A Predictive Model for Penetration Efficiency of Semi-Infinite Metallic Targets Based on Dimensional Constraints and Symbolic Regression

doi:10.12382/bgxb.2025.0425

Abstract

Abstract:

To address the limitations of traditional penetration efficiency prediction models, such as their reliance on empirical formulas, limited adaptability, and weak physical interpretability, this study proposes a modeling approach that integrates dimensional analysis with symbolic regression. A predictive model is developed for the penetration efficiency of rod projectiles impacting semi-infinite metal targets. Based on physical prior knowledge, seven original physical variables are transformed into four dimensionless control parameters with clear physical significance. Using 819 sets of experimental data, an analytical expression between the dimensionless parameters and penetration efficiency is constructed through a symbolic regression algorithm based on genetic programming, with a penalty mechanism introduced to ensure the participation of all control variables. The Results show that the proposed model performs well across various penetration conditions, with average coefficients of determination (R²) exceeding 0.8. The model accurately captures the nonlinear influence of each parameter on penetration efficiency. Compared to traditional empirical models, the proposed method offers improved predictive accuracy and adaptability, while producing physically meaningful and structurally clear expressions that provide insight into the role of key variables in the penetration process.

Key words: semi-infinite metal target, penetration efficiency, dimensionless parameters, machine learning, symbolic regression

CHEN Qingqing, ZHANG Jie, WANG Zhiyong, ZHAO Tingting, ZHANG Yuhang, WANG Zhihua. A Predictive Model for Penetration Efficiency of Semi-Infinite Metallic Targets Based on Dimensional Constraints and Symbolic Regression[J]. Acta Armamentarii, 2025, 46(10): 250425-.

Figures/Tables 9

References 35

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种类	侵彻方式	统计分析	杆弹长径比L/D	弹靶密度比 ρ_t/ρ_p	弹靶刚度比 HB_t/HB_p	Johnson破坏数 ρ_pV²/HB_t	侵彻效率 P/L
		最大值	9.99	2.90	5.8	1051.7	3.22
		最小值	1	0.35	0.14	2.38	0.01
	低速侵彻V<2000m/s	均值	3.50	1.01	1.13	115.3	0.61
		中位数	3	1	1	58.81	0.50
短杆弹L/D<10		标准差	1.82	0.62	1.13	154	0.51
		最大值	9.99	2.90	5.8	9859.6	7
		最小值	1	0.35	0.07	64.77	0.29
	高速侵彻V≥2000m/s	均值	3.59	0.85	0.96	930.26	1.69
		中位数	3	1	0.91	351.7	1.49
		标准差	2.39	0.53	0.86	1525.54	0.99
		最大值	32.04	4.15	1.32	349.40	2.18
		最小值	10	0.17	0.18	8.34	0.01
	低速侵彻V<1300m/s	均值	11.58	0.78	0.74	71.67	0.39
		中位数	10	0.46	0.63	60.7	0.31
长杆弹L/D≥10		标准差	4.69	0.84	0.32	62.23	0.40
		最大值	32.04	4.15	1.32	3836.7	3.61
		最小值	10	0.17	0.18	41.10	0.16
	高速侵彻V≥1300m/s	均值	12.56	0.74	0.71	355.88	1.12
		中位数	10	0.46	0.63	248.03	1.05
		标准差	5.32	0.80	0.29	444.01	0.56

种类	侵彻方式	统计分析	杆弹长径比L/D	弹靶密度比 ρ_t/ρ_p	弹靶刚度比 HB_t/HB_p	Johnson破坏数 ρ_pV²/HB_t	侵彻效率 P/L
		最大值	9.99	2.90	5.8	1051.7	3.22
		最小值	1	0.35	0.14	2.38	0.01
	低速侵彻V<2000m/s	均值	3.50	1.01	1.13	115.3	0.61
		中位数	3	1	1	58.81	0.50
短杆弹L/D<10		标准差	1.82	0.62	1.13	154	0.51
		最大值	9.99	2.90	5.8	9859.6	7
		最小值	1	0.35	0.07	64.77	0.29
	高速侵彻V≥2000m/s	均值	3.59	0.85	0.96	930.26	1.69
		中位数	3	1	0.91	351.7	1.49
		标准差	2.39	0.53	0.86	1525.54	0.99
		最大值	32.04	4.15	1.32	349.40	2.18
		最小值	10	0.17	0.18	8.34	0.01
	低速侵彻V<1300m/s	均值	11.58	0.78	0.74	71.67	0.39
		中位数	10	0.46	0.63	60.7	0.31
长杆弹L/D≥10		标准差	4.69	0.84	0.32	62.23	0.40
		最大值	32.04	4.15	1.32	3836.7	3.61
		最小值	10	0.17	0.18	41.10	0.16
	高速侵彻V≥1300m/s	均值	12.56	0.74	0.71	355.88	1.12
		中位数	10	0.46	0.63	248.03	1.05
		标准差	5.32	0.80	0.29	444.01	0.56

超参数名称与说明	不同侵彻工况下的超参数取值
超参数名称与说明	短杆弹低速	短杆弹高速	长杆弹低速	长杆弹高速
种群规模	960	820	920	930
迭代次数	472	350	430	456
惩罚项系数	0.006	0.004	0.01	0.07

超参数名称与说明	不同侵彻工况下的超参数取值
超参数名称与说明	短杆弹低速	短杆弹高速	长杆弹低速	长杆弹高速
种群规模	960	820	920	930
迭代次数	472	350	430	456
惩罚项系数	0.006	0.004	0.01	0.07

操作符	复杂度系数	操作符	复杂度系数
常数	1	除	2
输入变量	1	指数函数	4
加	1	幂函数	5
减	1	平方根	4
乘	1	绝对值	4