A method for estimating wind speed and direction of a spinning-stabilized projectile based on kernel limit learning machine.

Abstract

This invention discloses a method for estimating wind speed and direction of a rotating stable projectile based on a kernel limit learning machine (KLM). The method includes the following steps: establishing a four-degree-of-freedom kinematic model of a rotating stable projectile under windy conditions; constructing a KLM network model; estimating wind speed based on the constructed KLM network model; and determining only the connection weight matrices of the hidden and output layers, then solving for the model's output matrix to estimate wind speed and direction. This invention employs a multi-input multi-output model, avoiding the problem of only estimating one variable in a single estimation, thus reducing workload. Only the number of input features, the kernel function, and the number of output features need to be determined to establish the network model. There is no need to set the number of hidden layer nodes, thereby eliminating the need to set the initial weights and biases of the hidden layers. The output weights can be solved based on the least squares principle to estimate the wind speed and direction of the projectile.

Description

Technical Field

[0001] This invention belongs to the field of projectile wind speed and direction estimation, specifically involving a rotationally stable projectile wind speed and direction estimation method based on a kernel limit learning machine. Background Technology

[0002] Wind, as an important meteorological element, has a significant impact on the flight trajectory of uncontrolled rotating stable projectiles. Wind includes wind speed and wind direction; the direction from which the wind originates is usually called wind direction, and the angle from due north to the direction from which the wind originates is called the azimuth angle. The magnitude and speed of wind are mainly related to the magnitude and direction of the pressure gradient, the Coriolis inertial force, the air viscosity coefficient, and the roughness of the ground surface. Therefore, it is difficult to describe the distribution of wind using a single, unified mathematical formula.

[0003] While the navigation system onboard the uncontrolled spin-stabilized projectile provides some flight information, such as position and velocity, it does not provide information about the wind speed encountered during flight. In actual flight tests, wind speed information is generally obtained through weather balloons. After the balloon is released, parameters such as air pressure, temperature, humidity, wind speed, and wind direction can be measured from top to bottom.

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

[0005] To address the problem of estimating wind speed and direction of projectiles, He Hu et al., in "A Method for Estimating High-Altitude Wind Speed ​​and Direction of Guided Artillery Projectiles Based on GA-BP Neural Network" (Jiangsu Province: CN202310847494.6, 2023-10-27), proposed a method based on GA-BP neural network. However, this method requires multiple iterations during training, including selection, crossover, and mutation operations. Each iteration necessitates adjusting the network's weights and thresholds, and calculating the fitness value of each individual, resulting in a lengthy overall training time. Furthermore, this estimation method requires determining the number of neurons in the input, hidden, and output layers of the neural network, as well as parameters such as the activation function. It also requires setting parameters for the genetic algorithm, such as crossover and mutation probabilities. The model has a complex structure and numerous parameters, making the overall model relatively intricate. Summary of the Invention

[0006] The purpose of this invention is to provide a method for estimating wind speed and direction of a rotating stable projectile based on a nuclear limit learning machine. The method aims to use the flight data of the projectile under windy conditions to estimate the wind speed and direction experienced by the projectile based on the nuclear limit learning machine, thus providing a new approach to obtaining wind speed and direction.

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

[0008] Step (1): Establish a four-degree-of-freedom kinematic model of a rotating stable projectile under wind conditions;

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

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

[0011] Furthermore, step (1) establishes a four-degree-of-freedom kinematic model of a rotating stable projectile under wind conditions as follows:

[0012]

[0013]

[0014] In the formula, 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, and γ is the roll angle. Where ρ is the roll angular velocity, ρ is the air density, and V is the roll velocity. r Let W be the relative velocity of the projectile. x W z Let α be the component of wind speed W in the inertial coordinate system. W α represents the wind direction and the angle between the wind and due north. N Let α be the angle between the projectile and true north. ex α ey α ez For the dynamic equilibrium angle α e The component in the inertial coordinate system, C x0 C x2 These are the zero-lift drag coefficient and the induced drag coefficient, respectively, C' y C” is the derivative of the lift coefficient. z Let m' be the joint partial derivative of the Magnus force coefficients. xz is the derivative of the polar damping moment 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 to be the velocity component V of the projectile. x V y V z Range x, flight altitude y, and sideslip z;

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

[0019] A nuclear limit learning machine is used to estimate the wind speed experienced by the projectile, including both 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 dataset;

[0025] The min-max normalization method is used to map all data to the interval [0,1]. The normalization formula is as follows:

[0026]

[0027] Where, x i For the original input data, x min For the minimum input data, x max For the maximum input data, The input data is normalized;

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

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

[0030]

[0031] Choosing the Gaussian function as the kernel function, its expression is:

[0032]

[0033] Where 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] By setting the kernel function parameters σ and the regularization coefficient C, the connection weight matrix between the hidden layer and the output layer is obtained. The training process of the kernel extreme learning machine uses the least squares method to solve for the output weights 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 obtained as follows:

[0039]

[0040] Compared with the prior art, the significant advantages of this invention are:

[0041] (1) The method of this invention innovatively adopts the kernel extreme learning machine method to estimate the magnitude and direction of the wind speed experienced by the projectile. Compared with the multi-input single-output kernel extreme learning machine, considering the estimation of two variables, the magnitude and direction of the wind speed, it is innovatively improved into a multi-input multi-output model, 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, thus eliminating the need to set the initial weights and biases of the hidden layer, overcoming the problem that traditional intelligent algorithms have long estimation time and are prone to getting trapped in local optima. When this method is applied to the estimation of the wind speed experienced by the projectile, it can accurately and quickly identify the wind speed experienced by the projectile under high noise conditions, fully meeting the real-time and accuracy requirements of engineering.

[0042] (2) The method of this invention aims to estimate the wind speed and direction experienced by the projectile. To avoid excessive influencing factors that could lead to high collinearity and affect the network convergence speed, the method is based on a four-degree-of-freedom kinematic model, using the projectile's velocity component V. x V y V z The projectile's wind speed and direction were estimated using a nuclear limit learning machine, with range x, flight altitude y, and sideslip z as characteristic variables. A four-degree-of-freedom dynamic model was adopted, and the estimation time of the nuclear limit learning machine was much shorter than that of the six-degree-of-freedom kinematic model, with a relative error of less than 10% and good estimation accuracy.

[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 mapped to the [0,1] interval, eliminating the influence of different dimensions on the estimation results. Furthermore, the kernel function is used instead of the mapping function, which effectively overcomes the problem of function saturation that is easy to fall into when choosing the mapping function as the activation function, and further improves the estimation accuracy of the extreme learning machine.

[0044] (4) The method of the present invention introduces a regularization term when solving the output weights to reduce collinearity among influencing factors, thereby further improving the convergence speed and robustness of the model. Attached Figure Description

[0045] Figure 1 The network structure diagram of the kernel-based extreme learning machine.

[0046] Figure 2 A comparison chart showing the estimation of wind speed using the present invention.

[0047] Figure 3 A comparison chart showing the wind direction estimation using the present invention. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings.

[0049] A method for estimating the wind speed experienced by a projectile based on a kernel limit learning machine includes the following steps:

[0050] Step 1: Establish a four-degree-of-freedom kinematic model of a rotating stable projectile under wind conditions;

[0051] Specifically as follows:

[0052] A four-degree-of-freedom kinematic model is established in the inertial coordinate system, 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, and γ is the roll angle. Where ρ is the roll angular velocity, ρ is the air density, and V is the roll velocity. r Let W be the relative velocity of the projectile. x W z Let α be the component of wind speed W in the inertial coordinate system (ignoring vertical wind). W α represents the wind direction (the angle between the wind direction and due north). N α is the angle between the projectile and true north. ex α ey α ez For the dynamic equilibrium angle α e The component in the inertial coordinate system, C x0 C x2These are the zero-lift drag coefficient and the induced drag coefficient, respectively, C' y C” is the derivative of the lift coefficient. z Let m' be the joint partial derivative of the Magnus force coefficients. xz The derivative of the polar damping moment coefficient;

[0053]

[0054]

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

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

[0057] Specifically as follows:

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

[0059] The number of feature maps between the input and hidden layers of a nuclear extreme learning machine is determined based on the number of projectile flight parameters affected by wind speed. Based on the four-degree-of-freedom ballistic equations, the influencing factors are identified as the projectile's velocity component V. x V y V z The parameters are: range x, flight altitude y, and sideslip z. Therefore, the final number of nodes in the input layer of the network is determined to be I = 6.

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

[0061] The wind speed experienced by the projectile is estimated using a nuclear extreme learning machine. The wind speed includes both magnitude and direction. Therefore, 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] Based on the fundamental theory of neural networks, the kernel extreme learning machine can be viewed as a feedforward neural network with a single hidden layer. The entire network operation 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. Based on the determined connection weight matrix β, the prediction process solves for the model's output matrix to achieve the wind speed estimation function.

[0066] Step 3-1: Normalize the dataset;

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

[0068]

[0069] Where, x i For the original input data, x min For the minimum input data, x max For the maximum input data, The input data is normalized.

[0070] Step 3-2: Train the network and determine the output weights;

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

[0072]

[0073] Choosing the Gaussian function as the kernel function, its expression is:

[0074]

[0075] Where σ is the kernel parameter.

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

[0078]

[0079] Step 3-3: Network prediction to achieve wind speed estimation;

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

[0081]

[0082] Example 1

[0083] The following is a more detailed description with reference to the embodiments.

[0084] The parameters for the shells are shown in the table below:

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

[0086]

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

[0088] Table 2 Initial Launch Conditions of Projectiles

[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 extreme learning machine network has a 6-2 architecture. After solving the four-degree-of-freedom ballistic equations, 9282 sets of flight data were obtained. 6961 sets were selected as training samples, and 2321 sets were selected as prediction samples. The estimation results for wind speed and direction are as follows: Figure 2 and Figure 3 As shown, this verifies the effectiveness of the kernel limit learning machine in estimating wind speed and direction.

Claims

1. A method for estimating wind speed and direction of a rotating stable projectile based on a kernel limit learning machine, characterized in that, Includes the following steps: Step (1): Establish a four-degree-of-freedom kinematic model of a rotating stable projectile under wind conditions; Step (2): Construct the kernel extreme learning machine network model: determine the number of input layer nodes, kernel function, and number of output layer nodes; Step (3): Based on the constructed kernel extreme learning machine network model, wind speed is estimated: determine the kernel function parameter σ and the regularization coefficient C, and then solve the output matrix of the model to realize wind speed and wind direction estimation; Step (1) Establish the four-degree-of-freedom kinematic model of a rotating stable projectile under wind conditions as follows: In the formula, 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, and γ is the roll angle. Where ρ is the roll angular velocity, ρ is the air density, and V is the roll velocity. r Let W be the relative velocity of the projectile. x W z Let α be the component of wind speed W in the inertial coordinate system. W α represents the wind direction and the angle between the wind and due north. N Let α be the angle between the projectile and true north. ex α ey α ez For the dynamic equilibrium angle α e The component in the inertial coordinate system, C x0 C x2 These are the zero-lift drag coefficient and the induced drag coefficient, respectively, C' y C is the derivative of the lift coefficient. z " is the joint partial derivative of the Magnus force coefficients, m' xz The derivative of the polar damping moment coefficient; 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 to be the velocity component V of the projectile. x V y V z Range x, flight altitude y, and sideslip z; Step (22): Setting the number of output layer nodes A nuclear limit learning machine is used to estimate the wind speed experienced by the projectile, including both 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. The number of nodes in the input layer is I = 6; the number of nodes in the output layer is O = 2. Step (3) specifically includes the following steps: Step (31): Normalize the dataset; The min-max normalization method is used to map all data to the interval [0,1]. The normalization formula is as follows: Where, x i For the original input data, x min For the minimum input data, x max For the maximum input data, The input data is normalized; Step (32): Train the network and determine the output weights; The kernel function matrix is ​​defined as follows: Choosing the Gaussian function as the kernel function, its expression is: Where 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; By setting the kernel function parameters σ and the regularization coefficient C, the connection weight matrix between the hidden layer and the output layer is obtained. The training process of the kernel extreme learning machine uses the least squares method to solve for the output weights 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 obtained as follows:

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