Method for calculating firing data of guided rocket launcher based on surrogate model
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摘要:
针对制导火箭炮发射诸元的快速计算问题，提出了一种结合大样本数据和代理模型计算发射诸元的新方法。运用代理模型建立射角、无控弹道侧偏与炮位纬度、炮位高程、射向、射程、目标点高程及药温之间的函数关系，并根据射程和无控弹道侧偏的预测值对射向进行修正。仿真结果表明，高阶多项式响应面、相关函数为高斯函数的Kriging、高阶单项式径向基函数、核函数为高斯函数的最小二乘支持向量机、激活函数为正弦函数的超限学习机以及由上述单一代理模型构建的组合代理模型均具有较高的预测精度，各种单一代理模型对射角和无控弹道侧偏的预测时间均小于1 ms，证明了基于代理模型的射角和无控弹道侧偏预测方法切实可行，且通过对射向进行修正有效减小了由于地球自转引起的无控弹道侧偏。
Abstract:Aimed at the problem of rapid calculation of firing data of guided rocket launcher, a new method for calculating firing data based on large sample data and surrogate model is proposed. The surrogate models are used to establish the functional relations between the firing angle, uncontrolled lateral range and six influencing factors, including latitude of artillery location, elevation of artillery location, target azimuth, range between artillery location and target location, elevation of target location and propellant temperature, and the target azimuth is corrected according to the range and predicted value of the uncontrolled lateral range. The simulation results show that the high-order polynomial response surface, the Kriging with Gaussian correlation function, the radial basis function with high-order monomial, the least squares support vector machine with Gaussian kernel function, the extreme learning machine with sine activation function and an ensemble of the above individual surrogate models have higher prediction accuracy, and the execution time of each individual surrogate model for a prediction of firing angle or uncontrolled lateral range is less than 1 ms, which verifies the effectiveness and feasibility of the proposed method. Moreover, the uncontrolled lateral range due to the earth's rotation is effectively reduced after the target azimuth correction.
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Key words:
- guided rocket launcher /
- firing data /
- large sample data /
- surrogate model /
- target azimuth correction
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图 1 基于代理模型的制导火箭炮发射诸元计算流程
Figure 1. Process for calculating firing data of guided rocket launcher based on surrogate model
图 3 制导火箭弹在地面坐标系中的z轴分量随时间的变化关系
Figure 3. Variation of z-axis component of guided rocket in ground coordinate system with time
图 6 无控弹道侧偏的绝对误差小于10 m的测试样本占比
Figure 6. Percentage of testing samples with absolute error of uncontrolled lateral range less than 10 m
图 7 各种代理模型运行一次射角预测程序所需要的时间
Figure 7. Execution time of various surrogate models for running one-time firing angle prediction program
图 8 KRIGg对射角的预测精度随测试样本数量的变化
Figure 8. Variation of KRIGg prediction accuracy of firing angle with testing sample size
图 9 KRIGg对无控弹道侧偏的预测精度随测试样本数量的变化
Figure 9. Variation of KRIGg prediction accuracy of uncontrolled lateral range with testing sample size
图 10 射角的预测精度随训练样本数量的变化
Figure 10. Variation of prediction accuracy of firing angle with training sample size
图 11 由射角的预测误差引起的射程误差随训练样本数量的变化
Figure 11. Variation of range error due to prediction error of firing angle with training sample size
图 12 无控弹道侧偏的预测精度随训练样本数量的变化
Figure 12. Variation of prediction accuracy of uncontrolled lateral range with training sample size
表 1 各影响因素的变化范围
Table 1. Variation range of various influencing factors
因素 范围 B0/(°) [0, 60.00] H0/m [0, 5 000.00] AT/mil [0, 6 000.00) XG/km [80.00,300.00] HT/m [0, 5 000.00] TS/℃ [-40.00, 50.00] 
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表 2 阶数对PRS预测精度的影响
Table 2. Effect of order on prediction accuracy of PRS
阶数 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m 1 50.867 5.023 11.813 2455.38 606.87 17422.75 11.57 6658.22 2 24.550 3.211 7.545 1485.90 347.41 11483.88 8.50 4 490.55 3 9.817 1.236 2.385 914.41 185.51 4331.12 2.97 1368.86 4 6.167 0.652 1.245 509.76 94.03 2830.85 1.25 706.48 5 3.737 0.384 0.590 234.81 37.76 1298.65 0.77 320.38 6 2.333 0.240 0.323 99.02 16.15 768.27 0.47 172.21 7 1.476 0.151 0.186 49.15 7.01 519.29 0.23 95.82 8 1.085 0.111 0.120 25.06 3.46 343.80 0.15 61.56 9 0.667 0.068 0.084 13.76 1.41 208.69 0.13 44.40 10 0.792 0.078 0.088 18.10 1.93 245.16 0.14 46.51
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表 3 相关函数对Kriging预测精度的影响
Table 3. Effect of correlation function on prediction accuracy of Kriging
相关函数 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m Cubic 0.550 0.068 0.079 14.26 1.50 217.88 0.11 45.18 Exp 1.667 0.176 0.168 64.60 6.52 583.94 0.23 69.05 Gauss 0.483 0.051 0.064 6.64 0.65 182.31 0.09 33.45 Lin 1.567 0.164 0.174 65.82 5.84 564.56 0.22 76.00 Matern32 1.433 0.151 0.117 34.79 2.44 542.97 0.21 51.70 Matern52 1.183 0.124 0.099 16.82 1.25 449.70 0.17 48.59 Spherical 1.583 0.167 0.165 58.83 5.55 602.85 0.24 67.90 Spline 0.533 0.056 0.070 10.68 1.08 201.42 0.10 40.79
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表 4 基函数对RBF预测精度的影响
Table 4. Effect of basis function on prediction accuracy of RBF
基函数 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m Gauss 1.783 0.189 0.240 26.05 2.88 852.03 0.51 131.14 IMQ 1.350 0.165 0.182 23.69 2.64 680.56 0.53 101.25 MN 1.033 0.105 0.133 23.22 2.59 414.72 0.25 69.86 MQ 1.317 0.158 0.179 24.30 2.67 657.65 0.50 98.90 TPS 1.103 0.117 0.139 23.44 2.66 443.64 0.34 74.68
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表 5 核函数对LSSVM预测精度的影响
Table 5. Effect of kernel function on prediction accuracy of LSSVM
核函数 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m Lin 50.850 5.020 11.813 2455.39 606.87 17422.75 11.56 6658.22 Polynomial 1.017 0.106 0.120 24.49 3.50 365.25 0.17 61.98 Gauss 0.983 0.102 0.114 13.85 1.77 335.83 0.16 57.17
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表 6 激活函数对ELM预测精度的影响
Table 6. Effect of activation function on prediction accuracy of ELM
激活函数 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m Radbas 11.850 1.932 1.202 190.80 17.04 6 131.68 4.78 762.77 Sigmoid 1.167 0.135 0.157 33.68 3.15 640.92 0.44 85.99 Sine 1.117 0.115 0.130 24.18 2.65 337.00 0.22 66.95 Tanh 8.350 1.412 0.920 160.13 15.40 5692.56 3.86 581.62 Tribas 59.217 8.505 9.667 2 468.48 519.41 41920.08 31.48 6278.87
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表 7 单一代理模型和组合代理模型的预测精度
Table 7. Prediction accuracy of individual surrogate models and ensemble of surrogate models
模型类型 射角 无控弹道侧偏 射程 MAE/mil MRE/% RMSE/mil MAE/m RMSE/m MAE/m MRE/% RMSE/m PRSho 0.667 0.068 0.084 13.76 1.41 208.69 0.13 44.40 KRIGg 0.483 0.051 0.064 6.64 0.65 182.31 0.09 33.45 RBFm 1.033 0.105 0.133 23.22 2.59 414.72 0.25 69.86 LSSVMg 0.983 0.102 0.114 13.85 1.77 335.83 0.16 57.17 ELMs 1.117 0.115 0.130 24.18 2.65 337.00 0.22 66.95 EOSM 0.467 0.049 0.061 5.93 0.60 177.69 0.08 32.60
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表 8 射向修正法的修正效果
Table 8. Correction effect of target azimuth correction method
m 模型类型 (Δ z)Max (Δ z)Rmse (Δ x)Max PRSho 24.19 4.62 0.42 KRIGg 23.75 4.49 0.42 RBFm 28.72 5.05 0.50 LSSVMg 25.82 4.71 0.43 ELMs 33.13 5.18 0.48 EOSM 23.51 4.46 0.41
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