Projectile aerodynamic coefficient identification method based on butterfly algorithm optimization kernel extreme learning

Abstract

The invention relates to a projectile aerodynamic coefficient identification method based on butterfly algorithm optimized kernel extreme learning. Comprising the following steps: (1) establishing a projectile four-degree-of-freedom kinetic model; (2) constructing a kernel extreme learning network model; (3) optimizing the kernel extreme learning machine network model by using a butterfly algorithm to obtain a regularization coefficient and a kernel function parameter of an original kernel extreme learning machine network model, and substituting the regularization coefficient and the kernel function parameter into the kernel extreme learning machine network model to obtain an optimized butterfly algorithm kernel extreme learning machine network model; (4) inputting training sample data according to the optimized butterfly algorithm kernel extreme learning machine network model, and determining an output layer weight; and on the basis of determining the weight of the output layer, inputting prediction data, solving an output matrix of the model, and realizing parameter identification. According to the method, the regularization coefficient and the kernel function parameters are provided for the kernel extreme learning machine by using the butterfly optimization algorithm, and then the pneumatic parameters of the projectile are identified by using the kernel extreme learning, so that a new method is provided for obtaining the pneumatic parameters of the projectile.

Description

Technical Field

[0001] The present invention belongs to the field of projectile parameter identification, and specifically relates to a projectile aerodynamic coefficient identification method based on butterfly algorithm optimized kernel limit learning. Background Art

[0002] The accuracy of projectile aerodynamic coefficient identification affects the projectile ballistic trajectory and flight stability. In order to improve the projectile shooting accuracy, reduce the drop point dispersion and enhance the strike accuracy, it is very important to obtain the accurate aerodynamic parameters of the projectile.

[0003] At present, the main methods used for parameter identification are recursive least squares method, recursive maximum likelihood method, Kalman filter method and extreme learning machine method. Among them, the extreme learning machine method is becoming more and more well-known. For example, Xia Youran et al. proposed an improved particle swarm optimization extreme learning machine method to identify aerodynamic parameters in "Projectile Parameter Identification Based on Improved Particle Swarm Optimization Extreme Learning Machine" System Engineering and Electronic Technology, 2023, 45(02): 521-529. However, this method has many parameters, and the algorithm is greatly affected by the parameters. In addition, in the process of identifying the aerodynamic coefficients of the projectile, the kernel extreme learning machine randomly generates regularization coefficients and kernel function parameters, which makes the kernel extreme learning identification effect unstable. Summary of the invention

[0004] The object of the present invention is to provide a method for identifying aerodynamic coefficients of a projectile based on butterfly algorithm optimized kernel limit learning.

[0005] The technical solution to achieve the purpose of the present invention is: a projectile aerodynamic coefficient identification method based on butterfly algorithm optimized kernel limit learning, comprising the following steps:

[0006] Step (1): Establish a four-degree-of-freedom dynamic model of the projectile;

[0007] Step (2): construct a kernel extreme learning network model;

[0008] Step (3): Optimize the kernel extreme learning machine network model using the butterfly algorithm, obtain the regularization coefficient and kernel function parameters of the original kernel extreme learning machine network model, and bring them into the kernel extreme learning machine network model to obtain the optimized butterfly algorithm kernel extreme learning machine network model;

[0009] Step (4): According to the butterfly algorithm kernel extreme learning machine network model optimized in step (3), input the training sample data and determine the output layer weight w; based on the output layer weight w, input the prediction data, solve the output matrix of the model, and realize parameter identification.

[0010] Furthermore, step (1) "establishing a four-degree-of-freedom dynamic model of the projectile" is specifically as follows:

[0011] The four-degree-of-freedom dynamic model is established in the ground coordinate system. x 、V y 、V z are the velocity components of the projectile in the x, y, and z directions respectively; x, y, and z are the position coordinates of the projectile; γ is the roll angle; is the rolling angular velocity; m is the mass of the projectile; d is the maximum cross-sectional area of ​​the projectile; l is the length of the projectile; g is the acceleration of gravity; ρ is the air density; S is the characteristic area of ​​the projectile, which is taken as the maximum cross-sectional area of ​​the projectile; C x0 and C x2 are the zero-lift drag coefficient and the induced drag coefficient respectively; α e is the dynamic balance angle; V r is the speed of the projectile relative to the air; C y ′ is the lift coefficient derivative; C z ″ is the joint partial derivative of the Martensitic coefficients; C is the polar moment of inertia; m x ' z is the derivative of the extreme damping torque coefficient; W x and W z are the wind speeds in the x and y directions respectively; m′ y ′ is the joint partial derivative of the Magnus moment coefficient; m' z is the derivative of the static moment coefficient:

[0012]

[0013] The speed of the projectile relative to the air is

[0014]

[0015] The direct calculation formula for the dynamic balance angle is:

[0016]

[0017] The parameters in the direct calculation formula are:

[0018]

[0019] x2=(a a -a b )b y V r 2 (8)

[0020]

[0021]

[0022] V rx =V x -W x (12)

[0023] V ry =V y (13)

[0024] V rz =V z -W z (14).

[0025] Furthermore, step (2) "constructing a nuclear extreme learning network model" specifically includes the following steps:

[0026] Step (21): Setting input data;

[0027] Based on the four-degree-of-freedom trajectory model, the input data are determined to be V x 、V y 、V z , x, y, z;

[0028] Step (22): Calculate the kernel matrix based on the input data;

[0029] The learning objective function of the extreme learning machine is:

[0030] f(x)=H×β=T (15)

[0031] Among them, H is the output of the hidden layer node, β is the output weight, T is the expected output, and in order to enhance the stability of the neural network, the regularization coefficient C and the unit matrix I are introduced, then:

[0032]

[0033] Introduce the kernel matrix:

[0034] Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (17)

[0035] Among them, x i ,x j Input data for the experiment, K(x i ,x j ) is the Gaussian kernel function, and its expression is:

[0036]

[0037] Among them, γ is the kernel function parameter, ||xy|| is the Euclidean norm between samples;

[0038] Then the learning objective function is:

[0039]

[0040] Furthermore, step (3): "optimizing the kernel extreme learning machine network model using the butterfly algorithm to obtain the regularization coefficient and kernel function parameter of the original kernel extreme learning machine network model" specifically includes the following steps:

[0041] Step (31): normalize the data set;

[0042] Using the min-max normalization method, all data are mapped to the [0,1] interval. The normalization formula is:

[0043]

[0044] Among them, x j is the original input data, x min is the minimum input data, x max is the maximum input data, is the normalized input data;

[0045] Step (32): performing initial parameter setting;

[0046] Step (33): determine the fitness function and calculate the butterfly fitness value;

[0047] Select the mean square error function as the fitness function and calculate the fitness value of each butterfly

[0048]

[0049] Among them, M is the number of training sample data, T is the expected sample output value, Tn is the actual prediction value of the model, C is the regularization coefficient, S is the kernel parameter, and fitness is the fitness function value;

[0050] Step (34): Compare the fitness function values ​​of each butterfly to find the optimal value and optimal solution of the current butterfly;

[0051] f=c t I a (twenty two)

[0052] Among them, f is the amount of fragrance perception, c is the sensory form, t is the stimulus intensity, and a is the fragrance;

[0053] Step (35): Calculate the scent perception and update the position of the butterfly;

[0054]

[0055] represents the position of the tth butterfly in the t+1th generation, r is a random number in [0,1], g *Denotes the global optimal solution, f i Denotes the fragrance perception amount of the i-th butterfly;

[0056]

[0057] Respectively denote the positions of the i-th, j-th, and k-th butterflies in the t-th generation;

[0058]

[0059] b is a constant, c t Denotes the value in the t-th generation, N gen Is the maximum number of iterations;

[0060] Calculate the fragrance perception amount using Equation (22). If rand < p, then calculate using Equation (23) Otherwise, calculate using Equation (24)

[0061] Step (36): Recalculate the fitness value of each butterfly If Then replace the previous optimal value and optimal solution, where the optimal value includes the regularization coefficient and kernel function parameters;

[0062] Step (37): Update c, determine whether the maximum number of iterations is reached. If not, return to Step (35), otherwise end;

[0063] Step (38): Output the optimized regularization coefficient and kernel function parameters.

[0064] Furthermore, the initial parameter setting in Step (32) is specifically as follows:

[0065]

[0066] Furthermore, Step (4) specifically includes the following steps:

[0067] Step (41): Train the network and determine the output weights

[0068] The expression of the kernel extreme learning machine model is:

[0069]

[0070] Among them, I is the identity matrix, C is the regularization parameter, Ω ELM Is the kernel matrix, T is the output matrix;

[0071] Use N training samples (x i , t i ) to train the kernel extreme learning machine, where x i = [xi1 ,x i2 ,...,x in ] T ∈R n represents the input training sample data, t i =[t i1 ,t i2 ,...,t im ] T ∈R m Indicates the output of training sample data and calculates the kernel matrix of the training data:

[0072] Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (27)

[0073] Calculate the output weights:

[0074]

[0075] Step (42): Make predictions and use the output weights w to solve the output matrix of the model to achieve parameter identification

[0076] After the training is completed, the output weight w of the model is obtained. Assuming that M prediction samples are given at this time, the kernel matrix Ω of the prediction samples is calculated ELM , then the output matrix is:

[0077]

[0078] Compared with the prior art, the present invention has the following significant advantages:

[0079] The present invention is based on the flight data of the projectile, uses the butterfly optimization algorithm to provide regularization coefficients and kernel function parameters for the kernel extreme learning machine, and then uses the kernel extreme learning to identify the aerodynamic parameters of the projectile, thereby providing a new method for obtaining the aerodynamic parameters of the projectile. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 C of the present invention x0 Identify the results.

[0081] Figure 2 C of the present invention x2 Identify the results.

[0082] Figure 3 C of the present invention y 'Identification results.

[0083] Figure 4 m' of the present invention zIdentify the results.

[0084] Figure 5 The m of the present invention x ' z Identify the results.

[0085] Figure 6 C of the present invention z "Identification results.

[0086] Figure 7 is m' of the present invention y 'Identification results. DETAILED DESCRIPTION

[0087] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0088] A method for identifying aerodynamic coefficients of projectiles based on nuclear limit learning. Specifically, it includes the following steps:

[0089] Step 1: Establish a four-degree-of-freedom dynamic model of the projectile;

[0090] The details are as follows: The four-degree-of-freedom dynamic model is established in the ground coordinate system. x 、V y 、V z are the velocity components of the projectile in the x, y, and z directions respectively; x, y, and z are the position coordinates of the projectile; γ is the roll angle; is the rolling angular velocity; m is the mass of the projectile; d is the maximum cross-sectional area of ​​the projectile; l is the length of the projectile; g is the acceleration of gravity; ρ is the air density; S is the characteristic area of ​​the projectile, which is usually taken as the maximum cross-sectional area of ​​the projectile; C x0 and C x2 are the zero-lift drag coefficient and the induced drag coefficient respectively; α e is the dynamic balance angle; V r is the speed of the projectile relative to the air; C y ′ is the lift coefficient derivative; C z ″ is the joint partial derivative of the Martensitic coefficients; C is the polar moment of inertia; m x ' z is the derivative of the extreme damping torque coefficient; W x and W z are the wind speeds in the x and y directions respectively; m′ y ′ is the joint partial derivative of the Magnus moment coefficient; m' z is the derivative of the static moment coefficient:

[0091]

[0092]

[0093] The speed of the projectile relative to the air is

[0094]

[0095] The direct calculation formula for the dynamic balance angle is:

[0096]

[0097] The parameters in the direct calculation formula are:

[0098]

[0099] x2=(a a -a b )b y V r 2 (66)

[0100]

[0101] V rx =V x -W x

[0102] V ry =V y (70)

[0103] V rz =V z -W z (71)

[0104] Step 2: Construct a kernel extreme learning network model

[0105] When using kernel extreme learning machine to identify projectile aerodynamic parameters, it is necessary to determine the kernel function type.

[0106] The specific contents are as follows:

[0107] Step (21): input data setting;

[0108] Based on the four-degree-of-freedom trajectory model, the input data are determined to be V x 、V y 、V z , x, y, z;

[0109] Step (22): Calculate the kernel matrix based on the input data;

[0110] The learning objective function of the extreme learning machine is:

[0111] f(x)=H×β=T

[0112] Among them, H is the output of the hidden layer node, β is the output weight, T is the expected output, and in order to enhance the stability of the neural network, the regularization coefficient C and the unit matrix I are introduced, then:

[0113]

[0114] Introduce the kernel matrix:

[0115] Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (73)

[0116] Among them, x i ,x j Input data for the experiment, K(x i ,x j ) is the Gaussian kernel function, and its expression is:

[0117]

[0118] Among them, γ is the kernel function parameter, ||xy|| is the Euclidean norm between samples;

[0119] Then the learning objective function is:

[0120]

[0121] Step 3: Use the butterfly algorithm to optimize the kernel extreme learning machine network model and obtain the regularization coefficient and kernel function parameters of the original kernel extreme learning machine network model.

[0122] Step 3-1: Normalize the data set;

[0123] The data of the network has different physical meanings and dimensions. Different dimensions will affect the analysis results of the data. In order to eliminate the influence between different dimensions, the original data set needs to be normalized. The min-maxnormalization method is used to map all data to the [0,1] interval. The normalization formula is:

[0124]

[0125] Among them, x j is the original input data, x min is the minimum input data, x max is the maximum input data, is the normalized input data;

[0126] Step 3-2: Perform initial parameter settings;

[0127]

[0128] Step 3-3: Determine the fitness function and calculate the fitness value of the butterfly;

[0129] Select the mean square error function as the fitness function and calculate the fitness value of each butterfly

[0130]

[0131] where M is the number of training sample data, T is the expected sample output value, Tn is the actual predicted value of the model, C is the regularization coefficient, S is the kernel parameter, and fitness is the fitness function value.

[0132] Step 3-4: Compare the fitness function values of each butterfly and find the optimal value and optimal solution of the current butterfly from them;

[0133] f = c t I a (78)

[0134] where f is the fragrance perception amount, c is the sensory form, t is the stimulus intensity, and a is the fragrance;

[0135] Step 3-5: Calculate the fragrance perception amount and update the position of the butterfly.

[0136]

[0137] represents the position of the i-th butterfly in the (t + 1)-th generation, r is a random number in [0, 1], g * represents the global optimal solution, f i represents the fragrance perception amount of the i-th butterfly;

[0138]

[0139] represent the positions of the i-th, j-th, and k-th butterflies in the t-th generation respectively;

[0140]

[0141] b is a constant, c t represents the value in the t-th generation, N gen is the maximum number of iterations.

[0142] Calculate the fragrance perception amount using Equation (78). If rand < p, calculate using Equation (79) Otherwise, calculate using Equation (80)

[0143] Step 3-6: Recalculate the fitness value of each butterfly like Then replace the previous optimal value and optimal solution, where the optimal value includes the regularization coefficient and kernel function parameter.

[0144] Step 3-7: Update c and determine whether the maximum number of iterations has been reached. If not, return to step (35), otherwise end.

[0145] Step 3-8: Output the optimized regularization coefficient and kernel function parameters;

[0146] Step 4: Perform parameter identification based on the constructed BOA-KELM network model.

[0147] Step 4-1: Train the network and determine the output weights

[0148] The expression of the kernel extreme learning machine model is:

[0149]

[0150] Among them, I is the unit diagonal matrix, C is the regularization parameter, K(x,y) is the kernel function, Ω ELM is the kernel matrix and T is the output matrix.

[0151] Using N training samples (x i ,t i ), where x i =[x i1 ,x i2 ,...,x in ] T ∈R n represents the input training sample data, t i =[t i1 ,t i2 ,...,t im ] T ∈R m Indicates outputting training sample data to train the kernel extreme learning machine. Calculate the kernel matrix of the training data:

[0152] Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (83)

[0153] Calculate the output weights:

[0154]

[0155] Step 4-2: Make predictions and use the output weights w to solve the output matrix of the model to achieve parameter identification

[0156] After the training is completed, the output weight w of the model is obtained. Assuming that M prediction samples are given at this time, the kernel matrix Ω of the prediction samples is calculated ELM , then the output matrix is:

[0157]

[0158] Implementation Case 1

[0159] A more detailed description is given below in conjunction with embodiments.

[0160] The parameter settings of a certain type of shell are shown in the following table:

[0161] Table 1 Parameters of a certain type of projectile

[0162]

[0163]

[0164] Under the initial conditions in Table 2, the aerodynamic coefficients of the projectile are identified:

[0165] Table 2 Initial launch conditions of a certain type of projectile

[0166]

[0167] The aerodynamic parameters to be identified are: zero lift drag coefficient C x0 , induced drag coefficient C x2 , lift coefficient derivative C y ′, the joint partial derivative of the Marovnikov force coefficients C z ″, derivative of the polar damping torque coefficient m x ' z , the joint partial derivative of the Magnus moment coefficient m′ y ′, static moment coefficient derivative m' z The final identification result is as follows Figure 7 As shown in the figure, it can be seen that this method successfully identifies the aerodynamic coefficients of a certain type of projectile motion process.

Claims

1. A projectile aerodynamic coefficient identification method based on butterfly algorithm optimized kernel limit learning, characterized in that: The steps include: Step (1): Establish a four-degree-of-freedom dynamic model of the projectile; Step (2): construct a kernel extreme learning network model; Step (3): Optimize the kernel extreme learning machine network model using the butterfly algorithm, obtain the regularization coefficient and kernel function parameters of the original kernel extreme learning machine network model, and bring them into the kernel extreme learning machine network model to obtain the optimized butterfly algorithm kernel extreme learning machine network model; Step (4): According to the butterfly algorithm kernel extreme learning machine network model optimized in step (3), input the training sample data and determine the output layer weight w; based on the output layer weight w, input the prediction data, solve the output matrix of the model, and realize parameter identification.

2. The method according to claim 1, characterized in that Step (1) "establishing a four-degree-of-freedom dynamic model of the projectile" is specifically as follows: The four-degree-of-freedom dynamic model is established in the ground coordinate system. x 、V y 、V z are the velocity components of the projectile in the x, y, and z directions respectively; x, y, and z are the position coordinates of the projectile; γ is the roll angle; is the rolling angular velocity; m is the mass of the projectile; d is the maximum cross-sectional area of ​​the projectile; l is the length of the projectile; g is the acceleration of gravity; ρ is the air density; S is the characteristic area of ​​the projectile, which is taken as the maximum cross-sectional area of ​​the projectile; C x0 and C x2 are the zero-lift drag coefficient and the induced drag coefficient respectively; α e is the dynamic balance angle; V r is the speed of the projectile relative to the air; C y ′ is the lift coefficient derivative; C z ″ is the joint partial derivative of the Martensitic coefficients; C is the polar moment of inertia; m x ' z is the derivative of the extreme damping torque coefficient; W x and W z are the wind speeds in the x and y directions respectively; m′ y ′ is the joint partial derivative of the Magnus moment coefficient; m' z is the derivative of the static moment coefficient: The speed of the projectile relative to the air is The direct calculation formula for the dynamic balance angle is: The parameters in the direct calculation formula are: x2=(a a -a b )b y V r 2 (8) V rx =V x -W x (12) V ry =V y (13) V rz =V z -W z (14)。 3. The method according to claim 2, characterized in that Step (2) "constructing a nuclear extreme learning network model" specifically includes the following steps: Step (21): Setting input data; Based on the four-degree-of-freedom trajectory model, the input data are determined to be V x 、V y 、V z , x, y, z; Step (22): Calculate the kernel matrix based on the input data; The learning objective function of the extreme learning machine is: f(x)=H×β=T (15) Among them, H is the output of the hidden layer node, β is the output weight, T is the expected output, and in order to enhance the stability of the neural network, the regularization coefficient C and the unit matrix I are introduced, then: Introduce the kernel matrix: Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (17) Among them, x i ,x j Input data for the experiment, K(x i ,x j ) is the Gaussian kernel function, and its expression is: Among them, γ is the kernel function parameter, ||xy|| is the Euclidean norm between samples; Then the learning objective function is:

4. The method according to claim 3, characterized in that Step (3): "Using the butterfly algorithm to optimize the kernel extreme learning machine network model to obtain the regularization coefficient and kernel function parameters of the original kernel extreme learning machine network model" specifically includes the following steps: Step (31): normalize the data set; Using the min-max normalization method, all data are mapped to the [0,1] interval. The normalization formula is: Among them, x j is the original input data, x min is the minimum input data, x max is the maximum input data, is the normalized input data; Step (32): performing initial parameter setting; Step (33): determine the fitness function and calculate the butterfly fitness value; Select the mean square error function as the fitness function and calculate the fitness value of each butterfly Among them, M is the number of training sample data, T is the expected sample output value, Tn is the actual prediction value of the model, C is the regularization coefficient, S is the kernel parameter, and fitness is the fitness function value; Step (34): Compare the fitness function values ​​of each butterfly to find the optimal value and optimal solution of the current butterfly; f=c t I a (22) Among them, f is the amount of fragrance perception, c is the sensory form, t is the stimulus intensity, and a is the fragrance; Step (35): Calculate the scent perception and update the position of the butterfly; represents the position of the tth butterfly in the t+1th generation, r is a random number in [0,1], g * represents the global optimal solution, f i represents the scent perception of the i-th butterfly; Respectively represent the positions of the i, j, and k butterflies in the t generation; b is a constant, c t represents the value of the tth generation, N gen is the maximum number of iterations; Calculate the flavor perception amount using Equation (22). If rand < p, calculate using Equation (23). Otherwise, calculate using Equation (24). Step (36): Recalculate the fitness value of each butterfly like Then replace the previous optimal value and optimal solution, where the optimal value includes the regularization coefficient and kernel function parameter; Step (37): Update c and determine whether the maximum number of iterations has been reached. If not, return to step (35), otherwise end. Step (38): Output the optimized regularization coefficient and kernel function parameters.

5. The method according to claim 4, characterized in that The initial parameter setting of step (32) is specifically as follows:

6. The method according to claim 5, characterized in that Step (4) specifically includes the following steps: Step (41): Train the network and determine the output weights The expression of the kernel extreme learning machine model is: Where I is the identity matrix, C is the regularization parameter, Ω ELM is the kernel matrix, T is the output matrix; Using N training samples (x i ,t i ) to train the kernel extreme learning machine, where x i =[x i1 ,x i2 ,...,x in ] T ∈R n represents the input training sample data, t i =[t i1 ,t i2 ,...,t im ] T ∈R m Indicates the output of training sample data and calculates the kernel matrix of the training data: Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (27) Calculate the output weights: Step (42): Make predictions and use the output weights w to solve the output matrix of the model to achieve parameter identification After the training is completed, the output weight w of the model is obtained. Assuming that M prediction samples are given at this time, the kernel matrix Ω of the prediction samples is calculated ELM , then the output matrix is:

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