A multi-stage synchronous induction coil gun projectile outlet velocity prediction method and system

Abstract

The application discloses a kind of multistage synchronous induction coil cannon projectile outlet velocity prediction method and system, method includes: obtaining multistage synchronous induction coil cannon parameter sample set, and it is divided into training set and test set;Establish RNN model, input training set into RNN model and train, then test set is applied to the RNN model after training is completed and test, according to the evaluation index evaluation RNN model's prediction ability;If the prediction ability of RNN model meets the standard, then apply the RNN model after test to predict, otherwise, then using PSO optimization recurrent neural network model RNN is applied training set again training, select the hyperparameter of RNN, establish PSO-RNN model;Input test set to PSO-RNN model and test, according to the evaluation index evaluation PSO-RNN model's prediction ability, until the prediction ability meets the requirement, the optimal hyperparameter is brought into RNN model, obtains the best PSO-RNN model;Emitter parameter is input into the best PSO-RNN model, obtains the outlet velocity of projectile under current parameter, the present application can improve prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic launch technology, specifically to a method and system for predicting the exit velocity of projectiles using multi-stage synchronous induction coils. Background Technology

[0002] Synchronous induction coil guns are one of the important methods of electromagnetic launch. Their operation is as follows: After the energy storage capacitor is fully charged, a trigger discharge switch is activated according to a specific trigger control strategy, discharging the drive coil and generating a pulsed current, which in turn generates a pulsed magnetic field around the coil. According to the law of electromagnetic induction, the changing magnetic field induces eddy currents inside the launcher. These eddy currents interact with the radial component of the coil's magnetic field, generating an axial electromagnetic force that acts on the launcher, causing it to undergo variable acceleration.

[0003] The dynamic characteristics of synchronous induction coil guns are typically closely related to timing, including changes in the current and magnetic field of each driving coil stage, the projectile's motion, and the triggering time. Furthermore, the system parameters exhibit strong nonlinear characteristics. Currently, projectile exit velocity prediction for synchronous induction coil guns primarily relies on numerical analysis and finite element modeling. Both methods generally suffer from problems such as complex multi-physics coupling in modeling, long iterative calculation times, and low accuracy in exit velocity prediction due to system nonlinearity. Moreover, as the number of stages increases, the number of input parameters increases, the projectile velocity increases, and the triggering time of the coil becomes increasingly difficult to control accurately. Traditional methods require repeated, extensive iterative calculations, resulting in low computational efficiency. Furthermore, ensuring accurate exit velocity prediction places even higher demands on hardware. Therefore, a more efficient method is needed for modeling and predicting the exit velocity of the coil gun.

[0004] RNN neural networks excel at processing time-series data, capturing the nonlinear relationship between system inputs and outputs at different times. Moreover, RNN models do not rely on mathematical relationships but instead express the transmission relationship by analyzing and fitting the input and output to establish a "black box" model. Especially when dealing with multi-stage synchronous induction coil guns with many input parameters and complex coupling relationships, they can effectively improve computational efficiency, reduce hardware requirements, and achieve fast and accurate exit velocity prediction.

[0005] Furthermore, due to the large number of input and output parameters in a coilgun system and the highly nonlinear relationship between them, RNNs may experience poor prediction accuracy and instability during training. Therefore, it is necessary to introduce optimization algorithms to optimize the hyperparameters of the RNN model (the number of neurons in each layer and the regularization coefficient) to improve the prediction accuracy of the nonparametric model of a multi-stage synchronous induction coilgun. Thus, there is an urgent need for a method that can quickly and accurately model and predict the exit velocity of a multi-stage synchronous induction coilgun system. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the issues of low accuracy in predicting the exit velocity of projectiles using multi-stage synchronous induction coils and long modeling iteration times.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] A method for predicting the exit velocity of projectiles using multi-stage synchronous induction coils, comprising:

[0009] Obtain the parameter sample set of the multi-stage synchronous induction coil gun and divide it into training set and test set;

[0010] Build an RNN model, input the training set data into the RNN model for training, then use the test set to test the trained RNN model, and evaluate the predictive ability of the RNN model according to the evaluation metrics.

[0011] If the predictive ability of the RNN model meets the standard, the tested RNN model is used for prediction; otherwise, the PSO-optimized recurrent neural network model RNN is used, and the training set is used again for training to select the hyperparameters of the RNN and establish the PSO-RNN model.

[0012] The PSO-RNN model is tested using the input test set. The predictive ability of the PSO-RNN model is evaluated according to the evaluation metrics until the predictive ability meets the requirements. The optimal hyperparameters are then input into the RNN model to obtain the best PSO-RNN model.

[0013] Input the launcher parameters into the optimal PSO-RNN model to obtain the projectile's exit velocity under the current parameters.

[0014] In one embodiment of the present invention, the parameter sample set of the multi-stage synchronous induction coil gun is obtained by finite element simulation through orthogonal experiment combined with random experimental design.

[0015] In one embodiment of the present invention, each sample in the multi-stage synchronous induction coil gun parameter sample set takes the number of turns of each stage of the driving coil, the projectile triggering position, and the triggering time of each stage of the driving coil as input, and the projectile exit velocity as output.

[0016] In one embodiment of the present invention, evaluating the predictive ability of an RNN model based on an evaluation metric includes:

[0017] S1, Determine the structure of the RNN model: Initialize the various parameters of the RNN, including the input weights W. x Hidden state weight W h Output weight W y Input bias b x Hidden bias b h Output bias b y1. Initial hidden state h0, regularization parameters; 2. Determine the activation function of the hidden layer and the number of hidden layers;

[0018] S2, Input the training set and train the RNN model;

[0019] S3, Input the test set to test the RNN model, calculate the evaluation index and the percentage error between the predicted and simulated exit speed values;

[0020] S4. If the exit speed error percentage is less than 5%, the number of turns of each stage of the drive coil, the trigger position of the projectile, and the trigger time of each stage of the drive coil are directly input into the qualified RNN model to predict the exit speed of the projectile. If the exit speed error percentage is greater than 5%, the PSO algorithm is used to optimize the hyperparameters of the RNN model.

[0021] In one embodiment of the present invention, establishing a PSO-RNN model includes:

[0022] S10, Establish the correspondence between the PSO particle swarm algorithm and the hyperparameters of the RNN model;

[0023] S20, initialize the PSO algorithm, including population size, inertia weight, learning factor, maximum number of iterations, initial position and initial velocity of particles;

[0024] S30, using the root mean square error (RMSE) of the RNN model as the fitness function, calculate the particle fitness value;

[0025] S40, update particle position and velocity;

[0026] S50 is used to train the model using the training set. The optimized hyperparameters are then input into the RNN model to obtain the PSO-RNN model.

[0027] In one embodiment of the present invention, establishing the correspondence between the PSO particle swarm optimization algorithm and the hyperparameters of the RNN model includes:

[0028] The hyperparameters of the RNN model are mapped to the positions and velocities of particles in the particle swarm optimization algorithm. The hyperparameters of the RNN model include the number of neurons in each hidden layer and the regularization coefficient.

[0029] In one embodiment of the present invention, the particle fitness value is calculated using the following formula:

[0030]

[0031] In the formula, RMSE is the root mean square error, n is the sample size, and S is the mean square error. i and P i These are the simulated value and the predicted value of the i-th sample, respectively.

[0032] In one embodiment of the present invention, the particle position and velocity are updated using the following formula:

[0033] v id (t+1)=wv id (t)+c1r1(p id -x id )+c2r2(g d -x id );

[0034] x id (t+1)=x id (t)+v id (t+1);

[0035] In the formula, v id (t+1) and x id (t+1) represent the velocity and position of the i-th particle in the d-dimensional space at the (t+1)-th iteration; p id For the optimal position in the history of an individual particle, g d The global optimal position is represented by c1 and c2, which are two learning factors. r1 and r2 are random numbers uniformly distributed within the interval [0,1], and w is the inertia weight.

[0036] In one embodiment of the present invention, obtaining the optimal PSO-RNN model includes:

[0037] S60, Input the test set into the trained PSO-RNN model to obtain the prediction results of the test set; Calculate the evaluation index and error percentage based on the prediction results of the test set to determine whether the iteration has reached the termination condition.

[0038] If the termination condition is not met in S70, continue iterating from S30 to S60; if the termination condition is met, the final optimal hyperparameters are obtained. The optimal hyperparameters are then substituted into the RNN model to obtain the best PSO-RNN model.

[0039] This invention also proposes a multi-stage synchronous induction coil projectile exit velocity prediction system, which applies the above-described multi-stage synchronous induction coil projectile exit velocity prediction method, including:

[0040] The sample set module is used to acquire the parameter sample set of the multi-stage synchronous induction coil gun and divide it into a training set and a test set.

[0041] The RNN model module is used to build RNN models. It inputs training data into the RNN model for training, then uses the test set to test the trained RNN model, and evaluates the predictive ability of the RNN model based on evaluation metrics.

[0042] The initial PSO-RNN model module is used to determine whether the prediction ability of the RNN model meets the standard. If so, the tested RNN model is used for prediction. Otherwise, the PSO-optimized recurrent neural network model RNN is used, and the training set is applied again to select the optimal hyperparameters of the RNN and establish the PSO-RNN model.

[0043] The optimal PSO-RNN model module is used to test the PSO-RNN model by inputting a test set, evaluate the predictive ability of the PSO-RNN model according to the evaluation metrics, and continue until the predictive ability meets the requirements. Then, the optimal hyperparameters are input into the RNN model to obtain the optimal PSO-RNN model.

[0044] The prediction module is used to input the launcher parameters into the optimal PSO-RNN model to obtain the projectile's exit velocity under the current parameters.

[0045] Compared with existing technologies, the advantages of this invention are as follows: This invention solves the problems of multi-physics coupling, long iterative calculation time, and low accuracy of exit velocity prediction due to nonlinearity between system parameters in traditional synchronous induction coil gun modeling methods, achieving rapid prediction of exit velocity. The PSO algorithm addresses the problems of poor prediction accuracy and instability caused by nonlinearity between synchronous induction coil gun system parameters in the RNN algorithm, achieving accurate prediction of exit velocity. In summary, this invention can accurately predict the projectile exit velocity based on various parameters of the coil gun, providing accurate guidance for the parameter design of coil gun prototypes in engineering applications.

[0046] This invention employs a two-step parameter tuning and optimization method for RNN models. In the first stage, the RNN model is trained, and an evaluation metric is used to determine if the prediction error meets requirements. If it does, no second-stage parameter fine-tuning is needed. If not, the RNN model undergoes a second-stage parameter fine-tuning process. This second stage is based on the first-stage RNN model parameter optimization, and the PSO algorithm is applied to further fine-tune the RNN model's parameters. Compared to the current mainstream approach of directly building a prediction model combining at least two algorithms and then using a sample set for training and parameter optimization, this invention can improve computational efficiency or reduce computation time. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating a method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil, according to an embodiment of the present invention.

[0048] Figure 2 This is a comparison chart of the predicted output values ​​and simulated values ​​of the traditional RNN neural network and the PSO-RNN neural network in an embodiment of the present invention.

[0049] Figure 3This is a schematic diagram illustrating the error between the predicted output values ​​and simulated values ​​of the traditional RNN neural network and the PSO-RNN neural network in an embodiment of the present invention.

[0050] Figure 4 This is a block diagram of a multi-stage synchronous induction coil projectile exit velocity prediction system according to an embodiment of the present invention. Detailed Implementation

[0051] To facilitate understanding of the technical solution of the present invention by those skilled in the art, the technical solution of the present invention will now be further described in conjunction with the accompanying drawings.

[0052] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0053] Please see Figure 1 As shown, this invention provides a method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil, comprising:

[0054] S100 acquires the parameter sample set of the multi-stage synchronous induction coil gun and divides it into training set and test set.

[0055] In one embodiment of the present invention, the parameter sample set of the multi-stage synchronous induction coil gun is obtained by finite element simulation through orthogonal experiment combined with random experimental design.

[0056] In this embodiment, a three-stage synchronous induction coil gun is taken as an example. The system parameters and projectile parameters of the multi-stage synchronous induction coil gun are shown in Tables 1 and 2. 81 sets of sample data were obtained through orthogonal experiments as shown in Table 3, and 19 sets of sample data were obtained through random experiments as shown in Table 4. N1, N2, and N3 are the number of turns of the three-stage drive coil, respectively; P1 is the projectile trigger position; and T2 and T3 are the trigger times of the second and third stage drive coils, respectively.

[0057] Table 1 Parameters of Synchronous Induction Coil Gun System

[0058]

[0059] Table 2 Projectile Parameters

[0060]

[0061] Table 3 Sample Set for Orthogonal Experiments

[0062]

[0063] Table 4. Parameter Sample Set for Multi-Stage Synchronous Induction Coil Gun

[0064]

[0065] In this embodiment, each sample in the multi-stage synchronous induction coil gun parameter sample set takes the number of turns of each stage of the drive coil, the projectile trigger position, and the trigger time of each stage of the drive coil as input, and the projectile exit velocity as output.

[0066] In this embodiment, the obtained multi-stage synchronous induction coil gun parameter sample set is preprocessed, such as normalized, and the sample set is divided into a test set and a training set at a ratio of 1:4.

[0067] S200: Build an RNN model, input the training set data into the RNN model for training, then use the test set to test the trained RNN model, and evaluate the predictive ability of the RNN model based on the evaluation metrics.

[0068] In one embodiment of the present invention, evaluating the predictive ability of an RNN model based on an evaluation metric includes:

[0069] S1, Determine the structure of the RNN model: Initialize the various parameters of the RNN, including the input weights W. x Hidden state weight W h Output weight W y Input bias b x Hidden bias b h Output bias b y The initial hidden state h0 and regularization parameters are determined; the activation function and number of hidden layers are also determined. Specifically, the number of hidden layers is 3, and the activation function is Tanh.

[0070] S2, input the training set and train the RNN model.

[0071] S3, input the test set to test the RNN model, calculate the evaluation index and the percentage error between the predicted and simulated exit speed values.

[0072] In this embodiment, the evaluation metrics are, for example, mean square percentage error, mean absolute percentage error, and root mean square error.

[0073] S4. If the exit speed error percentage is less than 5%, the number of turns of each stage of the drive coil, the projectile trigger position, and the trigger time of each stage of the drive coil are directly input into the tested and qualified RNN model for projectile exit speed prediction. If the exit speed error percentage is greater than 5%, the PSO algorithm is used to optimize the hyperparameters of the RNN model.

[0074] S300. If the predictive ability of the RNN model meets the standard, the tested RNN model is used for prediction. Otherwise, the PSO-optimized recurrent neural network model RNN is used, and the training set is applied again for training. The hyperparameters of the RNN are selected, and the PSO-RNN model is established.

[0075] In one embodiment of the present invention, PSO specifically refers to the particle swarm optimization algorithm.

[0076] S400: Input the test set to test the PSO-RNN model, evaluate the predictive ability of the PSO-RNN model according to the evaluation index, until the predictive ability meets the requirements, and then input the optimal hyperparameters into the RNN model to obtain the best PSO-RNN model.

[0077] In one embodiment of the present invention, obtaining the optimal PSO-RNN model includes:

[0078] S10, Establish the correspondence between the PSO particle swarm algorithm and the hyperparameters of the RNN model.

[0079] In this embodiment, the hyperparameters of the RNN model, including the number of neurons in each hidden layer and the regularization coefficient, are mapped to the position and velocity of particles in the Particle Swarm Optimization (PSO) algorithm. Here, the particle is the basic individual in the algorithm, representing a potential solution in the solution space of the optimization problem. The particle gradually approaches the optimal solution by moving in the search space. The particle dimension D in the PSO algorithm is the dimension of the optimization object. In this embodiment, the optimization object includes the number of neurons in the three hidden layers and the regularization coefficient; therefore, D is 4 in this invention.

[0080] S20 initializes the PSO algorithm, including population size, inertia weight, learning factor, maximum number of iterations, initial position of particles, and initial velocity.

[0081] S30 uses the root mean square error (RMSE) of the RNN model as the fitness function to calculate the particle fitness value.

[0082] In this embodiment, the particle fitness value is calculated using the following formula:

[0083]

[0084] In the formula, RMSE is the root mean square error, n is the sample size, and S is the mean square error. i and P i These are the simulated value and the predicted value of the i-th sample, respectively, that is, the projectile exit velocity obtained from the simulation and the projectile exit velocity value predicted by the nonparametric model.

[0085] S40, update particle position and velocity.

[0086] In this embodiment, the particle position and velocity are updated according to the following formula:

[0087] v id (t+1)=wv id (t)+c1r1(p id -x id )+c2r2(g d -x id );

[0088] x id (t+1)=x id (t)+v id (t+1);

[0089] In the formula, v id (t+1) and x id (t+1) represent the velocity and position of the i-th particle in the d-dimensional space at the (t+1)-th iteration; p id For the optimal position in the history of an individual particle, g d The position is the global optimum; c1 and c2 are two learning factors, r1 and r2 are uniformly distributed random numbers in the interval [0,1], and w is the inertial weight. The particle velocity and position must be restricted within the defined domain.

[0090] S50, use the training set for training, input the optimized hyperparameters into the RNN model to obtain the PSO-RNN model.

[0091] In one embodiment of the present invention, the above describes the process of establishing a PSO-RNN model.

[0092] S60: Input the test set into the trained PSO-RNN model to obtain the prediction results of the test set; calculate the evaluation index and error percentage based on the prediction results of the test set, and determine whether the iteration has reached the termination condition.

[0093] In this embodiment, the evaluation index and error percentage are calculated based on the prediction results of the test set, and it is determined whether the iteration has reached the termination condition, that is, whether the error percentage between the predicted value and the simulated value of the exit speed is less than 5%.

[0094] If the termination condition is not met in S70, continue iterating from S30 to S60; if the termination condition is met, the final optimal hyperparameters are obtained, and the best PSO-RNN model is acquired.

[0095] In this embodiment, the final optimal hyperparameters are input into the RNN model, and the model is used to predict the exit velocity of the projectile from the multi-stage synchronous induction coil.

[0096] The S500 inputs the launcher parameters into the optimal PSO-RNN model to obtain the projectile's exit velocity under the current parameters.

[0097] In this embodiment, the test set is input into the traditional RNN neural network and the PSO-RNN model to obtain a comparison of the prediction results. Figure 2 It can be seen that the projectile exit velocity prediction model based on the PSO-RNN neural network is closer to the simulation value and the prediction result is more accurate than the prediction model of the traditional RNN neural network.

[0098] In this embodiment, Figure 3 A comparison of the prediction errors of traditional RNN neural networks and PSO-RNN neural networks shows that the maximum relative error of the PSO-RNN prediction model is 2.58, the average relative error is 0.95, and the maximum error percentage is 4.2%. The traditional RNN neural network prediction model has a maximum error of 6.5, an average relative error of 1.59, and a maximum error percentage of 11.7%. Considering the influence of actual measurement errors, an error percentage of less than 5% between the predicted and simulated projectile exit velocity is acceptable. In conclusion, the projectile exit velocity prediction result based on the PSO-RNN neural network for multi-stage synchronous induction coil guns is more accurate and has better generalization ability than the traditional RNN neural network prediction model.

[0099] Please see Figure 4 As shown, the present invention also provides a multi-stage synchronous induction coil projectile exit velocity prediction system, which applies the above-described multi-stage synchronous induction coil projectile exit velocity prediction method, including:

[0100] The sample set module is used to obtain the parameter sample set of the multi-stage synchronous induction coil gun and divide it into training set and test set.

[0101] The RNN model module is used to build RNN models. It inputs training data into the RNN model for training, then uses the test set to test the trained RNN model, and evaluates the predictive ability of the RNN model based on evaluation metrics.

[0102] The initial PSO-RNN model module is used to determine whether the prediction ability of the RNN model meets the standard. If so, the tested RNN model is used for prediction. Otherwise, the PSO-optimized recurrent neural network model RNN is used, and the training set is applied again to select the hyperparameters of the RNN and build the PSO-RNN model.

[0103] The optimal PSO-RNN model module is used to test the PSO-RNN model by inputting a test set, evaluate the predictive ability of the PSO-RNN model according to the evaluation metrics, and continue until the predictive ability meets the requirements. Then, the optimal hyperparameters are input into the RNN model to obtain the optimal PSO-RNN model.

[0104] The prediction module is used to input the launcher parameters into the optimal PSO-RNN model to obtain the projectile's exit velocity under the current parameters.

[0105] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0106] The above-described embodiments are merely examples of implementation methods of the invention. The scope of protection of the present invention is not limited to the above-described embodiments. For those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil, characterized in that, include: Obtain the parameter sample set of the multi-stage synchronous induction coil gun and divide it into training set and test set; Build an RNN model, input the training set data into the RNN model for training, then use the test set to test the trained RNN model, and evaluate the predictive ability of the RNN model according to the evaluation metrics. If the predictive ability of the RNN model meets the standard, the tested RNN model is used for prediction; otherwise, the PSO-optimized recurrent neural network model RNN is used, and the model is trained again using the training set. The hyperparameters of the RNN are selected, and the PSO-RNN model is established, including: S10, Establish the correspondence between the PSO particle swarm algorithm and the hyperparameters of the RNN model, and map the hyperparameters of the RNN model to the position and velocity of the particles in the particle swarm algorithm. The hyperparameters of the RNN model include: the number of neurons in each hidden layer and the regularization coefficient. S20, initialize the PSO algorithm, including population size, inertia weight, learning factor, maximum number of iterations, initial position and initial velocity of particles; S30, using the root mean square error (RMSE) of the RNN model as the fitness function, calculate the particle fitness value; S40, update particle position and velocity; S50, and use the training set for training, input the optimized hyperparameters into the RNN model to obtain the PSO-RNN model; The PSO-RNN model is tested using the input test set. The predictive ability of the PSO-RNN model is evaluated according to the evaluation metrics until the predictive ability meets the requirements. The optimal hyperparameters are then input into the RNN model to obtain the best PSO-RNN model. Input the launcher parameters into the optimal PSO-RNN model to obtain the projectile's exit velocity under the current parameters.

2. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, The parameter sample set of the multi-stage synchronous induction coil gun was obtained by finite element simulation through orthogonal experiments combined with random experimental design.

3. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, In the parameter sample set of the multi-stage synchronous induction coil gun, each sample takes the number of turns of the driving coil at each stage, the projectile trigger position, and the trigger time of the driving coil at each stage as input, and the projectile exit velocity as output.

4. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, The predictive power of RNN models is evaluated based on evaluation metrics, including: S1, Determine the structure of the RNN model: Initialize the various parameters of the RNN, including the input weights W. x Hidden state weight W h Output weight W y Input bias b x Hidden bias b h Output bias b y 1. Initial hidden state h0, regularization parameters; 2. Determine the activation function of the hidden layer and the number of hidden layers; S2, Input the training set and train the RNN model; S3, Input the test set to test the RNN model, calculate the evaluation index and the percentage error between the predicted and simulated exit speed values; S4. If the exit speed error percentage is less than 5%, the number of turns of each stage of the drive coil, the trigger position of the projectile, and the trigger time of each stage of the drive coil are directly input into the qualified RNN model to predict the exit speed of the projectile. If the exit speed error percentage is greater than 5%, the PSO algorithm is used to optimize the hyperparameters of the RNN model.

5. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, The particle fitness value is calculated using the following formula: In the formula, RMSE is the root mean square error, n is the sample size, and S is the mean square error. i and P i These are the simulated value and the predicted value of the i-th sample, respectively.

6. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, Update particle position and velocity using the following formula: v id (t+1)=wv id (t)+c1r1(p id -x id )+c2r2(g d -x id ); x id (t+1)=x id (t)+v id (t+1); In the formula, v id (t+1) and x id (t+1) represent the velocity and position of the i-th particle in the d-dimensional space at the (t+1)-th iteration; p id For the optimal position in the history of an individual particle, g d The global optimal position is represented by c1 and c2, which are two learning factors. r1 and r2 are random numbers uniformly distributed within the interval [0,1], and w is the inertia weight.

7. The method for predicting the exit velocity of a projectile using a multi-stage synchronous induction coil according to claim 1, characterized in that, To obtain the best PSO-RNN model, including: S60, Input the test set into the trained PSO-RNN model to obtain the prediction results of the test set; Calculate the evaluation index and error percentage based on the prediction results of the test set to determine whether the iteration has reached the termination condition. If the termination condition is not met in S70, continue iterating from S30 to S60; if the termination condition is met, the final optimal hyperparameters are obtained. The optimal hyperparameters are then substituted into the RNN model to obtain the best PSO-RNN model.

8. A multi-stage synchronous induction coil projectile exit velocity prediction system, characterized in that, The method for predicting the exit velocity of projectiles using a multi-stage synchronous induction coil, as described in any one of claims 1-7, is applied.

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