Rotation stable projectile wind speed and wind direction estimation method based on kernel extreme learning machine

Abstract

The invention relates to a rotating stable projectile wind speed and direction estimation method based on a kernel extreme learning machine. Comprising the following steps: establishing a four-degree-of-freedom kinematics model of the rotary stable projectile under a windy condition; constructing a kernel extreme learning machine network model; performing wind speed estimation according to the constructed kernel extreme learning machine network model; the method only needs to determine the connection weight matrix of the hidden layer and the output layer, solves the output matrix of the model on the basis of determining the connection weight matrix, and achieves the estimation of the wind speed and the wind direction. According to the method, a multi-input multi-output model is adopted, the problem that only one variable can be estimated through single estimation is avoided, and the workload is reduced; the network model can be established only by determining the number of the input features, the kernel function and the number of the output features; the number of nodes of the hidden layer does not need to be set, so that the initial weight and bias of the hidden layer do not need to be set, the output weight can be solved on the basis of the least square principle, and the wind speed and wind direction estimation of the projectile is achieved.

Description

Technical Field

[0001] The invention belongs to the field of projectile wind speed and direction estimation, and in particular relates to a rotationally stable projectile wind speed and direction estimation method based on a nuclear extreme learning machine. Background Art

[0002] As an important meteorological factor, wind has a significant impact on the flight trajectory of an uncontrolled rotating stabilized projectile. Wind includes wind speed and wind direction. The direction of the wind is usually called the wind direction, and the angle from the north clockwise to the direction of the wind is the wind direction azimuth. The wind direction and wind speed are mainly related to the size and direction of the pressure gradient, the Coriolis inertia force, the air viscosity coefficient, and the roughness of the surface. Therefore, it is difficult to use a unified mathematical formula to describe the distribution of wind.

[0003] Although the navigation system carried by the uncontrolled spin-stabilized projectile provides some flight information of the projectile, such as position and speed, it does not provide information about the wind speed to which the projectile is subject during flight. In actual flight tests, wind speed information is generally measured by sounding balloons. After the balloons are released, parameters such as air pressure, temperature, humidity, wind speed and direction can be measured from top to bottom.

[0004] In order to estimate the wind speed of a projectile, Wu Tao et al. used the output information of the onboard inertial navigation system to estimate the lateral wind speed in the horizontal plane in "Sidewind Calculation Method of Cluster Missile Based on SINS / GPS". Journal of Ballistics, 2011, 23(1):31-34+39. However, the model establishment of this method is relatively simple, and only the lateral wind speed is considered, which cannot better reflect the actual projectile system. Zhang Yanru et al. used an aerodynamic parameter identification algorithm to estimate the longitudinal wind speed in "Design of Ballistic Wind Speed ​​Estimation Algorithm Based on Aerodynamic Parameter Identification". Aerospace Control, 2014, 32(2):29-34. The longitudinal wind speed is estimated online based on the measured value of the onboard sensor and the theoretical value of the projectile drag coefficient. However, this method is only suitable for estimating the longitudinal wind speed and cannot estimate the lateral wind speed.

[0005] In response to the problem of estimating the wind speed and direction of projectiles, He Hu et al. proposed a method for estimating the high-altitude wind speed and direction of guided artillery shells based on GA-BP neural network, Jiangsu Province: CN202310847494.6, 2023-10-27. The GA-BP neural network requires multiple iterations during the training process, including selection, crossover, mutation and other operations. Each iteration requires adjusting the weights and thresholds of the network, and calculating the individual fitness values. The overall training time is relatively long. At the same time, the estimation method needs to determine the number of neurons in the input layer, hidden layer, and output layer of the neural network, as well as parameters such as the activation function. It is also necessary to set the parameters of the genetic algorithm such as the crossover probability and mutation probability. The model has many structures and parameters, and the overall model is relatively complex. Summary of the invention

[0006] The purpose of the present invention is to provide a method for estimating wind speed and direction of a rotationally stabilized projectile based on a nuclear extreme learning machine, which aims to utilize the flight data of the projectile under windy conditions to estimate the wind speed and direction experienced by the projectile based on a nuclear extreme learning machine, thereby providing a new way to obtain wind speed and direction.

[0007] The technical solution to achieve the purpose of the present invention is: a method for estimating wind speed and direction of a rotationally stable projectile based on a kernel extreme learning machine, comprising the following steps:

[0008] Step (1): Establish a four-degree-of-freedom kinematic model of a rotationally stabilized projectile under windy conditions;

[0009] Step (2): Construct a kernel extreme learning machine network model: determine the number of input layer nodes, kernel function, and the number of output layer nodes;

[0010] Step (3): Based on the constructed kernel extreme learning machine network model, the wind speed is estimated: the kernel function parameter σ and the regularization coefficient C are determined, and then the output matrix of the model is solved to realize the estimation of wind speed and wind direction.

[0011] Furthermore, step (1) establishes a four-degree-of-freedom kinematic model of a rotationally stabilized projectile under windy conditions:

[0012]

[0013]

[0014] Where g is the acceleration due to gravity, m is the mass of the projectile, S is the characteristic area of ​​the projectile, d is the diameter of the projectile, l is the characteristic length of the projectile, J is the axial moment of inertia of the projectile, γ is the roll angle, is the rolling angular velocity, ρ is the air density, V r is the relative velocity of the projectile, W x , W z is the component of wind speed W in the inertial coordinate system, α W is the wind direction, the angle with due north, α N is the angle between the direction and due north, α ex , α ey , α ez is the dynamic balance angle α e The component in the inertial coordinate system, C x0 , C x2 are the zero-lift drag coefficient and the induced drag coefficient, C' y is the lift coefficient derivative, C” z is the joint partial derivative of the Magnus force coefficients, m' xz is the derivative of the extreme damping torque coefficient.

[0015] Furthermore, step (2) specifically includes the following steps:

[0016] Step (21): Setting the number of input layer nodes

[0017] Based on the four-degree-of-freedom model, the influencing factors are determined as the velocity component V of the projectile x 、V y 、V z , range x, flight altitude y and lateral deviation z;

[0018] Step (22): Setting the number of output layer nodes

[0019] The kernel extreme learning machine is used to estimate the wind speed to which the projectile is subjected, including the magnitude and direction.

[0020] Step (23): Kernel function selection

[0021] By normalizing the input data, the size of the input data is mapped to the interval [0,1], and the Gaussian function is selected as the kernel function.

[0022] Furthermore, the number of nodes in the input layer is I=6; the number of nodes in the output layer is O=2.

[0023] Furthermore, step (3) specifically includes the following steps:

[0024] Step (31): normalize the data set;

[0025] Using the min-max normalization method, all data are mapped to the [0,1] interval. The normalization formula is:

[0026]

[0027] Among them, x i is the original input data, x min is the minimum input data, x max is the maximum input data, is the normalized input data;

[0028] Step (32): Train the network and determine the output weights;

[0029] The kernel function matrix is ​​defined as follows:

[0030]

[0031] The Gaussian function is selected as the kernel function, and its expression is:

[0032]

[0033] Among them, σ is the kernel function parameter;

[0034] The network model of the kernel extreme learning machine is Hβ=T, where H is the output matrix of the hidden layer, β is the connection weight matrix between the hidden layer and the output layer, and T is the output matrix;

[0035] The kernel function parameter σ and the regularization coefficient C are set to obtain the connection weight matrix between the hidden layer and the output layer; the training process of the kernel extreme learning machine uses the least squares method to solve the output weight β, specifically:

[0036]

[0037] Step (33): Network prediction to achieve parameter identification:

[0038] After the training process is completed, the output weight matrix β of the model is obtained. According to equations (4)-(6), the output of the kernel extreme learning machine is:

[0039]

[0040] Compared with the prior art, the present invention has the following significant advantages:

[0041] (1) The method of the present invention innovatively adopts the method of kernel extreme learning machine to estimate the magnitude and direction of the wind speed to which the projectile is subjected. Compared with the kernel extreme learning machine with multiple inputs and single outputs, the kernel extreme learning machine is innovatively improved into a multi-input multi-output model by taking into account the two variables of estimated wind speed magnitude and direction, thereby avoiding the problem that only one variable can be estimated in a single estimation and reducing the workload. Compared with the extreme learning machine, the kernel extreme learning machine does not need to set the number of hidden layer nodes, and thus does not need to set the initial weights and biases of the hidden layer, thus overcoming the problem that the traditional intelligent algorithm has a long estimation time and is prone to falling into local optimality. When the method is applied to the estimation of the wind speed to which the projectile is subjected, the wind speed to which the projectile is subjected can be accurately and quickly identified under high noise conditions, fully meeting the real-time and precision requirements of the project.

[0042] (2) The method of the present invention aims to estimate the wind speed and direction of the projectile. In order to avoid the high collinearity caused by too many influencing factors, which affects the network convergence speed, the velocity component V of the projectile is used as the basis of the four-degree-of-freedom kinematic model. x 、V y 、V z , range x, flight altitude y and lateral deviation z are used as feature variables, and the nuclear extreme learning machine is used to estimate the wind speed and direction of the projectile; using the four-degree-of-freedom dynamic model, the estimation time of the nuclear extreme learning machine is much lower than that of the six-degree-of-freedom kinematic model, the relative error is less than 10%, and the estimation accuracy is good.

[0043] (3) The method of the present invention takes into account that different data have different physical meanings and different dimensions, and different dimensions will affect the results of data analysis. The original data is normalized and the original data set is mapped to the interval [0,1], eliminating the influence of different dimensions on the estimation results. The kernel function is used instead of the mapping function, which effectively overcomes the problem of function saturation when selecting the mapping function as the activation function, and further improves the estimation accuracy of the extreme learning machine.

[0044] (4) When solving the output weight, the method of the present invention introduces a regularization term to reduce the collinearity between the influencing factors, thereby further improving the convergence speed and robustness of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is the network structure diagram of the core extreme learning machine.

[0046] Figure 2 This is a comparison diagram of wind speed estimation using the present invention.

[0047] Figure 3 This is a comparison diagram of wind direction estimation using the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0049] A method for estimating the wind speed of a projectile based on a kernel extreme learning machine comprises the following steps:

[0050] Step 1: Establish a four-degree-of-freedom kinematic model of the rotationally stabilized projectile under windy conditions;

[0051] The details are as follows:

[0052] A four-degree-of-freedom kinematic model is established in the inertial coordinate system, where g is the gravitational acceleration, m is the mass of the projectile, S is the characteristic area of ​​the projectile, d is the diameter of the projectile, l is the characteristic length of the projectile, J is the axial moment of inertia of the projectile, and γ is the roll angle. is the rolling angular velocity, ρ is the air density, V r is the relative velocity of the projectile, W x , W z is the component of wind speed W in the inertial coordinate system (ignoring vertical wind), α W is the wind direction (the angle with due north), α N is the direction (the angle with due north), α ex , α ey , α ez is the dynamic balance angle α e The component in the inertial coordinate system, C x0 , C x2are the zero-lift drag coefficient and the induced drag coefficient, C' y is the lift coefficient derivative, C” z is the joint partial derivative of the Magnus force coefficients, m' xz is the derivative of the polar damping torque coefficient;

[0053]

[0054]

[0055] Step 2: Build a kernel extreme learning machine network model;

[0056] When using the kernel extreme learning machine to estimate the wind speed of the projectile, it is necessary to determine the number of input layer nodes, the kernel function, and the number of output layer nodes.

[0057] The details are as follows:

[0058] (1) Setting the number of input layer nodes

[0059] The number of feature mappings between the input layer and the hidden layer of the kernel extreme learning machine is determined according to the number of projectile flight parameters affected by wind speed. Based on the four-degree-of-freedom trajectory equation, the influencing factors are determined as the velocity component V of the projectile x 、V y 、V z , range x, flight height y and lateral deviation z. Therefore, the number of nodes in the input layer of the network is finally determined to be I=6.

[0060] (2) Setting the number of output layer nodes

[0061] The kernel extreme learning machine is used to estimate the wind speed to which the projectile is subjected. The wind speed includes magnitude and direction, so the number of nodes in the output layer is selected as O=2.

[0062] (3) Kernel function selection

[0063] By normalizing the input data, the size of the input data is mapped to the interval [0,1], and the Gaussian function is selected as the kernel function.

[0064] Step 3: Estimate wind speed based on the constructed extreme learning machine network model;

[0065] According to the basic theory of neural networks, the kernel extreme learning machine can be regarded as a single hidden layer forward propagation neural network. The working process of the entire network can be divided into a training process and a prediction process. The main task of the network training process is to determine the connection weight matrix β between the hidden layer and the output layer. The prediction process solves the output matrix of the model on the basis of determining the connection weight matrix β to realize the wind speed estimation function.

[0066] Step 3-1, normalize the data set;

[0067] The data of the network has different physical meanings and different dimensions, and different dimensions will affect the results of data analysis. In order to eliminate the influence between different dimensions, the original data set needs to be normalized. After normalization, the convergence speed of the model can be further accelerated and the recognition accuracy can be improved. The min-max normalization method is used to map all data to the [0,1] interval. The normalization formula is:

[0068]

[0069] Among them, x i is the original input data, x min is the minimum input data, x max is the maximum input data, is the normalized input data.

[0070] Step 3-2, train the network and determine the output weight;

[0071] The kernel function matrix is ​​defined as follows:

[0072]

[0073] The Gaussian function is selected as the kernel function, and its expression is:

[0074]

[0075] Among them, σ is the kernel parameter.

[0076] The network model of the kernel extreme learning machine is Hβ=T, where H is the output matrix of the hidden layer, β is the connection weight matrix between the hidden layer and the output layer, and T is the output matrix.

[0077] The kernel function parameter σ and the kernel regularization coefficient C are set to obtain the connection weight matrix between the hidden layer and the output layer. The training process of the kernel extreme learning machine uses the least squares method to solve the output weight β, which is expressed as:

[0078]

[0079] Step 3-3, network prediction, realizing wind speed estimation;

[0080] After the training process is completed, the output weight matrix β of the model is obtained. According to formula (18-20), the output of the kernel extreme learning machine is obtained as

[0081]

[0082] Example 1

[0083] A more detailed description is given below in conjunction with embodiments.

[0084] The parameter settings of the shells are shown in the following table:

[0085] Table 1 Static parameters of a certain type of projectile

[0086]

[0087] Under the initial conditions in Table 2, the wind speed and direction are estimated:

[0088] Table 2 Initial launch conditions of the projectile

[0089]

[0090] The input feature vector is [V x ,V y ,V z ,x,y,z] T The parameters to be identified are wind speed W and wind direction α W , the network structure of the extreme learning machine is 6-2. After solving the four-degree-of-freedom trajectory equation, 9282 sets of flight data are obtained, 6961 sets are selected as training samples, and 2321 sets are selected as prediction samples. The estimated results of wind speed and direction are as follows Figure 2 and Figure 3 As shown, the effectiveness of the kernel extreme learning machine in estimating wind speed and direction is verified.

Claims

1. A method for estimating wind speed and direction of a rotationally stabilized projectile based on a kernel extreme learning machine, characterized in that: The steps include: Step (1): Establish a four-degree-of-freedom kinematic model of a rotationally stabilized projectile under windy conditions; Step (2): Construct a kernel extreme learning machine network model: determine the number of input layer nodes, kernel function, and the number of output layer nodes; Step (3): Based on the constructed kernel extreme learning machine network model, the wind speed is estimated: the kernel function parameter σ and the regularization coefficient C are determined, and then the output matrix of the model is solved to realize the estimation of wind speed and wind direction.

2. The method according to claim 1, characterized in that Step (1) Establish the four-degree-of-freedom kinematic model of the rotationally stabilized projectile under windy conditions: Where g is the acceleration of gravity, m is the mass of the projectile, S is the characteristic area of ​​the projectile, d is the diameter of the projectile, l is the characteristic length of the projectile, J is the axial moment of inertia of the projectile, γ is the roll angle, is the rolling angular velocity, r is the air density, V r is the relative velocity of the projectile, W x , W z is the component of wind speed W in the inertial coordinate system, α W is the wind direction, the angle with due north, α N is the angle between the direction and due north, α ex , α ey , α ez is the dynamic balance angle α e The component in the inertial coordinate system, C x0 , C x2 are the zero-lift drag coefficient and the induced drag coefficient, C' y is the lift coefficient derivative, C z ” is the joint partial derivative of the Magnus force coefficient, m' xz is the derivative of the extreme damping torque coefficient.

3. The method according to claim 2, characterized in that Step (2) specifically includes the following steps: Step (21): Setting the number of input layer nodes Based on the four-degree-of-freedom model, the influencing factors are determined as the velocity component V of the projectile x 、V y 、V z , range x, flight altitude y and lateral deviation z; Step (22): Setting the number of output layer nodes The kernel extreme learning machine is used to estimate the wind speed to which the projectile is subjected, including the magnitude and direction. Step (23): Kernel function selection By normalizing the input data, the size of the input data is mapped to the interval [0,1], and the Gaussian function is selected as the kernel function.

4. The method according to claim 3, characterized in that The number of nodes in the input layer is I=6; the number of nodes in the output layer is O=2.

5. The method according to claim 4, characterized in that Step (3) 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 i 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): Train the network and determine the output weights; The kernel function matrix is ​​defined as follows: The Gaussian function is selected as the kernel function, and its expression is: Among them, σ is the kernel function parameter; The network model of the kernel extreme learning machine is Hβ=T, where H is the output matrix of the hidden layer, β is the connection weight matrix between the hidden layer and the output layer, and T is the output matrix; The kernel function parameter σ and the regularization coefficient C are set to obtain the connection weight matrix between the hidden layer and the output layer; the training process of the kernel extreme learning machine uses the least squares method to solve the output weight β, specifically: Step (33): Network prediction to achieve parameter identification: After the training process is completed, the output weight matrix β of the model is obtained. According to equations (4)-(6), the output of the kernel extreme learning machine is:

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