CN114282310A - Aeroelastic structure coupling optimization method based on self-adaptive point-adding proxy model - Google Patents

Abstract

The invention discloses a coupling optimization method of a aeroelastic structure based on a self-adaptive point-adding agent model, which comprises the steps of firstly considering parameter uncertainty and model uncertainty, quantifying the uncertainty, providing a self-adaptive intelligent point-adding criterion based on a Kriging agent model, obtaining the upper and lower limits of the maximum stress and the flutter speed of an aircraft structure, and then considering a structural strength constraint condition and a aeroelastic constraint condition based on the self-adaptive point-adding agent model to optimally design the aircraft structure. The invention reduces the times of finite element analysis and aeroelasticity analysis in the optimization process of the aircraft structure, reduces the calculated amount, improves the optimization efficiency and provides a new thought for the optimization design of the aircraft structure.

Description

Aeroelastic structure coupling optimization method based on self-adaptive point-adding proxy model

Technical Field

The invention relates to the field of aeroelastic structure coupling optimization, in particular to an aeroelastic structure coupling optimization method based on a self-adaptive dotting agent model.

Background

The aeroelastic problem is widespread in aircraft design processes. Under the action of aerodynamic loads, the structure of the aircraft deforms and vibrates, and the deformation and the vibration of the structure influence the size and the distribution of the aerodynamic loads borne by the aircraft in turn, so that various aeroelasticity problems are generated when the aircraft performs flight tasks. The aeroelasticity problem is mainly divided into two types, namely the problem of static aeroelasticity, namely the displacement and deformation of an elastic body under the action of pneumatic load; the second is to study the dynamic response of the elastomer under the action of the pneumatic load, which is called the problem of the pneumatic elasticity.

The flutter phenomenon belongs to the aeroelasticity problem, is one of all the aeroelasticity problems which has the greatest harm to an aircraft, when the flight speed of the aircraft reaches a certain value, the lifting surface of the aircraft can vibrate greatly under the coupling action of aerodynamic force, elastic force and inertia force, and the phenomenon is called flutter. Flutter is a self-excited vibration that, once it occurs, often has catastrophic consequences for the aircraft and the pilot, even leading to aircraft and even death. Since international scholars have recognized the causes and hazards of flutter, strict specifications have been set, for example, in the airworthiness regulations of our country, the flutter phenomenon must not occur when an aircraft normally performs a mission within its flight envelope. At present, two methods for analyzing the flutter of the aircraft are mainly used, one is a wind tunnel test, a model is manufactured on the whole aircraft according to proportion according to a similar principle in aerodynamics, an actual blowing test is carried out on the model in a wind tunnel, and the flutter speed and the flutter frequency of the aircraft are obtained through calculation after test data are obtained. The other is a numerical simulation means, which processes the numerical model of the aircraft by using relevant approximate theories, such as a K method, a KE method, a PK method and the like, so as to calculate the flutter speed and the flutter frequency. The second method is widely used in flutter analysis because of its advantages such as low cost and short cycle time.

However, there are two major problems faced in the design of aircraft that actually take into account flutter. Firstly, although the adopted numerical simulation method has a short period and low cost compared with a wind tunnel test, a large amount of computing resources still need to be consumed, and a single analysis is short for several hours and long for several days; secondly, the actual design problem of the aircraft often needs to be calculated for finding the optimal design for multiple times, for example, when the optimization result does not meet the requirement, the optimization parameters need to be adjusted, and the optimization process is repeated. It is clear that if a single optimization takes up all the computational resources, then no more analytical studies will be performed subsequently or the analytical studies will be beyond a specified time limit. The basic idea of the proxy model is to spend resources and energy on building an efficient approximate mathematical model that can replace time-consuming numerical simulations, and once these proxy models are built, many curves can be drawn to better explore the trade-offs between multiple design goals and gain a deeper understanding of the problem, and if necessary, the proxy models can be updated to iterate until satisfied.

Most of the existing agent models are deterministic agent models, multi-source uncertainties such as material dispersibility and machining errors are not considered, the uncertainties have non-negligible influence on the performance of the aircraft structure, uncertainty propagation analysis is necessary, the agent models containing the uncertainties are built, and uncertainty intervals of structural response are obtained through the uncertainty agent models. In order to further reduce the calculation cost and reduce the number of required samples, bidirectional matching can be performed by using the uncertainty proxy model, and meanwhile, the proxy model is updated to finally obtain the upper and lower bounds of the structural response, so that the efficiency of uncertainty propagation analysis is improved.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method fully considers parameter uncertainty and model uncertainty commonly existing in engineering practical problems, adaptively adds sample points on the basis of an upper confidence boundary and a lower confidence boundary of a Kriging proxy model, updates the proxy model to obtain upper and lower boundaries of maximum stress and flutter speed of the aircraft structure, and comprehensively considers an intensity constraint condition and a aeroelasticity constraint condition to optimally design the aircraft structure. The method effectively reduces the times of finite element analysis and aeroelasticity analysis in the optimization process of the aircraft structure, reduces the calculated amount, improves the optimization efficiency, and provides a new thought for the optimization design of the aircraft structure.

The technical scheme adopted by the invention for solving the technical problems is as follows: a coupling optimization method of a gas-elastic structure based on a self-adaptive point-adding proxy model is realized by the following steps:

the first step is as follows: determining the elastic modulus of the aircraft structural material as an interval uncertain variable alpha, and determining the range alpha of the interval uncertain variable alpha^IAnd alpha are^IConversion to standard interval variable xi and range xi thereof^IGenerating an initial sample point xi of xi by adopting a test design method⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^T(m is the number of initial sample points). Taking a wing spar and a wing rib of the structure as design variables, and calculating the maximum stress and the flutter speed y of the aircraft structure at an initial sample point by finite element software at the current design point [ y ═ y⁽¹⁾,y⁽²⁾,…,y^(m)]^TY represents the maximum stress and the flutter speed;

the second step is that: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,…,y^(m)]^TConstructing a Kriging agent model, considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, and calculating the lower confidence boundary LCB of the Kriging agent model^k(xi), calculating using a global optimization algorithm such that LCB^k(xi) minimum sample point xi^(min)；

The third step: judging newly generated sample point xi^(min)And existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TThe most distant betweenSmall value min | | xi^(min)-ξ⁽ⁱ⁾If | (i ═ 1,2, …, m) is less than a predefined convergence threshold epsilon, and if not, then ξ^(min)Adding a new sample point and calculating the xi of the aircraft structure through a finite element^(min)Adding 1 to the iteration number k according to the maximum stress and the flutter speed, then returning to the second step, and if so, entering the next step, and resetting the iteration number k to be 1;

the fourth step: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m),ξ^(min)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,…,y^(m),y^(min)]^TConstructing a Kriging agent model, considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, and calculating the upper trust boundary UCB of the Kriging agent model^k(ξ), computing using a global optimization algorithm such that UCB is made^k(xi) maximum sample point xi^(max)；

The fifth step: judging newly generated sample point xi^(max)And existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TMinimum value min | | xi of distance between them^(max)-ξ⁽ⁱ⁾If | (i ═ 1,2, …, m) is less than a predefined convergence threshold epsilon, and if not, then ξ^(max)Adding a new sample point and calculating the xi of the aircraft structure through a finite element^(max)Adding 1 to the iteration number k according to the maximum stress and the flutter speed, then returning to the fourth step, and if so, entering the next step, and resetting the iteration number k to be 1;

and a sixth step: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,...,ξ^(m),ξ^(min),ξ^(max)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,...,y^(m),y^(min),y^(max)]^TConstructing a Kriging agent model as a final agent model, obtaining the maximum value and the minimum value of the agent model predicted value by adopting a global optimization algorithm, and taking the maximum value and the minimum value as the upper and lower boundaries of the maximum stress and the flutter speed of the aircraft structure to finish the self-adaptive point-adding agent modelConstructing a type;

the seventh step: and (3) respectively calculating the maximum stress and flutter speed constraint function values of the aircraft structure obtained in the sixth step based on the self-adaptive agent model, optimally designing the aircraft structure by taking the minimum total weight of the structure as a target function, searching a next design point by using a mature optimization algorithm if the optimal design result does not meet a convergence condition, and repeating the first step to the sixth step at the next design point until the optimal convergence is reached, thereby completing the optimization design of aeroelastic structure coupling.

In the first step to the sixth step, automatically selecting and adding sample points according to the existing agent model to finally obtain the maximum stress and flutter speed of the aircraft structure, and completing uncertainty propagation analysis, namely the self-adaptive point-adding agent model; in the seventh step, based on the adaptive agent model, the optimization design of the aeroelastic structure coupling is completed by using the existing optimization algorithm.

Further, the range alpha of the interval uncertain variable alpha in the first step^IRange xi converted to standard interval variable xi^I＝[-1,1]The specific method comprises the following steps:

α^I＝α^c+α^rξ^I (17)

wherein alpha is^cFor interval uncertainty of central value of variable alpha, alpha^IIs the interval radius of the interval uncertainty variable alpha, and the expression is:

in the formulaαAnd

respectively representing a lower interval bound and an upper interval bound of the interval uncertainty variable alpha.

Further, in the second step, a Kriging proxy model is constructed based on the existing sample points and the maximum stress and the flutter speed at the sample points, and the specific expression of the predicted value is as follows:

wherein the content of the first and second substances,

for the predicted maximum stress and flutter velocity, the proxy model is used to predict the value of the structural response at unknown points,

the response prediction value is expressed by the expression of the proxy model, and particularly in the invention patent, the structural response is the maximum stress and the flutter speed of the structure, and f (xi) ═ f₁(ξ),f₂(ξ),...,f_p(ξ)]Is a basis function, and p represents the number of basis functions;

herein, the

Is a correlation function with a correlation parameter theta; beta is a^*And gamma^*The expression of (a) is:

wherein the content of the first and second substances,

considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, the lower trust boundary LCB of the Kriging agent model^kThe specific expression of (ξ) is:

wherein the content of the first and second substances,

g represents the prediction uncertainty of the Kriging agent model; w represents the independent variable uncertainty of the Kriging agent model;

the variance is predicted by a Kriging agent model; k represents the kth iteration step; d and δ are constants, and are taken to be 1 in the present invention. The proxy model is an approximate relationship between the sample point and the function value at the sample point.

Is a predicted value, LCB, for other points^k(xi) is the lower confidence boundary of the predicted value after uncertainty is considered.

Further, in said third step, a newly generated sample point ξ^(min)Is to make LCB^k(ξ) the smallest point, and the specific expression of the convergence criterion is:

min||ξ^(min)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,m (24)

wherein ξ⁽ⁱ⁾(i ═ 1,2, …, m) represents the existing sample points, min | | ξ^(min)-ξ⁽ⁱ⁾| | denotes the newly generated sample point ξ^(min)And the minimum distance between the current sample point and the current sample point, wherein epsilon is a preset convergence threshold value and is 0.0001 in the invention.

Further, in the fourth step, a proxy model is constructed based on the existing sample points and the maximum stress and the flutter speed at the sample points, and the specific expression of the predicted value is as follows:

wherein the content of the first and second substances,

for the predicted maximum stress and flutter speed, f (ξ) ═ f₁(ξ),f₂(ξ),...,f_p(ξ)]Is a basis function, and p represents the number of basis functions;

herein, the

Is a correlation function with a correlation parameter theta; beta is a^*And gamma^*The expression of (a) is:

wherein the content of the first and second substances,

considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, the UCB of the upper signaling boundary of the Kriging agent model^kThe specific expression of (ξ) is:

wherein the content of the first and second substances,

g represents the prediction uncertainty of the Kriging agent model; w represents the independent variable uncertainty of the Kriging agent model;

is the predicted variance of the Kriging surrogate model; k represents the kth iteration step; d and delta are constants, both in the present inventionTake 1.

Further, a newly generated sample point ξ in the fifth step^(max)Is to make UCB^k(ξ) the largest point, and the specific expression of the convergence criterion is:

min||ξ^(max)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,m (30)

wherein ξ⁽ⁱ⁾(i ═ 1,2, …, m) represents the existing sample points, min | | ξ^(max)-ξ⁽ⁱ⁾| | denotes the newly generated sample point ξ^(max)And the minimum distance between the current sample point and the current sample point, wherein epsilon is a preset convergence threshold value and is 0.0001 in the invention.

Further, in the sixth step, the upper and lower boundaries of maximum stress and flutter speed of the aircraft structure

Andythe method is obtained by calculating the maximum value and the minimum value of the final Kriging agent model, namely:

whereby the uncertainty interval for the maximum stress and flutter speed of the aircraft structure is

Compared with finite element calculation, the Kriging agent model has low calculation time and calculation cost, so that the method for obtaining the uncertain interval of the maximum stress and the flutter speed is more efficient, and the efficiency of uncertainty propagation analysis is greatly improved. Compared with finite element calculation, the Kriging agent model has low calculation time and calculation cost, so that the method for obtaining the uncertain interval of the maximum stress and the flutter speed is more efficient, and the efficiency of uncertainty propagation analysis is greatly improved.

Further, the optimization in the seventh step is listed as:

where x is a design variable, taken in the present invention as the thickness of the spar and rib, x^LAnd x^URespectively a lower bound and an upper bound for the design variable; m (x) represents the total structural weight of the aircraft structure at design point x;

represents an upper bound on the maximum stress of the aircraft structure, [ sigma ]]Allowable stress;v _flutter(x) Lower bound, v, representing the flutter velocity of the aircraft structure_crThe minimum flutter speed required by aeroelasticity.

Compared with the prior art, the method has the advantages that a new idea of aircraft aeroelastic structure coupling optimization is provided, and the limitation of the traditional aircraft structure optimization design based on the deterministic agent model is made up and perfected. In the coupling optimization process of the aeroelastic structure of the aircraft, firstly, the independent variable uncertainty and the prediction uncertainty of a Kriging proxy model are considered, a self-adaptive intelligent point adding criterion based on the Kriging proxy model is provided, the upper and lower limits of the maximum stress and the flutter speed of the aircraft structure are obtained, the structural strength constraint condition and the aeroelastic constraint condition are considered, and the total times of finite element analysis and aeroelastic analysis in the optimization process are reduced on the premise of not losing the optimization precision, so that the calculated amount is reduced, and the optimization efficiency is improved.

Drawings

FIG. 1 is a finite element mesh model of an aircraft wing structure;

fig. 2 is a selection of a new sample point based on a lower signaling boundary LCB;

FIG. 3 is a proxy model after convergence of a lower trust boundary;

fig. 4 is a selection of a new sample point based on an upper signaling boundary UCB;

FIG. 5 is a proxy model after upper trust boundary convergence;

FIG. 6 is an upper and lower bound obtained based on a final proxy model for maximum stress of an aircraft wing structure;

FIG. 7 is an upper and lower bound obtained for aircraft wing structure flutter velocity based on a final proxy model;

FIG. 8 is a flow chart of an implementation of the aeroelastic structure coupling optimization method based on the adaptive dotting agent model.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.

Examples

As shown in fig. 8, the invention relates to a coupling optimization method for a gas-elastic structure based on an adaptive dotting agent model, which comprises the following steps:

step (1) takes the aircraft wing structure shown in figure 1 as an optimization object, and the uncertain variable interval is alpha^I＝[0,1]The material used for the structure is 2a12 aluminum alloy and the elastic modulus E of the structure with respect to the uncertain variable α is given by:

the structure consists of three parts, namely a skin, a wing beam and a wing rib, wherein the finite element grids of the three parts are all shell units, the thickness of the skin is 5.7mm, and the unit thickness of the wing beam is taken as a first design variable x₁Taking the cell thickness of the rib as a second design variable x₂And the initial value of the design variable is

The root of the wing structure of the aircraft is a fixed support end, the surface of the skin bears distributed aerodynamic loads, and the incoming flow speed is 4 Ma.

Firstly, an uncertain variable interval alpha is formed^ITransformation ofIs a standard interval xi^I＝[-1,1]，α^IAnd xi^IThe transformation relation between the two is as follows:

α^I＝0.5+0.5·ξ^I (34)

five sample points of xi obtained by uniform sampling are [ -1, -0.5,0,0.5,1]^TBy calling finite element analysis, the response value of the maximum stress of the structure at the sample point can be obtained as y_stress＝[236.43,231.70,233.84,223.48,247.65]^TMPa, response value of flutter speed of aircraft structure at sample point is y_vf＝[2281.1,2270.6,2275.0,2254.6,2329.8]^Tm/s。

Respectively constructing a Kriging proxy model based on the maximum stress and the flutter speed of the existing five sample point pairs, and calculating a lower confidence boundary LCB of the Kriging proxy model by considering the independent variable uncertainty and the prediction uncertainty of the proxy model^k(xi), calculating using a global optimization algorithm such that LCB^k(xi) minimum sample point xi^(min)The value of (c). For the maximum stress of the aircraft wing structure, the process is shown in fig. 2, the black solid line is a Kriging proxy model constructed according to the initial five sample points and the corresponding maximum stress, the black dotted line is a lower trust boundary, and the hollow point is an LCB (lower trust boundary)^k(xi) minimum sample point xi^(min)。

Step (3) because the newly generated sample point in step (2) is xi^(min)0.3568, the corresponding uncertain variable sample point is α^(min)0.6784, the convergence criterion is not fulfilled:

min||ξ^(min)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,5 (35)

therefore, the function response value corresponding to the newly generated sample point should be calculated, the iteration number k is set to 2, and the process of step (2) and step (3) is repeated until convergence. In the embodiment of the present invention, a total of seven iterations are performed, that is, convergence is achieved after seven sample points are added, and the number of iterations is reset to k 1 after convergence. For the maximum stress of the aircraft wing structure, the converged Kriging proxy model and the lower trust boundary LCB are shown in fig. 3, the solid points are all sample points after iteration, the black solid line is the Kriging proxy model constructed according to all 12 sample points, and the black dotted line is the lower trust boundary.

Step (4) constructing a Kriging proxy model based on the existing 12 sample points, considering the independent variable uncertainty and the prediction uncertainty of the proxy model, and calculating the upper signaling boundary UCB of the Kriging proxy model^k(ξ), computing using a global optimization algorithm such that UCB is made^k(xi) maximum sample point xi^(max)The value of (c). For the maximum stress of the aircraft wing structure, the process is shown in fig. 4, the black solid line is a Kriging agent model constructed according to all 12 sample points, the black dotted line is an upper confidence boundary, and the hollow point is an upper confidence boundary UCB^k(xi) maximum sample point xi^(max)。

Step (5) because the newly generated sample point in step (3) is xi^(max)0.8794, the corresponding uncertain variable sample point is α^(max)0.9397, the convergence criterion is not fulfilled:

min||ξ^(max)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,10 (36)

the function response value corresponding to the newly generated sample point should be calculated, the iteration number k is made to be 2, and the process of step (4) and step (5) is repeated until convergence. In the embodiment of the present invention, the iteration is performed twice in total, that is, convergence is achieved after two sample points are added, and the number of iterations is reset to k 1 after convergence. For the maximum stress of the aircraft wing structure, the converged Kriging proxy model and the upper trust boundary are shown in FIG. 5, the solid points are all the sample points after iteration, the black solid line is the Kriging proxy model constructed according to all the 14 sample points, and the black dotted line is the upper trust boundary.

Step (6) constructing Kriging surrogate model of maximum stress of structure based on existing 14 sample points, and taking the Kriging surrogate model as final refined surrogate model of maximum stress of structure

And using a global optimization algorithm to obtain

Maximum value of

And minimum value

As shown in fig. 6, the solid points are all the sample points after iteration, the black solid line is the Kriging surrogate model constructed from all the 14 sample points, and the maximum value and the minimum value of the surrogate model are also marked in the figure and are the upper bound and the lower bound of the maximum stress of the structure, respectively.

So that the uncertainty interval of the maximum stress of the structure is as follows:

similarly, for the flutter speed of the aircraft wing structure, as shown in fig. 7, the solid points are all sample points after iteration, the black solid line is a Kriging proxy model constructed according to all 15 sample points, the maximum value and the minimum value of the proxy model are also marked in the figure, and are respectively the upper bound and the lower bound of the structure flutter speed, so that the uncertainty interval of the structure flutter speed is:

and (7) calculating the value of a constraint function by using the upper limit of the maximum stress of the aircraft wing structure and the lower limit of the flutter speed, and optimally designing the aircraft structure by using the minimum total weight of the structure as an objective function. The allowable value of the maximum stress of the structure is set to 265MPa, the minimum flutter speed required by aeroelasticity is set to 1360m/s due to the incoming flow speed of 4Ma, and the optimization list is as follows:

the design variable of the final optimization result is x₁＝11.4615mm，x₂10.8718mm, the upper bound of the corresponding maximum stress of the structure is

The lower bound of the structural flutter velocity isy _flutter2143.6M/s, and 347.5kg of the total structure mass M. From the result of the constraint function, although the flutter speed of the wing structure of the aircraft is far away from the minimum value, the maximum stress reaches the vicinity of the allowable value, and no further optimization space exists; meanwhile, the total mass of the wing structure is reduced from 352.1kg before optimization to 347.5kg, and the effectiveness of the invention is illustrated. Compared with the traditional optimization method, the method provided by the invention has the advantages that the times of finite element analysis and aeroelasticity analysis are reduced, the calculated amount is reduced, the optimization efficiency is improved, and a new thought is provided for the optimization of the structural design of the aircraft.

The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.

The above are only the specific steps of the present invention, and the protection scope of the present invention is not limited in any way; the method can be expanded and applied to the field of efficient optimization of coupling of the aeroelastic structure, and all technical schemes formed by adopting equivalent transformation or equivalent replacement fall within the protection scope of the invention.

Claims (8)

1. A aeroelastic structure coupling optimization method based on a self-adaptive point-adding proxy model is characterized in that: the method is realized by adopting the self-adaptive dotting agent model designed by the invention, and comprises the following steps:

the first step is as follows: determining the elastic modulus of the aircraft structural material as an interval uncertain variable alpha, and determining the range alpha of the interval uncertain variable alpha^IAnd alpha are^IConversion to standard interval variable xi and range xi thereof^IGenerating an initial sample point xi of xi by adopting a test design method⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TM is the number of initial sample points; spars and ribs of structures as design variablesAnd at the current design point, calculating by finite element software to obtain the maximum stress and the flutter speed y of the aircraft structure at the initial sample point as [ y ═ y⁽¹⁾,y⁽²⁾,…,y^(m)]^TY represents the maximum stress and the flutter speed;

the second step is that: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,…,y^(m)]^TConstructing a Kriging agent model, and calculating a lower confidence boundary LCB of the Kriging agent model according to the independent variable uncertainty and the prediction uncertainty of the Kriging agent model^k(xi), calculating using a global optimization algorithm such that LCB^k(xi) minimum sample point xi^(min)Min means the minimum value, i.e. xi^(min)Make LCB^k(xi) taking a minimum value;

the third step: judging newly generated sample point xi^(min)And existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TMinimum value min | | xi of distance between them^(min)-ξ⁽ⁱ⁾If m is smaller than a predefined convergence threshold epsilon, if not, | i ═ 1,2, …, ξ^(min)Adding a new sample point and calculating the xi of the aircraft structure through a finite element^(min)The maximum stress and the flutter speed are processed, the iteration number k is added by 1, and then the step returns to the second step; if yes, entering the next step, and resetting the iteration number k to be 1;

the fourth step: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m),ξ^(min)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,…,y^(m),y^(min)]^TConstructing a Kriging agent model, considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, and calculating the upper trust boundary UCB of the Kriging agent model^k(ξ), computing using a global optimization algorithm such that UCB is made^k(xi) maximum sample point xi^(max)Max means the maximum value, i.e. ξ^(max)Make UCB^k(xi) taking a maximum value;

the fifth step: judging newly generated sample point xi^(max)And existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m)]^TMinimum value min | | xi of distance between them^(max)-ξ⁽ⁱ⁾If m is smaller than a predefined convergence threshold epsilon, if not, | i ═ 1,2, …, ξ^(max)Adding a new sample point and calculating the xi of the aircraft structure through a finite element^(max)Adding 1 to the iteration number k according to the maximum stress and the flutter speed, and then returning to the fourth step; if yes, entering the next step, and resetting the iteration number k to be 1;

and a sixth step: based on existing sample point [ xi⁽¹⁾,ξ⁽²⁾,…,ξ^(m),ξ^(min),ξ^(max)]^TAnd the corresponding maximum stress and flutter speed y ═ y⁽¹⁾,y⁽²⁾,…,y^(m),y^(min),y^(max)]^TConstructing a Kriging agent model as a final agent model, obtaining the maximum value and the minimum value of an agent model predicted value by adopting a global optimization algorithm, and taking the maximum value and the minimum value as the upper and lower boundaries of the maximum stress and the flutter speed of an aircraft structure to finish the construction of the self-adaptive point-adding agent model;

the seventh step: and (3) respectively calculating the maximum stress and flutter speed constraint function values of the aircraft structure obtained in the sixth step based on the self-adaptive agent model, optimally designing the aircraft structure by taking the minimum total weight of the structure as a target function, searching a next design point by using a mature optimization algorithm if the optimal design result does not meet a convergence condition, and repeating the first step to the sixth step at the next design point until the optimal convergence is reached, thereby completing the optimization design of aeroelastic structure coupling.

2. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: in the first step, the range alpha of the interval uncertain variable alpha is determined^IRange xi converted to standard interval variable xi^I＝[-1,1]The specific method comprises the following steps:

α^I＝α^c+α^rξ^I (1)

wherein alpha is^cFor interval uncertainty of central value of variable alpha, alpha^IIs the interval radius of the interval uncertainty variable alpha, and the expression is:

in the formulaαAnd

respectively representing a lower interval bound and an upper interval bound of the interval uncertainty variable alpha.

3. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: the second step is specifically realized as follows:

(1) constructing a proxy model based on the existing sample points and the maximum stress and the flutter speed at the sample points, wherein the specific expression of the predicted value is as follows: calculation of LCB in equation (6) requires

The expression in the formula (7) includes

w represents the independent variable uncertainty of the proxy model:

wherein the content of the first and second substances,

for the predicted maximum stress and flutter velocity, the proxy model is used to predict the value of the structural response at unknown points,

for the prediction of response, the structure response is the maximum stress and flutter speed of the structure, and f (xi) ═ f₁(ξ),f₂(ξ),...,f_p(ξ)]Is a basis function, and p represents the number of basis functions;

is a correlation function with a correlation parameter theta; beta is a^*And gamma^*The expression of (a) is:

wherein the content of the first and second substances,

(2) considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, the lower trust boundary LCB of the Kriging agent model^kThe specific expression of (ξ) is:

wherein the content of the first and second substances,

g represents the prediction uncertainty of the Kriging agent model; w represents the independent variable uncertainty of the Kriging agent model;

the variance is predicted by a Kriging agent model; k represents the kth iteration step; d and δ are constants, and are taken to be 1 in the present invention.

4. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: in the third step, a newly generated sample point ξ^(min)Is to make LCB^k(ξ) the smallest point, and the specific expression of the convergence criterion is:

min||ξ^(min)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,m (8)

wherein ξ⁽ⁱ⁾I ═ 1,2, …, m denotes existing sample points, min | | ξ^(min)-ξ⁽ⁱ⁾| | denotes the newly generated sample point ξ^(min)And the minimum distance between the current sample point and the current sample point, wherein epsilon is a preset convergence threshold value and is 0.0001 in the invention.

5. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: the fourth step is specifically realized as follows:

(1) constructing a proxy model based on the existing sample points and the maximum stress and the flutter speed at the sample points, wherein the specific expression of the predicted value is as follows:

wherein the content of the first and second substances,

for the predicted maximum stress and flutter speed, f (ξ) ═ f₁(ξ),f₂(ξ),…,f_p(ξ)]Is a basis function, and p represents the number of basis functions;

is a correlation function with a correlation parameter theta; beta is a^*And gamma^*The expression of (a) is:

wherein the content of the first and second substances,

(2) considering the independent variable uncertainty and the prediction uncertainty of the Kriging agent model, the UCB of the upper signaling boundary of the Kriging agent model^kThe specific expression of (ξ) is:

wherein the content of the first and second substances,

g represents the prediction uncertainty of the Kriging agent model; w represents the independent variable uncertainty of the Kriging agent model;

is the predicted variance of the Kriging surrogate model; k represents the kth iteration step; d and δ are constants, and are taken to be 1 in the present invention.

6. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: in the fifth step, a newly generated sample point ξ^(max)Is the point that maximizes, and the specific expression of the convergence criterion is:

min||ξ^(max)-ξ⁽ⁱ⁾||≤ε,i＝1,2,…,m (14)

wherein ξ⁽ⁱ⁾I ═ 1,2, …, m denotes existing sample points, min | | ξ^(max)-ξ⁽ⁱ⁾| | denotes the newly generated sample point ξ^(max)And the minimum distance between the current sample point, wherein epsilon is a preset convergence threshold value.

7. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: in the sixth step, the upper and lower boundaries of maximum stress and flutter speed of the aircraft structure

And y is obtained by calculating the maximum and minimum values of the final Kriging surrogate model, namely:

whereby the uncertainty interval for the maximum stress and flutter speed of the aircraft structure is

8. The aeroelastic structure coupling optimization method based on the adaptive dotting proxy model according to claim 1, characterized in that: in the seventh step, the list of the optimized design is as follows:

where x is a design variable, is the thickness of the spar and rib, x^LAnd x^URespectively a lower bound and an upper bound for the design variable; m (x) represents the total structural weight of the aircraft structure at design point x;

represents an upper bound on the maximum stress of the aircraft structure, [ sigma ]]Allowable stress;v _flutter(x) Lower bound, v, representing the flutter velocity of the aircraft structure_crThe minimum flutter speed required by aeroelasticity.

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