CN106446424A - Unsteady aerodynamic model parameter prediction method - Google Patents

Abstract

The invention discloses an unsteady aerodynamic model parameter prediction method, and relates to the technical field of aircraft modeling. Unsteady aerodynamic force is modeled and predicted through an ELM method on the basis of a large amount of wind tunnel test data, therefore, the advantages of being large in processing sample size, globally convergent, high in universality and prediction precision and the like are achieved, and unsteady aerodynamic force prediction under single-axle oscillation is achieved. Compared with other existing unsteady aerodynamic force prediction methods, the method has the advantages that the model precision is high, an accurate aerodynamic model is achieved under the condition of the large incidence angle and the great maneuver of an advanced fighter, great maneuver control can be better achieved, and therefore the favorable position is achieved in dogfight of future fighters.

Description

A kind of unsteady aerodynamic model parameter prediction method

Technical field

The present invention relates to aviation aircraft modeling technique field, particularly to a kind of unsteady aerodynamic model parameter prediction Method.

Background technology

Short range combat is the mark of advanced fighter super maneuver performance it is desirable to fighter plane still enables in low speed High Angle of Attack Controllable instruction tactical maneuver action post stall maneuver.Typical post stall maneuver have Cobra maneuver, He Baisite motor-driven, Vector cylinder etc., in post stall maneuver, it is straight that the gas of aerofoil surface flow to vortex motion, vortex breakdown by single attachment To developing into separated flow, gas flows and interferes between delayed and each part vortex system that ratio is more serious, and these result in aircraft The characteristic such as non-linear, the multiaxis coupling of the gentle kinetic moment of aerodynamic force and sluggishness during high maneuver.Therefore, traditional aerodynamic model exists No longer it is suitable for it is necessary to set up accurate unsteady aerodynamic model during High Angle of Attack.

For the modeling of unsteady aerodynamic force, conventional 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 single shaft vibration unsteady aerodynamic force modeling problem, but its modeling accuracy is not high, versatility is poor.

Content of the invention

Embodiments provide a kind of unsteady aerodynamic model parameter prediction method, in order to solve in prior art The problem existing.

A kind of unsteady aerodynamic model parameter prediction method, including：

Obtain and significantly vibrate wind tunnel test data, comprise three-axis force coefficient, three-axis force moment coefficient, the angle of pitch, rotating disk corner With shoe pole roll angle；

Relevant parameter when Unsteady Aerodynamic Modeling is obtained according to the described angle of pitch, rotating disk corner and shoe pole roll angle, including The angle of attack and yaw angle；

The input variable of selection limit learning machine ELM unsteady aerodynamic model is：The angle of attack, the first derivative of the angle of attack, side Sliding angle with reducing frequency, selection output variable is：Three-axis force coefficient, three-axis force moment coefficient, select kernel function be：Gaussian radial basis function Kernel function；

Set up and solve ELM unsteady aerodynamic model, according to the three-axis force coefficient obtaining in wind tunnel test and three-axis force Moment coefficient, and optimize ELM unsteady aerodynamic model using cross validation method；

Judge whether modeling accuracy reaches requirement, if reaching requirement, modeling and completing, otherwise re-use cross validation side Method selection parameter is modeled；

Obtain data to be predicted, including the angle of pitch to be predicted, rotating disk corner and shoe pole roll angle；

Obtained corresponding with described data to be predicted according to described data to be predicted and described ELM unsteady aerodynamic model Three-axis force coefficient and three-axis force moment coefficient.

Preferably, step obtains Unsteady Aerodynamic Modeling phase according to the described angle of pitch, rotating disk corner and shoe pole roll angle Related parameter specifically includes：

During for vertical dip mining, model formal dress, so angle of attack is mechanism's pitching angle theta_g, model yaw angle turns for rotating disk Angle ψ_g：

α=θ_g

β=ψ_g

For yaw oscillations, model side fills, and according to geometrical relationship, the angle of attack of model is rotating disk corner ψ_g, model Yaw angle is mechanism's pitching angle theta_g：

α=ψ_g

β=θ_g

Rolling is vibrated, model formal dress, because mechanism has the angle of pitch, so inertia coupling phenomenon occurs, i.e. mould The angle of attack of type and yaw angle hinge, at one piece, are derived by geometrical relationship, the angle of attack of model and yaw angle：

α=atan (cos (φ_g)·tan(θ_g))

β=asin (sin (φ_g)·sin(θ_g))

Wherein, φ_gFor shoe pole roll angle.

Preferably, the step setting up described 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 input layer with connection weight w of implicit interlayer is：

Wherein, w_jiRepresent the connection weight between i-th input variable of input layer and j-th input variable of hidden layer；

If hidden layer with connection weight β of output interlayer is：

Wherein, β_jkRepresent the connection weight between j-th input variable of hidden layer and k-th output variable of output layer；

If threshold value b of hidden layer input variable is：

Training set input matrix X and output matrix Y that setting tool has Q sample are respectively：

If the activation primitive of hidden layer input variable is g (x), the output T of model is：

T=[t₁t₂… t_Q]_m×Q

Wherein w_i=[w_i1w_i2… w_in], x_j=[x_1jx_2j… x_nj]^T, above formula can be written as：

H β=T^T

Wherein, H is referred to 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 enter Row adjustment, w and b can randomly choose before training, and keeps constant in the training process, and hidden layer and the company exporting interlayer Meet weights β to obtain by solving the least square solution of equation group：

Its solution：

H⁺Take Moore-Penrose generalized inverse.

Preferably, step optimizes ELM unsteady aerodynamic model using cross validation method and specifically includes：

The input variable sum of model is p, is randomly divided into q part, takes q-1 part as training sample, remaining 1 part of work For forecast sample, given prediction precision threshold simultaneouslyAnd initial predicted precision isIf hidden layer input variable Number is [p (q-1)/10q, 9p (q-1)/10q]；

Given hidden layer input variable number is N_hide=p (q-1)/10q, randomly selects the parameter input layer of ELM model With connection weight w of implicit interlayer and threshold value b of hidden layer input variable, averagely smart by providing predictive value after cross validation q time Degree R²If,ThenAnd by N now_hide, w and b record；Repeat this step N_hide/ 5 times；

Increase hidden layer input variable number N_hide=N_hide+ 2p (q-1)/25q, randomly chooses the parameter of ELM model again W and b, until hidden layer input variable number N_hide=p (q-1)/10q；

IfThen modeling terminates, and otherwise proceeds to the first step and continues.

Beneficial effects of the present invention are：The present invention on the basis of substantial amounts of wind tunnel test data, using ELM method to non- Unsteady Flow is modeled and predicts, has that process sample size is big, global convergence, highly versatile, precision of prediction height etc. are excellent Gesture it is achieved that the lower unsteady aerodynamic force of single shaft vibration is predicted, mould compared with other unsteady aerodynamic force Forecasting Methodologies existing Type precision higher so that there is Aerodynamic Model exactly under advanced fighter High Angle of Attack high maneuver, high maneuver is better achieved Control, thus occupying vantage point in following fighter plane short range combat.

Brief description

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing Have technology description in required use accompanying drawing be briefly described it should be apparent that, drawings in the following description be only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, acceptable Other accompanying drawings are obtained according to these accompanying drawings.

Fig. 1 is a kind of flow chart of steps of unsteady aerodynamic model parameter prediction method provided in an embodiment of the present invention；

Fig. 2 is that during sideslip angle beta=- 30 °, static pitching moment coefficient predicts the outcome；

Fig. 3 is that during sideslip angle beta=0 °, static pitching moment coefficient predicts the outcome；

Fig. 4 is that during sideslip angle beta=10 °, static pitching moment coefficient predicts the outcome；

Fig. 5 is sideslip angle beta=- 30 °, and significantly during frequency of oscillation f=0.4, pitching moment coefficient predicts the outcome；

Fig. 6 is sideslip angle beta=- 30 °, and significantly during frequency of oscillation f=0.6, pitching moment coefficient predicts the outcome；

Fig. 7 is sideslip angle beta=- 30 °, and significantly during frequency of oscillation f=0.8, pitching moment coefficient predicts the outcome；

Fig. 8 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.2, pitching moment coefficient predicts the outcome；

Fig. 9 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.4, pitching moment coefficient predicts the outcome；

Figure 10 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.5, pitching moment coefficient predicts the outcome；

Figure 11 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.6, pitching moment coefficient predicts the outcome；

Figure 12 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.7, pitching moment coefficient predicts the outcome；

Figure 13 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=0.8, pitching moment coefficient predicts the outcome；

Figure 14 is sideslip angle beta=0 °, and significantly during frequency of oscillation f=1, pitching moment coefficient predicts the outcome；

Figure 15 is sideslip angle beta=10 °, and significantly during frequency of oscillation f=0.4, pitching moment coefficient predicts the outcome；

Figure 16 is sideslip angle beta=10 °, and significantly during frequency of oscillation f=0.6, pitching moment coefficient predicts the outcome；

Figure 17 is sideslip angle beta=10 °, and significantly during frequency of oscillation f=0.8, pitching moment coefficient predicts the outcome.

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation description is it is clear that described embodiment is only a part of embodiment of the present invention, rather than whole embodiments.It is based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of not making creative work Embodiment, broadly falls into the scope of protection of the invention.

With reference to Fig. 1, embodiments provide a kind of unsteady aerodynamic model parameter prediction method, the method bag Include：

Obtain and significantly vibrate wind tunnel test data, comprise three-axis force coefficient, three-axis force moment coefficient, the angle of pitch, rotating disk corner With shoe pole roll angle；

Relevant parameter when obtaining Unsteady Aerodynamic Modeling according to the described angle of pitch, rotating disk corner and shoe pole roll angle, such as meets Angle and yaw angle；

The input variable of selection limit learning machine ELM unsteady aerodynamic model is：The angle of attack, the first derivative of the angle of attack, side Sliding angle with reducing frequency, selection output variable is：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), select kernel function be：Gaussian radial basis function Function；

Set up and solve ELM unsteady aerodynamic model, according to the three-axis force coefficient obtaining in wind tunnel test and three-axis force Moment coefficient, and optimize ELM unsteady aerodynamic model using cross validation method, judge whether modeling accuracy reaches requirement, If reaching requirement, modeling and completing, otherwise proceed to previous step and reselect parameter and be modeled；

Obtain data to be predicted, including the angle of pitch to be predicted, rotating disk corner and shoe pole roll angle；

Obtained corresponding with described data to be predicted according to described data to be predicted and described ELM unsteady aerodynamic model Three-axis force coefficient and three-axis force moment coefficient.

Below taking the unsteady aerodynamic force modeling of the pitching moment coefficient of pitching-rolling twin shaft coupled oscillationses as a example to this Bright method is described in detail：

Step 100, using the pitching moment coefficient under flow tunnel testing device acquisition single shaft vibration, the angle of pitch, rotating disk corner With shoe pole roll angle；

Step 200, to wind tunnel test data processing, relevant parameter when obtaining Unsteady Aerodynamic Modeling, such as angle of attack α, sideslip angle beta；

Specifically, step 200 includes：

During for vertical dip mining, model formal dress, so angle of attack is mechanism's pitching angle theta_g, model yaw angle turns for rotating disk Angle ψ_g：

α=θ_g

β=ψ_g

For yaw oscillations, model side fills, and according to geometrical relationship, the angle of attack of model is rotating disk corner ψ_g, model Yaw angle is mechanism's pitching angle theta_g：

α=ψ_g

β=θ_g

Rolling is vibrated, model formal dress, because mechanism has the angle of pitch, so inertia coupling phenomenon occurs, i.e. mould The angle of attack of type and yaw angle hinge are at one piece.Derived by geometrical relationship, the angle of attack of model and yaw angle：

α=atan (cos (φ_g)·tan(θ_g))

β=asin (sin (φ_g)·sin(θ_g))

Wherein, φ_gFor shoe pole roll angle.

Step 300, selects input variable it is contemplated that generally angle of attack α_iWith sideslip angle beta_iIt is impact three-axis force and three The factor of axle power moment coefficient, therefore selects angle of attack α first_iWith sideslip angle beta_iAs input variable.Secondly, from wind tunnel test data Analysis result is seen, its three-axis force and moment coefficient have hysteresis, therefore three-axis force and force coefficient and be subject to upper one to clap or a few bat state The impact of variable, so the first derivative by the angle of attackAs its input variable.Finally from test data, reduce frequency k_i Impact ratio to three-axis force and moment coefficient is larger, therefore also as input variable.Thus, for pitching-cross coupling The input variable of vibration unsteady aerodynamic model can be expressed as follows：

Select output variable, for output variable, due to the present invention it is important that unsteady aerodynamic force models, so its output Variable is three-axis force and three-axis force moment coefficient, that is,：

y_i∈{F_x,F_y,F_z,M_x,M_y,M_z}

Select kernel function, select following gaussian radial basis function：

G (x, w, b)=exp (- b | | x-w | |²)

Step 400, sets up ELM model：

Typically single hidden layer feedforward neural network SLFN is made up of input layer, hidden layer and output layer, input layer with hidden Entirely it is connected between output layer neuron containing layer, hidden layer.Wherein, input layer has n neuron, corresponding n input variable；Implicit Layer has l neuron, corresponding l input variable；Output layer has m neuron, corresponding m output variable.

Without loss of generality, if input layer with connection weight w of implicit interlayer is

Wherein, w_jiRepresent the connection weight between i-th input variable of input layer and j-th input variable of hidden layer.

If hidden layer with connection weight β of output interlayer is：

Wherein, β_jkRepresent the connection weight between j-th input variable of hidden layer and k-th output variable of output layer.

If threshold value b of hidden layer input variable is：

Training set input matrix X and output matrix Y that setting tool has Q sample are respectively：

If the activation primitive of hidden layer input variable, that is, kernel function is g (x), and the output T of network is：

T=[t₁t₂… t_Q]_m×Q

Wherein w_i=[w_i1w_i2… w_in], x_j=[x_1jx_2j… x_nj]^T.Above formula can be written as：

H β=T^T

Wherein, H is referred to as the hidden layer output matrix of neutral net, 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, w and b is before training Can randomly choose, and keep constant in the training process.And hidden layer with output interlayer connection weight β can by solve with The least square solution of lower equation group obtains：

Its solution：

H⁺Typically take Moore-Penrose generalized inverse.

Step 500, solves ELM model：

Number due in classical ELM method, simply requiring hidden layer neuron is less than number of samples, simultaneously for The biasing of the connection weight of input layer and output interlayer and hidden layer neuron is all random setting, and these result in ELM and exist During sample predictions, precision is poor.The present invention proposes a kind of method based on cross validation and determines this three class variable, and it is concrete Step is as follows：

The first step, the input variable sum of model is n, is randomly divided into q part, takes q-1 part as training sample, remaining 1 part as forecast sample, given prediction precision threshold simultaneouslyAnd initial predicted precision isIf hidden layer inputs The number of variable is [n (q-1)/10q, 9n (q-1)/10q]；

Second step, given hidden layer input variable number is N_hide=n (q-1)/10q, randomly selects the parameter of ELM model W and b, provides predictive value mean accuracy R by after cross validation q time²If,ThenAnd by now N_hide, w and b record；Repeat this step N_hide/ 5 times；

3rd step, increases hidden layer input variable number N_hide=N_hide+ 2n (q-1)/25q, repeats second step, until hidden The number N of input variable containing layer_hide=n (q-1)/10q；

4th step, ifThen modeling terminates, and otherwise proceeds to the first step and continues.

Step 600, obtains data to be predicted, including the angle of pitch to be predicted, rotating disk corner and shoe pole roll angle.

Step 700, obtains to be predicted with described according to described data to be predicted and described ELM unsteady aerodynamic model Data corresponding three-axis force coefficient and three-axis force moment coefficient.

For the precision of ELM model, using formula mean square error E and coefficient of determination formula R²Weighed, its calculating formula is as follows.

Wherein, r is sample set number, y_i(i=1,2 ..., r) be i-th sample actual value,For i-th The predictive value of individual sample.

Actual prediction precision is：E=8.7597e-6, R²=0.9994, the curve that predicts the outcome is shown in Fig. 2～Figure 17.By emulating The Forecasting Methodology degree of accuracy that result can be seen that the present invention is higher than existing Forecasting Methodology precision, and has preferably general Property.

Those skilled in the art are it should be appreciated that embodiments of the invention can be provided as method, system or computer program Product.Therefore, the present invention can be using complete hardware embodiment, complete software embodiment or the reality combining software and hardware aspect Apply the form of example.And, the present invention can be using in one or more computers wherein including computer usable program code The upper computer program implemented of usable storage medium (including but not limited to disk memory, CD-ROM, optical memory etc.) produces The form of product.

The present invention is the flow process with reference to method according to embodiments of the present invention, equipment (system) and computer program Figure and/or block diagram are describing.It should be understood that can be by each stream in computer program instructions flowchart and/or block diagram Flow process in journey and/or square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided The processor instructing general purpose computer, special-purpose computer, Embedded Processor or other programmable data processing device is to produce A raw machine is so that produced for reality by the instruction of computer or the computing device of other programmable data processing device The device of the function of specifying in present one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.

These computer program instructions may be alternatively stored in and can guide computer or other programmable data processing device with spy Determine in the computer-readable memory that mode works so that the instruction generation inclusion being stored in this computer-readable memory refers to Make the manufacture of device, this command device realize in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or The function of specifying in multiple square frames.

These computer program instructions also can be loaded in computer or other programmable data processing device so that counting On calculation machine or other programmable devices, execution series of operation steps to be to produce computer implemented process, thus in computer or On other programmable devices, the instruction of execution is provided for realizing in one flow process of flow chart or multiple flow process and/or block diagram one The step of the function of specifying in individual square frame or multiple square frame.

Although preferred embodiments of the present invention have been described, but those skilled in the art once know basic creation Property concept, then can make other change and modification to these embodiments.So, claims are intended to be construed to including excellent Select embodiment and fall into being had altered and changing of the scope of the invention.

Obviously, those skilled in the art can carry out the various changes and modification essence without deviating from the present invention to the present invention God and scope.So, if these modifications of the present invention and modification belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprise these changes and modification.

Claims (4)

1. a kind of unsteady aerodynamic model parameter prediction method is it is characterised in that include：

Obtain and significantly vibrate wind tunnel test data, comprise three-axis force coefficient, three-axis force moment coefficient, the angle of pitch, rotating disk corner and tail Support pole roll angle；

Relevant parameter when obtaining Unsteady Aerodynamic Modeling according to the described angle of pitch, rotating disk corner and shoe pole roll angle, including the angle of attack And yaw angle；

The input variable of selection limit learning machine ELM unsteady aerodynamic model is：The angle of attack, the first derivative of the angle of attack, yaw angle With reduction frequency, select output variable be：Three-axis force coefficient, three-axis force moment coefficient, select kernel function be：Gaussian radial basis function core letter Number；

Set up and solve ELM unsteady aerodynamic model, according to the three-axis force coefficient obtaining in wind tunnel test and three-axis force square system Number, and optimize ELM unsteady aerodynamic model using cross validation method, judge whether modeling accuracy reaches requirement, if reaching To requiring, model and complete, otherwise re-use cross validation method selection parameter and be modeled；

Obtain data to be predicted, including the angle of pitch to be predicted, rotating disk corner and shoe pole roll angle；

Obtained and described data corresponding three to be predicted according to described data to be predicted and described ELM unsteady aerodynamic model Axle power coefficient and three-axis force moment coefficient.

2. the method for claim 1 is it is characterised in that step is according to the described angle of pitch, rotating disk corner and shoe pole When roll angle obtains Unsteady Aerodynamic Modeling, relevant parameter specifically includes：

During for vertical dip mining, model formal dress, so angle of attack is mechanism's pitching angle theta_g, model yaw angle is rotating disk corner ψ_g：

α=θ_g

β=ψ_g

For yaw oscillations, model side fills, and according to geometrical relationship, the angle of attack of model is rotating disk corner ψ_g, the yaw angle of model For mechanism's pitching angle theta_g：

α=ψ_g

β=θ_g

For rolling vibration, model formal dress, because mechanism has the angle of pitch, so inertia coupling phenomenon occurs, i.e. model The angle of attack and yaw angle hinge, at one piece, are derived by geometrical relationship, the angle of attack of model and yaw angle：

α=atan (cos (φ_g)·tan(θ_g))

β=asin (sin (φ_g)·sin(θ_g))

Wherein, φ_gFor shoe pole roll angle.

3. the method for claim 1 is it is characterised in that the step setting up described ELM unsteady aerodynamic model is concrete Including：

Input layer has n input variable, and hidden layer has l input variable, and output layer has m output variable；

If input layer with connection weight w of implicit interlayer is：

$w={\left[\begin{array}{cccc}{w}_{11}& w_{12}& \mathrm{...}& w_{1n}\\ w_{21}& w_{22}& \mathrm{...}& w_{2n}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ w_{l1}& w_{l2}& \mathrm{...}& w_{ln}\end{array}\right]}_{l\×n}$

Wherein, w_jiRepresent the connection weight between i-th input variable of input layer and j-th input variable of hidden layer；

If hidden layer with connection weight β of output interlayer is：

$\mathrm{\β}={\left[\begin{array}{cccc}{\mathrm{\β}}_{11}& {\mathrm{\β}}_{12}& \mathrm{...}& {\mathrm{\β}}_{1m}\\ {\mathrm{\β}}_{21}& {\mathrm{\β}}_{22}& \mathrm{...}& {\mathrm{\β}}_{2m}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ {\mathrm{\β}}_{l1}& {\mathrm{\β}}_{l2}& \mathrm{...}& {\mathrm{\β}}_{lm}\end{array}\right]}_{l\×m}$

Wherein, β_jkRepresent the connection weight between j-th input variable of hidden layer and k-th output variable of output layer；

If threshold value b of hidden layer input variable is：

$b={\left[\begin{array}{c}{b}_1\\ b_2\\ .\\ .\\ .\\ b_l\end{array}\right]}_{l\×1}$

Training set input matrix X and output matrix Y that setting tool has Q sample are respectively：

$X={\left[\begin{array}{cccc}{x}_{11}& x_{12}& \mathrm{...}& x_{1Q}\\ x_{21}& x_{22}& \mathrm{...}& x_{2Q}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{n1}& x_{n2}& \mathrm{...}& x_{nQ}\end{array}\right]}_{n\×Q}$

$Y={\left[\begin{array}{cccc}{y}_{11}& y_{12}& \mathrm{...}& y_{1Q}\\ y_{21}& y_{22}& \mathrm{...}& y_{2Q}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ y_{m1}& y_{m2}& \mathrm{...}& y_{mQ}\end{array}\right]}_{m\×Q}$

If the activation primitive of hidden layer input variable is g (x), the output T of model is：

T=[t₁t₂… t_Q]_m×Q

$t_j={\left[\begin{array}{c}{t}_{1j}\\ t_{2j}\\ .\\ .\\ .\\ t_{mj}\end{array}\right]}_{m\×1}={\left[\begin{array}{c}\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\β}}_{i1}g(w_i{x}_j+b_i)\\ \underset{i=1}{\overset{l}{\Σ}}{\mathrm{\β}}_{i2}g(w_i{x}_j+b_i)\\ .\\ .\\ .\\ \underset{i=1}{\overset{l}{\Σ}}{\mathrm{\β}}_{im}g(w_i{x}_j+b_i)\end{array}\right]}_{m\×1},j=1,2,...,Q$

Wherein w_i=[w_i1w_i2… w_in], x_j=[x_1jx_2j… x_nj]^T, above formula can be written as：

H β=T^T

Wherein, H is referred to as hidden layer output matrix, and concrete form is as follows：

$H={\left[\begin{array}{cccc}g(w_1{x}_1+b_1)& g(w_2{x}_1+b_2)& \mathrm{...}& g(w_l{x}_1+b_l)\\ g(w_1{x}_2+b_1)& g(w_2{x}_2+b_2)& \mathrm{...}& g(w_l{x}_2+b_l)\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ g(w_1{x}_Q+b_1)& g(w_2{x}_Q+b_2)& \mathrm{...}& g(w_l{x}_Q+b_l)\end{array}\right]}_{Q\×l}$

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 randomly choose before training, and keeps constant in the training process, and hidden layer and the connection weight exporting interlayer Value β can be obtained by solving the least square solution of equation group：

$\underset{\mathrm{\β}}{min}\left|\right|H\mathrm{\β}-T^T\left|\right|$

Its solution：

$\widehat{\mathrm{\β}}=H^{+}{T}^T$

H⁺Take Moore-Penrose generalized inverse.

4. the method for claim 1 is it is characterised in that step utilizes cross validation method optimization ELM unsteady pneumatic Power model specifically includes：

The input variable sum of model is n, is randomly divided into q part, takes q-1 part as training sample, remaining 1 part as pre- Test sample basis, given prediction precision threshold simultaneouslyAnd initial predicted precision isIf the number of hidden layer input variable For [n (q-1)/10q, 9n (q-1)/10q]；

Given hidden layer input variable number is N_hide=n (q-1)/10q, randomly selects the parameter input layer of ELM model and implies Connection weight w of interlayer and threshold value b of hidden layer input variable, provide predictive value mean accuracy R by after cross validation q time²If,ThenAnd by N now_hide, w and b record；Repeat this step N_hide/ 5 times；

Increase hidden layer input variable number N_hide=N_hide+ 2n (q-1)/25q, again randomly choose ELM model parameter w and B, until hidden layer input variable number N_hide=n (q-1)/10q；

IfThen modeling terminates, and otherwise proceeds to the first step and continues.