peak-pursuit sampling approximate optimization method is a typical self-adaptive MBDO method, guides biased sampling in a design space by constructing a probability density function, and has the characteristics of high efficiency, support of parallel computing, strong robustness and the like. A series of methods are derived aiming at the problems of discrete continuous mixing, high dimension, strong constraint and the like on the basis of the standard MPS, and the method has obvious advantages in the aspects of optimizing efficiency and convergence performance. However, in most adaptive MBDO methods, including the MPS-derived method, proxy model construction relies on a single high-precision response message, and still consumes a large amount of computing resources.
In fact, there are often multiple source simulation models of different accuracy in aircraft engineering practice. The Multi-model Fusion method (MMF) is a surrogate model method for effectively fusing Multi-source model information, is applied to the field of aircraft engineering, but for the optimization problem related to a high-dimensional strong constraint complex aircraft system, the adaptive MBDO method based on Multi-model Fusion still faces the technical challenge of insufficient optimization efficiency and convergence performance.
Aiming at the problems, the invention introduces a Multi-Model Fusion method into a peak-pursuit Sampling frame, and provides a heterogeneous data-driven aircraft efficient approximate optimization method (MMF-MPS).
In order to better explain the technical scheme of the invention, the related agent model technology and method are introduced as follows.
(1) Co-Kriging agent model
Considering a high-precision sample point set XeAnd corresponding high-precision model response value YeLow-precision sample point set and corresponding low-precision model response value Y thereofcAnd taking the response value of the high-precision model and the low-precision model as obeying a cooperative Gaussian process to obtain a basic form of the Co-Kriging agent model as follows:
Ze(x)＝ηZc(x)+Zd(x) (1)
in the formula (1), eta is a proportionality coefficient, ZeAnd ZcRespectively representing Gauss processes, Z, obeyed by high and low precision model response valuesdRepresents ZeAnd eta ZcThe difference between them. According to the theory of Gaussian process, the predicted value expression of the Co-Kriging agent model is as follows:
Figure BDA0003204413730000021
in the formula (2), the reaction mixture is,
Figure BDA0003204413730000022
the predicted value of the Co-Kriging agent model is shown, C is a covariance matrix, and the expression is as follows:
Figure BDA0003204413730000023
in formula (3), phid(. phi.) and psicRespectively is a high-low precision sampleThe correlation matrix of the present set of points. The elements in the correlation matrix, i.e. the correlation functions, are typically in exponential form:
Figure BDA0003204413730000024
in the formula (4), nvIs the number of design variables, θkIs the correlation coefficient for the kth design variable,
Figure BDA0003204413730000025
is the kth design variable for the ith sample point.
Hyper-parameters of low-precision model Gaussian process
Figure BDA0003204413730000026
And thetacCan be obtained by maximum likelihood estimation, and the maximum likelihood function is:
Figure BDA0003204413730000027
similarly, the hyperparameters of the difference of the Gauss process of the high and low precision models
Figure BDA0003204413730000028
And thetadThe corresponding maximum likelihood function is:
Figure BDA0003204413730000031
(2) filter method
Constraint h according to optimization problemi(x) Defining the constraint violation function as:
Figure BDA0003204413730000032
in the formula (7), hmax(x) Is a constraint condition hi(x) Maximum value, ρ is the adjustment parameter, KS (x)>0 indicates that the sample point is not feasible, and KS (x)>A larger 0 indicates a less feasible sample point.
For arbitrary sample point x(i)And x(l)If and only if f (x)(i))≤f(x(l))∩KS(x(i))≤KS(x(l)) When it is called x(i)Dominating x(l)(ii) a Otherwise, it is called x(i)And x(l)Are not mutually exclusive. By definition, the dominant sample points are superior to the dominated sample points in terms of both objective function and constraint violation, while the two sets of non-dominated sample points dominate in terms of objective function or violation, respectively. Thereby giving the concept of a filter.
A filter is a set of a series of mutually non-dominant sample points, as shown in fig. 1. If a new sample point x is added(j)And all sample points in the filter are not mutually independent, then x is called(j)Current filters can be augmented; if the sample point x is newly added(j)Can dominate any one sample point in the filter, then we call x(j)The current filter can be updated. The solid dots in fig. 1 represent the non-dominant sample points that make up the filter. Augmenting the current filter when the newly added sample point is located at the black shadow position in fig. 1; when the newly added sample point is located at the position of the oblique line in fig. 1, the current filter is updated. Both of the above cases are referred to as new sample points accepted by the current filter. When the newly added sample point is located at the blank position in fig. 1, the newly added sample point is rejected by the filter. According to the analysis, in the design optimization process, the newly added sample points are screened by constructing the filter, and the current filter is expanded or updated, so that the elements in the filter are more and more close to a feasible global optimal solution.
(3) Fuzzy c-means clustering method
Fuzzy C-means Clustering methods (FCM) divide data into multiple clusters by minimizing the degree of difference of data under the same cluster. After the cluster number c is specified, the cluster center and the sample point in each cluster space are determined by solving the following optimization problem:
Figure BDA0003204413730000033
in the formula: u is m sample points xj(j ═ 1,2, …, m, x ∈ R); v ═ v (v)1,v2,…,vnc) Middle viRepresenting the ith clustering center, i is more than or equal to 1 and less than or equal to c; n is a constant greater than 1, typically taken as 2; mu.sijRepresenting the degree of membership of the jth sample point to the ith cluster space. The calculation formula of the standard Euclidean distance norm is
dij＝||xj-vi|| (9)
The lagrangian function of the constraint optimization problem construction represented by the formula (8) is represented by the formula (10).
Figure BDA0003204413730000041
To pair
Figure BDA0003204413730000042
Optimizing to obtain an optimal membership matrix U*And a clustering center v*And dividing each sample point into a clustering space with the maximum membership degree of the sample point.
Disclosure of Invention
Aiming at the problem that the existing peak-chasing sampling method and the derivative algorithm thereof are difficult to utilize the heterogeneous data in the engineering, the invention discloses a heterogeneous data driven aircraft high-efficiency approximate optimization method, which aims to solve the technical problems that: a Co-kriging agent model of the high-precision analysis model is constructed through high/low-precision sample points, multi-source simulation models with different precisions in engineering are fully utilized, precision-preserving quick response prediction of an aircraft complex engineering system is achieved, optimization efficiency of aircraft engineering optimization problems related to the high-time-consuming analysis model is improved, and quality of the aircraft complex engineering system is improved. The method is suitable for the field of aircraft complex engineering system optimization including high-precision analysis models, and solves the corresponding relevant engineering problems.
The field of aircraft complex engineering system optimization comprises aircraft structure optimization and aerodynamic configuration optimization.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a heterogeneous data driven high-efficiency approximate optimization method for an aircraft, which is characterized in that an agent model of a high-precision analysis model of an aircraft system is constructed through a radial basis function, a KS equation is adopted to aggregate a plurality of high-time-consumption constraints into a constraint violation degree function, a filter method is utilized to obtain a high-quality alternative sample point set with better feasibility and optimality from a simple sample point set generated by the disturbance of the current optimal point coordinate, a distance identification-based fuzzy clustering point selection strategy is adopted to select local high/low precision newly-added sample points according to the minimum Euclidean distance between the alternative sample points, a Co-Kriging agent model of the aircraft system is constructed in a sub-area to fully utilize different precision multisource simulation models existing in engineering, local optimization is carried out to obtain a pseudo-optimal solution, iteration is carried out until a given termination condition is met, and finally an optimization result is output. The method fully utilizes the high/low-precision heterogeneous data, can effectively reduce the calculation cost in the optimization process of the aircraft complex engineering system, and improves the quality of the optimization result and the optimization efficiency.
The invention discloses a high-efficiency approximate optimization method of an aircraft driven by heterologous data, which comprises the following steps:
step one, generating initial high-precision sample points in a design space by a standard Latin supersquare test design method, wherein the number of the initial high-precision sample points is Nini＝nv+1, wherein nvThe number of variables is designed. And judging whether feasible sample points meeting the constraint exist or not, and if not, executing the step two. If yes, adopting a standard Latin hyper-square test design method to continue sampling until the number of initial high-precision sample points reaches n0＝nv(nv+1)/2. Calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
Step two, based on the set YglobalRadial Basis Function (RBF) proxy model for constructing constraint function high-precision analysis model by using internal high-precision sample point information
Figure BDA0003204413730000051
And searching feasible sample points in the initial design space by the minimum constraint violation degree under the condition that the predicted value of the constraint function RBF is less than zero and the distance is greater than a given value. After the feasible sample point search is completed, if the set Y is setglobalThe number of internal high-precision sample points is less than n0Selecting n by adopting a standard Latin supersquare test design method0-nsubA high precision sample point, where nsubAs a set YglobalNumber of internal sample points. Otherwise, the sample point is not selected. Calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
The second step of realizing the method comprises the following steps: based on the set YglobalRadial basis function agent model of inner high-precision sample point information construction constraint function high-precision analysis model
Figure BDA0003204413730000052
Solving the optimization problem shown in equation (1)
Figure BDA0003204413730000053
Where rhonIs the KS equation parameter, xkIs YglobalInner sample point, TcoincideGiven a distance threshold. After the feasible sample point search is completed, if the set Y is setglobalThe number of internal high-precision sample points is less than n0Selecting n by adopting a standard Latin supersquare test design method0-nsubA high precision sample point, where nsubAs a set YglobalNumber of internal sample points. Otherwise, the sample point is not selected. Calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
Step three, based on the set YglobalInternal high-precision sample point information structureAnd (4) constructing an RBF proxy model of the target function and constraint function high-precision analysis model. The radial function takes the form of a multi-quadratic function and calculates a weight coefficient omega according to interpolation conditions, wherein the shape coefficient c is calculated by an empirical formula.
The third step is realized by the following steps: based on the set YglobalAnd constructing a target function and constraint function high-precision analysis model RBF agent model by using the internal high-precision sample point information. The radial function phi (r, c) takes the form of a multi-quadratic function
Figure BDA0003204413730000061
Where r is the Euclidean distance between sample points. The weight coefficient is calculated as equation (3) according to the interpolation condition.
Figure BDA0003204413730000062
In the formula FglobalA set of high-precision sample point response values, n being a set YglobalAnd counting the number of internal high-precision samples. The shape factor is calculated as equation (4).
Figure BDA0003204413730000063
Step four, if the current iteration times is 1, according to the set YglobalAnd determining a dominance relation between the objective function value of the inner high-precision sample point and the constraint violation degree, and constructing a filter. Otherwise, updating the filter according to the domination relationship between the newly-added sample point and the sample point in the filter.
And step five, obtaining a simple sample point set by a biased coordinate disturbance method. The method for applying the off-coordinate disturbance comprises two steps of determining the disturbance probability and generating a simple sample point set.
Step 5.1: if the iteration is the first iteration, a second order Polynomial Response Surface (PRSM) proxy model is not constructed, and the Method is based on the number of the existing high-precision sample points and the maximum equivalent high-precision proxy modelAnd (5) determining the disturbance probability p by the calling times of the degree model. Otherwise, determining the disturbance probability by comprehensively considering the optimality and the feasibility of the sample points, and respectively calculating the sensitivity indexes s of the objective function and the constraint function according to the PRSM (probabilistic fuzzy inference model) model coefficientsfAnd shAnd constructing a total sensitivity index
Figure BDA0003204413730000064
Index of total sensitivity
Figure BDA0003204413730000065
Normalized to [0,1]After the interval, according to the optimization, the situation C is not improvedstallAnd determining the calculated disturbance probability p.
Step 5.2: and applying the eccentric coordinate disturbance to the iterative optimal solution based on the disturbance probability p to generate a simple sample point set. In [0,1]]Internally generating neasy×nvA uniformly distributed random number dijWherein n iseasyThe number of simple sample points. Comparing random number with disturbance probability to determine biased coordinate disturbance component
Figure BDA0003204413730000066
If it is not
Figure BDA0003204413730000067
In the set {1, 2.,. nvRandomly select k in the sequence, order
Figure BDA0003204413730000068
Respectively taking 0 as the mean value and the step length sigmanGenerating normally distributed random numbers for variance in combination with off-coordinate perturbation components
Figure BDA0003204413730000069
And applying the eccentric coordinate disturbance to the iterative optimal solution to generate a simple sample point set. And if the simple sample point exceeds the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein n iseasy＝min{ne′asy·nv,ne″asyAt an initial step size of
Figure BDA0003204413730000071
To achieve the optimal performance of the heterogeneous data driven aircraft efficient approximate optimization method, preferably, where n iseasy＝min{100·nv5000, initial step size of
Figure BDA0003204413730000072
The method comprises the following steps: and obtaining a simple sample point set by a biased coordinate disturbance method. The method for applying the off-coordinate disturbance comprises two steps of determining the disturbance probability and generating a simple sample point set.
Step 5.1: if the iteration is the first iteration, a second order Polynomial Response Surface (PRSM) proxy model is not constructed, and the disturbance probability p is determined according to the number of the existing high-precision sample points and the number of times of calling the maximum equivalent high-precision model
Figure BDA0003204413730000073
Where n is the current set YglobalNumber of internal high-precision samples, NmaxAnd calling the maximum equivalent high-precision model. Otherwise, determining the disturbance probability by comprehensively considering the optimality and the feasibility of the sample points, and respectively calculating the sensitivity indexes s of the objective function and the constraint function according to the PRSM (probabilistic fuzzy inference model) model coefficientsfAnd sh
Figure BDA0003204413730000074
In the formula
Figure BDA0003204413730000075
And
Figure BDA0003204413730000076
for the objective function PRSM proxy model coefficients,
Figure BDA0003204413730000077
and
Figure BDA0003204413730000078
the PRSM proxy model coefficients are constraint functions. Index s of total sensitivity of construction
Figure BDA0003204413730000079
Normalizing the total sensitivity index s to the interval of [0,1]
Figure BDA00032044137300000710
According to the optimization not improving the situation CstallDetermining a calculated disturbance probability p
Figure BDA00032044137300000711
To achieve the optimal performance of the heterogeneous data driven aircraft efficient approximate optimization method, preferably, Cs′tall＝2
Step 5.2: and applying the eccentric coordinate disturbance to the iterative optimal solution based on the disturbance probability p to generate a simple sample point set. In [0,1]]Internally generating neasy×nvA uniformly distributed random number dijWherein n iseasyThe number of simple sample points. Comparing random number with disturbance probability to determine biased coordinate disturbance component
Figure BDA0003204413730000081
Figure BDA0003204413730000082
If it is not
Figure BDA0003204413730000083
In the set {1, 2.,. nvInner random }Select k, order
Figure BDA0003204413730000084
Respectively taking 0 as the mean value and the step length sigmanGenerating normally distributed random numbers for variance in combination with off-coordinate perturbation components
Figure BDA0003204413730000085
The iterative optimal solution is applied with the offset coordinate disturbance to generate a simple sample point set
yj＝xopt+z (11)
In the formula xoptFor iterative optimal solution, z is a normally distributed random number
Figure BDA0003204413730000086
And if the simple sample point exceeds the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein n iseasy＝min{ne′asy·nv,ne″asyAt an initial step size of
Figure BDA0003204413730000087
To achieve the optimal performance of the heterogeneous data driven aircraft efficient approximate optimization method, preferably, where n iseasy＝min{100·nv5000, initial step size of
Figure BDA0003204413730000088
Step six, screening the simple sample point set generated in the step five based on the filter determined in the step four to obtain a filter receiving sample point set Yaccept. If set YacceptThe number of the internal sample points is less than the number n of the newly added sample pointssEvaluation index T of prediction value criterionRBFAnd selecting the constraint violation degree function value to improve the feasibility of newly added sample points. Otherwise, the criterion evaluation index of the predicted value is selected as a target function value to improve the optimality of the newly added sample point. Distance criterion evaluation index TDISIs selected as set YacceptInner sample point and set YglobalThe minimum euclidean distance between inner high precision sample points. Optimizing the situation C not to be improved according to the current iteration timesstallAnd weight set
Figure BDA0003204413730000089
Determining an evaluation index weight coefficient omegasAnd calculating the total score. Selecting the sample point with the minimum total score as a newly added sample point, calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function, and adding a high-precision sample point set Yglobal. Removing set YacceptThe Euclidean distance between the existing high-precision sample points is less than a given threshold value TcoincideGenerating a set of candidate sample points Yselect。
In order to realize the optimal performance of the high-efficiency approximate optimization method of the aircraft driven by the heterogeneous data, the initial weight set omega is used as an optimizations,0＝{0.3,0.5,0.8,0.95}。
And seventhly, selecting local high/low-precision sample points from the alternative sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, and guiding the optimization process to quickly converge to a globally feasible optimal solution so as to improve the optimization efficiency. The fuzzy clustering point selection strategy based on distance identification comprises a high-precision sample point selection strategy and a low-precision sample point selection strategy.
Step 7.1: if set YselectThe minimum Euclidean distance between any sample point in the set and the rest sample points in the set is smaller than a given threshold value TcoincideUpdating the candidate sample point set Y by selecting the removed sample pointselect. According to the cost ratio tau calculated by the high/low precision sample points, determining the number n of the cluster center points of the high precision sample pointsadd＝nselectedτ +1, where nselectedFor the updated set of candidate sample points YselectNumber of internal sample points. Generating high-precision sample point clustering center point set Y according to clustering center point number and by adopting fuzzy C-means clustering analysis methode-fcmWhile removing set Ye-fcmA null value present therein. Updating high-precision sample point clustering centersPoint set Ye-fcmAnd nadd. Calculating any sample point in high-precision sample point clustering center point set
Figure BDA0003204413730000091
With alternative sample point set YselectMinimum Euclidean distance L between all points in the interior(i)Set of candidate sample points YselectInner and
Figure BDA0003204413730000092
the nearest point is recorded as
Figure BDA0003204413730000093
If L is(i)<TcoincideSelecting
Figure BDA0003204413730000094
Adding new high-precision sample points; otherwise, selecting
Figure BDA0003204413730000095
To newly add high-precision sample points.
Step 7.2: based on the updated set of alternative sample points YselectSelecting tau multiplied by n by adopting a fuzzy C mean value clustering analysis methodaddAnd generating new low-precision sample points by the clustering centers. Respectively calling high/low precision analysis models to calculate model response values of local high/low precision sample points, and adding the high precision sample points into a high precision sample point set YglobalAdding low-precision sample points into a low-precision sample point set Ycheap。
Based on the step 7.1 and the step 7.2, a fuzzy clustering point selection strategy based on distance identification is adopted, local high/low precision sample points are selected from the alternative sample point set by utilizing the fuzzy clustering point selection strategy, the optimization process is guided to be rapidly converged to a globally feasible optimal point, and the optimization efficiency is further improved.
Step eight, according to the set YglobalN with minimum inter-and iterative optimal solution distancek＝(nv+1)(nv+2)/2 sample points defining a sub-region Y of the geometric enveloperAnd use the areaDomain YrAll sample points within construct the PRSM proxy model.
Step nine, constructing a Co-Kriging agent model based on newly-increased high/low precision sample point information selected from the candidate sample point set in the step seven, fully utilizing aircraft multi-source simulation analysis models with different precisions through the Co-Kriging agent model, realizing precision-preserving fast response prediction of a complex aircraft engineering system, taking an iterative optimal solution as an optimization initial point and carrying out local optimization in a sub-area by adopting a sequence quadratic programming method to obtain a pseudo-optimal solution xoptCalling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set Yglobal。
Step ten, calculating the calling times N of the equivalent high-precision analysis model according to the calculation cost ratio tau of the high-precision sample points and the low-precision sample pointsequal＝Nglobal+NcheapTau is used. If N is presentequalAnd (5) the maximum equivalent high-precision analysis model calling times are reached, optimization is terminated, and the current optimal solution is output. Otherwise, repeating the three-valued step nine until N is metequalAnd when the maximum equivalent high-precision analysis model calling times are reached, solving the aircraft system optimization problem to obtain an aircraft system optimization scheme, namely, realizing the high-efficiency approximate optimization of the aircraft driven by the heterogeneous data.
Step eleven: according to the aircraft system optimization scheme obtained in the step ten, the system performance of the aircraft can be effectively improved, the aircraft research and development efficiency is improved, and the research and development cost is reduced. The aircraft system performance includes range/range of the aircraft, aerodynamic characteristics of the aircraft, and stiffness/strength of the aircraft.
Advantageous effects
1. The invention discloses a heterogeneous data driven aircraft high-efficiency approximate optimization method, which adopts a fuzzy clustering point selection strategy based on distance identification to select high-quality local high/low precision sample points with better feasibility and optimality from an alternative sample point set, and guides the optimization process to quickly converge towards a globally feasible optimal point; a Co-kriging agent model of an aircraft system analysis model is constructed through selected high/low precision sample points, multi-source simulation analysis models with different precisions in a project are fully utilized, precision-preserving quick response prediction of a complex aircraft engineering system is achieved, solving efficiency and robustness of aircraft system optimization problems related to high-time-consuming analysis models are improved, and performance of the complex aircraft system is improved.
2. The high-efficiency approximate optimization method of the aircraft driven by the heterogeneous data is based on the heterogeneous data to realize the high-efficiency approximate optimization of the aircraft, is particularly suitable for being applied to the field of design optimization of complex engineering systems of the aircraft comprising simulation analysis models with different precisions, and can effectively improve the system performance of the aircraft, improve the research and development efficiency of the aircraft and reduce the research and development cost. The aircraft system performance includes range/range of the aircraft, aerodynamic characteristics of the aircraft, and stiffness/strength of the aircraft. The method can be widely applied to the field of design optimization of complex engineering systems comprising simulation analysis models with different precisions, such as the engineering application fields of structural optimization containing large-scale finite element analysis, pneumatic optimization containing high-precision hydrodynamics analysis and the like.
Drawings
FIG. 1 is a schematic view of a filter;
FIG. 2 is a flow chart of a method for efficient approximate optimization of a heterogeneous data-driven aircraft.
Detailed Description
To further illustrate the objects and advantages of the present invention, the following description of the invention is provided in conjunction with specific embodiments and the overall performance of the invention is verified and analyzed by comparison with a baseline airfoil profile.
The specific implementation process is described below by taking an airfoil aerodynamic optimization example as an example.
The purpose of the airfoil aerodynamic optimization problem is to improve airfoil aerodynamic characteristics. The design variables of the airfoil aerodynamic optimization problem are ten airfoil function disturbance parameters. The optimization model expression is as follows:
Figure BDA0003204413730000111
wherein Cl is the coefficient of the lifting force,cd is the coefficient of resistance, tmaxThe maximum thickness of the airfoil is the maximum thickness,
Figure BDA0003204413730000112
to initial airfoil maximum thickness, Cd0Is the initial airfoil drag coefficient. The high-precision pneumatic analysis model adopts Fluent analysis software to carry out simulation analysis, the low-precision pneumatic analysis model adopts a surface element method to solve pneumatic parameters, and the calculation cost ratio tau of high-precision sample points to low-precision sample points is determined to be 6 by comparing the simulation time length of the high-precision pneumatic analysis model to the simulation time length of the low-precision pneumatic analysis model. Maximum equivalent high-precision analysis model calling times Nmax＝150。
Design variable n in this examplev10. As shown in fig. 2, the method for optimizing the high-efficiency approximation of the aircraft driven by the heterogeneous data disclosed in this embodiment includes the following specific steps:
step one, generating initial high-precision sample points in a design space by a standard Latin supersquare test design method, wherein the number of the initial high-precision sample points is Nini11. And judging whether feasible sample points meeting the constraint exist or not, and if not, executing the step two. If yes, adopting a standard Latin hyper-square test design method to continue sampling until the number of initial high-precision sample points reaches n055. Calling a high-precision pneumatic analysis model to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
Step two, based on the set YglobalRadial basis function agent model of inner high-precision sample point information construction constraint function high-precision analysis model
Figure BDA0003204413730000113
Solving the optimization problem shown in the formula (2)
Figure BDA0003204413730000121
After the feasible sample point search is completed, if the set Y is setglobalThe number of internal high-precision sample points is less than 55, and a standard Latin super-square test design method is adoptedMethod for selecting 55-nsubAnd (4) sampling points with high precision. Otherwise, the sample point is not selected. Calling a high-precision pneumatic analysis model to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
Step three, based on the set YglobalAnd constructing a target function and constraint function high-precision analysis model RBF agent model by using the internal high-precision sample point information. The radial function phi (r, c) takes the form of a multi-quadratic function
Figure BDA0003204413730000122
The weight coefficient is calculated as equation (4) according to the interpolation condition.
Figure BDA0003204413730000123
The shape factor is calculated by equation (5).
c＝((max(x)-min(x))/n)0.1 (5)
Step four, if the current iteration times is 1, according to the set YglobalAnd determining a dominance relation between the objective function value of the inner high-precision sample point and the constraint violation degree, and constructing a filter. Otherwise, updating the filter according to the domination relationship between the newly-added sample point and the sample point in the filter.
And step five, obtaining a simple sample point set by a biased coordinate disturbance method. The method for applying the off-coordinate disturbance comprises two steps of determining the disturbance probability and generating a simple sample point set.
Step 5.1: if the iteration is the first iteration, a second order Polynomial Response Surface (PRSM) proxy model is not constructed, and the disturbance probability p is determined according to the number of the existing high-precision sample points and the number of times of calling the maximum equivalent high-precision model
Figure BDA0003204413730000124
Otherwise, determining the disturbance probability by comprehensively considering the optimality and the feasibility of the sample points, and respectively calculating the sensitivity indexes s of the objective function and the constraint function according to the PRSM (probabilistic fuzzy inference model) model coefficientsfAnd sh
Figure BDA0003204413730000131
Index s of total sensitivity of construction
Figure BDA0003204413730000132
Normalizing the total sensitivity index s to the interval of [0,1]
Figure BDA0003204413730000133
According to the optimization not improving the situation CstallDetermining a calculated disturbance probability p
Figure BDA0003204413730000134
Step 5.2: and applying the eccentric coordinate disturbance to the iterative optimal solution based on the disturbance probability p to generate a simple sample point set. In [0,1]]Generates 1000 × 10 uniformly distributed random numbers dijComparing the random number with the disturbance probability to determine the disturbance component with biased coordinates
Figure BDA0003204413730000135
Figure BDA0003204413730000136
If it is not
Figure BDA0003204413730000137
Randomly choose k within the set {1, 2.. 10}, and order
Figure BDA0003204413730000138
Respectively taking 0 as the mean value and the step length sigmanGenerating normally distributed random numbers for variance in combination with off-coordinate perturbation components
Figure BDA0003204413730000139
The iterative optimal solution is applied with the offset coordinate disturbance to generate a simple sample point set
yj＝xopt+z (12)
In the formula xoptFor iterative optimal solution, z is a normally distributed random number
Figure BDA00032044137300001310
And if the simple sample point exceeds the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein the initial step size is
Figure BDA00032044137300001311
Step six, screening the simple sample point set generated in the step five based on the filter determined in the step four to obtain a filter receiving sample point set Yaccept。If set YacceptThe number of the internal sample points is less than the number n of the newly added sample pointssEvaluation index T of prediction value criterionRBFChosen as a constraint violation degree function value to improve feasibility. Otherwise, the criterion evaluation index of the predicted value is selected as the objective function value to improve optimality. Distance criterion evaluation index TDISIs selected as set YacceptInner sample point and set YglobalThe minimum euclidean distance between inner high precision sample points. Optimizing the non-improvement condition C according to the current iteration timesstallAnd weight set omegas,0The evaluation index weight coefficient ω is determined as {0.3,0.5,0.8,0.95}sAnd calculating the total score. Selecting the sample point with the minimum total score as a newly added sample point, calling a high-precision pneumatic analysis model to calculate the real response values of a target function and a constraint function, and adding a high-precision sample point set Yglobal. RemovingSet YacceptThe Euclidean distance between the existing high-precision sample points is smaller than a given threshold value 1.5811 multiplied by 10-4Generating a set of candidate sample points Yselect。
And seventhly, selecting local high/low-precision sample points from the alternative sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, and guiding the optimization process to quickly converge to a globally feasible optimal point so as to improve the optimization efficiency. The fuzzy clustering point selection strategy based on distance identification comprises a high-precision sample point selection strategy and a low-precision sample point selection strategy.
Step 7.1: if set YselectThe minimum Euclidean distance between any sample point in the set and the rest sample points in the set is smaller than a given threshold value 1.5811 multiplied by 10-4Updating the candidate sample point set Y by selecting the removed sample pointselect. Calculating the cost ratio 6 according to the high/low-precision sample points, and determining the number n of the clustering center points of the high-precision sample pointsadd＝nselected/6+1, wherein nselectedFor the updated set of candidate sample points YselectNumber of internal sample points. Generating high-precision sample point clustering center point set Y according to clustering center point number and by adopting fuzzy C-means clustering analysis methode-fcmWhile removing set Ye-fcmA null value present therein. Updating high-precision sample point clustering center point set Ye-fcmAnd nadd. Calculating any sample point in high-precision sample point clustering center point set
Figure BDA0003204413730000141
With alternative sample point set YselectMinimum Euclidean distance L between all points in the interior(i)Set of candidate sample points YselectInner and
Figure BDA0003204413730000142
the nearest point is recorded as
Figure BDA0003204413730000143
If L is(i)<1.5811×10-4Selecting
Figure BDA0003204413730000144
Adding new high-precision sample points; otherwise, selecting
Figure BDA0003204413730000145
To newly add high-precision sample points.
Step 7.2: based on the updated set of alternative sample points YselectAnd 6 Xn is selected by adopting a fuzzy C mean value clustering analysis methodaddAnd generating new low-precision sample points by the clustering centers. Respectively calling high/low precision analysis models to calculate model response values of local high/low precision sample points, and adding the high precision sample points into a high precision sample point set YglobalAdding low-precision sample points into a low-precision sample point set Ycheap。
Based on the step 7.1 and the step 7.2, a fuzzy clustering point selection strategy based on distance identification is adopted, local high/low precision sample points are selected from the alternative sample point set by utilizing the fuzzy clustering point selection strategy, the optimization process is guided to be rapidly converged to a globally feasible optimal point, and the optimization efficiency is further improved.
Step eight, according to the set YglobalN with minimum inter-and iterative optimal solution distancekThe geometric envelope formed by 66 sample points defines a sub-region YrAnd using the region YrAll sample points within construct the PRSM proxy model.
Step nine, constructing a Co-Kriging agent model based on newly-increased high/low precision sample point information selected from the candidate sample point set in the step seven, fully utilizing aircraft multi-source simulation analysis models with different precisions through the Co-Kriging agent model, realizing precision-preserving fast response prediction of a complex aircraft engineering system, taking an iterative optimal solution as an optimization initial point and carrying out local optimization in a sub-area by adopting a sequence quadratic programming method to obtain a pseudo-optimal solution xoptCalling a high-precision pneumatic analysis model to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set Yglobal。
Step ten, calculating the calling times N of the equivalent high-precision analysis model according to the calculation cost ratio tau of the high-precision sample points and the low-precision sample pointsequal＝Nglobal+Ncheap/6. If N is presentequalAnd (5) the maximum equivalent high-precision analysis model calling times are reached, optimization is terminated, and the current optimal solution is output. Otherwise, repeating the three-valued step nine until N is metequalAnd when the maximum equivalent high-precision analysis model calling times are reached, the airfoil aerodynamic optimization problem is solved to obtain an airfoil aerodynamic optimization scheme, namely the high-efficiency approximate optimization of the aircraft driven by the heterogeneous data is realized.
The method for efficiently approximating and optimizing the aircraft driven by the heterogeneous data solves the problem of aerodynamic optimization of the wing profile and compares the optimization result with the reference wing profile. The results are shown in Table 1.
TABLE 1 Airfoil aerodynamic optimization problem optimization results
Figure BDA0003204413730000151
As can be known from data in the table, compared with a reference airfoil, the lift-drag ratio of the optimized airfoil is improved by 33.4%, the aerodynamic characteristics of the airfoil are obviously improved, and the resistance coefficient and the maximum thickness of the optimized airfoil meet constraint conditions. In addition, 127 times of high-precision pneumatic analysis models and 144 times of low-precision pneumatic analysis models are respectively called in the optimization process, and pneumatic simulation analysis models with different precisions are fully utilized.
In order to better illustrate the advantages of MMF-MPS, 10 standard multi-precision examples are further selected for optimization, and are compared with a hybrid proxy model optimization algorithm (HSOSR) based on space reduction, a hierarchical particle swarm optimization algorithm (SHPSO) based on a proxy model, a differential evolution algorithm (S-JADE) based on a proxy model, a high-dimensional black box problem optimization algorithm (DYCORS) based on a proxy model of a radial basis function and dynamic coordinate search, an auxiliary modular differential evolution algorithm (MGPMDE) based on a multi-precision Gaussian process and a radial basis function, and an optimization algorithm (MF-GP-UCB) based on a multi-precision Bayesian process. Numerical test problems include F1-F10. For the above 10 test problems, the algorithm efficiency is measured by comparing the size of the near-optimal solution obtained at the end of the iteration. The maximum equivalent high-precision analysis model is called for 500 times, and the ratio tau of the calculation cost of the high-precision sample points to the calculation cost of the low-precision sample points is 10. To eliminate the influence of accidental factors, each algorithm was continuously optimized for each test problem 30 times. Mathematical models of 10 test questions are shown in equations (14) to (23).
F1：
Figure BDA0003204413730000161
F2：
Figure BDA0003204413730000162
F3：
Figure BDA0003204413730000163
F4：
Figure BDA0003204413730000171
F5：
Figure BDA0003204413730000172
F6:
Figure BDA0003204413730000173
F7:
Figure BDA0003204413730000174
F8:
Figure BDA0003204413730000181
F9:
Figure BDA0003204413730000182
F10:
Figure BDA0003204413730000183
TABLE 2 MMF-MPS, HSOSR, SHPSO, S-JADE optimization results
Figure BDA0003204413730000184
TABLE 3 DYCORS, MF-GP-UCB, MGPMDE optimization results
Figure BDA0003204413730000191
As can be seen from the data in tables 2 and 3, for all the calculation examples, under the same maximum equivalent high-precision analysis model calling times, the optimality of the MMF-MPS optimization result is superior to that of the methods HSOSR, SHPSO, S-JADE, DYCORS, MF-GP-UCB and MGPMDE. In the aspect of robustness, except for the F6 problem, the MMF-MPS optimization result is superior to HSOSR, SHPSO, S-JADE, DYCORS, MF-GP-UCB and MGPMDE methods. For the F6 problem, the MF-GP-UCB is slightly more robust than the MMF-MPS, but is negligible in the aircraft system optimization project.
From the above comparison, it can be easily seen that the MMF-MPS can improve the result optimality and optimization efficiency of the optimization problem in the process of solving the optimization design of the complex aircraft system, and can enhance the robustness of the optimization result. The MMF-MPS method is suitable for various aircraft system optimization fields with high computation time consumption, such as the aircraft system optimization fields of structural optimization design containing large-scale finite element analysis, pneumatic optimization design containing high-precision computational fluid mechanics and the like.
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 (10)

1. The high-efficiency approximate optimization method of the aircraft driven by the heterogeneous data is characterized by comprising the following steps: the method comprises the following steps:
step one, generating initial high-precision sample points in a design space by a standard Latin supersquare test design method, wherein the number of the initial high-precision sample points is Nini＝nv+1, wherein nvDesigning the number of variables; judging whether feasible sample points meeting the constraint exist or not, and if the feasible sample points do not exist, executing a second step; if yes, adopting a standard Latin hyper-square test design method to continue sampling until the number of initial high-precision sample points reaches n0＝nv(nv+ 1)/2; calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalExecuting the step three;
step two, based on the set YglobalRadial Basis Function (RBF) proxy model for constructing constraint function high-precision analysis model by using internal high-precision sample point information
Figure FDA0003204413720000011
Under the condition that the predicted value of a constraint function RBF is smaller than zero and the distance is larger than a given value, enabling the constraint violation degree to search for feasible sample points in the initial design space at the minimum; after the feasible sample point search is completed, if the set Y is setglobalThe number of internal high-precision sample points is less than n0Selecting n by adopting a standard Latin supersquare test design method0-nsubA high precision sample point, where nsubAs a set YglobalCounting the number of internal samples; otherwise, not selecting the sample point; calculating a target function by calling a high-precision analysis model of an aircraft systemAdding the true response value of the constraint function into a high-precision sample point set YglobalExecuting the step three;
step three, based on the set YglobalConstructing an RBF agent model of a target function and a constraint function high-precision analysis model by using the internal high-precision sample point information; the radial function adopts a multi-quadratic function form and calculates a weight coefficient omega according to an interpolation condition, wherein the shape coefficient c is calculated through an empirical formula;
step four, if the current iteration times is 1, according to the set YglobalDetermining a domination relation between the objective function value of the inner high-precision sample point and the constraint violation degree, and constructing a filter; otherwise, updating the filter according to the domination relationship between the newly-added sample point and the sample point in the filter;
step five, obtaining a simple sample point set by a biased coordinate disturbance method; the method for applying the eccentric coordinate disturbance comprises two steps of determining disturbance probability and generating a simple sample point set;
step six, screening the simple sample point set generated in the step five based on the filter determined in the step four to obtain a filter receiving sample point set Yaccept(ii) a If set YacceptThe number of the internal sample points is less than the number n of the newly added sample pointssEvaluation index T of prediction value criterionRBFSelecting a constraint violation degree function value to improve the feasibility of the newly added sample point; otherwise, selecting the criterion evaluation index of the predicted value as a target function value to improve the optimality of the newly added sample point; distance criterion evaluation index TDISIs selected as set YacceptInner sample point and set YglobalMinimum Euclidean distance between inner high-precision sample points; optimizing the situation C not to be improved according to the current iteration timesstallAnd weight set
Figure FDA0003204413720000012
Determining an evaluation index weight coefficient omegasCalculating a total score; selecting the sample point with the minimum total score as a newly added sample point, calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function, and adding a high-precision sample point set Yglobal(ii) a Removing set YacceptThe Euclidean distance between the existing high-precision sample points is less than a given threshold value TcoincideGenerating a set of candidate sample points Yselect；
Step seven, selecting local high/low precision sample points from the alternative sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, and guiding the optimization process to quickly converge to a globally feasible optimal solution so as to improve the optimization efficiency; the fuzzy clustering point selection strategy based on distance identification comprises a high-precision sample point selection strategy and a low-precision sample point selection strategy;
step eight, according to the set YglobalN with minimum inter-and iterative optimal solution distancek＝(nv+1)(nv+2)/2 sample points defining a sub-region Y of the geometric enveloperAnd using the region YrConstructing a PRSM (pseudo random SM) proxy model by all the sample points;
step nine, constructing a Co-Kriging agent model based on newly-increased high/low precision sample point information selected from the candidate sample point set in the step seven, fully utilizing aircraft multi-source simulation analysis models with different precisions through the Co-Kriging agent model, realizing precision-preserving fast response prediction of a complex aircraft engineering system, taking an iterative optimal solution as an optimization initial point and carrying out local optimization in a sub-area by adopting a sequence quadratic programming method to obtain a pseudo-optimal solution xoptCalling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set Yglobal；
Step ten, calculating the calling times N of the equivalent high-precision analysis model according to the calculation cost ratio tau of the high-precision sample points and the low-precision sample pointsequal＝Nglobal+Ncheapτ; if N is presentequalThe maximum equivalent high-precision analysis model calling times are reached, optimization is terminated, and the current optimal solution is output; otherwise, repeating the three-valued step nine until N is metequalAnd when the maximum equivalent high-precision analysis model calling times are reached, solving the aircraft system optimization problem to obtain an aircraft system optimization scheme, namely, realizing the high-efficiency approximate optimization of the aircraft driven by the heterogeneous data.
2. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 1, characterized by: and step eleven, according to the aircraft system optimization scheme obtained in the step eleven, the system performance of the aircraft can be effectively improved, the aircraft research and development efficiency is improved, and the research and development cost is reduced.
3. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 2, characterized by: the aircraft system performance includes range/range of the aircraft, aerodynamic characteristics of the aircraft, and stiffness/strength of the aircraft.
4. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 1,2 or 3, characterized by: the second step is realized by the method based on the set YglobalRadial basis function agent model of inner high-precision sample point information construction constraint function high-precision analysis model
Figure FDA0003204413720000031
Solving the optimization problem shown in equation (1)
Figure FDA0003204413720000032
Where rhonIs the KS equation parameter, xkIs YglobalInner sample point, TcoincideA given distance threshold; after the feasible sample point search is completed, if the set Y is setglobalThe number of internal high-precision sample points is less than n0Selecting n by adopting a standard Latin supersquare test design method0-nsubA high precision sample point, where nsubAs a set YglobalCounting the number of internal samples; otherwise, not selecting the sample point; calling a high-precision analysis model of the aircraft system to calculate the real response values of the target function and the constraint function and adding a high-precision sample point set YglobalAnd step three is executed.
5. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 4, characterized by: the third step is realized by the method based on the set YglobalConstructing a target function and constraint function high-precision analysis model RBF agent model by using the internal high-precision sample point information; the radial function phi (r, c) takes the form of a multi-quadratic function
Figure FDA0003204413720000033
Wherein r is the Euclidean distance between sample points; according to the interpolation condition, the weight coefficient is calculated according to the formula (3);
Figure FDA0003204413720000034
in the formula FglobalA set of high-precision sample point response values, n being a set YglobalCounting the number of internal high-precision samples; the shape coefficient is calculated according to the formula (4);
Figure FDA0003204413720000035
。
6. the method for efficient approximate optimization of heterologous data driven aircraft according to claim 5, characterized by: the fifth step is to realize that the method is that,
step 5.1: if the iteration is the first iteration, a quadratic Polynomial Response Surface (PRSM) proxy model is not constructed, and the disturbance probability p is determined according to the number of the existing high-precision sample points and the calling times of the maximum equivalent high-precision model; otherwise, determining the disturbance probability by comprehensively considering the optimality and the feasibility of the sample points, and respectively calculating the sensitivity indexes s of the objective function and the constraint function according to the PRSM (probabilistic fuzzy inference model) model coefficientsfAnd shAnd constructing a total sensitivity index
Figure FDA0003204413720000041
Index of total sensitivity
Figure FDA0003204413720000042
Normalized to [0,1]After the interval, according to the optimization, the situation C is not improvedstallDetermining a calculated disturbance probability p;
step 5.2: applying the eccentric coordinate disturbance to the iterative optimal solution based on the disturbance probability p to generate a simple sample point set; in [0,1]]Internally generating neasy×nvA uniformly distributed random number dijWherein n iseasyThe number of simple sample points; comparing random number with disturbance probability to determine biased coordinate disturbance component
Figure FDA0003204413720000043
If it is not
Figure FDA0003204413720000044
In the set {1, 2.,. nvRandomly select k in the sequence, order
Figure FDA0003204413720000045
Respectively taking 0 as the mean value and the step length sigmanGenerating normally distributed random numbers for variance in combination with off-coordinate perturbation components
Figure FDA0003204413720000046
Applying partial coordinate disturbance to the iterative optimal solution to generate a simple sample point set; if the simple sample point exceeds the boundary of the design space, mapping to the design space by adopting a coordinate reflection method; wherein n iseasy＝min{n′easy·nv,n″easyAt an initial step size of
Figure FDA0003204413720000047
7. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 6, characterized by: step 7.1: if set YselectAny one of themThe minimum Euclidean distance between the sample point and the rest sample points in the set is less than a given threshold value TcoincideUpdating the candidate sample point set Y by selecting the removed sample pointselect(ii) a According to the cost ratio tau calculated by the high/low precision sample points, determining the number n of the cluster center points of the high precision sample pointsadd＝nselectedτ +1, where nselectedFor the updated set of candidate sample points YselectCounting the number of internal samples; generating high-precision sample point clustering center point set Y according to clustering center point number and by adopting fuzzy C-means clustering analysis methode-fcmWhile removing set Ye-fcmA null value present therein; updating high-precision sample point clustering center point set Ye-fcmAnd nadd(ii) a Calculating any sample point in high-precision sample point clustering center point set
Figure FDA0003204413720000048
With alternative sample point set YselectMinimum Euclidean distance L between all points in the interior(i)Set of candidate sample points YselectInner and
Figure FDA0003204413720000049
the nearest point is recorded as
Figure FDA00032044137200000410
If L is(i)<TcoincideSelecting
Figure FDA00032044137200000411
Adding new high-precision sample points; otherwise, selecting
Figure FDA00032044137200000412
Adding new high-precision sample points;
step 7.2: based on the updated set of alternative sample points YselectSelecting tau multiplied by n by adopting a fuzzy C mean value clustering analysis methodaddGenerating new low-precision sample points by the clustering centers; respectively calling high/low precision analysis models to calculate model responses of local high/low precision sample pointsAdding the high-precision sample points into the high-precision sample point set YglobalAdding low-precision sample points into a low-precision sample point set Ycheap；
Based on the step 7.1 and the step 7.2, a fuzzy clustering point selection strategy based on distance identification is adopted, local high/low precision sample points are selected from the alternative sample point set by utilizing the fuzzy clustering point selection strategy, the optimization process is guided to be rapidly converged to a globally feasible optimal point, and the optimization efficiency is further improved.
8. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 7, wherein: the concrete implementation method of the step five is that,
step 5.1: if the iteration is the first iteration, a second order Polynomial Response Surface (PRSM) proxy model is not constructed, and the disturbance probability p is determined according to the number of the existing high-precision sample points and the number of times of calling the maximum equivalent high-precision model
Figure FDA0003204413720000051
Where n is the current set YglobalNumber of internal high-precision samples, NmaxCalling times for the maximum equivalent high-precision model; otherwise, determining the disturbance probability by comprehensively considering the optimality and the feasibility of the sample points, and respectively calculating the sensitivity indexes s of the objective function and the constraint function according to the PRSM (probabilistic fuzzy inference model) model coefficientsfAnd sh
Figure FDA0003204413720000052
In the formula
Figure FDA0003204413720000053
And
Figure FDA0003204413720000054
for objective function PRSM proxy modelThe coefficients of which are such that,
Figure FDA0003204413720000055
and
Figure FDA0003204413720000056
representing the coefficients of a PRSM proxy model as a constraint function; index s of total sensitivity of construction
Figure FDA0003204413720000057
Normalizing the total sensitivity index s to the interval of [0,1]
Figure FDA0003204413720000058
According to the optimization not improving the situation CstallDetermining a calculated disturbance probability p
Figure FDA0003204413720000059
Preferably, C 'is selected to achieve optimal performance of the heterologous data driven aircraft efficient approximate optimization method'stall＝2
Step 5.2: applying the eccentric coordinate disturbance to the iterative optimal solution based on the disturbance probability p to generate a simple sample point set; in [0,1]]Internally generating neasy×nvA uniformly distributed random number dijWherein n iseasyThe number of simple sample points; comparing random number with disturbance probability to determine biased coordinate disturbance component
Figure FDA0003204413720000061
Figure FDA0003204413720000062
If it is not
Figure FDA0003204413720000063
In the set {1, 2.,. nvRandomly select k in the sequence, order
Figure FDA0003204413720000064
Respectively taking 0 as the mean value and the step length sigmanGenerating normally distributed random numbers for variance in combination with off-coordinate perturbation components
Figure FDA0003204413720000065
The iterative optimal solution is applied with the offset coordinate disturbance to generate a simple sample point set
yj＝xopt+z (11)
In the formula xoptFor iterative optimal solution, z is a normally distributed random number
Figure FDA0003204413720000066
If the simple sample point exceeds the boundary of the design space, mapping to the design space by adopting a coordinate reflection method; wherein n iseasy＝min{n′easy·nv,n″easyAt an initial step size of
Figure FDA0003204413720000067
9. The method for efficient approximate optimization of heterologous data driven aircraft according to claim 8, wherein: for achieving the high-efficiency approximate optimization method of the aircraft driven by the heterogeneous data, the performance is optimal, wherein neasy＝min{100·nv5000, initial step size of
Figure FDA0003204413720000068
10. The heterologous gene of claim 8The high-efficiency approximate optimization method of the driven aircraft is characterized by comprising the following steps: in order to realize the optimal performance of the high-efficiency approximate optimization method of the aircraft driven by the heterogeneous data, the weight initial set omegas,0＝{0.3,0.5,0.8,0.95}。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114218686A (en) * 2022-02-21 2022-03-22 中国人民解放军国防科技大学 Multi-precision data smooth scale approximate modeling method for aircraft

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108459993A (en) * 2018-02-02 2018-08-28 北京理工大学 Based on the complicated High Dimensional Systems optimization method for quickly chasing after peak sampling
CN108491668A (en) * 2018-04-17 2018-09-04 北京理工大学 A kind of aerocraft system optimization method based on the fusion of dynamic multi-model
CN109918809A (en) * 2019-03-14 2019-06-21 北京理工大学 Aircraft near-optimal method based on filter and adaptive Kriging model
CN112231839A (en) * 2020-10-23 2021-01-15 北京理工大学 Intelligent exploration method for peak-tracking sampling of aircraft aiming at high time-consuming constraint

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108459993A (en) * 2018-02-02 2018-08-28 北京理工大学 Based on the complicated High Dimensional Systems optimization method for quickly chasing after peak sampling
CN108491668A (en) * 2018-04-17 2018-09-04 北京理工大学 A kind of aerocraft system optimization method based on the fusion of dynamic multi-model
CN109918809A (en) * 2019-03-14 2019-06-21 北京理工大学 Aircraft near-optimal method based on filter and adaptive Kriging model
CN112231839A (en) * 2020-10-23 2021-01-15 北京理工大学 Intelligent exploration method for peak-tracking sampling of aircraft aiming at high time-consuming constraint

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
WU YUFEI等: "Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization", JOURNAL OF MECHANICAL DESIGN, vol. 143, no. 4 *
龙腾;毛能峰;史人赫;武宇飞;沈敦亮: "考虑高耗时约束的追峰采样智能探索方法", 航空学报, no. 004 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114218686A (en) * 2022-02-21 2022-03-22 中国人民解放军国防科技大学 Multi-precision data smooth scale approximate modeling method for aircraft
CN114218686B (en) * 2022-02-21 2022-05-10 中国人民解放军国防科技大学 Multi-precision data smooth scale approximate modeling method for aircraft

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