An adaptive bias proportional guidance method based on neural network

Abstract

The present invention discloses a neural network-based adaptive bias proportional guidance method. For stationary fixed targets, a neural network is used to obtain the constant term in bias proportional guidance. The neural network is a BP neural network. The neural network inputs are the missile-target range, initial trajectory inclination, initial missile-target line-of-sight angle, and desired terminal intersection angle at the time of launch from the aircraft, and the output is the constant term. The neural network-based adaptive bias proportional guidance method disclosed in the present invention has high guidance accuracy and can complete the bias proportional guidance parameter solution online under different initial conditions and constraints. It is flexible to use and has low computational cost.

Description

Technical Field

[0001] The invention relates to an adaptive bias proportional guidance method based on a neural network, belonging to the technical field of aircraft control. Background Art

[0002] The selection of guidance law plays a key role in the accuracy of the terminal intersection angle.

[0003] At present, the biased proportional guidance method is widely used. It adds a constant bias term to the traditional proportional guidance law. This method has the advantages of less required information and simple structure. In particular, it does not require estimation of the remaining flight time, so it has obvious advantages in engineering applications.

[0004] However, the accuracy of the bias term directly affects the guidance accuracy. Traditional formulas have errors due to the application of the small angle assumption during derivation and the formula used to estimate the total flight time, which affects the accuracy of the terminal intersection angle.

[0005] In addition, the traditional formula derivation method requires professional technicians to temporarily calculate and derive the bias terms based on the actual initial conditions. It has many usage restrictions and a large workload for calculation and derivation.

[0006] Due to the above reasons, it is necessary to propose a bias proportional guidance method that can be quickly obtained online with high accuracy. Summary of the Invention

[0007] In order to overcome the above problems, the inventors conducted in-depth research and designed an adaptive bias proportional guidance method based on a neural network. For stationary fixed targets, the neural network is used to obtain the constant term in the bias proportional guidance.

[0008] Furthermore, the neural network is a BP neural network.

[0009] In a preferred embodiment, the input of the neural network is the missile-target distance r, the initial trajectory inclination angle θ0, the initial missile-target sight angle q0 and the desired terminal intersection angle θ when the aircraft is launched. f , the output of the BP neural network is the constant term b.

[0010] In a preferred embodiment, the guidance law of the biased proportional guidance is obtained according to the following formula:

[0011]

[0012] Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient.

[0013] In a preferred embodiment, the number of hidden layers of the BP neural network is 5.

[0014] In a preferred embodiment, the neural network needs to be trained before use, and trajectory simulation is used to obtain training samples.

[0015] In a preferred embodiment, the trajectory simulation is a nonlinear strike model simulation, and the nonlinear strike model can be expressed as:

[0016]

[0017]

[0018]

[0019]

[0020] η=θ-q

[0021] Among them, η is the angle between the aircraft speed and the sight line of sight, θ is the trajectory inclination angle, q is the sight line angle of sight, r is the distance between the missile and the target, v is the aircraft speed, and a M Overload command for the aircraft.

[0022] In a preferred embodiment, when establishing training samples, the setting parameters of the ballistic simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters. The setting parameters of the ballistic simulation include the initial projectile-target distance, the guidance coefficient, the initial ballistic inclination angle, and the initial projectile-target line of sight angle.

[0023] In a preferred embodiment, the initial projectile-target distance is 5,000 meters to 10,000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination angle is 10-20 degrees.

[0024] In a preferred embodiment, during the training of the neural network, the parameters of the neural network are updated using the Adam learning rate.

[0025] The beneficial effects of the present invention include:

[0026] (1) The BP neural network is used to achieve high-precision fitting approximation of the mapping, and the guidance accuracy is high;

[0027] (2) The bias proportional guidance parameter solution can be completed online under different initial conditions and constraints, which is flexible to use;

[0028] (3) It reduces the amount of calculation required to solve traditional formulas and reduces the computational cost in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A schematic flow chart of a neural network-based adaptive bias proportional guidance method according to a preferred embodiment of the present invention is shown;

[0030] Figure 2 The simulated ballistic trajectory of the guidance law in Example 1 is shown;

[0031] Figure 3 The simulated trajectory inclination angle of the guidance law in Example 1 is shown;

[0032] Figure 4 The simulated trajectory inclination angles in Example 2 and Comparative Example 1 according to the present invention are shown. DETAILED DESCRIPTION

[0033] The present invention will be described in further detail below with reference to the accompanying drawings and examples, through which the features and advantages of the present invention will become more clearly understood.

[0034] The word "exemplary" is used exclusively herein to mean "serving as an example, example, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0035] According to a neural network-based adaptive bias proportional guidance method provided by the present invention, a neural network is used to obtain bias proportional guidance for a stationary fixed target, thereby achieving precise landing constraint of the aircraft.

[0036] The guidance law of the biased proportional guidance can be expressed as:

[0037]

[0038] Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, N is the guidance coefficient, and b is the bias term.

[0039] In traditional bias proportional guidance, the bias term is generally obtained using the following formula:

[0040]

[0041] Among them, θ f is the terminal intersection angle, θ0 is the initial trajectory inclination angle, q0 is the initial missile-target line of sight angle, t0 is the initial launch time of the aircraft, t f is the terminal rendezvous time of the aircraft.

[0042] For t f -t0 can be obtained by the following traditional methods:

[0043] t=t f -t0

[0044] Among them, t is the flight time from the launch to the flight to the target position; f-t0 applies the small angle assumption and the estimation of the total remaining flight time, which leads to errors and the low accuracy of the biased proportional guidance law.

[0045] The inventors found that the t obtained by the traditional method f The error in -t0 can be compensated by adding the angle deviation term Δη and the time deviation term Δt:

[0046]

[0047] Among them, r is the distance between the missile and the target, v is the speed of the aircraft, are all positive, then |θ f | is a strictly monotone increasing function of b, and a strictly monotone function has a one-to-one mapping relationship, that is, |θ f There is a one-to-one mapping relationship between | and b, which can be expressed as:

[0048] b=f -1 (r,N,q0,θ0,θ f )

[0049] Furthermore, the BP neural network in the neural network can predict this mapping relationship more accurately. Therefore, in the present invention, the BP neural network is used to obtain the bias proportional guidance.

[0050] According to the present invention, the input of the neural network is the missile-target distance r, the initial trajectory inclination angle θ0, the initial missile-target sight angle q0 and the expected terminal intersection angle θ when the aircraft is launched. f ;

[0051] Different from the traditional method, the constant term is the initial sight angle q0, the initial trajectory inclination angle θ0, the expected terminal intersection angle θ f The present invention no longer uses the flight time t with a large error as the input of the neural network, but uses the missile-target distance r which is easier to measure as the input of the neural network, thereby further improving the guidance accuracy.

[0052] Furthermore, the output of the BP neural network is a constant term b, and the guidance law of the bias proportional guidance is obtained according to the following formula:

[0053]

[0054] Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient.

[0055] In a preferred embodiment, the number of hidden layers of the BP neural network is 5. The inventors found that when there are 5 hidden layers, the guidance law obtained based on the constant term output by the neural network is more accurate, and the calculation speed of the neural network is faster, which can achieve online solution.

[0056] Further preferably, the activation function of the BP neural network is a sigmoid function:

[0057]

[0058] Furthermore, the BP neural network needs to be trained before use. In the present invention, trajectory simulation is used to obtain training samples.

[0059] Specifically, the trajectory simulation is a nonlinear strike model simulation, and the nonlinear strike model can be expressed as:

[0060]

[0061]

[0062]

[0063]

[0064] η=θ-q

[0065] Among them, η is the angle between the aircraft speed and the sight line of sight, a M Overload command for the aircraft.

[0066] Furthermore, the integral in the nonlinear impact model is solved using the Runge-Kutta method, preferably with a solution step size of 0.05.

[0067] The Runge-Kutta method is an important implicit or explicit iterative method for solving nonlinear ordinary differential equations, which will not be described in detail in the present invention.

[0068] Furthermore, when establishing the training samples, the setting parameters of the trajectory simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters.

[0069] Furthermore, the setting parameters of the trajectory simulation include an initial projectile-target distance, a guidance coefficient, an initial trajectory inclination angle, and an initial projectile-target sight angle.

[0070] In a preferred embodiment, in the setting parameters, the initial projectile-target distance is 5000 meters to 10000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination angle is 10-20 degrees.

[0071] In a preferred embodiment, a set of data is taken every 200m of the initial projectile-target distance, the guidance coefficients are 2, 3, and 4 respectively, and a set of data is taken every 0.2° of the initial trajectory inclination angle as the setting parameters for the trajectory simulation, thereby obtaining a more comprehensive training sample.

[0072] In a preferred embodiment, the trajectory simulation parameters in the training samples are adjusted according to the initial projectile-target distance. When the initial projectile-target distance is greater than 7500m, a set of data is taken every 100m, with guidance coefficients of 2, 3, and 4, and an initial trajectory inclination angle of 0.2°. These are used as the trajectory simulation parameters to ensure that the trained neural network can achieve better accuracy.

[0073] When the initial missile-target distance is less than 7500m, a set of data is taken every 200m, with guidance coefficients of 2, 3, and 4, respectively, and a set of data is taken every 0.2° of the initial trajectory inclination angle as the setting parameters for the trajectory simulation. Since the initial missile-target distance is relatively close, the sample size can be appropriately reduced while ensuring guidance accuracy, thereby reducing the computational load of the neural network and the solving capability of the onboard computer. This means that a high-configuration onboard computer is not required, reducing costs.

[0074] According to the present invention, in the process of training a neural network, 60%-80% of the samples are selected from the training samples as a training set, for example, 70% of the samples are selected as a training set, 10%-20% of the samples are selected as a test set, for example, 15% of the samples are selected as a test set, and 10%-20% of the samples are selected as a validation set, for example, 15% of the samples are selected as a validation set.

[0075] Further preferably, in the process of training the neural network, the parameters of the neural network are updated using the Adam learning rate, and the updating process can be expressed as:

[0076]

[0077]

[0078] in, is the parameter before updating; is the updated parameter; κ is the learning rate; ε is the smoothing term to prevent division by zero; m′ t is the first-order moment estimate, v′ t is the second-order moment estimate; m t is the first-order moment of gradient, v t is the second-order moment of the gradient, and β1 and β2 are constant exponential decay rates.

[0079] According to the present invention, the initial ballistic inclination angle of the aircraft when launched is preferably 10-20°. The inventors found that the initial ballistic inclination angle has a great influence on the terminal intersection angle accuracy (i.e., the error between the actual terminal intersection angle and the expected terminal intersection angle). When the initial ballistic inclination angle is too small, the terminal intersection angle accuracy is significantly reduced. When the initial ballistic inclination angle is too large, it is not conducive to engineering launch and also affects the terminal intersection angle accuracy. More preferably, the initial ballistic inclination angle is 15-20°. Within this range, the accuracy of the terminal intersection angle is the best.

[0080] Example

[0081] Example 1

[0082] Adaptive bias proportional guidance is obtained based on the neural network. The guidance law of the bias proportional guidance is:

[0083]

[0084] The BP neural network is used to obtain the constant term b in the bias proportional guidance, where the number of hidden layers of the neural network is 5 and the activation function is the sigmoid function.

[0085] The training samples are obtained through ballistic simulation, which is a nonlinear strike model simulation. The nonlinear strike model is:

[0086]

[0087]

[0088]

[0089]

[0090] η=θ-q

[0091] The integral in the nonlinear strike model is solved using the Runge-Kutta method with a step size of 0.05. The set parameters for the ballistic simulation include the initial projectile-target distance, guidance coefficient, initial trajectory inclination, and initial projectile-target line of sight angle. Among them, the initial projectile-target distance is 5,000 meters to 10,000 meters, the guidance coefficient is 2-4, the initial trajectory inclination is 10-20°, and a set of data is taken every 200 meters for the initial projectile-target distance. The guidance coefficients are 2, 3, and 4 respectively, and the initial trajectory inclination is taken every 0.2°.

[0092] 70% of the samples are selected from the training samples as the training set, 15% of the samples are selected as the test set, and 15% of the samples are selected as the validation set.

[0093] In the process of training the neural network, the Adam learning rate is used to update the parameters of the neural network. The update process is expressed as:

[0094]

[0095]

[0096] The trained BP neural network is used for simulation, and the expected terminal intersection angle θ in the simulation parameters is f They are set to -30°, -60°, and -90° respectively. The other simulation parameters are shown in Table 1:

[0097] Table 1

[0098]

[0099] According to the above parameters, the input parameters of the neural network are: missile-target distance r = 10000, initial trajectory inclination angle θ0 = 10°, initial missile-target sight angle q0 = 0°, and expected terminal intersection angle θ f They are -30°, -60° and -90° respectively.

[0100] The biased proportional guidance law is obtained based on the BP neural network. The simulated trajectory of the guidance law is as follows: Figure 2 As shown, the trajectory inclination is Figure 3 As shown in the figure, it can be seen that the aircraft can reach the target position in all three cases, and the actual terminal intersection angles are: -29.9908°, -60.0016°, and -89.9976°, which are very close to the expected terminal intersection angles.

[0101] Example 2

[0102] The simulation is performed in the same manner as in Example 1, except that, in the simulation parameters, the expected terminal intersection angle θ is f They are set to -40° and -55° respectively, and the other simulation parameters are shown in Table 2:

[0103] Table 2

[0104]

[0105] The ballistic inclination trajectory obtained by simulation is as follows Figure 4 As shown, the actual terminal intersection angles of the aircraft are -40.21 and -54.97 degrees respectively.

[0106] Comparative Example 1

[0107] The same simulation experiment as in Example 2 was conducted, except that the conventional formula was used to solve the guidance law of biased proportional guidance. The simulated trajectory inclination of the guidance law is as follows: Figure 4 As shown, the actual terminal intersection angles of the aircraft are -41.95°-61.14° respectively.

[0108] By comparing the simulated trajectory inclination angles of Example 2 and Comparative Example 1, it can be seen that the guidance law of the biased proportional guidance obtained in Example 2 is more accurate, and the error between the actual intersection angle and the expected intersection angle is reduced by more than 9 times. In particular, when the expected terminal intersection angle is large, the error between the actual intersection angle and the expected intersection angle is reduced by nearly 38 times, and the error between the actual intersection angle and the expected intersection angle is as low as 0.05%, which significantly improves the guidance accuracy.

[0109] In the description of the present invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear" and the like, indicating positions or locations, are based on the operating state of the present invention and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0110] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention in specific contexts.

[0111] The present invention has been described above with reference to preferred embodiments, but these embodiments are merely exemplary and serve only as illustrations. On this basis, various replacements and improvements can be made to the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A neural network-based adaptive bias proportional guidance method, which uses a neural network to obtain the constant term in the bias proportional guidance for a stationary target; The neural network is a BP neural network; The input of the neural network is the missile-target distance r when the aircraft is launched, the initial trajectory inclination angle θ0, the initial missile-target line of sight angle q0 and the expected terminal intersection angle θ f , the output of the BP neural network is a constant term b; The guidance law of bias proportional guidance is obtained according to the following formula: in, θ is the trajectory inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient; Before using the neural network, it needs to be trained, and ballistic simulation is used to obtain training samples; The trajectory simulation is a nonlinear strike model simulation, which can be expressed as: η=θ-q Among them, η is the angle between the aircraft speed and the sight line of sight, θ is the trajectory inclination angle, q is the sight line angle of sight, r is the distance between the missile and the target, v is the aircraft speed, and a M Overload command for the aircraft.

2. The adaptive bias proportional guidance method based on neural network according to claim 1, characterized in that: The number of hidden layers of the BP neural network is 5.

3. The adaptive bias proportional guidance method based on neural network according to claim 1, characterized in that: When establishing training samples, the setting parameters of the trajectory simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters. The setting parameters of the trajectory simulation include the initial projectile-target distance, the guidance coefficient, the initial trajectory inclination angle, and the initial projectile-target line of sight angle.

4. The neural network-based adaptive bias proportional guidance method according to claim 3, characterized in that: The initial missile-target distance is 5,000 meters to 10,000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination is 10-20 degrees.

5. The adaptive bias proportional guidance method based on neural network according to claim 1, characterized in that: In the process of training the neural network, the Adam learning rate is used to update the parameters of the neural network.

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