A small sample trajectory prediction method and system based on data-model double driving

Abstract

The application provides a small sample trajectory prediction method and system based on data-model double driving, comprising: establishing a six-degree-of-freedom trajectory model; constructing a small sample trajectory prediction database including data driving and model driving, the data driving being observation data of a target trajectory, and the model driving being a full trajectory including all variable data of the six-degree-of-freedom trajectory model; constructing a trajectory prediction model based on a PINN model, and constructing physical constraints based on the data driving and the model driving in the small sample trajectory prediction database, embedding initial conditions, boundary conditions and the physical constraints into the trajectory prediction model as a loss function; and training the trajectory prediction model, and predicting the target trajectory through the trained trajectory prediction model. The application meets the trajectory prediction demand under the small sample condition.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of guided projectile trajectory prediction in dynamic environment, and particularly relates to a small sample trajectory prediction method and system based on data-model double driving. BACKGROUND

[0002] The guided projectile is a kind of low-cost precision strike ammunition developed on the basis of uncontrolled projectile by using precise guidance technology, adding precise guidance system or correction system. Due to the use of precise guidance technology, its hitting accuracy is greatly improved, which greatly improves the combat effectiveness of the artillery weapon system. According to the observation data of the own side, the trajectory prediction can accurately calculate the flight path of the guided projectile, effectively reduce the target error and improve the strike effect. Trajectory prediction allows rapid and flexible tactical decision-making in dynamic battlefield environment, and timely adjustment of the trajectory of the guided projectile. In the projectile development stage, accurate trajectory prediction can reduce the number of live ammunition tests, reduce development cost and shorten development cycle.

[0003] For the problem of trajectory prediction, the traditional methods are numerical integration and Kalman filter. Ji et al. proposed a numerical method based on 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 a trajectory object in the atmosphere. For each model, a different Extend Kalman Filter (EKF) is used to estimate the state, and then the model is used to identify the projectile to achieve impact point prediction. Deng et al. studied a trajectory estimation method without external velocity input, established a modified point-mass model of a spinning projectile with fixed canards, and estimated the real-time position and velocity of the projectile through an extended Kalman filter, with only position and rotation speed as input information. The numerical integration method and EKF algorithm often need to establish a complex dynamic model in advance according to different initial conditions and target types, and have many limitations in applicable scenarios, which is difficult to meet the needs of trajectory prediction in different environments.

[0004] To address the aforementioned issues, deep learning-based trajectory prediction methods can establish nonlinear trajectory prediction models using large amounts of trajectory data. Cai et al. proposed an environment-attention network model, overcoming the limitations imposed by dimensionality and structure when constructing a model of vehicle-environment interaction, effectively predicting vehicle trajectories. Fei et al. proposed a trajectory prediction method based on sequence models, which integrates CNN and LSTM neural networks, combining the spatial expansion of CNN and the temporal expansion of LSTM to predict the trajectories of surrounding vehicles; the hyperparameters of the model are optimized using a grid search algorithm to meet the requirements of both spatial and temporal precision prediction. Qin et al. combined Kalman Filter (KF) theory with LSTM neural networks to predict hurricane trajectories, preprocessing the data using one-hot encoding and filtering outliers, achieving prediction results superior to the improved LSTM neural network. However, the aforementioned deep learning-based trajectory prediction methods require large amounts of trajectory data, and collecting large amounts of high-quality shell trajectory data in practical applications can be very difficult or expensive. Therefore, this invention proposes a small-sample ballistic prediction method based on a data-model dual-drive approach. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention proposes a small-sample ballistic prediction method and system based on data-model dual-drive.

[0006] The technical solution to achieve the objective of this invention is:

[0007] A small-sample ballistic prediction method based on a data-model dual-drive approach includes:

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

[0009] A small-sample ballistic prediction database is constructed, which includes data-driven and model-driven approaches. The data-driven approach uses the observed data of the target ballistic trajectory, while the model-driven approach uses a known full trajectory that includes all variable data of a six-degree-of-freedom ballistic model.

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

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

[0012] Furthermore, the six-degree-of-freedom ballistic model is as follows:

[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 its flight; v is the velocity of the projectile relative to the ground, and θ is the velocity of the projectile relative to the ground. a ψ1 is the negative rotation angle of the velocity coordinate system about the Z-axis of the reference coordinate system, and ψ2 is the negative rotation angle of the velocity coordinate system about its own Y-axis. The angle is the negative rotation of the spring-axis coordinate system around the Z-axis of the reference coordinate system. δ1 is the negative rotation angle of the second projectile axis coordinate system about its own Y-axis, δ2 is the negative rotation angle of the second projectile axis coordinate system about its own Y-axis, and δ1 is the negative rotation angle of the second projectile axis coordinate system about the velocity coordinate system Z-axis. ξ ,ω η ,ω ζ γ represents the component of the total angular velocity in the projectile axis coordinate system, γ is the negative rotation angle of the projectile coordinate system around the projectile 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 and second projectile axes.

[0015] Furthermore, the loss function is:

[0016] MSE = MSE u +MSE f

[0017] Among them, MSE u The loss function representing the initial and boundary conditions, MSE f It is a physical loss function constructed from physical constraints.

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

[0019]

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

[0021] Furthermore, the loss function MSE f Including range physical loss MSE fX Physical loss at altitude MSE fY The physical losses due to lateral deviation are as follows:

[0022]

[0023]

[0024]

[0025] N f This represents the number of sampling points for the six-degree-of-freedom ballistic model.

[0026] Furthermore, the ballistic prediction model takes time t as input and outputs the projectile's coordinates x, y, z in the ground coordinate system. Each layer between the input and output, and the neurons in each layer, constitute a fully connected neural network structure. This network structure includes 5 fully connected layers, each with 40 neurons, using the hyperbolic tangent activation function. Residual blocks are added to the fully connected layers.

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

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

[0029] A small-sample ballistic prediction system based on a data-model dual-drive approach includes:

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

[0031] The database construction unit is used to build a small-sample ballistic prediction database that includes data-driven and model-driven methods. The data-driven method uses the observation data of the target ballistics, while the model-driven method uses a known full ballistic trajectory that includes all variable data of a six-degree-of-freedom ballistic model.

[0032] The prediction unit is used to construct a ballistic prediction model based on the PINN model, and to construct physical constraints based on data-driven and model-driven approaches from a small sample ballistic prediction database. The initial conditions, boundary conditions, and physical constraints are embedded as loss functions into the ballistic prediction model. The trained ballistic prediction model then predicts the target trajectory.

[0033] A computer storage medium storing an executable program, the executable program being executed by a processor to implement the steps of the small sample ballistic prediction method.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention is based on a six-degree-of-freedom ballistic model to build a small sample ballistic prediction database, which solves the problem that it is very difficult or expensive to collect a large amount of high-quality projectile trajectory data in practical applications; (2) PINN is introduced to embed the ballistic boundary constraints and ballistic physical model constraints in the neural network, and the efficient training of the model is achieved through automatic differentiation technology to meet the ballistic prediction requirements under small sample conditions; (3) The present invention is applicable to the ballistic prediction of guided projectiles in dynamic battlefield environments. Attached Figure Description

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

[0036] Figure 2 This is a schematic diagram of a small sample database.

[0037] Figure 3 Data + Model Dual-Driven Prediction Framework Diagram.

[0038] Figure 4 PINN model structure diagram for ballistic prediction.

[0039] Figure 5 This is an overall flowchart of the method of the present invention. Detailed Implementation

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

[0041] Combination Figure 1 and Figure 5 This invention designs a small-sample ballistic prediction method based on a data-model dual-drive approach, comprising:

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

[0043] When studying projectile flight trajectories, a nonlinear six-degree-of-freedom ballistic model is employed, which is the most commonly used method for describing projectile motion 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 its flight; where v is the velocity of the projectile relative to the ground, and θ is the velocity of the projectile relative to the ground. a ψ1 is the negative rotation angle of the velocity coordinate system about the Z-axis of the reference coordinate system, and ψ2 is the negative rotation angle of the velocity coordinate system about its own Y-axis. The angle is the negative rotation of the spring-axis coordinate system around the Z-axis of the reference coordinate system. δ1 is the negative rotation angle of the second projectile axis coordinate system about its own Y-axis, δ2 is the negative rotation angle of the second projectile axis coordinate system about its own Y-axis, and δ1 is the negative rotation angle of the second projectile axis coordinate system about the velocity coordinate system Z-axis. ξ ,ω η ,ω ζ γ represents the component of the total angular velocity in the projectile axis coordinate system, γ is the negative rotation angle of the projectile coordinate system around the projectile 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 and second projectile axes.

[0046] 2. Construct a small sample database

[0047] Combination Figure 2 The small sample database consists of data-driven and model-driven approaches. Data-driven approaches are obtained by radar or missile-borne sensors, which provide trajectory data of the target ballistics for the first few seconds, including range X, altitude Y, and lateral deviation Z. Model-driven approaches are a complete ballistic trajectory with known data, including the 15 variable data in equation (1), which can be measured in a known environment. The ballistic equations are solved offline to obtain the derivatives of the ballistic variables with respect to time, which together with the trajectory data for the first few seconds constitute the small sample database.

[0048] Data-driven and model-driven constraints from a small sample database are constructed and embedded as a loss function into the PINN model. Its integration with the ballistic model is as follows:

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

[0050] μ t +N(u;λ)=0,x∈Ω,t∈[0,T] (2)

[0051] In the formula, 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 ballistic model. The neural network uses automatic differentiation techniques. Based on the chain rule, the partial differential relationship between the output and input of the neural network model can be obtained using the backpropagation algorithm of the neural network.

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

[0053] f≡μ t +N(u;λ) (3)

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

[0055]

[0056] in, The initial and boundary training data for the solution of the equation. The data output by the neural network, Let N be the sampling points of f(t,x). uN represents the number of initial and boundary training data points. f This represents the number of sampling points for the ballistic model.

[0057] MSE in ballistic prediction f It consists of three parts: MSE fX MSE fY MSE fZ These are the physical losses from range, altitude, and lateral deviation, respectively.

[0058]

[0059] 3. Construct a PINN ballistic trajectory prediction model

[0060] The process of the PINN ballistic trajectory prediction model is attached. Figure 4 Choosing time t as input and positions x, y, z as output, each layer between input and output and each layer of neurons constitutes a fully connected neural network structure. The dynamic model of the ballistics should be transformed into equation (1). The network structure includes 5 fully connected layers, each with 40 neurons, using the hyperbolic tangent activation function. The output of the neural network is used as the solution to the differential equation, and the derivative with respect to time is calculated using automatic differentiation. The dynamic model is embedded into the loss function to calculate the physics-based loss function. The output of the neural network and the partial observation data of the target trajectory constitute the boundary loss. The physics 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 objective function of the loss, equation (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 that the neural network converges faster. To avoid gradient explosion and gradient vanishing, a residual neural network is added to the fully connected network in PINN. After the PINN model is trained, the time-series data of the target trajectory is used as input to obtain the predicted value of the target trajectory.

[0061] In the PINN model, the output of the fully connected network and the trajectory data of the target ballistics in the first few seconds of the small sample database constitute the PINN boundary loss. The output of the fully connected network, after automatic differentiation, and the derivative of the variables constitute the PINN physical loss. The boundary loss and the physical loss together constitute the loss function of the PINN model. By minimizing the loss function, the network parameters are updated to obtain the optimal network. The predicted value of the target ballistics is obtained by inputting the time series of the trajectory to be predicted.

[0062] See appendix Figure 3This invention provides a data + model dual-driven ballistic prediction system, comprising a ballistic model and a neural network. Ballistic data and the ballistic model provide additional physical information input for ballistic prediction; the neural network learns the dynamic nonlinear characteristics of the ballistic trajectory, exhibiting features such as feature extraction, reduction of model parameters, and description of temporal dependencies. A small sample database provides ballistic boundary constraints and ballistic physical model constraints for the PINN model through offline solution of ballistic equations. PINN utilizes these constraints to construct a loss function, optimize parameters, obtain the optimal network, and achieve ballistic prediction.

[0063] This invention provides a small-sample ballistic prediction system based on a data-model dual-drive approach, comprising:

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

[0065] The database construction unit is used to build a small-sample ballistic prediction database that includes data-driven and model-driven methods. The data-driven method uses the observation data of the target ballistics, while the model-driven method uses a known full ballistic trajectory that includes all variable data of a six-degree-of-freedom ballistic model.

[0066] The prediction unit is used to construct a ballistic prediction model based on the PINN model, and to construct physical constraints based on data-driven and model-driven approaches from a small sample ballistic prediction database. The initial conditions, boundary conditions, and physical constraints are embedded as loss functions into the ballistic prediction model. The trained ballistic prediction model then predicts the target trajectory.

[0067] This invention provides a computer storage medium storing an executable program that is executed by a processor to implement the steps of the small-sample ballistic prediction method. These computer program instructions can also be loaded onto a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable device for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0068] This invention mainly comprises two parts: constructing a small sample database and a PINN prediction model. Based on a six-degree-of-freedom ballistic model, a small sample ballistic prediction database is constructed. PINN is introduced to embed ballistic boundary constraints and ballistic physical model constraints into the neural network. The model is trained efficiently through automatic differentiation technology to meet the ballistic prediction requirements under small sample conditions. This method is suitable for ballistic prediction of guided artillery shells in dynamic battlefield environments.

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

Claims

1. A small sample trajectory prediction method based on data-model double driving, characterized in that, The method comprises the following steps: establishing a six-degree-of-freedom trajectory model; constructing a small-sample trajectory prediction database comprising data-driven and model-driven data, wherein the data-driven data is observation data of a target trajectory, and the model-driven data is a full trajectory comprising all variable data of the six-degree-of-freedom trajectory model; constructing a trajectory prediction model based on a PINN model, and constructing physical constraints based on the data-driven and model-driven data in the small-sample trajectory prediction database, wherein the initial conditions, boundary conditions and physical constraints are embedded into the trajectory prediction model as a loss function; wherein the output of a full connection network in the PINN model and the trajectory data of the target trajectory for a plurality of seconds before the target trajectory in the small-sample trajectory prediction database constitute a PINN boundary loss, and the output of the full connection network after automatic differentiation and the variable derivative constitute a PINN physical loss; the boundary loss and the physical loss jointly constitute the loss function of the PINN model, the network parameters are updated by minimizing the loss function, and an optimal network is obtained; inputting a time sequence of a trajectory to be predicted, a prediction value of the target trajectory is obtained; training the trajectory prediction model, and predicting the target trajectory by using the trained trajectory prediction model; the six-degree-of-freedom trajectory model is as follows: In the formula, v, θ a , ψ2, δ2, δ1, ω ξ , ω η , ω ζ , γ, x, y, z, β are respectively variables of the projectile in the flight process; v is the projectile speed relative to the ground, θ a is the negative rotation angle of the speed coordinate system around the Z axis of the reference coordinate system, ψ2 is the negative rotation angle of the speed coordinate system around the Y axis of itself, is the negative rotation angle of the projectile axis coordinate system around the Z axis of the reference coordinate system, is the negative rotation angle of the projectile axis coordinate system around the Y axis of itself, δ2 is the negative rotation angle of the second projectile axis coordinate system around the Y axis of itself, δ1 is the negative rotation angle of the second projectile axis coordinate system around the Z axis of the speed coordinate system, ω ξ , ω η , ω ζ is the component of the total angular velocity in the projectile axis coordinate system, γ is the negative rotation angle of the projectile body coordinate system around the projectile axis coordinate system, x, y, z are the coordinates of the projectile in the ground coordinate system, and β is the negative rotation angle of the first projectile axis and the second projectile axis.

2. The small sample ballistic prediction method based on data-model double driving according to claim 1, characterized in that, the loss function is as follows: MSE = MSE u + MSE f where MSE u is the loss function representing the initial conditions and boundary conditions, MSE f is the physical loss function constructed from the physical constraints.

3. The small sample ballistic prediction method based on data-model dual driving according to claim 2, characterized in that, The loss function MSE u is: wherein, is initial and boundary training data for the equation solution, is data output by the neural network, N u is the number of initial and boundary training data points.

4. The small sample ballistic prediction method based on data-model dual driving according to claim 2, characterized in that, The loss function MSE f including a range physical loss MSE fX , a height physical loss MSE fY , and a cross bias physical loss MSE fZ , respectively, are: N f is the number of sample points for the six-degree-of-freedom ballistic model.

5. The small sample ballistic prediction method based on data-model dual driving according to claim 1, characterized in that, the input of the trajectory prediction model is time t, and the output is coordinates x, y and z of the cannonball in a ground coordinate system; each layer and each neuron of each layer between the input and the output constitute a full connection neural network structure, the network structure comprises five full connection layers, each layer has 40 neurons, a hyperbolic tangent activation function is used, and a residual block is added to the full connection layer.

6. The small sample ballistic prediction method based on data-model dual driving according to claim 5, characterized in that, The Adam optimizer is used to optimize the loss function during the training of the trajectory prediction model.

7. The small sample ballistic prediction method based on data-model dual driving according to claim 6, characterized in that, The initial weight and bias of the trajectory prediction model are determined by using the Xavier method.

8. A small sample trajectory prediction system based on data-model dual driving, which implements the method of any one of claims 1-7, characterized in that, The method comprises the following steps: a model construction unit is configured to establish a six-degree-of-freedom trajectory model; a database construction unit is configured to construct a small-sample trajectory prediction database comprising data-driven and model-driven data, wherein the data-driven data is observation data of a target trajectory, and the model-driven data is a full trajectory comprising all variable data of the six-degree-of-freedom trajectory model; a prediction unit is configured to construct a trajectory prediction model based on a PINN model, and to construct physical constraints based on the data-driven and model-driven data in the small-sample trajectory prediction database, wherein the initial conditions, boundary conditions and physical constraints are embedded into the trajectory prediction model as a loss function; the trained trajectory prediction model is used to predict a target trajectory.

9. 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 in any one of claims 1-7.

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