Small sample trajectory prediction method and system based on data-model dual drive

Abstract

The invention provides a small sample trajectory prediction method and system based on data-model dual drive. The method comprises the following steps: establishing a six-degree-of-freedom trajectory model; a small sample trajectory prediction database comprising data driving and model driving is constructed, the data driving is observation data of a target trajectory, and the model driving is a known whole trajectory comprising all variable data of a six-degree-of-freedom trajectory model; a trajectory prediction model is constructed based on a PINN model, physical constraints are constructed based on data driving and model driving in the small sample trajectory prediction database, and initial conditions, boundary conditions and the physical constraints are used as loss functions to be embedded into the trajectory prediction model; and training the trajectory prediction model, and predicting a target trajectory through the trained trajectory prediction model. The ballistic prediction requirement under the small sample condition is met.

Description

Technical Field

[0001] The present invention belongs to the field of guided projectile trajectory prediction in a dynamic environment, and in particular relates to a small sample trajectory prediction method and system based on data-model dual drive. Background Art

[0002] Guided artillery shells are a type of low-cost precision strike ammunition developed on the basis of uncontrolled artillery shells by adopting precision guidance technology and adding precision guidance systems or correction systems. Due to the use of precision guidance technology, its hit accuracy has been greatly improved, greatly improving the combat effectiveness of artillery weapon systems. Trajectory prediction based on one's own observation data can accurately calculate the flight path of guided artillery shells, which can effectively reduce target errors and improve strike effects. Trajectory prediction allows for fast and flexible tactical decisions in a dynamic battlefield environment and timely adjustment of the trajectory of guided artillery shells. In the artillery shell development stage, accurate trajectory prediction can reduce the number of live-fire tests, reduce development costs, and shorten the development cycle.

[0003] Traditional methods for trajectory prediction include numerical integration and Kalman filtering. Ji et al. proposed a numerical method based on the high-precision Runge-Kutta recursive formula to solve high-order uncertain differential equations. Ravindra et al. proposed a multi-model program for estimating the state of ballistic objects in the atmosphere. For each model, a different extended Kalman filter (EKF) was used for state estimation, and then the model was used to identify the projectile to achieve impact point prediction. Deng et al. studied a trajectory estimation method without external velocity input, established a corrected point-mass model for a rotating projectile with fixed canards, and estimated its real-time position and velocity through an extended Kalman filter. The input information is only position and rotation speed. Numerical integration methods and EKF algorithms often need to pre-establish complex dynamic models based on different initial conditions and target types, and have many limitations on applicable scenarios, making it difficult to meet the needs of trajectory prediction in different environments.

[0004] In view of the above problems, the trajectory prediction method based on deep learning can establish a nonlinear trajectory prediction model through a large amount of trajectory data. Cai et al. proposed an environment-attention network model, which solved the limitations of dimensionality and structural influence when building a model of interaction between vehicles and the surrounding environment, and effectively predicted the trajectory of vehicles. Fei et al. proposed a trajectory prediction method based on a sequence model, which combines two neural networks, CNN and LSTM, and predicts the trajectory of surrounding vehicles by combining the characteristics of CNN spatial expansion and LSTM temporal expansion; the hyperparameters of the model are optimized according to the grid search algorithm to meet the requirements of spatial and temporal double-precision prediction. Qin et al. combined the Kalman filter (KF) theory and the LSTM neural network to predict the hurricane trajectory, preprocessed the data by one-hot encoding, and screened the predicted outliers. The prediction results were better than the improved LSTM neural network. However, the above trajectory prediction method based on deep learning requires a large amount of trajectory data. In practical applications, it may be very difficult or expensive to collect a large amount of high-quality artillery trajectory data. For this reason, the present invention proposes a small sample trajectory prediction method based on data-model dual drive. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention proposes a small sample trajectory prediction method and system based on data-model dual drive.

[0006] The technical solution for achieving the purpose of the present invention is:

[0007] A small sample trajectory prediction method based on data-model dual drive, including:

[0008] Establish a six-degree-of-freedom trajectory model;

[0009] Construct a small sample trajectory prediction database including data-driven and model-driven. The data-driven one is the observation data of the target trajectory, and the model-driven one is a known full trajectory including all variable data of the six-degree-of-freedom trajectory model.

[0010] A trajectory prediction model is constructed based on the PINN model, and physical constraints are constructed based on data-driven and model-driven methods in a small sample trajectory prediction database. Initial conditions, boundary conditions, and physical constraints are embedded into the trajectory prediction model as loss functions.

[0011] The trajectory prediction model is trained, and the target trajectory is predicted by the trained trajectory prediction model.

[0012] Furthermore, the six-degree-of-freedom trajectory model is:

[0013]

[0014] In the formula, v,θ a,ψ2, δ2,δ1,ω ξ ,ω η ,ω ζ ,γ,x,y,z,β are the variables of the projectile during flight; v is the speed of the projectile relative to the ground, θ a is the negative rotation angle of the velocity coordinate system around the Z axis of the reference coordinate system, ψ2 is the negative rotation angle of the velocity coordinate system around its own Y axis, It is the negative rotation angle of the elastic axis coordinate system around the Z axis of the reference coordinate system. is the negative rotation angle of the elastic axis coordinate system around its own Y axis, δ2 is the negative rotation angle of the second elastic axis coordinate system around its own Y axis, δ1 is the negative rotation angle of the second elastic axis coordinate system around the Z axis of the velocity coordinate system, ω ξ ,ω η ,ω ζ is the component of the total angular velocity in the missile axis coordinate system, γ is the negative rotation angle of the missile body coordinate system around the missile axis coordinate system, x, y, z are the coordinates of the projectile in the ground coordinate system, and β is the negative rotation angle between the first missile axis and the second missile axis.

[0015] Furthermore, the loss function is:

[0016] MSE = MSE u +MSE f

[0017] Among them, MSE u Represents the loss function of initial conditions and boundary conditions, MSE f is the physical loss function constructed by physical constraints.

[0018] Furthermore, the loss function MSE u for:

[0019]

[0020] in, are the initial and boundary training data for the solution of the equation, is the data output by the neural network, N u is the number of initial and boundary training data points.

[0021] Furthermore, the loss function MSE f Includes range physical loss MSE fX , Shooting height physical loss MSE fY and lateral physical losses, respectively:

[0022]

[0023]

[0024]

[0025] N f is the number of sampling points of the six-degree-of-freedom trajectory model.

[0026] Furthermore, the input of the trajectory prediction model is time t, and the output is the coordinates x, y, z of the projectile in the ground coordinate system. Each layer and each layer of neurons between the input and output constitute a fully connected neural network structure. The network structure includes 5 fully connected layers, each with 40 neurons, using a hyperbolic tangent activation function, and a residual block is added to the fully connected layer.

[0027] Furthermore, the Adam optimizer is used to optimize the loss function during the training of the trajectory prediction model.

[0028] Furthermore, the Xavier method is used to determine the initial weights and deviations of the trajectory prediction model.

[0029] A small sample trajectory prediction system based on data-model dual drive, comprising:

[0030] A model building unit, used to build a six-degree-of-freedom trajectory model;

[0031] A database construction unit is used to construct a small sample trajectory prediction database including data-driven and model-driven ones, wherein the data-driven one is the observation data of the target trajectory, and the model-driven one is a known full trajectory including all variable data of the six-degree-of-freedom trajectory model;

[0032] The prediction unit is used to build a trajectory prediction model based on the PINN model, and to build physical constraints based on data-driven and model-driven methods in the small sample trajectory prediction database, and to embed initial conditions, boundary conditions and physical constraints into the trajectory prediction model as loss functions; the trained trajectory prediction model is used to predict the target trajectory.

[0033] A computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the small sample trajectory prediction method.

[0034] Compared with the prior art, the present invention has the following advantages: (1) The present invention constructs a small sample trajectory prediction database based on a six-degree-of-freedom ballistic model, which solves the problem that it is very difficult or expensive to collect a large amount of high-quality artillery trajectory data in practical applications; (2) PINN is introduced to embed the ballistic boundary constraints and the ballistic physical model constraint relationship in the neural network, and the efficient training of the model is achieved through automatic differentiation technology to meet the ballistic prediction needs in the case of small samples; (3) The present invention is suitable for guided artillery trajectory prediction in a dynamic battlefield environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A small sample trajectory prediction framework based on data-model dual drive.

[0036] Figure 2 Schematic diagram of a small sample database.

[0037] Figure 3 Diagram of the data + model dual-driven prediction framework.

[0038] Figure 4 Diagram of the PINN model structure for trajectory prediction.

[0039] Figure 5 The figure is an overall flow chart of the method of the present invention. DETAILED DESCRIPTION

[0040] Next, the implementation of the present invention will be described in detail with reference to the accompanying drawings.

[0041] Combination Figure 1 and Figure 5 The present invention designs a small sample trajectory prediction method based on data-model dual drive, including:

[0042] 1. Establish a six-degree-of-freedom trajectory model

[0043] When studying the flight trajectory of a projectile, a nonlinear six-degree-of-freedom ballistic model is used, which is the most commonly used method to describe the motion of a projectile in the air. First, a six-degree-of-freedom ballistic model is established:

[0044]

[0045] In the formula, v,θ a ,ψ2, δ2,δ1,ω ξ ,ω η ,ω ζ ,γ,x,y,z,β are the variables of the projectile during flight; v is the velocity of the projectile relative to the ground, θ a is the negative rotation angle of the velocity coordinate system around the Z axis of the reference coordinate system, ψ2 is the negative rotation angle of the velocity coordinate system around its own Y axis, It is the negative rotation angle of the elastic axis coordinate system around the Z axis of the reference coordinate system. is the negative rotation angle of the elastic axis coordinate system around its own Y axis, δ2 is the negative rotation angle of the second elastic axis coordinate system around its own Y axis, δ1 is the negative rotation angle of the second elastic axis coordinate system around the Z axis of the velocity coordinate system, ω ξ ,ω η ,ω ζ is the component of the total angular velocity in the missile axis coordinate system, γ is the negative rotation angle of the missile body coordinate system around the missile axis coordinate system, x, y, z are the coordinates of the projectile in the ground coordinate system, and β is the negative rotation angle between the first missile axis and the second missile axis.

[0046] 2. Build a small sample database

[0047] Combination Figure 2 The small sample database is composed of data-driven and model-driven. The data-driven one is to obtain the trajectory data of the target several seconds before the trajectory through radar or missile-borne sensors, including range X, altitude Y and lateral deviation Z. The model-driven one is a full trajectory with all known data, including the 15 variable data in formula (1), which can be measured in a known environment and solved offline through the trajectory equation to obtain the derivative of the trajectory variable with respect to time, which together with the trajectory data of several seconds constitutes the small sample database.

[0048] The data-driven and model-driven models in the small sample database are constructed as constraints and embedded into the PINN model as loss functions. Its combination with the ballistic model is as follows:

[0049] We assume that the parameterized nonlinear partial differential equation has the following simple form:

[0050] μ t +N(u;λ)=0,x∈Ω,t∈[0,T] (2)

[0051] Where μ(t,x) is the implicit solution of the partial differential equation, N(u;λ) is a nonlinear operator parameterized by λ, and u is a variable in the six-degree-of-freedom trajectory model. Automatic differentiation technology is used in neural networks. Based on the chain rule, the partial differential relationship between the output and input of the neural network model can be obtained by using the back propagation algorithm of the neural network.

[0052] The physical problem is transformed into the form of formula (2), and its solution is calculated by minimizing the loss function of the neural network. The objective function of the loss is the mean square error loss, as shown in formula (4), which consists of two parts. u represents the loss function of initial conditions and boundary conditions, and MSE f is the physical loss of the target partial differential equation.

[0053] f≡μ t +N(u;λ) (3)

[0054] MSE = MSE u +MSE f (4)

[0055]

[0056] in, are the initial and boundary training data for the solution of the equation, is the output data of the neural network, is the sampling point of f(t,x), N uis the number of initial and boundary training data points, N f is the number of sampling points of the trajectory model.

[0057] MSE in trajectory prediction f It consists of three parts: fX , MSE fY , MSE fZ , are the physical losses of range, height and lateral deviation respectively:

[0058]

[0059] 3. Construct PINN ballistic trajectory prediction model

[0060] The process of PINN ballistic trajectory prediction model is attached Figure 4 . Select time t as input, position x, y, z as output, and each layer and each layer of neurons between input and output constitute a fully connected neural network structure. The dynamic model of the trajectory should be transformed into equation (1). The structure of the network includes 5 fully connected layers, each with 40 neurons, and a hyperbolic tangent activation function. The output of the neural network is used as the solution of the differential equation, and the automatic differentiation technique is used to calculate the derivative with respect to time. The dynamic model is embedded in the loss function to calculate the physics-based loss function. The output of the neural network and part of the observed data of the target trajectory constitute the boundary loss. The physical loss and the boundary loss constitute the loss of the neural network and the weights of the neuron nodes in the fully connected layer are updated by minimizing the loss function. In order to reduce the error of the loss function, the Adam optimizer is used to optimize the loss objective function (4). During the learning process, the Adam optimizer can continuously adjust the learning rate as the situation changes. The "Xavier" method is used to determine the initial weights and biases. It is a weight initialization method commonly used in training deep learning models proposed by Xavier Glorot and Yoshua Bengio in 2010 to ensure faster convergence of the neural network. In order to avoid gradient explosion and gradient vanishing, a residual neural network is added to the fully connected network in PINN. After the PINN model training is completed, the time series data of the target trajectory is used as input to obtain the predicted value of the target trajectory.

[0061] The output of the fully connected network in the PINN model and the trajectory data of the target trajectory several seconds before in the small sample database constitute the PINN boundary loss. The output of the fully connected network constitutes the PINN physical loss with the variable derivative after automatic differentiation. The boundary loss and the physical loss together constitute the loss function of the PINN model. By minimizing the loss function and updating the network parameters, the optimal network is obtained. The time series of the trajectory to be predicted is input to obtain the predicted value of the target trajectory.

[0062] See attached Figure 3The present invention provides a data + model dual-driven trajectory prediction including a trajectory model and a neural network. The trajectory data and the trajectory model can provide additional physical information input for trajectory prediction; the neural network learns the dynamic nonlinear characteristics of the trajectory, and has the characteristics of extracting features, reducing model parameters, and describing time series dependencies. The small sample database provides the PINN model with trajectory boundary constraints and trajectory physical model constraints through offline solution of the trajectory equation. PINN uses constraints to construct a loss function, optimize parameters, obtain the optimal network, and realize trajectory prediction.

[0063] The present invention provides a small sample trajectory prediction system based on data-model dual drive, comprising:

[0064] A model building unit, used to build a six-degree-of-freedom trajectory model;

[0065] A database construction unit is used to construct a small sample trajectory prediction database including data-driven and model-driven ones, wherein the data-driven one is the observation data of the target trajectory, and the model-driven one is a known full trajectory including all variable data of the six-degree-of-freedom trajectory model;

[0066] The prediction unit is used to build a trajectory prediction model based on the PINN model, and to build physical constraints based on data-driven and model-driven methods in the small sample trajectory prediction database, and to embed initial conditions, boundary conditions and physical constraints into the trajectory prediction model as loss functions; the trained trajectory prediction model is used to predict the target trajectory.

[0067] The present invention provides a computer storage medium storing an executable program, which is executed by a processor to implement the steps of the small sample trajectory prediction method. These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions executed on the computer or other programmable device for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0068] The present invention mainly includes two parts: constructing a small sample database and a PINN prediction model. Based on a six-degree-of-freedom trajectory model, a small sample trajectory prediction database is constructed. PINN is introduced to embed the trajectory boundary constraints and the trajectory physical model constraint relationship in the neural network. The automatic differentiation technology is used to realize efficient model training to meet the trajectory prediction needs under small sample conditions. This method is suitable for guided artillery projectile trajectory prediction in a dynamic battlefield environment.

[0069] The description of the above preferred embodiments enables those skilled in the art to make or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without using creative capabilities. Therefore, the present invention is not limited to the embodiments shown herein, but conforms to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A small sample trajectory prediction method based on data-model dual drive, characterized in that: include: Establish a six-degree-of-freedom trajectory model; Construct a small sample trajectory prediction database including data-driven and model-driven. The data-driven one is the observation data of the target trajectory, and the model-driven one is a known full trajectory including all variable data of the six-degree-of-freedom trajectory model. A trajectory prediction model is constructed based on the PINN model, and physical constraints are constructed based on data-driven and model-driven methods in a small sample trajectory prediction database. Initial conditions, boundary conditions, and physical constraints are embedded into the trajectory prediction model as loss functions. The trajectory prediction model is trained, and the target trajectory is predicted by the trained trajectory prediction model.

2. According to claim 1, a small sample trajectory prediction method based on data-model dual drive is characterized in that: The six-degree-of-freedom trajectory model is: In the formula, v,θ a ,ψ2, δ2,δ1,ω ξ ,ω η ,ω ζ ,γ,x,y,z,β are the variables of the projectile during flight; v is the speed of the projectile relative to the ground, θ a is the negative rotation angle of the velocity coordinate system around the Z axis of the reference coordinate system, ψ2 is the negative rotation angle of the velocity coordinate system around its own Y axis, It is the negative rotation angle of the elastic axis coordinate system around the Z axis of the reference coordinate system. is the negative rotation angle of the elastic axis coordinate system around its own Y axis, δ2 is the negative rotation angle of the second elastic axis coordinate system around its own Y axis, δ1 is the negative rotation angle of the second elastic axis coordinate system around the Z axis of the velocity coordinate system, ω ξ ,ω η ,ω ζ is the component of the total angular velocity in the missile axis coordinate system, γ is the negative rotation angle of the missile body coordinate system around the missile axis coordinate system, x, y, z are the coordinates of the projectile in the ground coordinate system, and β is the negative rotation angle between the first missile axis and the second missile axis.

3. The small sample trajectory prediction method based on data-model dual drive according to claim 1 is characterized in that: The loss function is: MSE=MSE u +MSE f Among them, MSE u Represents the loss function of initial conditions and boundary conditions, MSE f It is the physical loss function constructed by physical constraints.

4. The small sample trajectory prediction method based on data-model dual drive according to claim 3 is characterized in that: The loss function MSE u for: in, are the initial and boundary training data for the solution of the equation, is the data output by the neural network, N u is the number of initial and boundary training data points.

5. The small sample trajectory prediction method based on data-model dual drive according to claim 3 is characterized in that: The loss function MSE f Includes range physical loss MSE fX , Shooting height physical loss MSE fY and lateral physical losses, respectively: N f is the number of sampling points of the six-degree-of-freedom trajectory model.

6. The small sample trajectory prediction method based on data-model dual drive according to claim 1 is characterized in that: The input of the trajectory prediction model is time t, and the output is the coordinates x, y, z of the projectile in the ground coordinate system. Each layer and each layer of neurons between the input and output constitute a fully connected neural network structure. The network structure includes 5 fully connected layers, each layer has 40 neurons, and a hyperbolic tangent activation function is used. A residual block is added to the fully connected layer.

7. A small sample trajectory prediction method based on data-model dual drive according to claim 6, characterized in that: The Adam optimizer is used to optimize the loss function during the training of the trajectory prediction model.

8. The small sample trajectory prediction method based on data-model dual drive according to claim 7 is characterized in that: The Xavier method is used to determine the initial weights and deviations of the trajectory prediction model.

9. A small sample trajectory prediction system based on data-model dual drive for implementing any of the methods described in claims 1-8, characterized in that: include: A model building unit, used to build a six-degree-of-freedom trajectory model; A database construction unit is used to construct a small sample trajectory prediction database including data-driven and model-driven ones, wherein the data-driven one is the observation data of the target trajectory, and the model-driven one is a known full trajectory including all variable data of the six-degree-of-freedom trajectory model; The prediction unit is used to build a trajectory prediction model based on the PINN model, and to build physical constraints based on data-driven and model-driven methods in the small sample trajectory prediction database, and to embed initial conditions, boundary conditions, and physical constraints into the trajectory prediction model as loss functions; The trained trajectory prediction model is used to predict the target trajectory.

10. A computer storage medium, characterized in that: The computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the small sample trajectory prediction method described in any one of claims 1-8.

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