Boost-glide trajectory prediction method based on physical information neural network

Abstract

The invention provides a boosting-gliding trajectory prediction method based on a physical information neural network. According to the method, a neural network is adopted as a boosting-gliding trajectory rapid prediction model, and the neural network inputs trajectory scheme design parameters and outputs a predicted trajectory voyage sequence and a height sequence. A parameter prediction sequence scheme is adopted, trajectory prediction starting from a launching point with trajectory scheme parameters as input can be achieved, and prediction of large-batch trajectory voyages and heights can be efficiently processed through neural network modeling. According to the scheme, physical information is introduced in a network training process, and a speed sequence and a trajectory inclination angle sequence are used as the physical information for loss calculation, so that the precision of trajectory voyage and height prediction is improved.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft system design, and particularly relates to a boost-glide trajectory prediction method based on a physics-informed neural network. Background Art

[0002] Hypersonic boost-glide vehicles have received extensive attention from domestic and foreign research institutions in recent years due to their characteristics such as rocket boost, reentry glide, and rapid penetration, and have good application prospects in fields such as area denial / anti-access operations. Due to constraints such as the handover point between the boost phase trajectory and the glide phase trajectory, it exacerbates the complexity of the trajectory scheme design and the high time-consuming nature of solving the trajectory simulation analysis model. Therefore, it is necessary to realize the prediction of hypersonic boost-glide trajectories through the nonlinear fitting ability and generalization ability of deep neural networks.

[0003] Existing trajectory prediction technologies take the trajectory sequence tracked by radar as the input and the subsequent trajectory sequence as the output, so as to realize the prediction of the trajectory sequence, and cannot realize the trajectory prediction with the trajectory scheme parameters as the input starting from the launch point.

[0004] At the same time, since the hypersonic boost-glide vehicle uses rocket boost in the boost phase and Sanger ballistic skip flight in the glide phase, it has characteristics such as long flight time, large change in trajectory altitude, and difficult feature extraction. Single surrogate model technologies such as BPNN have large prediction errors for it and cannot effectively perform trajectory prediction. Summary of the Invention

[0005] In view of this, the present invention provides a boost-glide trajectory prediction method based on a physics-informed neural network. This method adopts a parameter prediction sequence scheme, which can perform trajectory prediction with the trajectory scheme parameters as the input starting from the launch point; neural network modeling can efficiently process the prediction of a large number of trajectory ranges and altitudes; introducing physical information during the network training process can improve the trajectory prediction accuracy.

[0006] In order to solve the above technical problems, the present invention is implemented as follows.

[0007] A boost-glide trajectory prediction method based on a physics-informed neural network, comprising:

[0008] Step 1: Obtain multiple groups of trajectory scheme design parameters; use the hypersonic boost-glide vehicle trajectory simulation analysis model to solve the trajectory, and obtain the trajectory data corresponding to each group of trajectory scheme design parameters, including the range sequence R output , altitude sequence H output , speed sequence V output , ballistic inclination angle sequence Θ output ; the trajectory scheme design parameters and the trajectory data form training samples;

[0009] Step 2: Use the training samples to train the ballistic prediction neural network; the input of the ballistic prediction neural network structure is the ballistic scheme design parameters, and the output is the predicted ballistic flight program sequence and altitude sequence; during training, the velocity sequence V in the training samples output and the ballistic inclination angle sequence Θ output are used as physical information for loss calculation;

[0010] Step 3: Use the trained ballistic prediction neural network to predict the flight program sequence and altitude sequence of the boost-glide ballistic trajectory.

[0011] Preferably, in the above Step 2, the ballistic prediction neural network includes a first ballistic prediction neural network net for predicting the flight program sequence 1 and a second ballistic prediction neural network net for predicting the altitude sequence 2 ;

[0012] The loss of the first ballistic prediction neural network net 1 consists of two parts, including the root mean square error between the network prediction output and the true output and the network error ε calculated based on physical information pys1 :

[0013]

[0014] wherein, is the velocity sequence data after normalization processing, is the ballistic inclination angle sequence data after normalization processing; is the predicted value of the ballistic flight program sequence; the above formula represents the sum after calculating the data at the corresponding moments in the sequence;

[0015] The loss of the second ballistic prediction neural network net 2 consists of two parts, including the root mean square error between the network prediction output and the true output and the network error ε calculated based on physical information pys2 :

[0016]

[0017] wherein, is the velocity sequence data after normalization processing, is the ballistic inclination angle sequence data after normalization processing; is the predicted value of the ballistic altitude sequence; the above formula represents the sum after calculating the data at the corresponding moments in the sequence.

[0018] Preferably, the first ballistic prediction neural network net 1 and the second ballistic prediction neural network net for predicting the altitude sequence 2They have the same structure, all including an input layer, multiple hidden layers and an output layer; there are 5 hidden layers, and each hidden layer contains 1 fully connected layer, 1 ReLU activation function layer and 1 Dropout layer.

[0019] Preferably, among the 5 hidden layers, the number of neurons in the fully connected layers are successively fc 1 = 3200, fc 2 = 8000, fc 3 = 6400, fc 4 = 6400 and fc 5 = 3200, and the dropout ratios of the Dropout layers are respectively dp 1 = 0.2, dp 2 = 0.2, dp 3 = 0.1, dp 4 = 0.1 and dp 5 = 0.1.

[0020] Preferably, the root mean square error in the loss and the network error are weighted to obtain the loss value; the weighting coefficient of the root mean square error is 0.67, and the weighting coefficient of the network error is 0.33.

[0021] Preferably, in the training samples, the ballistic data are intercepted according to the set maximum prediction duration t max , t max covers all the boost segments, glide segments and part of the dive and press-down segments of each ballistic trajectory, and satisfies t max being less than the ballistic terminal time t end .

[0022] Preferably, in step 1, the ballistic scheme design parameters include the first-stage charge mass m 1 of the solid rocket engine, the second-stage charge mass m 2 of the solid rocket engine, the third-stage charge mass m 3 of the solid rocket engine, the expected altitude at the end of the boost segment the expected ballistic inclination at the end of the boost segment

[0023] Preferably, in step 1, the solution of the ballistic trajectory using the hypersonic boost-glide vehicle ballistic simulation analysis model is as follows:

[0024] Step a: Establish the dynamics model of the boost-glide vehicle as:

[0025]

[0026] Wherein, t is time, v is the speed of the aircraft, Θ is the ballistic inclination angle, ψ is the course angle, r is the distance from the center of the earth, λ is the longitude, φ is the latitude, D and L are the aerodynamic drag and lift, T is the thrust of the solid rocket motor, m is the mass of the aircraft, α is the angle of attack, σ is the bank angle, ω E is the angular velocity of the earth's rotation, g r and g ω are the components of the gravitational acceleration along the direction of the vector from the center of the earth and the direction of the angular velocity of the earth's rotation, respectively;

[0027] According to the mass m 1 of the first-stage charge of the solid rocket motor, the mass m 2 of the second-stage charge of the solid rocket motor, and the mass m 3 of the third-stage charge of the solid rocket motor, calculate the mass m of the aircraft and the thrust T of the solid rocket motor, and substitute them into formula (I);

[0028] Based on the Haversine formula, calculate the range R of the aircraft according to the longitude λ and the latitude φ; subtract the radius r E of the earth from the distance r from the center of the earth as the height H of the aircraft;

[0029] The R, H, v, and Θ at each moment form a flight procedure sequence R output of the height sequence H output of the speed sequence V output and the pitch angle sequence Θ output ;

[0030] Step b. Establish the control equation of the boost-phase trajectory: Based on the pitch program angle divide the boost-phase trajectory into five stages, namely: the vertical takeoff stage t ∈ [0, t 1 , the angle-of-attack turning stage t ∈ (t 1 , t 2 , the gravity-turning stage t ∈ (t 2 ~t 3 , the constant pitch angle flight stage t ∈ (t 3 ~t 4 , and the constant pitch angle rate flight stage t ∈ (t 4 ~t 5 ;

[0031]

[0032] Wherein, t is time, θ(t) is the inclination angle of the aircraft speed, is the pitch angle rate, and α(t) is the angle-of-attack function as shown in formula (III);

[0033]

[0034] Wherein, α mis the maximum negative angle of attack, k is the turning parameter, and π is the ratio of the circumference of a circle to its diameter;

[0035] Step c: Based on formulas (I) to (III), use the Runge-Kutta method to integrate and solve the boost-phase trajectory, and optimize the pitch program angle parameter α based on the Newton iteration method m and such that the terminal height h of the boost-phase trajectory 1 and the flight path angle Θ 1 have the smallest deviation from the expected terminal height and the flight path angle ;

[0036] Step d: Based on the boost-phase trajectory, use the Runge-Kutta method to integrate and solve the glide-phase and dive-down phase trajectories, and obtain the trajectory data of the complete trajectory composed of the boost-phase, glide-phase, and dive-down phase.

[0037] Preferably, in step 1, obtaining multiple trajectory scheme design parameters is as follows: obtaining N sets of trajectory scheme design parameters from the upper and lower bounds of the trajectory scheme design parameter values based on the Latin hypercube sampling method p ;

[0038] Preferably, the method further includes: dividing the training samples into a training set and a test set;

[0039] Using the training set to train the trajectory prediction neural network in this step 2;

[0040] Using the trained trajectory prediction neural network to process the trajectory scheme design parameters in the test set, and outputting the predicted trajectory data; calculating the Euclidean distance between the corresponding moments of the real trajectory data and the predicted trajectory data of the test set as the error, and statistically calculating the maximum error D of each trajectory max ; Judging whether the trajectory prediction accuracy meets the requirements according to the maximum error.

[0041] Advantageous effects:

[0042] (1) A fast prediction method for boost-glide trajectories based on a physics-informed neural network disclosed by the present invention realizes, through training a trajectory prediction neural network, taking trajectory scheme design parameters as inputs and predicting the trajectory height sequence and flight program sequence, providing a scheme for predicting parameter sequences. This scheme can perform trajectory prediction starting from the launch point with trajectory scheme parameters as inputs, without using the "sequence" input and cyclic prediction methods, and there is no cumulative error in trajectory prediction, enabling long-term range prediction. At the same time, from the perspective of overall trajectory design, there is no need to obtain "sequence" inputs through methods such as radar tracking, and a direct prediction process from trajectory design parameters to the entire trajectory sequence is established, with a wider application scenario.

[0043] (2) To improve the accuracy of the parameter prediction sequence scheme, the present invention embeds physical information in the neural network through a custom loss function to improve the prediction accuracy of the ballistic flight program sequence and the altitude sequence. When predicting the flight program sequence, the horizontal velocity component prediction sequence is obtained by differentiating the flight program sequence, and the true horizontal velocity component sequence is obtained by multiplying the velocity by the cosine value of the ballistic inclination angle. The square root of the difference between the horizontal velocity component prediction sequence and the true sequence is used as the physical loss and embedded in the loss function. Similarly, when predicting the altitude, the vertical velocity component prediction sequence is obtained by differentiating the altitude sequence, and the true vertical velocity component sequence is obtained by multiplying the velocity by the sine value of the ballistic inclination angle. The square root of the difference between the vertical velocity component prediction sequence and the true sequence is used as the physical loss and embedded in the loss function.

[0044] (3) When constructing the training samples, since the flight times of the ballistic trajectories in the sample set are different, it is necessary to intercept the data to the same length. Considering that the boost phase contains the input parameters of the ballistic prediction and the ballistic launch point, the glide phase contains the main features of the ballistic shape, and the dive phase often uses guidance and control for terminal maneuvers in engineering practice, the interception starts from the boost phase, so that the true output of each sample covers the entire boost phase, glide phase, and part of the dive phase of each ballistic trajectory.

[0045] (4) A fast prediction method for boost-glide ballistic trajectories based on a physics-informed neural network disclosed by the present invention uses a deep neural network to fit the boost-glide ballistic trajectory simulation analysis model, avoiding the repeated iterative solution of the boost phase control parameters that meet the constraints using the Newton iteration method and the high time consumption of integrating the ballistic trajectory using the Runge-Kutta method, saving the time cost of ballistic trajectory simulation analysis, and being able to efficiently process the prediction of a large number of ballistic trajectories' ranges and altitudes. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the schematic diagram of the principle of the present invention;

[0047] Figure 2 is the flow chart of the boost-glide ballistic trajectory prediction based on a physics-informed neural network;

[0048] Figure 3 is the schematic diagram of the ballistic trajectory of a hypersonic boost-glide vehicle;

[0049] Figure 4 is the pitch program angle-time graph of the boost phase;

[0050] Figure 5 is the angle of attack-velocity curve graph of the glide phase;

[0051] Figure 6 is the structural diagram of the ballistic trajectory prediction neural network;

[0052] Figure 7It is a comparison diagram of the predicted trajectory and the true trajectory;

[0053] Figure 8 It is a distribution diagram of the ballistic prediction error. Specific implementation manner

[0054] The present invention will be described in detail below in conjunction with the accompanying drawings and by way of examples.

[0055] In order to solve the problems existing in the existing methods for solving the trajectory of hypersonic boost-glide vehicles, such as the complex iteration of active section control parameters and the high time consumption of dynamic integration, the present invention provides a boost-glide trajectory prediction method based on a physics-informed neural network. Its basic principle is as Figure 1 shown, and it includes the following main steps:

[0056] Step 1: Obtain multiple ballistic scheme design parameters; use the hypersonic boost-glide vehicle trajectory simulation analysis model to solve the trajectory, and obtain the trajectory data corresponding to each set of ballistic scheme design parameters, including the flight program sequence R output , altitude sequence H output , speed sequence V output , and ballistic inclination angle sequence Θ output ; the ballistic scheme design parameters and the trajectory data form the training samples;

[0057] Step 2: Use the training samples to train the ballistic prediction neural network; the input of the ballistic prediction neural network structure is the ballistic scheme design parameters, and the output is the ballistic flight program sequence and altitude sequence; during training, the speed sequence V output and the ballistic inclination angle sequence Θ output in the training samples are used to calculate the loss function;

[0058] Step 3: Use the trained ballistic prediction neural network to predict the flight program sequence and altitude sequence in the boost-glide trajectory.

[0059] It can be seen that this method uses a neural network as the prediction model, and realizes the prediction of the ballistic altitude sequence and flight program sequence with the ballistic scheme design parameters as the input by training the neural network. It provides a scheme of "parameters" predicting "sequences". Compared with the scheme of "sequences" predicting "sequences", the present invention does not adopt the method of "sequence" input and cyclic prediction, and there is no cumulative error in ballistic prediction, and long-term range prediction can be carried out; at the same time, starting from the overall ballistic design perspective, the present invention does not need to obtain "sequence" input through methods such as radar tracking, and establishes a direct prediction process from ballistic design parameters to the whole-course ballistic sequence, with a wider application scenario. Therefore, the present invention can be applied to the overall ballistic design process, thereby greatly reducing the calculation time cost of hypersonic boost-glide trajectories and improving the design efficiency of hypersonic boost-glide ballistic schemes.

[0060] To make up for the missing timing of the parameters as outputs, the present invention further embeds physical information in the loss function of the deep neural network. Through the further constraint and guidance of the physical information, the generalization ability of the deep neural network is improved, so as to accurately fit the boost-glide trajectory simulation analysis model, thus alleviating the problem of high time consumption in the large-scale calculation of the trajectory scheme.

[0061] In the present invention, the outputs of the trajectory prediction only include the flight program sequence and altitude sequence of the boost phase, glide phase and part of the dive and press-down phase.

[0062] Figure 2 Shows a complete implementation process of the boost-glide trajectory rapid prediction method based on the physical information neural network of the present invention. The method of the present invention constructs the dynamics, kinematics equations and trajectory models of the aircraft including the boost phase, glide phase and dive and press-down phase; Latin hypercube samples several groups of trajectory scheme design parameters, and solves the trajectory data based on the Newton iteration method and numerical integration method; constructs a trajectory prediction network based on the neural network, and uses the obtained trajectory data to train and verify the prediction accuracy of the trajectory prediction network.

[0063] See Figure 2 , the specific implementation steps of this scheme are as follows:

[0064] Step A: Determine the relevant parameters of the hypersonic boost-glide vehicle, and design the trajectory scheme design parameters and their value ranges.

[0065] The relevant parameters of the hypersonic boost-glide vehicle include the initial velocity of v 0 , the initial ballistic inclination angle of Θ 0 , the initial heading angle of ψ 0 , the initial longitude and latitude are λ 0 , φ 0 , the initial geocentric distance is r 0 , the initial range and initial altitude are x 0 , y 0 ; the initial time is t 0 , the terminal time is t end ; the working time of the first stage of the solid rocket engine is t gr1 , the working time of the second stage is t gr2 , the working time of the third stage is t gr3 .

[0066] The trajectory scheme design parameters are designed as including the first-stage charge mass m of the solid rocket engine 1 , the second-stage charge mass m of the solid rocket engine 2 , the third-stage charge mass m of the solid rocket engine 3 , the expected altitude at the end of the boost-phase trajectory Desired Ballistic Inclination at the Terminal of the Boost Phase Its dimension is The upper and lower bounds of the value are

[0067] In this embodiment, the initial velocity of the hypersonic boost-glide vehicle is determined to be v 0 = 0.01 m / s, the initial ballistic inclination is Θ 0 = 90°, the initial heading angle is ψ 0 = 90°, the initial longitude and latitude are λ 0 = 100°, φ 0 = 40°, the initial geocentric distance is r 0 = 6378637 m, the initial range and initial altitude are x 0 = 0 m, y 0 = 500 m; the initial time is t 0 = 0 s, the terminal time is t end ; the working time of the first stage of the solid rocket engine is t gr1 = 65 s, the working time of the second stage is t gr2 = 55 s, the working time of the third stage is t gr3 = 40 s. Ballistic scheme design parameters The dimension is The upper and lower bounds of the value are where m UB1 = 24000 kg, m UB2 = 13000 kg, m UB3 = 6000 kg, m LB1 = 22000 kg, m LB2 = 11000 kg, m LB3 = 4500 kg,

[0068] Step B: Establish a ballistic simulation analysis model for the hypersonic boost-glide vehicle and solve the trajectory based on the Newton iteration method and the Runge-Kutta integration method. Determine the time step of the Runge-Kutta method to be t step = 0.1 s. The schematic diagram of the hypersonic boost-glide vehicle trajectory is as shown in Figure 3 shown.

[0069] The implementation method of Step B is as follows:

[0070] Step B-1: Establish a dynamics model of the boost-glide vehicle, as shown in formula (1). In the present invention, considering the earth as a rotating ellipsoid and the vehicle having no sideslip angle, a longitudinal plane dynamics equation set of the boost-glide vehicle is established, as shown in formula (1).

[0071]

[0072] In the formula, \(t\) is time, \(v\) is the vehicle velocity, \(\Theta\) is the ballistic inclination angle, \(\psi\) is the course angle, \(r\) is the geocentric distance, \(\lambda\) is the longitude, \(\varphi\) is the latitude, \(D\) and \(L\) are the aerodynamic drag and lift, \(T\) is the solid rocket motor thrust, \(m\) is the vehicle mass, \(\alpha\) is the angle of attack, \(\sigma\) is the bank angle, \(\omega\) E = 7.292115×10 -5 rad / s is the angular velocity of the Earth's rotation, \(g\) r and \(g\) ω are the components of the gravitational acceleration along the geocentric vector direction and the angular velocity direction of the Earth's rotation, respectively. In addition, based on the Haversine formula, the vehicle range \(R\) is obtained with \(\lambda\) and \(\varphi\) as inputs; the vehicle altitude \(H\) is taken as the geocentric distance \(r\) minus the Earth's radius \(r\) E = 6378 km; the vehicle mass \(m\) and the solid rocket motor thrust \(T\) are related to the mass \(m\) 1 of the first-stage charge of the solid rocket motor, the mass \(m\) 2 of the second-stage charge of the solid rocket motor, and the mass \(m\) 3 of the third-stage charge of the solid rocket motor, and can be calculated using existing technologies, i.e., \([m, T]=f(m\) 1 , \(m\) 2 , \(m\) 3 , \(t)\). This functional relationship \(f\) varies for different vehicles, and the calculation scheme can be referred to in Document 1 (Zhai Yiyun, Long Teng, Liu Zhenyu, et al. Multi-objective approximate optimization of the ballistic scheme of boost-glide variant vehicles [J]. Aerospace Shanghai, 2024, 41(3): 110-20.). The \(R\), \(H\), \(v\), and \(\Theta\) at each moment form the flight program sequences \(R\) output , the altitude sequence \(H\) output , the velocity sequence \(V\) output and the pitch angle sequence \(\Theta\) output .

[0073] Step B-2: Establish the control equations for the boost-phase trajectory.

[0074] For the boost-phase trajectory, the three-stage solid rocket motor ignites sequentially, and the pitch program angle control is adopted to make the boost-phase trajectory meet the terminal expected altitude and the local velocity inclination angle. Based on the pitch program angle, the boost-phase trajectory is divided into five stages, namely: the vertical takeoff stage \(t\in[0, t\) 1 , the angle-of-attack turning stage \(t\in(t\) 1 , \(t\) 2 , the gravity-turning stage \(t\in(t\) 2 ~\(t\) 3 , the constant pitch angle flight stage \(t\in(t\) 3 ~\(t\) 4 , and the constant pitch angle rate flight stage \(t\in(t\) 4 ~\(t\) 5; In this embodiment, t 1 = 5 s, t 2 = 25 s, t 3 = 110 s, t 4 = 122 s, t 5 = 160 s. The pitch program angle design scheme is shown in Equation (2).

[0075]

[0076] In the formula, t is time, is the pitch program angle, θ(t) is the vehicle speed inclination angle, is the pitch angle rate, and α(t) is the angle of attack function shown in Equation (3).

[0077]

[0078] In the formula, α m is the maximum negative angle of attack, k = 0.5 is the turning parameter, and π is the pi. The pitch program angle - time graph is as Figure 4 shown.

[0079] Step B - 3: Based on Formulas (1) to (3), use the Runge - Kutta method to integrate and solve the boost - phase trajectory, and optimize the pitch program angle parameters α m and to make the terminal altitude h 1 and the trajectory inclination Θ 1 of the boost - phase trajectory have the minimum deviation from the expected terminal altitude and the trajectory inclination . The optimization problem model is shown in Equation (4).

[0080]

[0081] In the formula, α m,min = 0° and α m,max = 25° are the lower and upper bounds of the value of α m , and are the lower and upper bounds of the value of .

[0082] Step B - 4: Based on the boost - phase trajectory, use the Runge - Kutta method to integrate and solve the glide - phase and dive - down - pressure - phase trajectories.

[0083] The hypersonic vehicle mainly realizes flight control through the angle of attack and bank angle in the glide - phase. In this invention, for the trajectory in the longitudinal plane, the bank angle is set to be constantly 0°. The angle of attack is set as a two - stage profile function that changes with speed. When in the high - altitude re - entry glide phase, the vehicle has a large angle of attack α g1Fly at 19°. When the aircraft speed decreases to the end speed v of high-altitude reentry gliding, gα1 which is below 4000 m / s, the angle of attack decreases linearly. When the speed decreases to the start speed v of low-altitude reentry gliding, gα2 which is 3400 m / s, the aircraft maintains a constant value α g2 of 12° until the end of the reentry gliding section. During the dive and press-down section, the aircraft reenters to the ground with a zero angle of attack. The angle-of-attack vs. speed curve in the gliding section is as shown in Figure 5 Figure.

[0084] Step C: Based on the Latin hypercube sampling method, obtain N p = 200 sets of ballistic design parameters within the upper and lower bounds of the ballistic design parameter values determined in Step A; solve the corresponding ballistic data according to the model and method mentioned in Step B, including the flight path sequence R output , altitude sequence H output , speed sequence V output , and ballistic inclination angle sequence Θ output . Save the ballistic design parameters and ballistic data as a sample set. Among them, the flight path sequence R output and altitude sequence H output are used as the true outputs of the ballistic prediction neural network of the present invention, and the speed sequence V output and ballistic inclination angle sequence Θ output are used for loss calculation.

[0085] Step D: Preprocess the data in the sample set.

[0086] In this embodiment, the preprocessing includes data truncation, data normalization, and data partitioning.

[0087] The implementation method of Step D is as follows:

[0088] Step D-1: Since the flight times of each ballistic in the sample set are different, it is necessary to set the maximum prediction duration t max , and truncate each set of ballistic data to ensure that the dimension of the ballistic data is t max which should cover the entire boost section, gliding section, and part of the dive and press-down section of each ballistic, and satisfy t max < t end .

[0089] In this embodiment, t max = 1824.1 s,

[0090] Step D-2: Randomly select N p sets from the N train sets of inputs and outputs as the training set, and the remaining sets of data as the test set.

[0091] In this embodiment, N train = 180, N test = N P - N train = 20.

[0092] Step D-3: Normalize the ballistic scheme design parameters in the training set as shown in Equation (5) to obtain as the input for neural network training.

[0093]

[0094] where x LB and x UB are the minimum and maximum values of x input respectively.

[0095] Step D-4: Use the min-max normalization method to normalize the range R output , altitude H output , velocity V output , and ballistic inclination angle Θ output in the ballistic data in the training set respectively, and obtain the normalized range altitude velocity ballistic inclination angle as the output of neural network training; as physical information for calculating the loss of network training.

[0096] Step E: Determine the structure of the ballistic prediction neural network and determine the network training parameters.

[0097] In this embodiment, the designed ballistic prediction neural network adopts a deep neural network model and embeds physical information in the loss function. The network structure includes an input layer, multiple hidden layers, and an output layer, aiming to effectively process the prediction of boost-glide trajectories. The structure diagram of the ballistic prediction neural network is as shown in Figure 6 shown.

[0098] The implementation method of Step E is as follows:

[0099] Step E-1: Determine that the input layer of the network is a feature input layer, which receives the normalized ballistic scheme design parameters as the network input. The size of the input layer (i.e., the number of features) is equal to the dimension of the ballistic scheme design parameters

[0100] Step E-2: Determine that the hidden layer of the network has 5 layers, and each hidden layer contains 1 fully connected layer, 1 ReLU activation function layer, and 1 dropout layer to improve the generalization ability of the network and reduce overfitting. In this embodiment, determine that the number of neurons in the 5 fully connected layers are fc 1 = 3200, fc 2 = 8000, fc 3 = 6400, fc 4 = 6400, and fc 5 = 3200, and the dropout ratios of the dropout layers are dp 1 = 0.2, dp 2 = 0.2, dp 3 = 0.1, dp 4 = 0.1, and dp 5 = 0.1.

[0101] Step E-3: Determine that the output layer of the network is 1 fully connected layer to output the prediction result. In this embodiment, the size of the output layer is equal to the dimension of the ballistic output data

[0102] Step E-4: Determine the custom neural network loss function. The loss ε consists of two parts, including the root mean square error ε pred between the network predicted output and the true output and the network error ε pys calculated based on physical information, as shown in Equation (6).

[0103] ε = ω 1 ε pred + ω 2 ε pys (6)

[0104] In the formula, ω 1 and ω 2 are weight coefficients. Preferably, ω 1 = 0.67 and ω 2 = 0.33.

[0105] Step E-5: Determine that the network parameter optimization function is Adaptive Moment Estimation (Adam), determine that the maximum number of training epochs of the network is E max , the initial learning rate is LR init , the learning rate decay period is E step , and the learning rate decay coefficient is F drop .

[0106] In this embodiment, determine that the maximum number of training epochs of the network is E max = 2000, and the initial learning rate is LR init= 0.001, the learning rate decay period is E step = 400, the learning rate decay coefficient is F drop = 0.5.

[0107] Step F: Train the ballistic range and altitude prediction neural networks respectively.

[0108] The implementation method of Step F is as follows:

[0109] Step F-1: Use the normalized ballistic scheme design parameters in the training set as the training input, and the range as the training output to train the ballistic prediction neural network net 1 , and obtain the ballistic range prediction value Among them, the network error ε based on physical information pys1 is calculated as shown in Equation (7). For , the differential derivative is used to obtain the predicted sequence of the horizontal velocity component. The product of the velocity and the cosine value of the ballistic inclination is used to obtain the true sequence of the horizontal velocity component. The square root of the difference between the predicted sequence and the true sequence of the horizontal velocity component is used as the physical loss to embed in the loss function.

[0110]

[0111] Among them, is the velocity sequence data after normalization processing, is the ballistic inclination sequence data after normalization processing; is the predicted value of the ballistic range sequence; the above formula represents the sum after calculating the data at the corresponding moments in the sequence;

[0112] Step F-2: Use the normalized ballistic scheme design parameters in the training set as the training input, and the altitude as the training output to train the ballistic prediction neural network net 2 , and obtain the ballistic altitude prediction value Among them, the network error ε based on physical information pys2 is calculated as shown in Equation (8). For , the differential derivative is used to obtain the predicted sequence of the vertical velocity component. The product of the velocity and the sine value of the ballistic inclination is used to obtain the true sequence of the vertical velocity component. The square root of the difference between the predicted sequence and the true sequence of the vertical velocity component is used as the physical loss to embed in the loss function.

[0113]

[0114] Among them, ​​is the velocity sequence data after normalization processing, is the ballistic inclination angle sequence data after normalization processing; is the predicted value of the ballistic height sequence; the above formula represents the sum after calculating the data at the corresponding time in the sequence.

[0115] Step G: Establish a rapid prediction process for hypersonic boost-glide trajectories with ballistic design parameters as inputs and ballistic height and flight program sequences as outputs, and perform ballistic prediction and verify the error based on the test set data.

[0116] The implementation method of Step G is as follows:

[0117] Step G-1: Perform the normalization processing on the ballistic design parameters x input in the test set as shown in Equation (6) to obtain as the prediction input.

[0118] Step G-2: Based on the well-trained ballistic prediction neural networks net 1 and net 2 in Step F, obtain the predicted values of the ballistic range and height

[0119] Step G-3: Perform the inverse normalization on to obtain R pred and H pred .

[0120] Step G-4: Calculate the Euclidean distance D at each corresponding time between the true ballistic P true =[R output ,H output and the predicted ballistic P pred =[R pred ,H pred as the error, and statistically calculate the maximum error D max of each ballistic trajectory.

[0121] It also includes Step H: Judge whether the ballistic prediction accuracy meets the engineering requirements according to the results of Step G-4.

[0122] Finally, obtain the ballistic prediction neural networks net 1 and net 2 that meet the engineering requirements. In actual use, input the ballistic design parameters into the neural network, and the predicted results of the flight program sequence and height sequence of the ballistic trajectory can be obtained.

[0123] To better demonstrate the effectiveness and engineering practicability of the present invention, the following takes the ballistic prediction problem of hypersonic boost-glide vehicles as an example, and further illustrates the present invention in combination with the attached drawings and tables.

[0124] In this case, the ballistic design parameters The value of is: m 1 ∈ [22000 kg, 24000 kg 2 ∈ [11000 kg, 13000 kg], m 3 ∈ [4500 kg, 6000 kg], Based on the trained ballistic prediction neural network, taking the ballistic scheme design parameters in the test set as the input, the ballistic height and flight program sequence are output to obtain the predicted ballistic. The comparison between the predicted ballistic and the real ballistic is as Figure 7 shown; the predicted ballistic is smooth, and the changes in each stage of the ballistic are basically the same as those of the real ballistic. The maximum value, average value and minimum value of the prediction error of each ballistic are shown in Table 1, and the error distribution is as Figure 8 shown; it meets the accuracy requirements of engineering applications. Calculate the average time taken to solve the ballistic through the ballistic simulation analysis model and to predict the ballistic through the ballistic prediction process, as shown in Table 2; the method proposed in the present invention has a significant improvement in efficiency and is applicable to the rapid prediction of a large number of ballistics.

[0125] Table 1 Maximum value, average value and minimum value of the prediction error of each ballistic

[0126]

[0127] Table 2 Comparison of ballistic solution time consumption

[0128]

[0129] The above ballistic prediction results show that the present invention can quickly predict the flight range and height sequence of the ballistic based on the ballistic prediction neural network with a small computational cost, achieving the expected invention purpose and verifying the rationality, effectiveness and engineering practicability of the present invention.

[0130] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in this description can be different and are not limited. Therefore, those skilled in the art of the present invention can modify or equivalently replace the technical solutions recorded in the foregoing embodiments; and these modifications and replacements do not depart from the spirit and technical solutions of the present invention and should all fall within the protection scope of the present invention.

Claims

1. A boost-glide trajectory prediction method based on physical information neural network, characterized in that: include: Step 1: Obtain multiple sets of trajectory design parameters; The trajectory simulation analysis model of the hypersonic boost-glide vehicle is used to solve the trajectory and obtain the trajectory data corresponding to each set of trajectory design parameters, including the flight sequence R output , height sequence H output , speed sequence V output 、Ballistic inclination sequence Θ output ;Trajectory design parameters and trajectory data constitute training samples; Step 2: Use the training samples to train the trajectory prediction neural network; the input of the trajectory prediction neural network structure is the trajectory design parameters, and the output is the predicted trajectory course sequence and height sequence; during training, the velocity sequence V in the training sample output and the ballistic inclination sequence Θ output Used as physical information for loss calculation; Step 3: Use the trained trajectory prediction neural network to predict the flight sequence and altitude sequence of the boost-glide trajectory.

2. The method according to claim 1, characterized in that In step 2, the trajectory prediction neural network includes a first trajectory prediction neural network net1 for predicting the flight sequence and a second trajectory prediction neural network net2 for predicting the height sequence; The first trajectory predicts that the loss of the neural network net1 consists of two parts, including the root mean square error between the network prediction output and the true output and the network error ε calculated based on physical information pys1 : in, is the speed series data after normalization, is the normalized trajectory inclination angle series data; is the predicted value of the ballistic flight sequence; the above formula represents the sum of the corresponding time data in the sequence after calculation; The second trajectory indicates that the loss of the neural network net2 consists of two parts, including the root mean square error between the network prediction output and the true output and the network error ε calculated based on physical information pys2 : in, is the speed series data after normalization, is the normalized trajectory inclination angle series data; is the predicted value of the trajectory height sequence; the above formula represents the calculation and summation of the data at corresponding moments in the sequence.

3. The method according to claim 2, characterized in that The first trajectory prediction neural network net1 and the second trajectory prediction neural network net2 for predicting height sequence have the same structure, both including an input layer, multiple hidden layers and an output layer; the hidden layers are 5 layers, each of which includes 1 fully connected layer, 1 ReLU activation function layer and 1 temporary dropout layer Dropout.

4. The method according to claim 3, characterized in that Among the five hidden layers, the number of neurons in the fully connected layer is fc1=3200, fc2=8000, fc3=6400, fc4=6400 and fc5=3200 respectively, and the dropout ratios of the temporary dropout layer are dp1=0.2, dp2=0.2, dp3=0.1, dp4=0.1 and dp5=0.1 respectively.

5. The method according to claim 1, characterized in that The root mean square error and network error in the loss are weighted to obtain the loss value; the weighting coefficient of the root mean square error is 0.67, and the weighting coefficient of the network error is 0.

33.

6. The method according to claim 1, characterized in that The trajectory data in the training sample is based on the set maximum prediction time t max To intercept, t max Covering all boost phases, gliding phases and part of the dive phases of each trajectory, and satisfying t max Less than the ballistic terminal time t end .

7. The method according to claim 1, characterized in that In step 1, the trajectory design parameters include the mass of the solid rocket motor first stage charge m1, the mass of the solid rocket motor second stage charge m2, the mass of the solid rocket motor third stage charge m3, the expected height of the booster stage trajectory terminal Expected trajectory inclination at the end of the boost phase 8. The method according to claim 7, characterized in that In step 1, the trajectory is solved by using the hypersonic boost-glide vehicle trajectory simulation analysis model as follows: Step a: Establish the boost-glide vehicle dynamics model as follows: Where t is time, v is the speed of the aircraft, θ is the ballistic inclination angle, ψ is the heading angle, r is the distance from the center of the earth, λ is the longitude, φ is the latitude, D and L are the aerodynamic drag and lift, T is the thrust of the solid rocket engine, m is the mass of the aircraft, α is the angle of attack, σ is the tilt angle, ω is E is the angular velocity of the Earth's rotation, g r and g ω They are the components of gravitational acceleration along the direction of the geocentric vector and the direction of the earth's rotation angular velocity respectively; Calculate the vehicle mass m and the solid rocket engine thrust T according to the solid rocket engine first-stage charge mass m1, the solid rocket engine second-stage charge mass m2, and the solid rocket engine third-stage charge mass m3, and substitute them into formula (I); Based on the Haversine formula, the aircraft range R is calculated based on the longitude λ and latitude φ; the distance from the center of the earth r minus the radius of the earth r E As the aircraft height H; R, H, v and θ at each moment constitute the flight sequence R output , height sequence H output , speed sequence V output and the pitch angle sequence Θ output ; Step b: Establish the control equation of the boost phase trajectory: Based on the pitch program angle The boost phase trajectory is divided into five stages: vertical take-off stage t∈[0,t1], angle of attack turning stage t∈(t1,t2], gravity turning stage t∈(t2~t3], constant pitch angle flight stage t∈(t3~t4] and constant pitch angle rate flight stage t∈(t4~t5]; Where t is time, θ(t) is the velocity angle of the aircraft, is the pitch angle rate, α(t) is the angle of attack function as shown in formula (III); In the formula, α m is the maximum negative angle of attack, k is the turning parameter, and π is the circumference of a circle; Step c: Based on formulas (I) to (III), the boost phase trajectory is solved by using the Runge-Kutta method, and the pitch program angle parameter α is optimized based on the Newton iteration method. m and Make the boost phase trajectory terminal height h1, trajectory inclination angle θ1 and the desired terminal height Ballistic inclination Minimal deviation; Step d: Based on the boost stage trajectory, the Runge-Kutta method is used to integrally solve the gliding stage and the diving stage trajectory to obtain the trajectory data of the complete trajectory consisting of the boost stage, the gliding stage, and the diving stage.

9. The method according to claim 1, characterized in that In step 1, multiple trajectory design parameters are obtained as follows: N is obtained from the upper and lower bounds of trajectory design parameters based on the Latin hypercube sampling method. p Set of ballistic design parameters.

10. The method according to claim 1, characterized in that The method further includes: dividing the training samples into a training set and a test set; The trajectory prediction neural network training of step 2 is performed using the training set; The trajectory prediction neural network trained is used to process the trajectory design parameters in the test set and output the predicted trajectory data. The Euclidean distance between the real trajectory data and the predicted trajectory data of the test set is calculated as the error, and the maximum error D of each trajectory is calculated. max ; Determine whether the trajectory prediction accuracy meets the requirements based on the maximum error.

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