CN106446424B - A kind of unsteady aerodynamic force parameter prediction method - Google Patents
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Abstract
The invention discloses a kind of unsteady aerodynamic model parameter prediction methods, are related to aviation aircraft modeling technique field.On the basis of a large amount of wind tunnel test data, unsteady aerodynamic force is modeled and predicted using ELM method, big, global convergence, the advantages such as versatile, precision of prediction is high with processing sample size, realize the unsteady aerodynamic force prediction under uniaxial oscillation, model accuracy is higher compared with other existing unsteady aerodynamic force prediction techniques, so that having accurately Aerodynamic Model under advanced fighter High Angle of Attack high maneuver, high maneuver control is better achieved, to occupy vantage point in the following fighter plane short range combat.
Description
Technical field
The present invention relates to aviation aircraft modeling technique field, in particular to a kind of unsteady aerodynamic force parameter prediction side
Method.
Background technique
Short range combat is the mark of advanced fighter super maneuverability energy, it is desirable that fighter plane is still able to achieve in low speed High Angle of Attack
Controllable instruction tactical maneuver movement --- post stall maneuver.Typical post stall maneuver have Cobra maneuver, He Baisite it is motor-driven,
Vector roller etc., in post stall maneuver, it is straight that the gas of aerofoil surface by single attachment flow to vortex motion, vortex breakdown
It is separation flowing to development, interferes with each other between gas flowing lag and each component vortex system than more serious, these result in aircraft
The characteristics such as the non-linear of aerodynamic and aerodynamic torque, multiaxis coupling and sluggishness when high maneuver.Therefore, traditional aerodynamic model exists
It is no longer applicable in when High Angle of Attack, it is necessary to establish accurate unsteady aerodynamic model.
Modeling for unsteady aerodynamic force, common method have Step Function Model, algebraic polynomial model,
Fourier Functional Analysis model, state-space model, difference equation model and fuzzy logic model etc., although these methods are all
Solve uniaxial oscillation unsteady aerodynamic force modeling problem, but its modeling accuracy is not high, versatility is poor.
Summary of the invention
The embodiment of the invention provides a kind of unsteady aerodynamic model parameter prediction methods, to solve in the prior art
There are the problem of.
A kind of unsteady aerodynamic model parameter prediction method, comprising:
It obtains and substantially vibrates wind tunnel test data, include three-axis force coefficient, three-axis force moment coefficient, pitch angle, turntable corner
With shoe strut roll angle；
Relevant parameter when obtaining Unsteady Aerodynamic Modeling according to the pitch angle, turntable corner and shoe strut roll angle, including
The angle of attack and yaw angle；
The input variable of selection limit learning machine ELM unsteady aerodynamic model are as follows: the angle of attack, the first derivative of the angle of attack, side
Sliding angle and reduction frequency, select output variable are as follows: three-axis force coefficient, three-axis force moment coefficient select kernel function are as follows: gaussian radial basis function
Kernel function；
ELM unsteady aerodynamic model is established and solves, according to the three-axis force coefficient and three-axis force obtained in wind tunnel test
Moment coefficient, and optimize ELM unsteady aerodynamic model using cross validation method；
Judge whether modeling accuracy reaches requirement, completion is modeled if reaching requirement, otherwise re-uses cross validation side
Method selection parameter is modeled；
Data to be predicted are obtained, including pitch angle to be predicted, turntable corner and shoe strut roll angle；
It is obtained according to the data to be predicted and the ELM unsteady aerodynamic model corresponding with the data to be predicted
Three-axis force coefficient and three-axis force moment coefficient；
Wherein, step is specifically included using cross validation method optimization ELM unsteady aerodynamic model:
The input variable sum of the first step, model is n, is randomly divided into q parts, takenq- 1 part is used as training sample, remaining
1 part be used as forecast sample, while given prediction precision threshold Ro 2, and initial predicted precision isIf hidden layer inputs
The number of variable is [n (q-1)/10q, 9n (q-1)/10q]；
Second step, giving hidden layer input variable number is Nhide=n (q-1)/10q, randomly selects the parameter of ELM model
Input layer and the connection weight w of the implicit interlayer and threshold value b of hidden layer input variable, by providing predicted value after cross validation q times
Mean accuracy R2IfThenAnd by N at this timehide, w and b record；Repeat this step Nhide/ 5 times；
Third step increases hidden layer input variable number Nhide=Nhide+ 2n (q-1)/25q randomly chooses ELM mould again
The parameter w and b of type, until hidden layer input variable number Nhide=n (q-1)/10q；
4th step, ifThen modeling terminates, and is otherwise transferred to first step continuation.
Preferably, step obtains Unsteady Aerodynamic Modeling phase according to the pitch angle, turntable corner and shoe strut roll angle
Parameter is closed to specifically include:
When for vertical dip mining, model formal dress, so angle of attack is mechanism pitching angle thetag, model yaw angle is turntable turn
Angle ψg:
α=θg
β=ψg
For yaw oscillations, model side dress, according to geometrical relationship it is found that the angle of attack of model is turntable corner ψg, model
Yaw angle is mechanism pitching angle thetag:
α=ψg
β=θg
Rolling is vibrated, model formal dress, since mechanism has pitch angle, so will appear inertia coupling phenomenon, i.e. mould
The angle of attack and yaw angle hinge of type are derived at one piece by geometrical relationship, the angle of attack and yaw angle of model:
α=atan (cos (φg)·tan(θg))
β=asin (sin (φg)·sin(θg))
Wherein, φgFor shoe strut roll angle.
Preferably, the step of establishing the ELM unsteady aerodynamic model specifically includes:
Input layer has n input variable, and hidden layer has l input variable, and output layer has m output variable；
If the connection weight w of input layer and implicit interlayer are as follows:
Wherein, wlnIndicate the connection weight between first of input variable of n-th of input variable of input layer and hidden layer；
If the connection weight β of hidden layer and output interlayer are as follows:
Wherein, βlmIndicate the connection weight between m-th of output variable of first of input variable of hidden layer and output layer；
If the threshold value b of hidden layer input variable are as follows:
Setting tool has the training set input matrix X of Q sample and output matrix Y to be respectively as follows:
If the activation primitive of hidden layer input variable is g (x), the output T of model are as follows:
T=[t1 t2 … tQ]m×Q
Wherein wi=[wi1 wi2 … win], xj=[x1j x2j … xnj]T, above formula is writeable are as follows:
H β=TT
Wherein, H is known as hidden layer output matrix, and concrete form is as follows:
When activation primitive g (x) infinitely can be micro-, the parameter of single hidden layer feedforward neural network SLFN do not need all into
Row adjustment, w and b can be randomly selected before training, and remain unchanged in the training process, and the company of hidden layer and output interlayer
Meeting weight β can be obtained by solving the least square solution of equation group:
It is solved:
H+Take Moore-Penrose generalized inverse.
The invention has the benefit that the present invention is on the basis of a large amount of wind tunnel test data, using ELM method to non-
Unsteady Flow modeled and predicted, has big processing sample size, global convergence, that versatile, precision of prediction is high etc. is excellent
Gesture realizes the unsteady aerodynamic force prediction under uniaxial oscillation, the mould compared with other existing unsteady aerodynamic force prediction techniques
Type precision is higher, so that having accurately Aerodynamic Model under advanced fighter High Angle of Attack high maneuver, high maneuver is better achieved
Control, to occupy vantage point in the following fighter plane short range combat.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of step flow chart of unsteady aerodynamic force parameter prediction method provided in an embodiment of the present invention；
Static state pitching moment coefficient prediction result when Fig. 2 is β=- 30 ° of yaw angle；
Static state pitching moment coefficient prediction result when Fig. 3 is yaw angle β=0 °；
Static state pitching moment coefficient prediction result when Fig. 4 is yaw angle β=10 °；
Fig. 5 is β=- 30 ° of yaw angle, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.4；
Fig. 6 is β=- 30 ° of yaw angle, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.6；
Fig. 7 is β=- 30 ° of yaw angle, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.8；
Fig. 8 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.2；
Fig. 9 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.4；
Figure 10 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.5；
Figure 11 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.6；
Figure 12 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.7；
Figure 13 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.8；
Figure 14 is yaw angle β=0 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=1；
Figure 15 is yaw angle β=10 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.4；
Figure 16 is yaw angle β=10 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.6；
Figure 17 is yaw angle β=10 °, substantially pitching moment coefficient prediction result when frequency of oscillation f=0.8.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Referring to Fig.1, the embodiment of the invention provides a kind of unsteady aerodynamic force parameter prediction methods, this method comprises:
It obtains and substantially vibrates wind tunnel test data, include three-axis force coefficient, three-axis force moment coefficient, pitch angle, turntable corner
With shoe strut roll angle；
Relevant parameter when obtaining Unsteady Aerodynamic Modeling according to the pitch angle, turntable corner and shoe strut roll angle, such as meets
Angle and yaw angle；
The input variable of selection limit learning machine ELM unsteady aerodynamic model are as follows: the angle of attack, the first derivative of the angle of attack, side
Sliding angle and reduction frequency, select output variable are as follows: three-axis force coefficient (axial force coefficient, sideway force coefficient and normal force coefficient),
Three-axis force moment coefficient (pitching moment coefficient, rolling moment coefficient and yawing moment coefficient) selects kernel function are as follows: gaussian radial basis function
Function；
ELM unsteady aerodynamic model is established and solves, according to the three-axis force coefficient and three-axis force obtained in wind tunnel test
Moment coefficient, and optimize ELM unsteady aerodynamic model using cross validation method, judge whether modeling accuracy reaches requirement,
Completion is modeled if reaching requirement, is otherwise transferred to previous step and is reselected parameter and is modeled；
Data to be predicted are obtained, including pitch angle to be predicted, turntable corner and shoe strut roll angle；
It is obtained according to the data to be predicted and the ELM unsteady aerodynamic model corresponding with the data to be predicted
Three-axis force coefficient and three-axis force moment coefficient.
Below to this hair by taking the modeling of the unsteady aerodynamic force of pitching-rolling twin shaft coupled oscillations pitching moment coefficient as an example
Bright method is described in detail:
Step 100, pitching moment coefficient, the pitch angle, turntable corner under uniaxial oscillation are obtained using flow tunnel testing device
With shoe strut roll angle；
Step 200, to wind tunnel test data processing, relevant parameter when obtaining Unsteady Aerodynamic Modeling, such as angle of attack α, yaw angle β；
Specifically, step 200 includes:
When for vertical dip mining, model formal dress, so angle of attack is mechanism pitching angle thetag, model yaw angle is turntable turn
Angle ψg:
α=θg
β=ψg
For yaw oscillations, model side dress, according to geometrical relationship it is found that the angle of attack of model is turntable corner ψg, model
Yaw angle is mechanism pitching angle thetag:
α=ψg
β=θg
Rolling is vibrated, model formal dress, since mechanism has pitch angle, so will appear inertia coupling phenomenon, i.e. mould
The angle of attack and yaw angle hinge of type are at one piece.It is derived by geometrical relationship, the angle of attack and yaw angle of model:
α=atan (cos (φg)·tan(θg))
β=asin (sin (φg)·sin(θg))
Wherein, φgFor shoe strut roll angle.
Step 300, input variable is selected, it is contemplated that angle of attack α under normal circumstancesiWith yaw angle βiIt is to influence three-axis force and three
The factor of axle power moment coefficient, therefore angle of attack α is selected firstiWith yaw angle βiAs input variable.Secondly, from wind tunnel test data
Analysis result sees that three-axis force and torque coefficient have hysteresis, therefore three-axis force and force coefficient are by a upper bat or a few bat states
The influence of variable, so by the first derivative of the angle of attackAs its input variable.Finally by test data it is found that reduction frequency ki
Influence to three-axis force and torque coefficient is bigger, therefore also as input variable.To for pitching-cross coupling
The input variable of oscillation unsteady aerodynamic model can be expressed as follows:
Output variable is selected, for output variable, since emphasis of the present invention is unsteady aerodynamic force modeling, so it is exported
Variable is three-axis force and three-axis force moment coefficient, it may be assumed that
yi∈{Fx,Fy,Fz,Mx,My,Mz}
Kernel function is selected, following gaussian radial basis function is selected:
G (x, w, b)=exp (- b | | x-w | |2)
Step 400, ELM model is established:
Typical list hidden layer feedforward neural network SLFN is made of input layer, hidden layer and output layer, input layer with it is hidden
Containing being connected entirely between layer, hidden layer and output layer neuron.Wherein, input layer has n neuron, corresponding n input variable；It is implicit
Layer has l neuron, corresponding l input variable；Output layer has m neuron, corresponding m output variable.
Without loss of generality, if the connection weight w of input layer and implicit interlayer is
Wherein, wlnIndicate the connection weight between first of input variable of n-th of input variable of input layer and hidden layer.
If the connection weight β of hidden layer and output interlayer are as follows:
Wherein, βlmIndicate the connection weight between m-th of output variable of first of input variable of hidden layer and output layer.
If the threshold value b of hidden layer input variable are as follows:
Setting tool has the training set input matrix X of Q sample and output matrix Y to be respectively as follows:
If the activation primitive of hidden layer input variable, i.e. kernel function are g (x), the output T of network are as follows:
T=[t1 t2 … tQ]m×Q
Wherein wi=[wi1 wi2 … win], xj=[x1j x2j … xnj]T.Above formula is writeable are as follows:
H β=TT
Wherein, H is known as the hidden layer output matrix of neural network, and concrete form is as follows:
When activation primitive g (x) infinitely can be micro-, the parameter of SLFN does not need all to be adjusted, and w and b are before training
It can be randomly selected, and remain unchanged in the training process.And hidden layer and output interlayer connection weight β can by solve with
The least square solution of lower equation group obtains:
It is solved:
H+Generally take Moore-Penrose generalized inverse.
Step 500, ELM model is solved:
Due in classical ELM method, only requiring the number of hidden layer neuron to be no more than number of samples, simultaneously for
The biasing of the connection weight and hidden layer neuron of input layer and output interlayer is all set at random, these result in ELM and exist
Precision is poor when sample predictions.These three types of variables are determined based on the method for cross validation the invention proposes a kind of, it is specific
Steps are as follows:
The input variable sum of the first step, model is n, is randomly divided into q parts, takenq- 1 part is used as training sample, remaining
1 part be used as forecast sample, while given prediction precision thresholdAnd initial predicted precision isIf hidden layer is defeated
The number for entering variable is [n (q-1)/10q, 9n (q-1)/10q]；
Second step, giving hidden layer input variable number is Nhide=n (q-1)/10q, randomly selects the parameter of ELM model
W and b, by providing predicted value mean accuracy R after cross validation q times2IfThenAnd it will at this time
Nhide, w and b record；Repeat this step Nhide/ 5 times；
Third step increases hidden layer input variable number Nhide=Nhide+ 2n (q-1)/25q repeats second step, until hidden
The number of input variable containing layer Nhide=n (q-1)/10q；
4th step, ifThen modeling terminates, and is otherwise transferred to first step continuation.
Step 600, data to be predicted are obtained, including pitch angle to be predicted, turntable corner and shoe strut roll angle.
Step 700, according to the data to be predicted and the ELM unsteady aerodynamic model obtain with it is described to be predicted
The corresponding three-axis force coefficient of data and three-axis force moment coefficient.
For the precision of ELM model, formula mean square error E and coefficient of determination formula R are utilized2It is measured, calculating formula is as follows.
Wherein, r is sample set number, yi(i=1,2 ..., r) is the true value of i-th of sample,It is
The predicted value of i sample.
Actual prediction precision are as follows: E=8.7597e-6, R2=0.9994, prediction result curve is shown in Fig. 2~Figure 17.By emulating
As a result as can be seen that prediction technique accuracy of the invention is higher than existing prediction technique precision, and have preferably general
Property.
It should be understood by those skilled in the art that, the embodiment of the present invention can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the present invention
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the present invention, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The present invention be referring to according to the method for the embodiment of the present invention, the process of equipment (system) and computer program product
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
Although preferred embodiments of the present invention have been described, it is created once a person skilled in the art knows basic
Property concept, then additional changes and modifications may be made to these embodiments.So it includes excellent that the following claims are intended to be interpreted as
It selects embodiment and falls into all change and modification of the scope of the invention.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
Mind and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (3)
1. a kind of unsteady aerodynamic model parameter prediction method characterized by comprising
It obtains and substantially vibrates wind tunnel test data, include three-axis force coefficient, three-axis force moment coefficient, pitch angle, turntable corner and tail
Support strut roll angle；
Relevant parameter when obtaining Unsteady Aerodynamic Modeling according to the pitch angle, turntable corner and shoe strut roll angle, including the angle of attack
And yaw angle；
The input variable of selection limit learning machine ELM unsteady aerodynamic model are as follows: the angle of attack, the first derivative of the angle of attack, yaw angle
With reduction frequency, output variable is selected are as follows: three-axis force coefficient, three-axis force moment coefficient select kernel function are as follows: gaussian radial basis function core letter
Number；
ELM unsteady aerodynamic model is established and solves, according to the three-axis force coefficient and three-axis force square system obtained in wind tunnel test
Number, and optimize ELM unsteady aerodynamic model using cross validation method, judge whether modeling accuracy reaches requirement, if reaching
To requiring, completion is modeled, cross validation method selection parameter is otherwise re-used and is modeled；
Data to be predicted are obtained, including pitch angle to be predicted, turntable corner and shoe strut roll angle；
It is obtained and the data corresponding three to be predicted according to the data to be predicted and the ELM unsteady aerodynamic model
Axle power coefficient and three-axis force moment coefficient；
Wherein, step is specifically included using cross validation method optimization ELM unsteady aerodynamic model:
The first step, the input variable sum of model are n, are randomly divided into q part, take q-1 parts to be used as training sample, remaining 1
Part is used as forecast sample, while given prediction precision thresholdAnd initial predicted precision isIf hidden layer input becomes
The number of amount is [n (q-1)/10q, 9n (q-1)/10q]；
Second step, giving hidden layer input variable number is Nhide=n (q-1)/10q randomly selects the parameter input of ELM model
Layer and the connection weight w of the implicit interlayer and threshold value b of hidden layer input variable, are averaged by providing predicted value after cross validation q times
Precision R2IfThenAnd by N at this timehide, w and b record；Repeat this step Nhide/ 5 times；
Third step increases hidden layer input variable number Nhide=Nhide+ 2n (q-1)/25q randomly chooses ELM model again
Parameter w and b, until hidden layer input variable number Nhide=n (q-1)/10q；
4th step, ifThen modeling terminates, and is otherwise transferred to first step continuation.
2. the method as described in claim 1, which is characterized in that step is according to the pitch angle, turntable corner and shoe strut
Relevant parameter specifically includes when roll angle obtains Unsteady Aerodynamic Modeling:
When for vertical dip mining, model formal dress, so angle of attack is mechanism pitching angle thetag, model yaw angle is turntable corner ψg:
α=θg
β=ψg
For yaw oscillations, model side dress, according to geometrical relationship it is found that the angle of attack of model is turntable corner ψg, the yaw angle of model
For mechanism pitching angle thetag:
α=ψg
β=θg
Rolling is vibrated, model formal dress, since mechanism has pitch angle, so will appear inertia coupling phenomenon, i.e. model
The angle of attack and yaw angle hinge are derived at one piece by geometrical relationship, the angle of attack and yaw angle of model:
α=atan (cos (φg)·tan(θg))
β=asin (sin (φg)·sin(θg))
Wherein, φgFor shoe strut roll angle.
3. the method as described in claim 1, which is characterized in that the step of establishing the ELM unsteady aerodynamic model is specific
Include:
Input layer has n input variable, and hidden layer has l input variable, and output layer has m output variable；
If the connection weight w of input layer and implicit interlayer are as follows:
Wherein, wlnIndicate the connection weight between first of input variable of n-th of input variable of input layer and hidden layer；
If the connection weight β of hidden layer and output interlayer are as follows:
Wherein, βlmIndicate the connection weight between m-th of output variable of first of input variable of hidden layer and output layer；
If the threshold value b of hidden layer input variable are as follows:
Setting tool has the training set input matrix X of Q sample and output matrix Y to be respectively as follows:
If the activation primitive of hidden layer input variable is g (x), the output T of model are as follows:
T=[t1 t2 … tQ]m×Q
Wherein wi=[wi1 wi2 … win], xj=[x1j x2j … xnj]T, above formula is writeable are as follows:
H β=TT
Wherein, H is known as hidden layer output matrix, and concrete form is as follows:
When activation primitive g (x) infinitely can be micro-, the parameter of single hidden layer feedforward neural network SLFN does not need all to be adjusted
Whole, w and b can be randomly selected before training, and remain unchanged in the training process, and the connection weight of hidden layer and output interlayer
Value β can be obtained by solving the least square solution of equation group:
It is solved:
H+Take Moore-Penrose generalized inverse.
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| CN107886126B (en) * | 2017-11-10 | 2018-11-20 | 哈尔滨工业大学（威海） | Aerial engine air passage parameter prediction method and system based on dynamic integrity algorithm |
| CN108345755B (en) * | 2018-03-07 | 2021-06-11 | 北京顺恒达汽车电子股份有限公司 | Method and device for optimally designing strut moment of electric strut system of automobile tail gate |
| CN111160631B (en) * | 2019-12-17 | 2024-01-19 | 西北工业大学 | Conflict detection and resolution method based on four-dimensional track operation |
| CN111176329B (en) * | 2020-02-12 | 2020-09-18 | 中国空气动力研究与发展中心高速空气动力研究所 | Formation flight mixing performance function construction method based on wind tunnel test data |
| CN111241762A (en) * | 2020-03-03 | 2020-06-05 | 成都陆面体科技有限公司 | Method for predicting gap between model tail cavity and strut for wind tunnel test |
| CN112446091A (en) * | 2020-11-19 | 2021-03-05 | 中国航天空气动力技术研究院 | Artificial neural network-based pulsating pressure prediction method |
| CN115343012B (en) * | 2022-07-07 | 2023-04-07 | 中国航空工业集团公司哈尔滨空气动力研究所 | Unsteady-state large-amplitude oscillation test method |
| CN116956471B (en) * | 2023-09-19 | 2024-01-12 | 中国空气动力研究与发展中心计算空气动力研究所 | Aerodynamic force prediction method, device, equipment and medium for large-scale conveyor |
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