CN109033678A - A kind of aircraft near-optimal design method generated based on virtual sample - Google Patents
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Abstract
A kind of aircraft near-optimal method generated based on virtual sample disclosed by the invention, belongs to the design optimizing field in Flight Vehicle Design.The present invention carries out approximate modeling to high accuracy analysis model using RBF, and is designed optimization instead of archetype；The effective update and management for realizing RBF agent model are generated by virtual sample, are improved local search ability and global exploring ability, are constructed in virtual sample generation comprising LSSVM classifier training and virtual sample；In near-optimal design process, it makes full use of and has construction sample point information, it is generated by virtual sample and constantly updates RBF model, to guide and ensure that optimization process rapidly converges to globally optimal solution, aircraft high accuracy analysis model call number is reduced, is of great significance to alleviating structure small sample problem, reducing to calculate cost, improve optimization efficiency etc..The present invention is suitable for that there are the aerospace field of high time consuming analysis model or correlation engineering optimization design fields, and solves the problems, such as correlation engineering.
Description
Technical field
The present invention relates to a kind of aircraft near-optimal design methods generated based on virtual sample, belong to Flight Vehicle Design
In design optimizing field.
Background technique
With the development of computer technology, high accuracy analysis model is widely used in Flight Vehicle Design, such as
Computation fluid dynamics model, finite element analysis FEA model etc..High accuracy analysis model can in raising analysis precision and design
While reliability, also increase calculating cost, for example, using CFD model complete an aerodynamics simu1ation analysis generally require it is several small
When.Conventional aircraft design method often calls directly exploration of the high accuracy analysis model realization to design space, so that calculating
Cost is difficult to receive and design efficiency is lower, extends the design cycle of aircraft.In order to reduce in conventional aircraft design
Cost is calculated, the design optimization strategy (MBDO) based on agent model is widely applied in field of flight vehicle design.It should
Method is intended to carry out approximation to original optimization problem by mathematical measure, and optimizes instead of high accuracy analysis model.However,
It is less to the sampling of high accuracy analysis model (i.e. small sample problem) that aircraft optimization designs initial stage, and tradition MBDO strategy is to
There are the Land use systems of sample information more single (such as modeling and exploring design space), so that tradition MBDO strategy is flying
There is still a need for a large amount of management and update for calling high accuracy analysis model realization agent model in device design process, cause to calculate cost
Still higher, there are still rooms for promotion for design efficiency.In recent years, small-sample learning problem obtains widely in machine learning field
Concern.On the one hand, the support vector machines based on Statistical Learning Theory and its mutation are applied in fields such as pattern-recognition, fault detections
It is more.On the other hand, virtual sample generates the information structuring virtual sample by sufficiently excavating existing sample, spread training collection with
Learning performance is improved, there is directive significance for processing small sample problem.Therefore, with reference to small-sample learning the relevant technologies, having must
Develop the course of new aircraft near-optimal design method that a kind of computational efficiency is high, global convergence is strong, to alleviate aircraft
Near-optimal designs the small sample problem faced.
Technical solution in order to better illustrate the present invention is below briefly situated between to involved related mathematical tool
It continues:
(1) radial basis function agent model
Radial basis function RBF is a kind of interpolation type agent model, shown in citation form such as formula (1)
Wherein nsFor sample point quantity, φ (| | x-xi| |), i=1,2..nsFor basic function, β is RBF coefficient vector.It is common
Basic function type it is as shown in table 1.
RBF needs meet interpolation condition shown in formula (2) at sample point
WhereinFor the true model response at sample point.
Table 1 often uses radial basis function type
(2) Kriging agent model
Kriging model KRG is a kind of unbiased optimal estimation interpolation model for spatial distribution data, such as formula (3) institute
Show
In formula, g (x) is multinomial overall situation approximate model, if the numerical characteristic of target is unknown, can use constant μ.Partial deviations
Z (x) be mean value be 0, variance σ2, covariance non-zero random process.Wherein, g (x) reflects approximate target in design space
In general morphologictrend, Z (x) determine KRG approximate ability.The covariance matrix of Z (x) is represented by
Cov[Z(xi),Z(xj)]=σ2R[R(xi,xj)] (4)
In formula, R is Gauss correlation function, and R is symmetrical correlation matrix.
Parameter μ and σ2Formula (6) can be solved by least square method to obtain.
Parameter θkIt can be obtained by the optimization problem in maximum-likelihood method solution formula.
The dependent vector r (x) of arbitrary point x is
To which KRG model can be rewritten as
(3) least square method supporting vector machine
Support vector machines are proposed by Vapnik et al., according to structural risk minimization principle, by solving formula (10)
Problem obtains hyperplane, realizes classification learning.
In formula, w is the normal vector of hyperplane, and c is normal number, ξiIt is relaxation factor,It is kernel function, yiIt is i-th
The class label of training sample.By introducing least square, formula (10) inequality constraints is rewritten as equation about by Suykens et al.
Beam, as shown in formula (11).
In formula, eiIt is tolerance, γ is relatively small normal number.The problem of to solve formula (11), construct a Lagrange
Function, such as formula (12)
In formula, αiThe Lagrange multiplier being positive.According to KKT condition, available formula (13)
By eliminating the available linear problem of w and e such as formula (14)
Wherein, Y=[y1,...,yn],α=[α1,...,αn],
1=[11,...,1n].And define kernel function Ω (xk,xl) be
By solving formula (14), disaggregated model can be expressed as
Wherein, { -1 ,+1 } sign (x) ∈, x are test samples.
Summary of the invention
Cause aircraft close using insufficient existing sample point for traditional proxy modelling optimisation strategy (MBDO)
It is disclosed by the invention a kind of based on virtual sample like the defect for still needing to call more high accuracy analysis model in process of optimization
Aircraft near-optimal method (the Sequential Radial Basis Function Using Virtual of generation
Sample Generation, SRBF-VSG), technical problems to be solved are: it is sufficiently sharp that realization has construction sample point information
With, ensure design optimization optimality and it is constringent under the premise of, reduce aircraft near-optimal design process in divide in high precision
Model call number is analysed, the design cycle is shortened.The present invention is suitable for there are the aerospace fields or phase of high time consuming analysis model
Optimum design of engineering structure field is closed, correlation engineering problem is able to solve.
The purpose of the present invention is what is be achieved through the following technical solutions.
A kind of aircraft near-optimal method generated based on virtual sample disclosed by the invention, using RBF to high-precision
Analysis model carries out approximate modeling, and is designed optimization instead of archetype；It is generated by virtual sample and realizes that RBF acts on behalf of mould
Effective update and the management of type, to improve local search ability and global exploring ability, in the virtual sample generation in the present invention
It is constructed comprising LSSVM classifier training and virtual sample.In aircraft near-optimal design process, makes full use of and have construction
Sample point information is generated by virtual sample and constantly updates RBF model, to guide and ensure that optimization process rapidly converges to entirely
Office's optimal solution, reduces high accuracy analysis model call number in aircraft near-optimal design process, for alleviating structure small sample
Problem, reduction calculate cost, raising optimization efficiency etc. and are of great significance.
A kind of aircraft near-optimal design method generated based on virtual sample disclosed by the invention, including walk as follows
It is rapid:
Step A: the basic parameter of the aircraft near-optimal design method generated based on virtual sample, including design are determined
Space size, the number of initial samples, the number of simple sample point, the number and preset receipts of maximum newly-increased virtual sample
Hold back criterion.
Step B: initial sample point is generated in design space using the super side's experimental design OLHD of optimal Latin, and is calculated just
The response of corresponding high accuracy analysis model at beginning sample.Authentic specimen point is added in initial sample point and corresponding response
In set, and initialization of virtual sample point set.
Step C: the sample point concentrated based on authentic specimen point set and virtual sample point and corresponding response, jointly constructs
Or update the RBF agent model of objective function or constraint function.
Step D: using Genetic Algorithms or sequential quadratic programming SQP to the RBF generation of current goal function and constraint function
Reason model optimizes, and obtains current RBF agent model optimal solution.Calculate the high-precision at current RBF agent model optimal solution
The true response of analysis model, and authentic specimen point set is added in current RBF agent model optimal solution and corresponding response
In, that is, realize the update to authentic specimen point set.
Step E: check whether convergence criterion meets.If current iteration result meets convergence criterion, current RBF generation is exported
Model optimal solution is managed as aircraft final design as a result, solving the corresponding engineering problem of field of flight vehicle design；It is on the contrary then enter
Step F.
Step F: being generated by virtual sample, obtains newly-increased virtual sample point, and obtained newly-increased virtual sample point is added
In virtual sample point set after entering initialization, the update to virtual sample point set, void of the return step C based on update are realized
Quasi- sample point set and authentic specimen point set are updated current RBF agent model.
Virtual sample, which is generated, in step F constructs two steps, specific implementation comprising LSSVM classifier training and virtual sample
Steps are as follows:
Step F-1:LSSVM classifier training.Response and constraint based on sample point in authentic specimen point set are violated
It spends and 0-1 division is carried out to the sample point in authentic specimen point set, the wherein representative of label 1 near globe optimum and may accord with
The potential high-quality point of contract beam, label 0 represent point inferior.The training using the sample point in authentic specimen point set as training sample
LSSVM classifier, and a large amount of simple sample points are tested using trained classifier, obtain one group of potential newly-increased sample
Point.
Step F-2: virtual sample construction.The KRG agency of objective function is constructed according to updated authentic specimen point set
Model, and calculate the corresponding approximate response of potential newly-increased sample point obtained in step F-1.According to the optimal of approximate response
Property and the number of maximum newly-increased virtual sample determine newly-increased virtual sample point, and by newly-increased virtual sample point and corresponding approximate ring
It should be worth in the virtual sample point set after initialization is added, that is, complete the update of virtual sample point set.
The utility model has the advantages that
1, a kind of aircraft near-optimal design method generated based on virtual sample disclosed by the invention, by construction
The information excavating and recycling of sample point, can alleviate need to call asking for more high accuracy analysis model because of sample point deficiency
Topic is of great significance for improve optimization efficiency, accelerate convergence rate etc..
2, a kind of aircraft near-optimal design method generated based on virtual sample disclosed by the invention, passes through virtual sample
This generation, in conjunction with virtual sample point and authentic specimen point management and renewal agency model, during capable of alleviating Flight Vehicle Design
The small sample problem encountered, is suitably applied that there are the aerospace field of high time consuming analysis model or correlation engineering optimization designs
Field.
3, a kind of aircraft near-optimal design method generated based on virtual sample disclosed by the invention, due to based on void
What quasi- sample generated has versatility and universality like optimum design method, can expand and be applied to following engineering fields: contain
Optimal Structure Designing, the Aerodynamic optimization design containing high-precision flow dynamics analysis and the flight of extensive finite element analysis
The multidisciplinary design optimization etc. of the complex engineerings system such as device, automobile, ship, can alleviate the sample faced in Optimum design of engineering structure
This problem.
Detailed description of the invention
Fig. 1 is the aircraft near-optimal design method flow chart generated based on virtual sample；
Fig. 2 is the geometry comparison of optimal aerofoil profile and initial aerofoil profile；
Fig. 3 is the pressure coefficient comparison of optimal aerofoil profile and initial aerofoil profile；
Specific embodiment
Objects and advantages in order to better illustrate the present invention are described in detail below with reference to the accompanying drawings and in conjunction with the embodiments
The present invention.
A kind of aircraft near-optimal design method generated based on virtual sample disclosed in the present embodiment, is suitable for calculating
Time-consuming engineering design optimization problem can be effectively reduced and calculate cost, shorten the design cycle.The present embodiment specific embodiment
It is as follows:
Step A: the basic parameter of optimization method, including design space size [x are determinedLB,xUB], the numbers of initial samples
nis, simple sample point number nc, maximum newly-increased virtual sample number nvirAnd preset convergence criterion.Partial parameters are set
It sets as shown in formula (17).
Wherein, s is the dimension of problem；bmaxIt is the full-size in all dimensions in design space, precision 0.01.
Step B: according to determining initial sample point quantity nis, empty in design using the super side's experimental design OLHD of optimal Latin
It is interior to generate initial sample point Xr, and calculate initial sample XrLocate the response Y of corresponding high accuracy analysis modelr.By initial sample
Authentic specimen point set S is added in this point and corresponding responserIn, and initialization of virtual sample point setSetting changes
Generation number k=1.
Step C: it is based on authentic specimen point set SrWith virtual sample point set SvIn sample point and corresponding response, jointly
Construction or the RBF agent model for updating objective function and constraint function.Wherein, the construction sample of objective function includes set SrWith
Set SvSample, the construction sample of constraint function is only set Sr。
Step D: solving the optimization problem in formula (18) using Genetic Algorithms or sequential quadratic programming SQP, wherein
For the RBF agent model of objective function,The RBF agent model constrained for i-th.Using optimum results as current optimal
PointAnd it calculatesThe true response f (x of the high accuracy analysis model at place(k)) and g (x(k)), and it is added into authentic specimen
Point set SrIn, it realizes to authentic specimen point set SrUpdate.
Step E: check whether the convergence criterion in formula (19) meets.If current iteration result meets convergence criterion, defeated
Current optimal solution is as final optimization pass result out；It is on the contrary then enter step F.
Wherein, eps is optimality criterion, usually takes 0.001；Err is current optimum pointApproximate error, expression formula
As shown in (20)；Err_max is the approximate error upper limit, usually takes 0.01；nallIt is the number of authentic specimen point, nmaxIt is true sample
The maximum number of this point.
Step F: initialization of virtual sample point set firstThen it is generated by virtual sample, obtains newly-increased void
Quasi- sample point, and obtained newly-increased virtual sample point is added in virtual sample point set, it realizes to virtual sample point set
It updates, virtual sample point set and authentic specimen point set of the return step C based on update are updated RBF agent model.
Specific step is as follows:
Step F-1:LSSVM classifier training.According to current authentic specimen point set SrThe result of middle authentic specimen point is most
Sample point set is divided into two classes by dominance and constraint degree of violating, and label is respectively 0 and 1, and the wherein representative of label 1 may be in the overall situation
Optimum point is neighbouring and meets the potential high-quality point of constraint, and label 0 represents point inferior.Constraint degree of violating h (x) is defined as follows:
Wherein, gi(x(k)) it is point x(k)The true response of i-th of constraint.In general, h (x)=0 illustrates that the point meets
Constraint.It is chosen from authentic specimen point set according to formula (21) and meets the point of constraint and be put into set SpIn, if current collection SrIn do not have
There is the point for meeting h (x)=0, then chooses the corresponding sample point of smaller h (x) and be put into set SpIn.Then according to set SpMiddle sample
It is as follows that the response of point defines a threshold value P:
P=min (Ypp)+ηn(max(Ypp)-min(Ypp)) (22)
Wherein ηnIt is a zoom factor.From set SpMiddle selection meets yrThe sample point of < P meets y if not findingr<P
Sample point, then by coefficient ηnAmplification.The process is repeated, meets y until findingrThe sample point of < P.By yrThe sample point of < P is corresponding
Label be set as 1, set SrIn the labels of other sample points be set as 0.So far, set SrMiddle sample point adds class label 0
Or 1.
LSSVM is trained based on the authentic specimen point classified, realizes and design space is divided, find global optimum
Solve region that may be present.Using trained LSSVM classifier, simple sample point is tested, obtains one group of contingency table
The sample point set X that label are 1pc.Wherein, simple sample point based on the equally distributed method of sampling in initial designs space by being adopted
Sample.
Step F-2: virtual sample construction.First according to authentic specimen point set SrMiddle sample point and corresponding response structure
The KRG agent model of objective function is made, and calculates sample point set X using the KRG agent model of constructionpcMiddle sample point is corresponding close
Like target response value Ypc.From sample point set XpcMiddle selection ypc< P sample point is put into conjunction with XpvIn.If XpvThe number of middle sample point
Amount is greater than nvir, then to sample set XpvCluster, finds out nvirA cluster centre Xc, and utilize the KRG agent model meter constructed
Calculate corresponding approximate objective function Yc, by XcAnd YcNewly-increased virtual sample point set S is addedc；Conversely, by XpvWith corresponding YpvAdd
Enter newly-increased virtual sample point set Sc。
Step F-3: the newly-increased virtual sample point set S that will be obtained in step F-2cVirtual sample point set S is addedv, i.e., in fact
Now to the update of virtual sample point set, authentic specimen point set S of the k=k+1 return step C based on update is enabledrWith virtual sample point
Collect SvCurrent RBF agent model is updated.
Purpose and advantage in order to better illustrate the present invention, below by standard testing example and field of flight vehicle design
Typical Airfoil Design Optimal Example, in conjunction with attached drawing, the present invention will be further described with table.
Embodiment 1: standard engineering tests example
In order to verify advantage of the invention, selection standard example of engineering calculation is to disclosed by the invention a kind of raw based on virtual sample
At aircraft near-optimal design method (SRBF-VSG) tested, and with several famous agent model optimization methods into
Row performance comparison, including ARSM-ISES and CiMPS.Standard engineering tests mathematical model such as formula (23) and formula (24) institute of example
Show.
Spring design test problem (SD)
Design of pressure vessels problem (PVD)
Using different optimisation strategies to above-mentioned standard testing example Filled function 10 times, much suboptimization is optimal for statistics
The median f* of value, average target function call times N fe, average constraint function call number Nce, average maximum constrained value
Optimal value f in MCV, multiple optimum resultsoAnd corresponding objective function call number Nfeo, constraint function call number
NceoWith maximum constrained value MCVo, statistical result is as shown in table 1.Wherein, foReflect the optimizing of MBDO strategy, f* reflects MBDO
The optimization convergence of strategy, the optimization efficiency of Nfe and Nce reflection MBDO strategy.MCV is in the corresponding constraint function value of optimal solution
Maximum value, reflection MBDO strategy seek optimal solution feasibility.
In table 1, N/A indicates no corresponding result.Statistical result showed near-optimal method disclosed by the invention is sought
Optimal solution foIt is suitable or more excellent with CiMPS and ARSM-ISES, but corresponding model call number (Nfeo+Nceo) be considerably less than
CiMPS and ARSM-ISES is able to verify that the high efficiency of optimization method disclosed by the invention.Maximum constrained value MCVoShow SRBF-
The optimal solution f that VSG strategy is soughtoMeet constraint, the f that CiMPS and ARSM-ISES are soughtoIt is not to be inconsistent contract on stricti jurise
Beam.From f*, Nfe, Nce and MCV it can be found that the aircraft near-optimal disclosed by the invention generated based on virtual sample is set
Meter method for solve standard engineering example have some superiority, ensure to optimize it is constringent simultaneously, with less model tune
The optimal solution f* of feasible (MCV < 0) is found with number (Nfe+Nce).
1 standard engineering example optimum results of table statistics
Embodiment 2: aerofoil profile aerodynamic optimization example
Choose NACA0012 aerofoil profile as it is initial 2 dimension aerofoil profile, choose 10 parameters by shape function method of perturbation to aerofoil profile into
Row updates, and as design variable, i.e. xui,xli(i=1,2,3,4,5).The mathematical model of aerofoil profile aerodynamic optimization problem is such as
Under:
Wherein, CL/DIndicate lift resistance ratio, CDIndicate resistance coefficient, CLIndicate lift coefficient,Indicate initial lift system
Number, tmaxIndicate the maximum gauge of aerofoil profile,Indicate that the maximum gauge of initial aerofoil profile, x are design variable, xlbAnd xupIt is respectively
The lower bound of design space and the upper bound.
For Mach 2 ship 0.8, flight operating condition when the angle of attack is 2.5 °, using SRBF-VSG strategy disclosed by the invention,
SRBF-SVM strategy carries out the aerodynamic optimization of 10 aerofoil profiles respectively, and as a result statistics is as shown in table 2.
2 aerofoil profile aerodynamic optimization Comparative result of table
It can be seen from Table 2 that the lift resistance ratio AC that SRBF-VSG strategy obtainsL/D16 are all larger than, better than SRBF-SVM strategy
Obtained optimal result.And the tactful required averaging model call number Nfe of SRBF-VSG is only SRBF-SVM strategy
83.1%, it is able to verify that feasibility and practicability of the present invention in practical implementation.
The optimal aerofoil profile and initial aerofoil profile that comparison SRBF-VSG strategy obtains, partial parameters are as shown in table 3.Optimal aerofoil profile
The more initial aerofoil profile of lift coefficient can be improved 60.6%, and the more initial aerofoil profile of resistance coefficient can be with reduction by 10.4%, maximum gauge
9.5% can be reduced, lift resistance ratio can be improved 79.2%.Fig. 2 is obtained optimal aerofoil profile and just after SRBF-VSG policy optimization
The comparison of beginning aerofoil profile, Fig. 3 are the comparison of pressure coefficient and initial value under optimal aerofoil profile.
The optimal aerofoil profile of table 3 and initial airfoil section parameter comparison
Compared by above-mentioned two classes optimal inspection problem, compared to existing MBDO strategy, a kind of base that the present invention announces
Available data information can be more fully hereinafter utilized in the aircraft near-optimal design method (SRBF-VSG) that virtual sample generates,
Under the premise of ensuring optimum results convergence and optimality, reaching reduces model call number, improves optimization efficiency, and shortening is set
The purpose for counting optimizing cycle, can be realized expected goal of the invention and beneficial effect, and sufficiently verify reasonability of the invention, have
Effect property and engineering practicability.
Above-described specific descriptions have carried out further specifically the purpose of invention, technical scheme and beneficial effects
It is bright, it should be understood that above is only a specific embodiment of the present invention, being used to explain the present invention, it is not used to limit this
The protection scope of invention, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should all
It is included within protection scope of the present invention.
Claims (4)
1. a kind of aircraft near-optimal design method generated based on virtual sample, it is characterised in that: include the following steps,
Step A: the basic parameter of the aircraft near-optimal design method generated based on virtual sample, including design space are determined
Size, the number of initial samples, the number of simple sample point, the number of maximum newly-increased virtual sample and preset convergence are quasi-
Then；
Step B: initial sample point is generated in design space using the super side's experimental design OLHD of optimal Latin, and calculates initial sample
The response of corresponding high accuracy analysis model at this；Authentic specimen point set is added in initial sample point and corresponding response
In, and initialization of virtual sample point set；
Step C: the sample point concentrated based on authentic specimen point set and virtual sample point and corresponding response, jointly constructs or more
The RBF agent model of fresh target function or constraint function；
Step D: mould is acted on behalf of to the RBF of current goal function and constraint function using Genetic Algorithms or sequential quadratic programming SQP
Type optimizes, and obtains current RBF agent model optimal solution；Calculate the high accuracy analysis at current RBF agent model optimal solution
The true response of model, and current RBF agent model optimal solution and corresponding response are added in authentic specimen point set, i.e.,
Realize the update to authentic specimen point set；
Step E: check whether convergence criterion meets；If current iteration result meets convergence criterion, exports current RBF and act on behalf of mould
Type optimal solution is as aircraft final design as a result, solving the corresponding engineering problem of field of flight vehicle design；It is on the contrary then enter step
F；
Step F: being generated by virtual sample, obtains newly-increased virtual sample point, and obtained newly-increased virtual sample point is added just
In virtual sample point set after beginningization, the update to virtual sample point set, virtual sample of the return step C based on update are realized
This point set and authentic specimen point set are updated current RBF agent model.
2. a kind of aircraft near-optimal design method generated based on virtual sample as described in claim 1, feature are existed
In: virtual sample, which is generated, in step F constructs two steps comprising LSSVM classifier training and virtual sample, implements step
It is as follows:
Step F-1:LSSVM classifier training；Response and constraint degree of violating pair based on sample point in authentic specimen point set
Sample point in authentic specimen point set carries out 0-1 division, and the wherein representative of label 1 near globe optimum and may meet about
The potential high-quality point of beam, label 0 represent point inferior；The training using the sample point in authentic specimen point set as training sample
LSSVM classifier, and a large amount of simple sample points are tested using trained classifier, obtain one group of potential newly-increased sample
Point；
Step F-2: virtual sample construction；The KRG agent model of objective function is constructed according to updated authentic specimen point set,
And calculate the corresponding approximate response of potential newly-increased sample point obtained in step F-1；According to the optimality of approximate response and
The number of the newly-increased virtual sample of maximum determines newly-increased virtual sample point, and by newly-increased virtual sample point and corresponding approximate response
In virtual sample point set after initialization is added, that is, complete the update of virtual sample point set.
3. a kind of aircraft near-optimal design method generated based on virtual sample as claimed in claim 1 or 2, feature
It is: is generated by virtual sample, in conjunction with virtual sample point and authentic specimen point management and renewal agency model, can be alleviated winged
The small sample problem encountered in row device design process, is suitably applied that there are the aerospace fields or phase of high time consuming analysis model
Close Optimum design of engineering structure field.
4. a kind of aircraft near-optimal design method generated based on virtual sample as claimed in claim 1 or 2, feature
It is: since what is generated based on virtual sample has versatility and universality like optimum design method, can expands and be applied to down
Engineering field is stated, the Optimal Structure Designing containing extensive finite element analysis contains the pneumatic excellent of high-precision flow dynamics analysis
The multidisciplinary design optimization for changing the complex engineerings systems such as design and aircraft, automobile, ship, can alleviate engineering optimization and set
The small sample problem faced in meter.
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| CN114118365A (en) * | 2021-11-08 | 2022-03-01 | 北京理工大学 | Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network |
| EP4095733A1 (en) * | 2021-05-21 | 2022-11-30 | Raytheon Technologies Corporation | Gradient free design environment including adaptive design space |
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| EP4095733A1 (en) * | 2021-05-21 | 2022-11-30 | Raytheon Technologies Corporation | Gradient free design environment including adaptive design space |
| CN114118365A (en) * | 2021-11-08 | 2022-03-01 | 北京理工大学 | Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network |
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