CN104834772B - Aircraft wing based on artificial neural network/wing inverse design method - Google Patents
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- 238000013461 design Methods 0.000 title claims abstract description 69
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Abstract
The invention belongs to airplane design technical field, the specially a kind of aircraft wing based on artificial neural network/wing inverse design method.The inventive method includes：Using the expression way of aerofoil profile/wing PARSEC parametric methods reconstruct aerofoil profile/wing, pass through artificial neural network（ANN）Algorithm, realize mimetic design technology.The present invention bypassed traditional aerofoil profile/wing design it is cumbersome and inefficient enumerate alternative manner（cut‑and‑try）, the relation of aerofoil profile/wing aerodynamic performance and aerofoil profile/wing geometric shape is directly established, realizes the aerofoil profile based on artificial neural network/wing parametrization mimetic design.Feature of the present invention：When it is quick, it is quite suitable in the master-plan especially initial designs of aircraft；Two be due to using artificial neural network algorithm in place so that caused result is very accurate.
Description
Technical field
The invention belongs to airplane design technical field, and in particular to a kind of aircraft wing/wing inverse design method.
Background technology
Mimetic design method in aircraft components design, i.e., a kind of " required i.e. gained ", can be pneumatic directly according to what is given
Performance requirement obtains the geometric data of satisfactory aircraft components.At present, the method for common aircraft wing/wing design
It is traditional, cumbersome and inefficient to enumerate-alternative manner（cut-and-try）, i.e., by the way that aircraft wing/wing is calculated
Design result aeroperformance, be fed back to and new change made to geometric data（Often such change and pneumatic property
The relevance of energy is not very strong, and shows larger randomness）, then carry out new aeroperformance and calculate, so repeatedly
Iteration meets new aerofoil/wing of required aeroperformance until obtaining.Because such design method specific aim is not strong
Reason, the time quantum of consumption is larger, is unfavorable for the job requirement in airplane design work especially initial design stage.
Mimetic design method on aerofoil profile/wing of aircraft, it is therefore an objective to directly constitute aircraft wing/wing aerodynamic performance with
The contact of geometric data, the direct correlation from aeroperformance to geometric data is realized, it is more quick, more direct so as to obtain
Aerofoil profile/Wing design method.At present, the technology in aircraft components mimetic design field usually utilizes various intelligent algorithms, carries out pneumatic
The mapping of performance data and geometry data.But it is limited to aircraft components design the complex nature of the problem, the intelligence calculation taken
Method is not quite similar, and obtained effect is also unsatisfactory.Based on this present situation, the present invention proposes the aircraft based on artificial neural network
Aerofoil profile/wing inverse design method.
The content of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention proposes a kind of aircraft wing based on artificial neural network
Type/wing inverse design method.
Aircraft wing based on artificial neural network/wing inverse design method provided by the invention, it is broadly divided into 5 steps
Suddenly：
（1）First, aerofoil profile/wing PARSEC (Sobieczky H. Parametric airfoils and are utilized
wings[M]//Recent Development of Aerodynamic Design Methodologies. Vieweg+
Teubner Verlag, 1999:71-87.) the expression way of parametric method reconstruct aerofoil profile, i.e., with 11 PARSEC profiles
Parameter（Leading-edge radius rle, up/down aerofoil maximum gauge XupAnd Xlo, up/down aerofoil maximum gauge correspondence position ZupAnd Zlo, it is upper/
Lower aerofoil vertex curvature ZxxupAnd Zxxlo, trailing edge width △ ZTE, trailing edge vertical height ZTE, trailing edge angle of wedge βTE, trailing edge deflection
αTE）To simulate airfoil geometry situation, with 6 Aerodynamics（Lift coefficient CL, resistance coefficient CD, moment coefficient CM, cruise
Efficiency MCL/CD, coefficient of frictional resistance CDF, drag due to shock wave coefficient CDW）To summarize the aeroperformance of aerofoil profile.
Top airfoil and lower aerofoil parameter of curve expression formula are formula（1）It is shown：
（1）
a n For multinomial coefficient, for top airfoil, coefficient a n By matrix equation（2）Provide：
（2）
For lower aerofoil, coefficient a n By matrix equation（3）Provide, it is similar with top airfoil, top airfoil configuration spy will be characterized
The parameter of sign amount changes the corresponding parameter of lower aerofoil into：
（3）
Fitting coefficient is obtained, can be to establish contacting for geometric parameter and actual aerofoil profiles.
On the basis of PARSEC geometric parameter methods, to aerofoil profile/wing inverse design using geometric parameter as optimization object.
（2）Then, different length positions are moulded by the selection and size scaling of aerofoil profile with the geometric parameter data of aerofoil profile
The wing section put；With reference to the wing relative thickness parameter and torsion angular dimensions of different length opening positions（General 6 i.e. can reach it is pre-
Phase precision）, it is wing using spline curve fitting wing, the geometric data of wing is obtained, implementing procedure is referring to Fig. 3.Corresponding
The parameter of wing aerodynamic performance description includes：Cruise efficiency MCL/CD, airfoil lift coefficient CLWING, wing drag coefficient
CDWING, pressure drag coefficient CDP, induced drag coefficient CDI, drag due to shock wave coefficient CDW and wing moment coefficient CMQING.
（3）Then, according to preceding step obtain on aerofoil profile and the geometric data result of wing, applied to substantial amounts of
On aerofoil profile, to form airfoil geometry database.Can the success or not of the technology depends on geometric database accomplish：It is 1. pneumatic
Data and geometric data cover sufficiently large scope so that the mimetic design technology can have use value；2. database is at certain
Whether data under one classification enrich enough, to ensure next the（4）The study of artificial neural network required for step can
Not only it is complete but also accurate.At present, number of training purpose determines no general method, it is considered that, sample is very few may to make net
The expression of network is not abundant enough, and so as to cause the extrapolability of network inadequate, sample redundancy phenomena excessively occurs in sample, both increases
Network training burden, information content surplus is likely to occur again, network over-fitting is occurred, database passes through ANN
The training of network, form available mimetic design artificial neural network.User now sets required mimetic design in input again
Aerodynamic, then mimetic design artificial neural network now can export automatically meets that wing/airfoil geometry of this performance is joined
Number.User can obtain the profile of wing/aerofoil profile according to this result, further be used for design work.
, it is necessary to carry out for its geometric data before the database that application has arranged carries out artificial neural network training
Classification, the aerofoil profile data of the training input to ensure as mimetic design artificial neural network geometrically can connect as far as possible
Closely.This way is based on considering on a mechanics：The aeroperformance that similar geometric shape is formed should be close.
Such understanding, help to lower the training difficulty of artificial neural network.Sorting technique uses SOM algorithms（Kohonen T,
Hynninen J, Kangas J. et al. Som pak: The self-organizing map program package
[J]. Report A31, Helsinki University of Technology, Laboratory of Computer
and Information Science, 1996.）.
（4）Then on this basis, artificial neural network is passed through（ANN）Algorithm（Zeidenberg M. Neural
networks in artificial intelligence[M]. Ellis Horwood, 1990.）, in order to realize mimetic design,
Carry out the training of related artificial neural network.On the training method of neutral net, using GRNN algorithms (Specht D F. A
general regression neural network. Neural Networks[J], IEEE Transactions on,
1991. 2(6): p. 568-576.)（By comparing, its target coefficient correlation is horizontal and network generalization is superior to BP calculations
Method and RBF algorithms）：Input is the aeroperformance of wing/aerofoil profile（It can be accepted or rejected according to the demand of mimetic design, than like flying
Lift-drag ratio coefficient can be chosen during machine initial designs）, output end is the geometric data of corresponding wing/aerofoil profile.
（5）After mimetic design artificial neural network, which is trained, to be completed, the artificial neural network that can be finished with training herein
On carry out the work of mimetic design, i.e. user in the required aerofoil profile/wing aerodynamic performance parameter of the input input of network, this
When output end result be exactly Aerodynamic required by required correspondence aerofoil profile geometric parameter.Pass through step
（1）In aerofoil restoring method（That is formula（1））, it is possible to obtain final result.
Compared with prior art, it is cumbersome and inefficient by mimetic design to have bypassed traditional aerofoil profile/wing design by the present invention
Enumerate-alternative manner（cut-and-try）, but directly establish aerofoil profile/wing aerodynamic performance and aerofoil profile/wing geometric shape
Relation.It is different with general database search simultaneously：It can utilize the intellectual technology height of artificial neural network " to insert
Value " obtains required result.The features of the present invention：On the one hand it is quick, is quite suitable for the master-plan of aircraft especially
Among the process of initial designs；On the other hand due to application artificial neural network algorithm in place so that caused result is very accurate
Really.The technology is examined in numerical simulation：It is Mach number 0.75 for operating mode, 2.53 ° of the angle of attack, Reynolds number 23,
000,000, lift-drag ratio 25.8, lift coefficient 0.5, type resistance coefficient is 0.0105, induced drag coefficient 0.009, shock wave
Resistance coefficient is 0.00017, moment coefficient 0.23；Airfoil lift coefficient is 0.43, and resistance coefficient is 0.0095 and torque system
Number designs for -0.13 wing profile supercritical wing, the wing that the technology application obtains with it is contemplated that phase on aerodynamic parameter
It is as a result satisfactory to error within 2%（Refer to " embodiment " part hereinafter）.
Brief description of the drawings
Fig. 1 is aerofoil profile/wing inverse design concept map.
Fig. 2 is GRNN network modes figure used in aerofoil profile/wing inverse design.
Fig. 3 is conversion process figure of the aerofoil profile/wing inverse design aerofoil profile parameter to wing geometric parameter, and it corresponds to step 2.
Fig. 4 is the manifestation mode of wing PARSEC parameters in the present invention.
Fig. 5 is that mimetic design obtains aerofoil profiles in specific example.
Fig. 6 is wing section geometric configuration.
Fig. 7 is the relative thickness distribution in prediction wing section（It is left）It is distributed with torsion angle（It is right）.
Fig. 8 is distributed for wing isobar.
Fig. 9 is the pressure distribution in 6 wing sections.
Embodiment
Embodiment 1：
Design requirement：Under one cruise Mach number Ma=0.785, design point is the aerofoil profile of parameters described below：
Design Mach numberMa=0.71
Design angle of attack á=2.53
Reynolds numberRe=23,000,000
Initially set up airfoil database.On the construction of profile, aerofoil profile is relatively simple.In this example in airfoil database
Include 208 reconstruct aerofoil profiles.Each aerofoil profile in database will have good aeroperformance；And the geometry structure of aerofoil profile
Type will have span as big as possible, that is, have obvious shape differentiation between aerofoil profile.It so just can guarantee that aerofoil profile data
The high efficiency and integrality in storehouse.Tables 1 and 2 is respectively that the span of aerofoil profile moving parameter and formal parameter collects.
The aerofoil profile aerodynamic parameter of table 1 collects
The aerofoil profiles parameter of table 2 collects
| Minimum Value | Maximum Value | |
| r le | 0.0034 | 0.0306 |
| X up | 0.2927 | 0.5074 |
| X lo | 0.275 | 0.4577 |
| Z up | 0.0301 | 0.1116 |
| |Z lo | | 0.0186 | 0.0923 |
| |Z xxup | | 0.02 | 1.1086 |
| Z xxlo | 0.096 | 0.919 |
| △Z TE | 0 | 0.0163 |
| Z TE | -0.0419 | 0.0082 |
| β TE | 0.01 | 8.4622 |
| α TE | 2.1599 | 16.6992 |
Using the artificial neural network based on mimetic design（Input and output mode is as shown in Figure 1）, be trained and input and
The desired aeroperformance of this example, the aerofoil profile result of mimetic design is obtained, as shown in table 3 and Fig. 5：
The Airfoil Inverse Design result of table 3
。
After mimetic design aerofoil profiles are obtained, to it carry out Flow Field Calculation, calculate gained design aerodynamic parameter and
The expection aerodynamic parameter of target call is contrasted.The relative error of major design aerodynamic parameter is all within allowed band.
The Airfoil Inverse Design error analysis of table 4
。
Embodiment 2：
Design requirement：It is 25.8 to design lift-drag ratio, lift coefficient 0.5, and type resistance coefficient is 0.0105, induced drag system
Number is 0.009, and drag due to shock wave coefficient is 0.00017, moment coefficient 0.23；Airfoil lift coefficient is 0.43, and resistance coefficient is
0.0095 and moment coefficient be -0.13 wing profile.
Wherein main aerodynamic parameter（Wing lift-drag ratio and lift coefficient）Itd is proposed by designer, remaining secondary aerodynamic parameter
Provided with interpolation method with reference to 214 groups of pneumatic input ranges in main aerodynamic parameter and database, such as table 5.
The wing aerodynamic parameter of table 5 collects
。
First the wing data in database are classified according to aeroperformance with SOM neutral nets, it is pneumatic to take out target
One group of corresponding data of input, select GRNN neutral nets to be calculated.
Aeroperformance is expected according to wing with mimetic design method, 78 wing formal parameters are calculated, according to parametrization
Method and wing construction method construct wing profile with formal parameter.Wherein, the geometric configuration in 6 wing sections is respectively such as Fig. 6
It is shown；The relative thickness distribution in each wing section and torsion angle are distributed as shown in fig. 7, corresponding aeroperformance is as shown in Figure 9；It is whole
The form and aeroperformance of individual wing are as shown in Figure 8.
The expection aerodynamic parameter of the design aerodynamic parameter and target call that calculate gained is contrasted.The phase of efficiency factor
It is 0.39% to error, the relative error of multi-wall interference lift coefficient is 2.22%, and the error of airfoil lift coefficient is 1.33%.
The relative error of three main aerodynamic parameters is all within allowed band.
The wing formal parameter of table 6 predicts error analysis
。
Claims (1)
- A kind of 1. aircraft wing based on artificial neural network/wing inverse design method, it is characterised in that concretely comprise the following steps：(1) first, the expression way of aerofoil profile is reconstructed using aerofoil profile/wing PARSEC parametric methods, i.e., with outside 11 PARSEC Shape parameter：Leading-edge radius rle, up/down aerofoil maximum gauge xupAnd xlo, up/down aerofoil maximum gauge correspondence position zupAnd zlo、 Up/down aerofoil vertex curvature zxxupAnd zxxlo, trailing edge width △ zte, trailing edge vertical height zte, trailing edge angle of wedge βte, trailing edge deflection αteTo simulate airfoil geometry situation, with 6 Aerodynamics：Lift coefficient CL, resistance coefficient CD, moment coefficient CM, cruise Efficiency M (CL/CD), coefficient of frictional resistance CDF, drag due to shock wave coefficient CDW describe the aeroperformance of aerofoil profile；Then, top airfoil It is shown in formula (1) with lower aerofoil parameter of curve expression formula：<mrow> <mi>z</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>6</mn> </munderover> <msub> <mi>a</mi> <mi>n</mi> </msub> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>anFor multinomial coefficient, for top airfoil, coefficient anProvided by matrix equation (2)：<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> 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<mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>15</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>35</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>63</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>99</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>4</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>5</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>6</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msqrt> <mrow> <mn>2</mn> <msub> <mi>r</mi> <mrow> <mi>l</mi> <mi>e</mi> </mrow> </msub> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&Delta;z</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>tan</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&beta;</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mrow> <mi>x</mi> <mi>x</mi> <mi>u</mi> <mi>p</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>For lower aerofoil, coefficient anProvided by matrix equation (3)：<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> <mtd> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> </msubsup> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>9</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>15</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>35</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>63</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>99</mn> <mn>4</mn> </mfrac> <msubsup> <mi>x</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>4</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>5</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>6</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msqrt> <mrow> <mn>2</mn> <msub> <mi>r</mi> <mrow> <mi>l</mi> <mi>e</mi> </mrow> </msub> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&Delta;z</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mrow> <mi>l</mi> <mi>o</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>tan</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&beta;</mi> <mrow> <mi>t</mi> <mi>e</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mrow> <mi>x</mi> <mi>x</mi> <mi>l</mi> <mi>o</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Fitting coefficient is obtained, just sets up contacting for geometric parameter and actual aerofoil profiles；On the basis of PARSEC geometric parameter methods, to aerofoil profile/wing inverse design using geometric parameter as optimization object；(2) then, different length positions are moulded by the selection and size scaling of aerofoil profile using the geometric parameter data of aerofoil profile Wing section；With reference to the wing relative thickness parameter and torsion angular dimensions of different length opening positions, spline curve fitting machine is utilized Thriving shape, obtain the geometric data of wing；The parameter of corresponding wing aerodynamic performance description includes：Cruise efficiency M (CL/ CD), airfoil lift coefficient CLWING, wing drag coefficient CDWING, pressure drag coefficient CDP, induced drag coefficient CDI, swash Wave resistance force coefficient CDW and wing moment coefficient CMQING；(3) then, according to preceding step obtain on aerofoil profile and the result of the geometric data of wing, applied to substantial amounts of aerofoil profile On, to form airfoil geometry database；It is required that accomplish：(A) aerodynamic data and geometric data cover sufficiently large scope, make Obtaining the mimetic design technology can be with practical value；(B) data of the database under a certain classification are enriched enough, to ensure to walk below Suddenly the study of the artificial neural network required for (4) can be not only complete but also accurate；Database passes through the training of artificial neural network, Form available mimetic design artificial neural network；Using SOM algorithms, classify for airfoil geometry data, the training to ensure as mimetic design artificial neural network is defeated Enter the aerofoil profile data at end geometrically can be close as far as possible；(4) on this basis, artificial neural network algorithm, the training of progress mimetic design artificial neural network are passed through；Wherein, On the training of neutral net, using GRNN algorithms：Input be wing/aerofoil profile aeroperformance data, the aeroperformance number According to can be accepted or rejected according to the demand of mimetic design, output end is the geometric data of corresponding wing/aerofoil profile；(5) after mimetic design artificial neural network, which is trained, to be completed, train carried out instead on the artificial neural network finished herein The work of design, i.e. user are in the required aerofoil profile/wing aerodynamic performance parameter of the input input of network, now output end As a result the geometric parameter of the aerofoil profile of the Aerodynamic required by correspondence required for being exactly；Pass through the aerofoil in (1) step Restoring method, obtain final result.
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