A High-spinning Projectile Aerodynamic Modeling Method Combining System Identification and Transfer Learning

doi:10.12382/bgxb.2023.0127

Abstract

Abstract:

Computational fluid dynamics andrigid body dynamics(CFD/RBD) coupling simulation is a common method for evaluating the flight performance of spinning projectiles, which is quite inefficient due to huge amount of CFD simulations. An efficient and accurate aerodynamic model with strong generalization ability is established to significantly improve the simulation efficiency by replacing the CFD module in coupling simulation. An aerodynamic modeling method combining system identification and transfer learning is proposed to address the above-mentioned problem. First, the samples of spinning projectile are obtained by CFD/RBD coupling simulations under the given initial conditions. Then the autoregressive moving average method is used to build an original aerodynamic model, and the long short-term memory network is utilized to build a state prediction model. In condition of small variation of initial state, the original aerodynamic model remains valid; however in case of large variation of initial state, the state prediction model is transferred to the corresponding initial state, and then an aerodynamic model is built by using the autoregressive moving average method based on the predicted state parameters. The results show that the proposed method is suitable for accurate aerodynamic modeling of high-spinning projectile under the large variations of initial angular velocity and pitch angle. In comparison with the autoregressive moving average method based on direct CFD/RBD coupling simulations, the modeling efficiency of the proposed method is doubled.

Key words: high-spinning projectile, aerodynamic modeling, autoregressive moving average, long short-term memory network, transfer learning

CLC Number:

TJ410.1

JI Wen, LI Chunna, JIA Xuyi, WANG Gang, GONG Chunlin. A High-spinning Projectile Aerodynamic Modeling Method Combining System Identification and Transfer Learning[J]. Acta Armamentarii, 2024, 45(7): 2197-2208.

Figures/Tables 15

Fig.1 Coupled CFD/RBD simulation process

Fig.2 Process of TL-ARMA

Fig.3 Typical LSTM network architecture

Fig.4 Transfer learning model based on pre-training method

Fig.5 Model geometry

Fig.6 Mesh at nearfield of spinning projectile

Table 1 Initial conditions of coupled CFD/RBD simulation

方向	位置/m	速度/ (m·s^-1)	姿态角/ (°)	角速度/ (rad·s^-1)
x	4.593	1030.81	0	2518.39
y	-0.2	22.064	5	-52.802
z	-0.159	86.278	1.317	22.233

Table 2 Modeling errors of NCarma at different initial angular velocities

初始转速/ (rad·s^-1)	误差	力			力矩
初始转速/ (rad·s^-1)	误差	F_x	F_y	F_z	M_x	M_y	M_z
2518.39	δ_RMSE	0.0271	0.0357	0.0325	0.0003	0.0009	0.0009
	δ_MAPE	0.09%	3.35%	0.5%	2.15%	0.95%	3.45%
2100	δ_RMSE	0.0413	0.0438	0.0453	0.0004	0.0012	0.0014
	δ_MAPE	0.14%	4.59%	0.52%	3.22%	0.53%	4.49%
2 900	δ_RMSE	0.0471	0.0583	0.0596	0.0006	0.0014	0.0016
	δ_MAPE	0.17%	6.82%	0.68%	4.88%	0.62%	1.95%
2 000	δ_RMSE	0.0352	0.0402	0.0379	0.0004	0.001	0.0013
	δ_MAPE	0.12%	10.29%	0.86%	7.78%	1.49%	11.58%
3 000	δ_RMSE	0.0258	0.0463	0.0422	0.0004	0.0011	0.0011
	δ_MAPE	0.09%	11.11%	1.45%	6.27%	1.07%	10.16%
1 800	δ_RMSE	0.0331	0.0514	0.0494	0.0003	0.0013	0.0017
	δ_MAPE	0.11%	21.31%	1.24%	2.97%	0.89%	21.98%

Table 3 Modeling errors of NCarma at different initial pitch angles

初始俯仰角/(°)	误差	力			力矩
初始俯仰角/(°)	误差	F_x	F_y	F_z	M_x	M_y	M_z
5	δ_RMSE	0.0271	0.0357	0.0325	0.0003	0.0009	0.0009
	δ_MAPE	0.09%	3.35%	0.5%	2.15%	0.95%	3.45%
4	δ_RMSE	0.0414	0.0557	0.0534	0.0005	0.0013	0.0013
	δ_MAPE	0.15%	1.82%	0.68%	4.48%	0.41%	1.73%
6	δ_RMSE	0.0814	0.0676	0.0761	0.0009	0.0016	0.0015
	δ_MAPE	0.31%	4.65%	1.01%	5.64%	0.27%	1.18%
2	δ_RMSE	0.0807	0.1041	0.3602	0.0009	0.0163	0.0029
	δ_MAPE	0.29%	1.97%	5.96%	17.70%	8.47%	1.79%
3	δ_RMSE	0.0779	0.099	0.3412	0.0008	0.0159	0.0027
	δ_MAPE	0.28%	2.71%	16.97%	19.90%	10.63%	2.58%
7	δ_RMSE	0.1242	0.0800	0.1503	0.0023	0.0030	0.0016
	δ_MAPE	0.43%	9.23%	0.74%	8.72%	1.66%	1.71%

Fig.7 Comparison between the predicted and true values of different methods at the initial of 1800rad/s

Table 4 Comparison of model errors corresponding to different methodsat theinitial of 1800rad/s

方法	误差	力			力矩
方法	误差	F_x	F_y	F_z	M_x	M_y	M_z
TL-ARMA	δ_RMSE	0.01	0.011	0.0466	0.0002	0.0019	0.0004
	δ_MAPE	0.03%	5.74%	0.96%	1.53%	1.09%	4.78%
ARMA	δ_RMSE	0.0193	0.0156	0.022	0.0004	0.0007	0.0006
	δ_MAPE	0.06%	6.47%	0.54%	4.66%	0.44%	5.42%
$N C a r m a$	δ_RMSE	0.0331	0.0514	0.0494	0.0003	0.0013	0.0017
	δ_MAPE	0.11%	21.31%	1.24%	2.97%	0.89%	21.98%

Table 4 Comparison of model errors corresponding to different methodsat theinitial of 1800rad/s

方法	误差	力			力矩
方法	误差	F_x	F_y	F_z	M_x	M_y	M_z
TL-ARMA	δ_RMSE	0.01	0.011	0.0466	0.0002	0.0019	0.0004
	δ_MAPE	0.03%	5.74%	0.96%	1.53%	1.09%	4.78%
ARMA	δ_RMSE	0.0193	0.0156	0.022	0.0004	0.0007	0.0006
	δ_MAPE	0.06%	6.47%	0.54%	4.66%	0.44%	5.42%
$N C a r m a$	δ_RMSE	0.0331	0.0514	0.0494	0.0003	0.0013	0.0017
	δ_MAPE	0.11%	21.31%	1.24%	2.97%	0.89%	21.98%

Table 5 Comparison of modeling times for different methods

方法	样本计算时间	建模时间	总时间
TL-ARMA	3h56min	10min23s	约4h6min
ARMA	9h51min		9h51min

Fig.8 Comparison between the predicted and true values of different methods at the initial θ of 2°

Table 6 Comparison of model errors corresponding to different methodsat the initial θ of 2°

方法	误差	力			力矩
方法	误差	F_x	F_y	F_z	M_x	M_y	M_z
TL-ARMA	δ_RMSE	0.0162	0.0166	0.0211	0.0002	0.001	0.0008
	δ_MAPE	0.05%	0.44%	0.23%	7.29%	0.25%	0.61%
ARMA	δ_RMSE	0.0232	0.0253	0.0727	0.0004	0.0025	0.0007
	δ_MAPE	0.08%	0.57%	0.96%	8.69%	0.63%	0.53%
$N C a r m a$	δ_RMSE	0.0807	0.1041	0.3602	0.0009	0.0163	0.0029
	δ_MAPE	0.29%	1.97%	5.96%	17.70%	8.47%	1.79%

Table 6 Comparison of model errors corresponding to different methodsat the initial θ of 2°

方法	误差	力			力矩
方法	误差	F_x	F_y	F_z	M_x	M_y	M_z
TL-ARMA	δ_RMSE	0.0162	0.0166	0.0211	0.0002	0.001	0.0008
	δ_MAPE	0.05%	0.44%	0.23%	7.29%	0.25%	0.61%
ARMA	δ_RMSE	0.0232	0.0253	0.0727	0.0004	0.0025	0.0007
	δ_MAPE	0.08%	0.57%	0.96%	8.69%	0.63%	0.53%
$N C a r m a$	δ_RMSE	0.0807	0.1041	0.3602	0.0009	0.0163	0.0029
	δ_MAPE	0.29%	1.97%	5.96%	17.70%	8.47%	1.79%

Table 7 Comparison of modeling times for different methods

方法	样本计算时间	建模时间	总时间
TL-ARMA	4h50min	13min37s	约5h3min
ARMA	9h40min		9h40min

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