基于量纲约束与符号回归的半无限金属靶板侵彻效率预测模型

doi:10.12382/bgxb.2025.0425

摘要/Abstract

摘要： 针对传统侵彻效率预测模型依赖经验公式、适应性差且物理解释力不足的问题,采用一种融合量纲约束与符号回归算法的建模方法,构建了杆弹侵彻半无限金属靶板的侵彻效率预测模型。首先,基于物理先验知识将金属靶板侵彻过程中涉及的7个原始物理变量转化为4个具有明确物理意义的无量纲控制参数;随后,利用收集的819组实验数据,采用引入惩罚机制的遗传编程符号回归算法建立无量纲变量与侵彻效率之间的解析表达式。结果表明:在不同的侵彻工况下,所构建模型在拟合精度、泛化能力与表达结构简洁性方面均表现优异,平均决定系数R²均超过0.8,且能准确捕捉各无量纲参数对侵彻效率的非线性影响。该方法兼具预测精度与跨工况适应性,还可生成结构明确、物理含义清晰的解析表达式,有助于进一步理解各物理参量在侵彻响应过程中的作用机制。

关键词: 半无限金属靶, 侵彻效率, 无量纲量, 机器学习, 符号回归

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

陈青青, 张杰, 王志勇, 赵婷婷, 张煜航, 王志华. 基于量纲约束与符号回归的半无限金属靶板侵彻效率预测模型[J]. 兵工学报, 2025, 46(10): 250425-.

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-.

图/表 9

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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