CN113657029B - Efficient approximate optimization method for heterogeneous data driven aircraft - Google Patents
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Abstract
The invention discloses a heterogeneous data driven aircraft efficient approximate optimization method, and belongs to the technical field of aircraft engineering optimization. According to the invention, a fuzzy clustering point selection strategy based on distance identification is adopted to select high-quality local high/low-precision sample points with better feasibility and optimality from the candidate sample point set, and the optimization process is guided to quickly converge towards a global feasible optimal point; the Co-kriging proxy model of the aircraft system analysis model is constructed through the selected high/low-precision sample points, the multisource simulation analysis models with different precision existing in the engineering are fully utilized, the precision-keeping quick response prediction of the complex aircraft engineering system is realized, the efficiency and the robustness of solving the aircraft system optimization problem related to the high-time-consumption analysis model are improved, and the performance of the complex aircraft system is improved. The method is suitable for being applied to the field of aircraft complex engineering system optimization comprising high-precision analysis models, and solves corresponding related engineering problems.
Description
Technical Field
The invention relates to a heterogeneous data driven aircraft efficient approximate optimization method, and belongs to the technical field of aircraft engineering optimization.
Background
With the development of discipline modeling techniques, numerical computing techniques, and computer software and hardware, high-precision analytical models are increasingly being used in the engineering practice of aircraft optimization, such as the computational fluid dynamics (Computational Fluid Dynamics, CFD) model of aerodynamic disciplines, the finite element analysis (FINITE ELEMENT ANALYSIS, FEA) model of structural disciplines, and the like. The application of the high-precision analysis model can improve the reliability of results and the quality of the aircraft, but simultaneously increases the calculation cost. In addition, the high-precision analysis model is repeatedly called in the aircraft optimization process to find an optimal scheme, so that the calculation complexity is further increased. In order to alleviate the above problems, a surrogate model-based Optimization method (Metamodel-based DESIGN AND Optimization, MBDO) has been studied in depth, and aims to guide the Optimization process to quickly converge to an optimal solution by constructing a reasonable approximation model, thereby reducing the calculation cost and shortening the design period. The optimization method (also called as a self-adaptive MBDO method) based on the dynamic proxy model can effectively improve the optimization efficiency and the global convergence, and becomes a current research hotspot.
The peak-tracking sampling approximate optimization method is a typical self-adaptive MBDO method, and the biased sampling in the design space is guided by constructing a probability density function, so that the method has the characteristics of high efficiency, parallel calculation support, strong robustness and the like. A series of methods are derived on the basis of standard MPS aiming at the problems of discrete continuous mixing, high dimension, strong constraint and the like, and the method has remarkable advantages in the aspects of optimizing efficiency and convergence performance. However, in most adaptive MBDO methods, including MPS-derived methods, proxy model construction relies on a single high-precision response message, and still requires a significant amount of computational resources.
Indeed, there are often multiple source simulation models of varying accuracy in aircraft engineering practice. The Multi-model Fusion (MMF) is a proxy model method for effectively fusing Multi-source model information, which has been applied in the field of aircraft engineering, but for the optimization problem related to Gao Weijiang constraint complex aircraft systems, the Multi-model Fusion-based adaptive MBDO method still faces the technical challenges of insufficient optimization efficiency and convergence performance.
Aiming at the problems, the invention introduces a Multi-model fusion method into a peak tracking sampling framework and provides a heterogeneous data driven aircraft efficient approximate optimization method (Multi-Model Fusion based Mode Pursuing Sampling method, MMF-MPS).
In order to better explain the technical scheme of the invention, the related agent model technology and method are described as follows.
(1) Co-Kriging proxy model
Considering the high-precision sample point set X e and a corresponding high-precision model response value Y e thereof, the low-precision sample point set and a corresponding low-precision model response value Y c thereof, and regarding the high-precision model response value and the low-precision model response value as obeying a collaborative Gaussian process, the Co-Kriging proxy model is obtained in the basic form as follows:
Ze(x)＝ηZc(x)+Zd(x) (1)
In the formula (1), η is a proportionality coefficient, Z e and Z c respectively represent gaussian processes to which high-low precision model response values obey, and Z d represents a difference between Z e and ηz c. According to Gaussian process theory, the Co-Kriging agent model predictive value expression is:
In the formula (2), the amino acid sequence of the compound, The predicted value of the Co-Kriging agent model is represented by the formula:
In the formula (3), ψ d (·, ·) and ψ c (·, ·) are the correlation matrices of high and low precision sample point sets, respectively. The elements in the correlation matrix, i.e. the correlation functions, are typically in the form of exponentials:
In the formula (4), n v is the number of design variables, θ k is the correlation coefficient of the kth design variable, Is the kth design variable for the ith sample point.
Super-parameters of low-precision model Gaussian processAnd θ c can be obtained by maximum likelihood estimation, the maximum likelihood function is:
similarly, the hyper-parameters of the high and low accuracy model Gaussian process differences The maximum likelihood function corresponding to θ d is:
(2) Filter method
According to constraint condition h i (x) of the optimization problem, defining a constraint violation function as follows:
In the formula (7), h max (x) is the maximum value of the constraint h i (x), ρ is the adjustment parameter, KS (x) >0 indicates that the sample point is not feasible, and a larger KS (x) >0 indicates that the sample point is less feasible.
For any sample points x (i) and x (l), if and only if f (x (i))≤f(x(l))∩KS(x(i))≤KS(x(l)), x (i) is said to dominate x (l); otherwise, it is said that x (i) and x (l) are mutually exclusive. By definition, dominant sample points are superior to dominant sample points in both objective function and constraint violations, while two sets of sample points that are mutually exclusive are dominant in objective function or violations, respectively. Giving the concept of a filter.
A filter is a collection of a series of mutually exclusive sample points, as shown in fig. 1. If the newly added sample point x (j) and all sample points in the filter do not govern each other, then x (j) is said to be able to augment the current filter; if the newly added sample point x (j) can dominate any sample point in the filter, then x (j) is said to be able to update the current filter. The solid dots in fig. 1 represent mutually exclusive sample dots that make up the filter. When the newly added sample point is located at the black shadow position in fig. 1, the current filter is enhanced; when the newly added sample point is located at the diagonal line position in fig. 1, the current filter is updated. Both of the above cases are referred to as the new sample point being accepted by the current filter. When the new sample point is located at the blank position in fig. 1, the new sample point is rejected by the filter. According to the analysis, in the design optimization process, newly added sample points are screened by constructing a filter, and the current filter is amplified or updated, so that elements in the filter are enabled to approach a feasible global optimal solution more and more.
(3) Fuzzy c-means clustering method
Fuzzy C-means clustering (Fuzzy C-means Clustering Method, FCM) divides data into clusters by minimizing the degree of variance of the data under the same cluster. After the cluster number c is specified, the cluster center and the sample points in each cluster space are determined by solving the following optimization problem:
Wherein: u is a membership matrix of m sample points x j (j=1, 2, …, m, x e R); v i in v= (v 1,v2,…,vnc) represents the ith cluster center, i is more than or equal to 1 and less than or equal to c; n is a constant greater than 1, typically taking n=2; mu ij represents the membership degree 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 is constructed for the constraint optimization problem represented by equation (8) as shown in equation (10).
For a pair ofAnd optimizing to obtain an optimal membership matrix U * and a clustering center v *, and dividing each sample point into a clustering space with the largest membership of the sample point.
Disclosure of Invention
Aiming at the problem that the existing peak tracking sampling method and the derivative algorithm thereof are difficult to utilize heterologous data existing in engineering, the technical problem to be solved by the method for optimizing the efficient approximation of the aircraft driven by the heterologous data disclosed by the invention is as follows: the Co-kriging proxy model of the high-precision analysis model is constructed through the high/low-precision sample points, the multi-source simulation models with different precision existing in the engineering are fully utilized, the precision-keeping quick response prediction of the complex engineering system of the aircraft is realized, the optimization efficiency of the engineering optimization problem of the aircraft related to the high-time-consumption analysis model is improved, and the quality of the complex engineering system of the aircraft is improved. The method is suitable for being applied to the field of aircraft complex engineering system optimization comprising high-precision analysis models, and solves corresponding related engineering problems.
The field of aircraft complex engineering system optimization comprises aircraft structure optimization and aerodynamic profile optimization.
The aim of the invention is achieved by the following technical scheme.
The invention discloses a heterogeneous data-driven efficient approximate optimization method for an aircraft, which comprises the steps of constructing a proxy model of a high-precision analysis model of the aircraft system through a radial basis function, adopting a KS equation to aggregate a plurality of high-time-consuming constraints into constraint violation functions, utilizing a filter method to obtain a high-quality alternative sample point set with better feasibility and optimality from a simple sample point set generated by current optimal point coordinate disturbance, adopting a fuzzy clustering point selection strategy based on distance identification to select local high/low-precision newly-increased sample points according to the minimum Euclidean distance between the alternative sample points, constructing a Co-Kriging proxy model of the aircraft system in a subarea so as to fully utilize different precision multisource simulation models existing in engineering, carrying out local optimization to obtain pseudo-optimal solutions, iterating until a given termination condition is met, and finally outputting an optimization result. The method and the device fully utilize high/low-precision heterogeneous data, can effectively reduce the calculation cost in the optimization process of the complex engineering system of the aircraft, and improve the quality and the optimization efficiency of the optimization result.
The invention discloses a method for optimizing the high-efficiency approximation 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 super test design method, wherein the number of the initial high-precision sample points is N ini＝nv +1, and N v is the number of design variables. Judging whether feasible sample points meeting the constraint exist or not, and if not, executing the second step. If the sample is present, the standard Latin over-square test design method is adopted to continue sampling until the number of initial high-precision sample points reaches n 0＝nv(nv +1)/2. And D, invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
Constructing a radial basis function (Radial basis function, RBF) proxy model of a constraint function high-precision analysis model based on high-precision sample point information in the set Y global And enabling the constraint violation degree to minimum search feasible sample points in the initial design space under the condition that the RBF predicted value of the constraint function is smaller than zero and the distance is larger than a given value. After the search of the feasible sample points is completed, if the number of high-precision sample points in the set Y global is smaller than n 0, selecting n 0-nsub high-precision sample points by adopting a standard Latin square test design method, wherein n sub is the number of sample points in the set Y global. Otherwise, no sample point is selected. And D, invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
The implementation method of the second step is as follows: radial basis function proxy model for constructing constraint function high-precision analysis model based on high-precision sample point information in set Y global Solving the optimization problem shown in (1)
Where ρ n is the KS equation parameter, x k is the sample point in Y global, and T coincide is the given distance threshold. After the search of the feasible sample points is completed, if the number of high-precision sample points in the set Y global is smaller than n 0, selecting n 0-nsub high-precision sample points by adopting a standard Latin square test design method, wherein n sub is the number of sample points in the set Y global. Otherwise, no sample point is selected. And D, invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
And thirdly, constructing an RBF proxy model of the objective function and constraint function high-precision analysis model based on the high-precision sample point information in the set Y global. The radial function takes the form of a multiple quadratic function and calculates the weight coefficient ω according to the interpolation condition, where the shape coefficient c is calculated by an empirical formula.
The implementation method of the third step is as follows: and constructing an RBF proxy model of the objective function and constraint function high-precision analysis model based on the high-precision sample point information in the set Y global. The radial function phi (r, c) adopts a multi-quadratic function form
Where r is the Euclidean distance between sample points. According to the interpolation condition, the weight coefficient is calculated according to the formula (3).
Wherein F global is a high-precision sample point response value set, and n is the high-precision sample point number in the set Y global. The shape factor is calculated according to equation (4).
And step four, if the current iteration number is 1, determining a dominant relationship according to the objective function value and the constraint violation degree of the high-precision sample points in the set Y global, and constructing a filter. Otherwise, according to the dominant relation between the newly added sample points and the sample points in the filter, the filter is updated.
And fifthly, acquiring a simple sample point set through 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 5.1: if the first iteration is performed, a quadratic polynomial response surface (Polynomial Response Surface Method, PRSM) proxy model is not constructed yet, and the disturbance probability p is determined according to the number of existing high-precision sample points and the number of times of the maximum equivalent high-precision model call. Otherwise, comprehensively considering the optimality and feasibility of the sample points to determine disturbance probability, respectively calculating sensitivity indexes s f and s h of the objective function and the constraint function according to PRSM proxy model coefficients and constructing a total sensitivity indexTotal sensitivity index/>After normalization to the [0,1] interval, the calculated disturbance probability p is determined according to the optimization non-improvement condition C stall.
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. N easy×nv uniformly distributed random numbers d ij are generated within [0,1], where n easy is the number of simple sample points. Determining a biased disturbance component by comparing the random number and the disturbance probabilityIf/>Randomly selecting k in the set {1,2,. }, n v } to let/>Respectively taking 0 as a mean value, taking the step length sigma n as a variance to generate a normal distribution random number and combining with a eccentric disturbance component/>And applying the eccentric disturbance to the iterative optimal solution to generate a simple sample point set. If the simple sample points exceed the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein n easy＝min{ne′asy·nv,ne″asy, the initial step size is/>
The performance of the method is optimal for realizing the efficient approximate optimization of the aircraft driven by the heterologous data, wherein n easy＝min{100·nv, 5000}, and the initial step size is as follows
The fifth implementation method comprises the following steps: and 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 5.1: if the first iteration is performed, a quadratic polynomial response surface (Polynomial Response Surface Method, PRSM) proxy model is not constructed yet, and the disturbance probability p is determined according to the existing high-precision sample points and the maximum equivalent high-precision model call times
Where N is the number of high-precision sample points in the current set Y global, and N max is the number of times of invoking the maximum equivalent high-precision model. Otherwise, comprehensively considering the optimality and feasibility of the sample points to determine disturbance probability, and respectively calculating sensitivity indexes s f and s of the objective function and the constraint function according to PRSM proxy model coefficients h
In the middle ofAnd/>Proxy model coefficients for objective function PRSM,/>And/>Model coefficients are proxied for constraint functions PRSM. Structure total sensitivity index s
Normalizing the total sensitivity index s to the [0,1] interval
Determining the calculated disturbance probability p according to the optimized non-improved condition C stall
Optimal performance for achieving a heterogeneous data-driven aircraft efficient approximate optimization method is preferred, wherein C s′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. N easy×nv uniformly distributed random numbers d ij are generated within [0,1], where n easy is the number of simple sample points. Determining a biased disturbance component by comparing the random number and the disturbance probability
If it isRandomly selecting k in the set {1,2,. }, n v } to let/>Respectively taking 0 as a mean value, taking the step length sigma n as a variance to generate a normal distribution random number and combining with a eccentric disturbance component/>Generating a simple sample point set by applying eccentric disturbance to an iterative optimal solution
yj＝xopt+z (11)
Wherein x opt is an iterative optimal solution, and z is a normal distribution random number
If the simple sample points exceed the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein n easy＝min{ne′asy·nv,ne″asy, the initial step size is
The performance of the method is optimal for realizing the efficient approximate optimization of the aircraft driven by the heterologous data, wherein n easy＝min{100·nv, 5000}, and the initial step size is as follows
And 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 acceptance sample point set Y accept. If the number of the sample points in the set Y accept is smaller than the number n s of the newly added sample points, the predicted value criterion evaluation index T RBF is selected as the constraint violation degree function value to improve the feasibility of the newly added sample points. Otherwise, the predicted value criterion evaluation index is selected as the objective function value to improve the optimality of the newly added sample point. The distance criterion evaluation index T DIS is selected as the minimum euclidean distance between the sample points in set Y accept and the high-precision sample points in set Y global. According to the current iteration times, optimizing the non-improved condition C stall and the weight setAnd determining an evaluation index weight coefficient omega s, and calculating a total score. And selecting a sample point with the smallest 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 objective function and the constraint function, and adding the real response values into a high-precision sample point set Y global. Sample points with Euclidean distance smaller than a given threshold T coincide between the set Y accept and the existing high-precision sample points are removed, and an alternative sample point set Y select is generated.
To achieve optimal performance of the heterogeneous data driven aircraft efficient approximate optimization method, the initial set of weights ω s,0 = {0.3,0.5,0.8,0.95} is preferable.
And step seven, selecting local high/low-precision sample points from the candidate sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, guiding the optimization process to quickly converge towards a globally feasible optimal solution, and further improving the optimization efficiency. The fuzzy clustering point selection strategy based on distance recognition comprises a high-precision sample point selection strategy and a low-precision sample point selection strategy.
Step 7.1: if the minimum Euclidean distance between any sample point in the set Y select and the rest of the sample points in the set is less than the given threshold T coincide, selecting to remove the sample points and update the alternative sample point set Y select. And calculating the cost ratio tau according to the high/low precision sample points, and determining the clustering center point number n add＝nselected/tau+1 of the high precision sample points, wherein n selected is the sample point number in the updated candidate sample point set Y select. And generating a high-precision sample point clustering center point set Y e-fcm by adopting a fuzzy C-means clustering analysis method according to the clustering center point number, and simultaneously removing null values in the set Y e-fcm. And updating the high-precision sample point cluster center point sets Y e-fcm and n add. Calculating any sample point in a high-precision sample point clustering center point setMinimum Euclidean distance L (i) between the candidate sample point set Y select and all points in the candidate sample point set Y select and/>The nearest point is noted/>If L (i)<Tcoincide, choose/>The method is a newly added high-precision sample point; otherwise, choose/>Is a new high-precision sample point.
Step 7.2: based on the updated candidate sample point set Y select, selecting tau multiplied by n add clustering centers by adopting a fuzzy C-means clustering analysis method, and generating a new added low-precision sample point. And respectively calling a high/low precision analysis model to calculate model response values of local high/low precision sample points, adding the high precision sample points into a high precision sample point set Y global, and adding the low precision sample points into a low precision sample point set Y cheap.
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 candidate sample point set by utilizing the fuzzy clustering point selection strategy, and the optimization process is guided to quickly converge towards the global feasible optimal point, so that the optimization efficiency is improved.
And step eight, defining a subarea Y r according to a geometric envelope formed by n k＝(nv+1)(nv +2)/2 sample points with the smallest distance from the iterative optimal solution in the set Y global, and constructing PRSM a proxy model by utilizing all sample points in the area Y r.
Step nine, constructing a Co-Kriging proxy model based on newly-added high/low precision sample point information selected from the candidate sample point set in step seven, fully utilizing the multi-source simulation analysis model of the aircraft with different precision through the Co-Kriging proxy model, realizing the precision-keeping quick response prediction of the complex aircraft engineering system, taking the iterative optimal solution as an optimization initial point, adopting a sequence quadratic programming method to carry out local optimization in a subarea to obtain a pseudo-optimal solution x opt, calling the high-precision analysis model of the aircraft system to calculate the real response values of an objective function and a constraint function, and adding the real response values into the high-precision sample point set Y global.
And step ten, calculating the equivalent high-precision analysis model calling times N equal＝Nglobal+Ncheap/tau according to the high/low-precision sample point calculation cost ratio tau. If N equal reaches the maximum equivalent high-precision analysis model calling times, optimizing and terminating and outputting the current optimal solution. Otherwise, repeating the step III and the step III until N equal reaches the maximum equivalent high-precision analysis model calling times, and completing the aircraft system optimization problem solving to obtain an aircraft system optimization scheme, namely realizing the efficient 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 development efficiency of the aircraft is improved, and the development cost is reduced. The aircraft system performance includes range/course of the aircraft, aerodynamic properties of the aircraft, and stiffness/strength of the aircraft.
Advantageous effects
1. According to the method for optimizing the high-efficiency approximation of the heterogeneous data-driven aircraft, disclosed by the invention, a fuzzy clustering point selection strategy based on distance recognition is adopted to select high-quality local high/low-precision sample points with better feasibility and optimality from the candidate sample point set, and the optimization process is guided to quickly converge towards a global feasible optimal point; the Co-kriging proxy model of the aircraft system analysis model is constructed through the selected high/low-precision sample points, the multisource simulation analysis models with different precision existing in the engineering are fully utilized, the precision-keeping quick response prediction of the complex aircraft engineering system is realized, the efficiency and the robustness of solving the aircraft system optimization problem related to the high-time-consumption analysis model are improved, and the performance of the complex aircraft system is improved.
2. The method for optimizing the high-efficiency approximate of the aircraft driven by the heterologous data realizes the high-efficiency approximate optimization of the aircraft based on the heterologous data driving, is particularly suitable for being applied to the field of design optimization of complex engineering systems of the aircraft comprising different precision simulation analysis models, 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/course of the aircraft, aerodynamic properties of the aircraft, and stiffness/strength of the aircraft. The invention can be applied to the field of design optimization of complex engineering systems comprising different precision simulation analysis models, such as the field of engineering application including structural optimization comprising large-scale finite element analysis, pneumatic optimization comprising high-precision hydrodynamic analysis and the like.
Drawings
FIG. 1 is a schematic diagram of a filter;
FIG. 2 is a flow chart of a method for efficient approximate optimization of a heterologous data driven aircraft.
Detailed Description
To further illustrate the objects and advantages of the present invention, the present invention is further described below in connection with specific examples, and the overall performance of the present invention is verified by comparison with a baseline airfoil.
The following describes the implementation by way of an airfoil aerodynamic optimization example as an example.
The goal of airfoil aerodynamic optimization problems is to improve airfoil aerodynamic characteristics. The design variable of the aerofoil aerodynamic optimization problem is ten profile function disturbance parameters of the aerofoil. The optimization model expression is as follows:
Wherein Cl is lift coefficient, cd is drag coefficient, t max is airfoil maximum thickness, Cd 0 is the initial airfoil drag coefficient for the initial airfoil maximum thickness. The high-precision pneumatic analysis model adopts Fluent analysis software to carry out simulation analysis, the low-precision pneumatic analysis model adopts a face element method to solve pneumatic parameters, and the high/low-precision sample point calculation cost ratio tau=6 is determined by comparing the simulation time length of the high/low-precision pneumatic analysis model. The maximum equivalent high-precision analysis model call number N max =150.
In this embodiment, the design variable n v =10 is taken. As shown in fig. 2, the method for optimizing the efficiency approximation of the aircraft driven by the heterologous data disclosed in the embodiment is implemented by the following steps:
Step one, generating initial high-precision sample points in a design space by a standard Latin square test design method, wherein the number of the initial high-precision sample points is N ini =11. Judging whether feasible sample points meeting the constraint exist or not, and if not, executing the second step. If the sample is present, the standard Latin over-square test design method is adopted to continue sampling until the number of initial high-precision sample points reaches n 0 =55. And D, calling a high-precision pneumatic analysis model to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
Step two, constructing a radial basis function proxy model of a constraint function high-precision analysis model based on high-precision sample point information in the set Y global Solving the optimization problem shown in (2)
After the search of the feasible sample points is completed, if the number of high-precision sample points in the set Y global is smaller than 55, 55-n sub high-precision sample points are selected by adopting a standard Latin square test design method. Otherwise, no sample point is selected. And D, calling a high-precision pneumatic analysis model to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
And thirdly, constructing an RBF proxy model of the objective function and constraint function high-precision analysis model based on the high-precision sample point information in the set Y global. The radial function phi (r, c) adopts a multi-quadratic function form
According to the interpolation condition, the weight coefficient is calculated according to the formula (4).
The shape factor is calculated according to equation (5).
c＝((max(x)-min(x))/n)0.1 (5)
And step four, if the current iteration number is 1, determining a dominant relationship according to the objective function value and the constraint violation degree of the high-precision sample points in the set Y global, and constructing a filter. Otherwise, according to the dominant relation between the newly added sample points and the sample points in the filter, the filter is updated.
And fifthly, acquiring a simple sample point set through 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 5.1: if the first iteration is performed, a quadratic polynomial response surface (Polynomial Response Surface Method, PRSM) proxy model is not constructed yet, and the disturbance probability p is determined according to the existing high-precision sample points and the maximum equivalent high-precision model call times
Otherwise, comprehensively considering the optimality and feasibility of the sample points to determine disturbance probability, and respectively calculating sensitivity indexes s f and s of the objective function and the constraint function according to PRSM proxy model coefficients h
Structure total sensitivity index s
Normalizing the total sensitivity index s to the [0,1] interval
Determining the calculated disturbance probability p according to the optimized non-improved condition C stall
/>
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. Generating 1000×10 uniformly distributed random numbers d ij in [0,1], comparing the random numbers with the disturbance probability to determine the disturbance component with eccentric coordinates
If it isRandomly selecting k in the set {1,2,.,. 10} to let/>Respectively taking 0 as a mean value, taking the step length sigma n as a variance to generate a normal distribution random number and combining with a eccentric disturbance component/>Generating a simple sample point set by applying eccentric disturbance to an iterative optimal solution
yj＝xopt+z (12)
Wherein x opt is an iterative optimal solution, and z is a normal distribution random number
If the simple sample points exceed the boundary of the design space, mapping to the design space by adopting a coordinate reflection method. Wherein the initial step length is
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 accepted sample point set Y accept., and if the number of sample points in the set Y accept is smaller than the number of newly added sample points n s, selecting a predicted value criterion evaluation index T RBF as a constraint violation degree function value to improve feasibility. Otherwise, the predictive value criterion evaluation index is selected as the objective function value to improve the optimality. The distance criterion evaluation index T DIS is selected as the minimum euclidean distance between the sample points in set Y accept and the high-precision sample points in set Y global. And determining an evaluation index weight coefficient omega s according to the current iteration times and the optimization non-improvement condition C stall and the weight set omega s,0 = {0.3,0.5,0.8,0.95} and calculating a total score. And selecting a sample point with the smallest total score as a new sample point, calling a high-precision pneumatic analysis model to calculate the real response values of the objective function and the constraint function, and adding the real response values into a high-precision sample point set Y global. Sample points with Euclidean distance between the set Y accept and the existing high-precision sample points smaller than a given threshold 1.5811 multiplied by 10 -4 are removed, and an alternative sample point set Y select is generated.
And step seven, selecting local high/low-precision sample points from the candidate sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, guiding the optimization process to quickly converge towards a global feasible optimal point, and further improving the optimization efficiency. The fuzzy clustering point selection strategy based on distance recognition comprises a high-precision sample point selection strategy and a low-precision sample point selection strategy.
Step 7.1: if the minimum Euclidean distance between any sample point in the set Y select and the rest of the sample points in the set is less than a given threshold 1.5811 ×10 -4, the sample point is selected to be removed and an alternative sample point set Y select is updated. And (3) determining the clustering center point number n add＝nselected/6+1 of the high-precision sample points according to the high/low-precision sample point calculation cost ratio 6, wherein n selected is the sample point number in the updated candidate sample point set Y select. And generating a high-precision sample point clustering center point set Y e-fcm by adopting a fuzzy C-means clustering analysis method according to the clustering center point number, and simultaneously removing null values in the set Y e-fcm. And updating the high-precision sample point cluster center point sets Y e-fcm and n add. Calculating any sample point in a high-precision sample point clustering center point setMinimum Euclidean distance L (i) between the candidate sample point set Y select and all points in the candidate sample point set Y select and/>The nearest point is noted/>If L (i)<1.5811×10-4, choose/>The method is a newly added high-precision sample point; otherwise, choose/>Is a new high-precision sample point.
Step 7.2: based on the updated candidate sample point set Y select, 6 multiplied by n add clustering centers are selected by adopting a fuzzy C-means clustering analysis method, and a new low-precision sample point is generated. And respectively calling a high/low precision analysis model to calculate model response values of local high/low precision sample points, adding the high precision sample points into a high precision sample point set Y global, and adding the low precision sample points into a low precision sample point set Y cheap.
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 candidate sample point set by utilizing the fuzzy clustering point selection strategy, and the optimization process is guided to quickly converge towards the global feasible optimal point, so that the optimization efficiency is improved.
And step eight, defining a subarea Y r according to a geometric envelope formed by n k =66 sample points with the smallest distance from the iterative optimal solution in the set Y global, and constructing PRSM a proxy model by utilizing all sample points in the area Y r.
And step nine, constructing a Co-Kriging proxy model based on newly-added high/low precision sample point information selected from the candidate sample point set in the step seven, fully utilizing the multi-source simulation analysis model of the aircraft with different precision through the Co-Kriging proxy model, realizing the precision-preserving quick response prediction of the complex aircraft engineering system, taking the iterative optimal solution as an optimization initial point, adopting a sequence quadratic programming method to carry out local optimization in a subarea to obtain a pseudo-optimal solution x opt, calling a high-precision pneumatic analysis model to calculate the true response values of an objective function and a constraint function, and adding the real response values into the high-precision sample point set Y global.
And step ten, calculating the equivalent high-precision analysis model calling times N equal＝Nglobal+Ncheap/6 according to the high/low-precision sample point calculation cost ratio tau. If N equal reaches the maximum equivalent high-precision analysis model calling times, optimizing and terminating and outputting the current optimal solution. Otherwise, repeating the step III and the step III until N equal reaches the maximum equivalent high-precision analysis model calling times, and completing the aerofoil aerodynamic optimization problem solution to obtain an aerofoil aerodynamic optimization scheme, namely realizing the efficient approximate optimization of the aircraft driven by the heterologous data.
The method for the efficient approximate optimization of the heterogeneous data driven aircraft solves the pneumatic optimization problem of the airfoil, and compares the optimization result with a reference airfoil. The results are shown in Table 1.
Table 1 aerofoil aerodynamic optimization problem optimization results
As shown by the 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 precision are fully utilized.
In order to better illustrate the advantages of MMF-MPS, 10 standard multi-precision examples are further selected for optimization, and compared with a hybrid proxy model optimization algorithm (HSOSR) based on space reduction, a layered 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 radial basis function proxy model and dynamic coordinate search, an auxiliary model 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 questions included F1-F10. For the 10 test problems described above, the algorithm efficiency is measured by comparing the magnitude of the near-optimal solution obtained at the end of the iteration. The maximum equivalent high-precision analysis model call number is 500, and the high/low-precision sample point calculation cost ratio tau=10. To eliminate the influence of accidental factors, each algorithm was continuously optimized 30 times for each test question. Mathematical models of 10 test questions are shown in equations (14) to (23).
F1：
F2：
F3：
F4：
F5：
F6:
F7:
F8:
F9:
F10:
TABLE 2 MMF-MPS, HSOSR, SHPSO, S-JADE optimization results
TABLE 3 DYCORS, MF-GP-UCB, MGPMDE optimization results
As can be seen from the data in tables 2 and 3, the optimality of the MMF-MPS optimization results is better than the HSOSR, SHPSO, S-JADE, DYCORS, MF-GP-UCB and MGPMDE methods for all the calculation examples under the same maximum equivalent high-precision analysis model call times. In terms of robustness, the MMF-MPS optimization results are superior to HSOSR, SHPSO, S-JADE, DYCORS, MF-GP-UCB and MGPMDE methods except for the F6 problem. For the F6 problem, the MF-GP-UCB is slightly more robust than the MMF-MPS, but is negligible in the aircraft system optimization engineering.
The comparison can easily show that in the process of solving the optimal design of the complex aircraft system, the MMF-MPS can improve the result optimality and the optimization efficiency of the optimization problem, and can enhance the robustness of the optimization result. The MMF-MPS method is suitable for the optimization fields of various aircraft systems with high calculation time consumption, such as the optimization fields of the aircraft systems including structural optimization design containing large-scale finite element analysis, pneumatic optimization design containing high-precision computational fluid mechanics and the like.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (10)
1. The method for the efficient approximate optimization of the heterogeneous data driven aircraft is characterized by comprising the following steps of: the method comprises the following steps:
Generating initial high-precision sample points in a design space by a standard Latin super square test design method, wherein the number of the initial high-precision sample points is N ini＝nv +1, and N v is the number of design variables; judging whether feasible sample points meeting the constraint exist or not, and if not, executing the second step; if the sample number exists, continuing to sample by adopting a standard Latin overestimation design method until the initial high-precision sample number reaches n 0＝nv(nv +1)/2; invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step;
Constructing a radial basis function (Radial basis function, RBF) proxy model of a constraint function high-precision analysis model based on high-precision sample point information in the set Y global Enabling the constraint violation degree to minimum search feasible sample points in the initial design space under the condition that the RBF predicted value of the constraint function is smaller than zero and the distance is larger than a given value; after the search of the feasible sample points is finished, if the number of high-precision sample points in the set Y global is smaller than n 0, selecting n 0-nsub high-precision sample points by adopting a standard Latin super square test design method, wherein n sub is the number of sample points in the set Y global; otherwise, not selecting a sample point; invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step;
Constructing an RBF proxy model of a high-precision analysis model of the objective function and the constraint function based on high-precision sample point information in the set Y global; the radial function adopts a multi-quadratic function form and calculates a weight coefficient omega according to interpolation conditions, wherein a shape coefficient c is calculated through an empirical formula;
Step four, if the current iteration number is 1, determining a dominant relationship according to the objective function value and the constraint violation degree of the high-precision sample points in the set Y global, and constructing a filter; otherwise, according to the dominant relation between the newly added sample points and the sample points in the filter, updating the filter is realized;
Step five, obtaining a simple sample point set by a biased coordinate disturbance method; the method for applying the eccentric coordinate disturbance comprises the 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 acceptance sample point set Y accept; if the number of the sample points in the set Y accept is smaller than the number n s of the newly added sample points, selecting a predicted value criterion evaluation index T RBF as a constraint violation degree function value to improve the feasibility of the newly added sample points; otherwise, selecting the predictive value criterion evaluation index as a target function value to improve the optimality of the newly added sample point; the distance criterion evaluation index T DIS is selected as the minimum Euclidean distance between the sample points in the set Y accept and the high-precision sample points in the set Y global; according to the current iteration times, optimizing the non-improved condition C stall and the weight set Determining an evaluation index weight coefficient omega s, and calculating a total score; selecting a sample point with the smallest total score as a newly added sample point, calling a high-precision analysis model of the aircraft system to calculate real response values of an objective function and a constraint function, and adding a high-precision sample point set Y global; removing sample points with Euclidean distance smaller than a given threshold T coincide between the set Y accept and the existing high-precision sample points, and generating an alternative sample point set Y select;
Step seven, selecting local high/low precision sample points from the candidate sample point set by adopting a fuzzy clustering point selection strategy based on distance identification, guiding the optimization process to quickly converge towards a globally feasible optimal solution, and further improving 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, defining a subarea Y r according to a geometric envelope formed by n k＝(nv+1)(nv +2)/2 sample points with the minimum distance from the iterative optimal solution in the set Y global, and constructing PRSM an agent model by utilizing all sample points in the area Y r;
Constructing a Co-Kriging proxy model based on newly-added high/low precision sample point information selected from the candidate sample point set in the step seven, fully utilizing the multi-source simulation analysis model of the aircraft with different precision through the Co-Kriging proxy model, realizing the precision-keeping quick response prediction of the complex aircraft engineering system, taking an iterative optimal solution as an optimization initial point, adopting a sequence quadratic programming method to carry out local optimization in a subarea to obtain a pseudo-optimal solution x opt, calling the high-precision analysis model of the aircraft system to calculate the real response values of an objective function and a constraint function, and adding the real response value into the high-precision sample point set Y global;
Step ten, calculating the equivalent high-precision analysis model calling times N equal＝Nglobal+Ncheap/tau according to the high/low-precision sample point calculation cost ratio tau; if N equal reaches the maximum equivalent high-precision analysis model calling times, optimizing and terminating and outputting the current optimal solution; otherwise, repeating the steps three to nine until the number of times of invoking the maximum equivalent high-precision analysis model is reached by N equal, and then completing the solution of the aircraft system optimization problem to obtain an aircraft system optimization scheme, namely realizing the efficient approximate optimization of the aircraft driven by the heterogeneous data.
2. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 1, wherein: the method further comprises a step eleven, and according to the aircraft system optimization scheme obtained in the step eleven, the system performance of the aircraft can be effectively improved, the development efficiency of the aircraft is improved, and the development cost is reduced.
3. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 2, wherein: the aircraft system performance includes range/course of the aircraft, aerodynamic properties of the aircraft, and stiffness/strength of the aircraft.
4. A method of efficient approximate optimization of a heterologous data driven aircraft as set forth in claim 1,2, or 3, wherein: the second implementation method is that a radial basis function proxy model of a constraint function high-precision analysis model is constructed based on high-precision sample point information in a set Y global Solving the optimization problem shown in (1)
Wherein ρ n is a KS equation parameter, x k is a sample point in Y global, and T coincide is a given distance threshold; after the search of the feasible sample points is finished, if the number of high-precision sample points in the set Y global is smaller than n 0, selecting n 0-nsub high-precision sample points by adopting a standard Latin super square test design method, wherein n sub is the number of sample points in the set Y global; otherwise, not selecting a sample point; and D, invoking a high-precision analysis model of the aircraft system to calculate the real response values of the objective function and the constraint function, adding a high-precision sample point set Y global, and executing the third step.
5. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 4, wherein: constructing an RBF proxy model of a high-precision analysis model of an objective function and a constraint function based on high-precision sample point information in a set Y global; the radial function phi (r, c) adopts a multi-quadratic function form
Wherein r is Euclidean distance between sample points; according to interpolation conditions, calculating a weight coefficient according to a formula (3);
Wherein F global is a high-precision sample point response value set, and n is the number of high-precision sample points in the set Y global; the shape factor is calculated according to formula (4);
。
6. the method for efficient approximate optimization of a heterologous data driven aircraft of claim 5, wherein: the fifth implementation method is that,
Step 5.1: if the iteration is the first iteration, a quadratic polynomial response surface (Polynomial Response Surface Method, PRSM) proxy model is not constructed yet, and disturbance probability p is determined according to the number of existing high-precision sample points and the number of times of calling the maximum equivalent high-precision model; otherwise, comprehensively considering the optimality and feasibility of the sample points to determine disturbance probability, respectively calculating sensitivity indexes s f and s h of the objective function and the constraint function according to PRSM proxy model coefficients and constructing a total sensitivity indexTotal sensitivity index/>After normalization to the [0,1] interval, determining and calculating disturbance probability p according to the optimized non-improved condition C stall;
Step 5.2: applying eccentric coordinate disturbance to the iterative optimal solution based on disturbance probability p to generate a simple sample point set; generating n easy×nv uniformly distributed random numbers d ij within [0,1], where n easy is the number of simple sample points; determining a biased disturbance component by comparing the random number and the disturbance probability If/>Randomly selecting k in the set {1,2,. }, n v } to let/>Respectively taking 0 as a mean value, taking the step length sigma n as a variance to generate a normal distribution random number and combining with a eccentric disturbance component/>Applying a biased 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 the simple sample point to the design space by adopting a coordinate reflection method; wherein n easy＝min{n′easy·nv,n″easy, the initial step size is/>
7. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 6, wherein: step 7.1: if the minimum Euclidean distance between any sample point in the set Y select and the rest sample points in the set is smaller than a given threshold T coincide, selecting to remove the sample points and update an alternative sample point set Y select; calculating a cost ratio tau according to the high/low precision sample points, and determining the clustering center point number n add＝nselected/tau+1 of the high precision sample points, wherein n selected is the sample point number in the updated candidate sample point set Y select; generating a high-precision sample point clustering center point set Y e-fcm according to the clustering center point number and by adopting a fuzzy C-means clustering analysis method, and simultaneously removing null values in the set Y e-fcm; updating a high-precision sample point clustering center point set Y e-fcm and n add; calculating any sample point in a high-precision sample point clustering center point setMinimum Euclidean distance L (i) between the candidate sample point set Y select and all points in the candidate sample point set Y select and/>The nearest point is marked asIf L (i)＜Tcoincide, choose/>The method is a newly added high-precision sample point; otherwise, choose/>The method is a newly added high-precision sample point;
Step 7.2: selecting tau multiplied by n add clustering centers based on the updated candidate sample point set Y select and by adopting a fuzzy C-means clustering analysis method, and generating a new added low-precision sample point; respectively calling a high/low precision analysis model to calculate model response values of local high/low precision sample points, adding the high precision sample points into a high precision sample point set Y global, and adding the low precision sample points into a low precision sample point set Y cheap;
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 candidate sample point set by utilizing the fuzzy clustering point selection strategy, and the optimization process is guided to quickly converge towards the global feasible optimal point, so that the optimization efficiency is improved.
8. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 7, wherein: the fifth concrete implementation method is that,
Step 5.1: if the first iteration is performed, a quadratic polynomial response surface (Polynomial Response Surface Method, PRSM) proxy model is not constructed yet, and the disturbance probability p is determined according to the existing high-precision sample points and the maximum equivalent high-precision model call times
N is the number of high-precision sample points in the current set Y global, and N max is the number of times of invoking the maximum equivalent high-precision model; otherwise, comprehensively considering the optimality and feasibility of the sample points to determine disturbance probability, and respectively calculating sensitivity indexes s f and s of the objective function and the constraint function according to PRSM proxy model coefficients h
In the middle ofAnd/>Proxy model coefficients for objective function PRSM,/>And/>Agent model coefficients for constraint functions PRSM; structure total sensitivity index s
Normalizing the total sensitivity index s to the [0,1] interval
Determining the calculated disturbance probability p according to the optimized non-improved condition C stall
Optimal performance for achieving a heterogeneous data driven aircraft efficient approximate optimization method, wherein C' stall = 2
Step 5.2: applying eccentric coordinate disturbance to the iterative optimal solution based on disturbance probability p to generate a simple sample point set; generating n easy×nv uniformly distributed random numbers d ij within [0,1], where n easy is the number of simple sample points; determining a biased disturbance component by comparing the random number and the disturbance probability
If it isRandomly selecting k in the set {1,2,. }, n v } to let/>Respectively taking 0 as a mean value, taking the step length sigma n as a variance to generate a normal distribution random number and combining with a eccentric disturbance component/>Generating a simple sample point set by applying eccentric disturbance to an iterative optimal solution
yj＝xopt+z (11)
Wherein x opt is an iterative optimal solution, and z is a normal distribution random number
If the simple sample point exceeds the boundary of the design space, mapping the simple sample point to the design space by adopting a coordinate reflection method; wherein n easy＝min{n′easy·nv,n″easy, the initial step size is
9. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 8, wherein: the performance of the aircraft efficient approximate optimization method driven by the heterogeneous data is optimal, wherein n easy＝min{100·nv, 5000}, and the initial step size is that
10. The method for efficient approximate optimization of a heterologous data driven aircraft of claim 8, wherein: to achieve optimal performance of the heterogeneous data driven aircraft efficient approximate optimization method, the initial set of weights ω s,0 = {0.3,0.5,0.8,0.95}.
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