A shell trajectory prediction method using support vector machines
Patent Information
- Application Number
- CN202610926084.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-25
- Publication Date
- 2026-10-20
AI Technical Summary
但神经网络模型的训练依赖大规模历史炮弹轨迹数据，在数据量有限的场景下难以获得高精度的预测模型，限制了其在实际应用中的推广
[0029]1.本发明通过结合传统物理模型生成的轨迹数据与真实历史数据训练 SVM 模型，有效降低了对大规模真实历史数据的依赖，解决了现有神经网络技术在数据量有限场景下预测精度不足的问题。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of projectile trajectory prediction, and more specifically to a projectile trajectory prediction method using support vector machines (SVM). Background Technology
[0002] Traditional projectile trajectory prediction methods are primarily based on the classical parabolic motion model. While this model is computationally simple, its accuracy is limited, and it fails to adequately account for the impact of air resistance on projectile motion. Current mainstream projectile trajectory prediction technologies have shifted to using dynamic models that incorporate air resistance coefficients for trajectory calculation. However, accurately obtaining and optimizing the parameters of these dynamic models remains a core technical challenge limiting the improvement of prediction accuracy. Furthermore, the computational complexity of dynamic models is high, placing certain demands on hardware computing resources.
[0003] To address the aforementioned issues, existing technologies have introduced neural network techniques to construct adaptive parameter adjustment mechanisms, which to some extent reduce computational resource requirements and improve prediction accuracy. However, the training of neural network models relies on large-scale historical shell trajectory data, making it difficult to obtain high-precision prediction models in scenarios with limited data, thus limiting their widespread application. Therefore, how to achieve high-precision shell trajectory prediction using limited historical data has become a pressing technical problem to be solved in this field. Summary of the Invention
[0004] To overcome the shortcomings of existing technologies, this invention provides a projectile trajectory prediction method using support vector machines. By combining data generated by traditional physical models with real historical data to train the SVM model, the dependence on large-scale historical data is effectively reduced, while ensuring the accuracy and reliability of trajectory prediction.
[0005] The technical solution adopted in this invention is: a projectile trajectory prediction method using support vector machines, comprising the following steps:
[0006] Step 1. Determine the initial parameters for projectile trajectory prediction, and establish a wind resistance model and a projectile dynamic model that consider air density changes at altitude;
[0007] Step 2. Using the projectile motion model obtained in Step 1, calculate the projectile trajectory data under different initial conditions and generate a projectile trajectory dataset;
[0008] Step 3. Mix the shell trajectory dataset generated in Step 2 with real historical shell trajectory data according to a preset ratio to construct a training dataset for training the Support Vector Machine (SVM) model;
[0009] Step 4. Compare the predicted trajectory of the SVM model trained in Step 3 with the actual projectile trajectory to evaluate the model performance; if the model performance does not meet the preset requirements, repeat Step 2 to Step 3 to retrain the model.
[0010] Step 5: Determine the SVM model that meets the preset performance requirements obtained in Step 4 as the final projectile trajectory prediction model, and its parameters are the final model parameters.
[0011] In step 1, the initial parameters include muzzle velocity, launch angle, and trajectory prediction step size; the trajectory prediction step size is the proportional division step size of the projectile from exiting the muzzle to landing.
[0012] In step 1, the expression for the wind resistance model is:
[0013] F = 0.5 × ρ × v² × C_d × A
[0014] Where ρ is air density, v is velocity, C_d is drag coefficient, A is frontal area, and ρ is a function of altitude.
[0015] ρ(h) = ρ0 × exp(-h / H),
[0016] Where ρ0 is the air density at sea level, h is the current altitude, and H is the atmospheric scale altitude.
[0017] Therefore, the dynamic model of the projectile in the x and y directions are as follows:
[0018] m×dvx / dt=-0.5×ρ(h)×v²×C_d×A×vx / |v|
[0019] m×dvy / dt=-m×g-0.5×ρ(h)×v²×C_d×A×vy / |v|
[0020] v = sqrt(vx² + vy²),
[0021] Where m is the mass of the projectile, ρ(h) is the air density as a function of altitude, g is the gravitational acceleration, h is the current altitude, v is the velocity, vx is the horizontal x-component of the velocity, vy is the vertical y-component of the velocity, C_d is the drag coefficient, and A is the frontal area.
[0022] In step 2, the constraint ranges for the different initial conditions are: the firing angle constraint range is 0° to 90°, and the muzzle velocity constraint range is 150 m / s to 850 m / s.
[0023] In step 3, the mixing ratio of the generated shell trajectory dataset to the real historical shell trajectory data is 8:2; the SVM model uses the radial basis function as the kernel function, the kernel width search range is set to 0.1 to 100, and the regularization parameter search range is set to 0.1 to 10.
[0024] In step 4, the preset requirements for model performance include:
[0025] (1) The predicted trajectory conforms to the laws of physics, that is, it conforms to the laws of parabolic motion, and the wind resistance effect conforms to the conventional ballistic physics phenomena.
[0026] (2) The coefficient of determination of the goodness of fit between the predicted trajectory and the actual trajectory is greater than 0.95.
[0027] The SVM model achieves single-step or multi-step prediction based on the trajectory prediction step size, corresponding to short-time trajectory prediction or full-process trajectory prediction.
[0028] The projectile trajectory prediction method using support vector machines designed according to the above technical solution of this invention has the following advantages:
[0029] 1. This invention effectively reduces the reliance on large-scale real historical data by training an SVM model using trajectory data generated by a traditional physical model and real historical data, thus solving the problem of insufficient prediction accuracy of existing neural network technologies in scenarios with limited data.
[0030] 2. The wind resistance model established in this invention takes into account the change of air density with altitude, which improves the accuracy of the physical model and provides a high-quality training data foundation for the SVM model.
[0031] 3. This invention uses support vector machines as the prediction model, which has good generalization ability and small sample learning ability. While ensuring prediction accuracy, it reduces the demand for computing resources and improves prediction efficiency.
[0032] 4. By setting strict model evaluation criteria, this invention ensures that the predicted trajectory meets both numerical accuracy requirements and conforms to the laws of physics, thereby improving the reliability of the prediction results.
[0033] 5. This invention can flexibly realize single-step prediction and multi-step prediction, and is suitable for the needs of projectile trajectory prediction in different scenarios, and has broad application prospects. Attached Figure Description
[0034] Figure 1 The flowchart for the projectile trajectory prediction model using support vector machines in this invention is shown below.
[0035] Figure 2 This is a schematic diagram of the 50 projectile trajectories generated by the wind resistance model and dynamic model of this invention;
[0036] Figure 3 This is a schematic diagram of the unqualified curve of the SVM training projectile trajectory prediction result of the present invention;
[0037] Figure 4This is a schematic diagram of the qualified curve of the SVM training projectile trajectory prediction result of the present invention. Detailed Implementation
[0038] The following description, in conjunction with the accompanying drawings, details a projectile trajectory prediction method using support vector machines according to the present invention.
[0039] This invention discloses a projectile trajectory prediction method using support vector machines, see [link to relevant documentation]. Figures 1 to 4 This includes the following steps:
[0040] Step 1: Determining initial parameters and establishing the model
[0041] Initial parameters: muzzle velocity, launch angle, and trajectory prediction step size (divided proportionally from muzzle exit to landing).
[0042] Wind resistance model:
[0043] F = 0.5 * ρ * v² * C_d * A
[0044] Where ρ is air density, v is velocity, C_d is drag coefficient (set to 0.5 in this invention), and A is frontal area (set to 0.1 in this invention). Note that ρ is a function of altitude.
[0045] ρ(h) = ρ0 * exp(-h / H),
[0046] Where ρ0 is the air density at sea level, approximately 1.225 kg / m³, h is the current altitude, and H is the atmospheric altitude (set to 8 kilometers in this invention).
[0047] Therefore, the dynamic model of the projectile in the x and y directions are as follows:
[0048] m * dvx / dt = -0.5 * ρ(h) * v² * C_d * A * vx / |v|
[0049] m * dvy / dt = -m * g -0.5 * ρ(h) * v² * C_d * A * vy / |v|
[0050] v = sqrt(vx² + vy²),
[0051] Where m is the mass of the projectile (set to 10kg in this invention), ρ(h) is the air density function as a function of altitude, g is the gravitational acceleration (set to 9.81m / s²), h is the current altitude, v is the velocity, vx is the x-direction (i.e., horizontal) component of the velocity, vy is the y-direction (i.e., vertical horizontal) component of the velocity, C_d is the drag coefficient, and A is the frontal area.
[0052] In step 1 of this invention, the initial parameters—muzzle velocity, firing angle, and trajectory prediction step size—are the input parameters of the SVM model, and the output parameters of the SVM model are the distances from the current x and y values to the origin. It should be noted that the SVM model outputs of the distances from the current x and y values to the origin are affected by the trajectory prediction step size, allowing for single-step or multi-step prediction, thus achieving various prediction methods including short-time trajectory prediction and full-range prediction.
[0053] Step 2: Using the projectile motion model obtained in Step 1, calculate different trajectory data under different initial conditions to obtain the projectile trajectory dataset (e.g., Figure 2 As shown in the figure, the launch angle is constrained from 0° to 90°, and the initial velocity is constrained from 150m / s to 850m / s.
[0054] Step 3: Mix the shell trajectory dataset obtained in Step 2 with real historical data (ratio 8:2) to train the SVM model. The kernel function uses the radial basis function, the kernel width search range is set to 0.1 to 100, and the regularization parameter search range is set to 0.1 to 10.
[0055] Step 4: Compare the trajectory prediction of the SVM model obtained in Step 3 with the actual trajectory to observe whether the predicted model curve conforms to the laws of physics. Simultaneously, the goodness-of-fit index (determination coefficient) should be greater than 0.95. Otherwise, repeat Steps 2 and 3 until the requirements are met. In this invention, conforming to the laws of physics means that the predicted result should conform to a parabolic law, and the influence of wind resistance should conform to conventional ballistic physics phenomena, for example… Figure 3 As shown, this does not conform to the laws of physics. Specifically, the x-axis velocity, affected by air resistance, is less in the later stages of the trajectory than in the earlier stages. The y-axis velocity is zero at the highest point of the trajectory, but the x-axis velocity is greater in the later stages than in the earlier stages. A normal trajectory should be as follows... Figure 4 As shown.
[0056] Step 5: Determine the SVM model obtained in Step 4 as the final prediction model, and its parameters are the final model parameters.
Claims
1. A projectile trajectory prediction method using support vector machines, characterized in that... Includes the following steps: Step 1. Determine the initial parameters for projectile trajectory prediction, and establish a wind resistance model and a projectile dynamic model that consider air density changes at altitude; Step 2. Using the projectile motion model obtained in Step 1, calculate the projectile trajectory data under different initial conditions and generate a projectile trajectory dataset; Step 3. Mix the shell trajectory dataset generated in Step 2 with real historical shell trajectory data according to a preset ratio to construct a training dataset for training the Support Vector Machine (SVM) model; Step 4. Compare the predicted trajectory of the SVM model trained in Step 3 with the actual projectile trajectory to evaluate the model performance; if the model performance does not meet the preset requirements, repeat Step 2 to Step 3 to retrain the model. Step 5: Determine the SVM model that meets the preset performance requirements obtained in Step 4 as the final projectile trajectory prediction model, and its parameters are the final model parameters.
2. The projectile trajectory prediction method using support vector machines according to claim 1, characterized in that in step 1, the initial parameters include muzzle velocity, launch angle and trajectory prediction step size; the trajectory prediction step size is the proportional division step size of the projectile from exiting the muzzle to landing.
3. The projectile trajectory prediction method using support vector machines according to claim 1, characterized in that, in step 1, the expression of the wind resistance model is: F = 0.5 × ρ × v² × C_d × A Where ρ is air density, v is velocity, C_d is drag coefficient, A is frontal area, and ρ is a function of altitude. ρ(h) = ρ0 × exp(-h / H), in, ρ0 is the air density at sea level, h is the current altitude, and H is the atmospheric scale height. Therefore, the dynamic model of the projectile in the x and y directions are as follows: m×dvx / dt=-0.5×ρ(h)×v²×C_d×A×vx / |v| m×dvy / dt=-m×g-0.5×ρ(h)×v²×C_d×A×vy / |v| v = sqrt(vx² + vy²), Where m is the mass of the projectile, ρ(h) is the air density as a function of altitude, g is the gravitational acceleration, h is the current altitude, v is the velocity, vx is the horizontal x-component of the velocity, vy is the vertical y-component of the velocity, C_d is the drag coefficient, and A is the frontal area.
4. The projectile trajectory prediction method using support vector machine according to claim 1, characterized in that in step 2, the constraint range of the different initial conditions is: the firing angle constraint range is 0° to 90°, and the muzzle initial velocity constraint range is 150m / s to 850m / s.
5. The method for predicting projectile trajectories using support vector machines according to claim 1, characterized in that in step 3, the mixing ratio of the generated projectile trajectory dataset and the real historical projectile trajectory data is 8:2; the SVM model uses radial basis functions as kernel functions, the kernel width search range is set to 0.1 to 100, and the regularization parameter search range is set to 0.1 to 10.
6. The projectile trajectory prediction method using support vector machines according to claim 1, Its characteristic is that, in step 4, the preset requirements for model performance include: (1) The predicted trajectory conforms to the laws of physics, that is, it conforms to the laws of parabolic motion, and the wind resistance effect conforms to the conventional ballistic physics phenomena. (2) The coefficient of determination of the goodness of fit between the predicted trajectory and the actual trajectory is greater than 0.
95. The SVM model achieves single-step or multi-step prediction based on the trajectory prediction step size, corresponding to short-time trajectory prediction or full-process trajectory prediction.