Prediction Model of Concrete Penetration Depth Based on Unbiased Feature Selection

doi:10.12382/bgxb.2025.0019

Abstract

Abstract:

To address the challenges of insufficient data,complex feature selection,and limited applicability of traditional empirical formulas in the prediction of concrete penetration depth,this paper proposes a concrete penetration depth prediction model based on deep learning and optimization strategies.Initially,218 sets of concrete penetration test data are collected,and the size and diversity of dataset are expanded through the integration of multi-stage empirical formulas.To enhance the accuracy of feature selection,an XGBoost (eXtreme Gradient Boosting) model combined with SHAP (SHapley Additive exPlanations) values is employed for feature screening and dimensionality reduction,thereby identifying the key features that are correlated with penetration depth.A multi-layer perceptron (MLP) model for penetration depth prediction is constructed based on these selected key features.Further,Bayesian optimization method is applied to fine-tune the hyperparameters of the MLP model,and its generalization capability is evaluated through K-fold cross-validation.The results demonstrate that the proposed model performs better than the traditional empirical formula under various conditions,its prediction accuracy and stability are significantly improved,and it shows good generalization ability and adaptability.In addition,compared with the traditional empirical formulas,the proposed model also shows better prediction effect in the applicable range of the empirical formulas.

Key words: concrete, penetration depth prediction, unbiased feature selection, Bayesian optimization

CLC Number:

O385

ZHANG Xiuli, ZHANG Jie, QI Xiaopeng, WANG Zhiyong, LIU Zhifang, WANG Zhihua. Prediction Model of Concrete Penetration Depth Based on Unbiased Feature Selection[J]. Acta Armamentarii, 2025, 46(11): 250019-.

Figures/Tables 15

References 24

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数据来源	数据数量	弹体质量 m/kg	弹体直径 d/mm	弹体长度 l/mm	曲率半径与弹径之比CRH	靶板厚度 h/mm	靶板强度 f_c/MPa	靶板密度 ρ_c/(kg·m^-3)	侵彻速度 v/(m·s^-1)	侵彻深度 x/mm
Forrestal等^[9]	9	0.478~1.608	20.3~30.5	203.2~304.8	3	910~2 130	51~62.8	2300	450~821	300~1230
Frew等^[10]	7	12.89~13.08	76.2	530.73	3	910~1830	23		164~337	310~1020
Forrestal等^[11]	17	0.904~0.906	26.9	242.4	2	760~1830	32.4~108.3		277~800	173~958
Frew等^[12]	8	0.478~1.62	20.3~30.5	203.2~304.7	3	940~2240	58.4	2300	442~815	287~1230
Forrestal等^[13]	15	12.9~13.158	76.2	530.73	3~6	1220~1830	23~39	2040~2250	139.3~456.4	240~1250
Gomez等^[14]	14	0.0144~0.0153	6.4	64.34	4.8	406	38.15	2337	183~616	24.26~135.13
Wu等^[15]	20	0.333~0.346	25.3	151.9	3	650	67.5~125.2		510~850	116~346
Zhang等^[16]	17	0.015	12.6	23.93	2.5	150	45.5~112.5		657.9~694.4	28.5~48.5
齐爱东等^[17]	10	4.43	57	465	4	600~1000	30	2600	340.2~497.2	290~500
柴传国^[18]	6	1.394~1.41	40	213	2~4.55	1200	14.8	2238	419~780	384~1019
沈河涛^[19]	9	2.83~2.9	50.8	339	5.157	800~1000	30	2400	497.5~637.3	626~821
刘士践等^[20]	12	0.48	30	195	3	800	85	2560	315~664	90~247
王磊^[21]	21	0.0639~0.098	12.66~14.48	76.25~95.32	2~3	360~400	30.8	2 300	283.5~565.5	73.25~239.53
黄民荣^[22]	5	4.43	57	456.4	4	600~1200	35	2 450	340.2~590	310~625
李清献^[23]	5	0.241	27.3	220.7	8.54		24.1	2356	398~465	155~201
周宁等^[24]	5	25	100	666		3000	35		310~468	590~1190
邓佳杰^[25]	13	0.0655~0.541	14.5~30	87~180	4	1000	40.3~45.1		523.1~797.8	127~450

数据来源	数据数量	弹体质量 m/kg	弹体直径 d/mm	弹体长度 l/mm	曲率半径与弹径之比CRH	靶板厚度 h/mm	靶板强度 f_c/MPa	靶板密度 ρ_c/(kg·m^-3)	侵彻速度 v/(m·s^-1)	侵彻深度 x/mm
Forrestal等^[9]	9	0.478~1.608	20.3~30.5	203.2~304.8	3	910~2 130	51~62.8	2300	450~821	300~1230
Frew等^[10]	7	12.89~13.08	76.2	530.73	3	910~1830	23		164~337	310~1020
Forrestal等^[11]	17	0.904~0.906	26.9	242.4	2	760~1830	32.4~108.3		277~800	173~958
Frew等^[12]	8	0.478~1.62	20.3~30.5	203.2~304.7	3	940~2240	58.4	2300	442~815	287~1230
Forrestal等^[13]	15	12.9~13.158	76.2	530.73	3~6	1220~1830	23~39	2040~2250	139.3~456.4	240~1250
Gomez等^[14]	14	0.0144~0.0153	6.4	64.34	4.8	406	38.15	2337	183~616	24.26~135.13
Wu等^[15]	20	0.333~0.346	25.3	151.9	3	650	67.5~125.2		510~850	116~346
Zhang等^[16]	17	0.015	12.6	23.93	2.5	150	45.5~112.5		657.9~694.4	28.5~48.5
齐爱东等^[17]	10	4.43	57	465	4	600~1000	30	2600	340.2~497.2	290~500
柴传国^[18]	6	1.394~1.41	40	213	2~4.55	1200	14.8	2238	419~780	384~1019
沈河涛^[19]	9	2.83~2.9	50.8	339	5.157	800~1000	30	2400	497.5~637.3	626~821
刘士践等^[20]	12	0.48	30	195	3	800	85	2560	315~664	90~247
王磊^[21]	21	0.0639~0.098	12.66~14.48	76.25~95.32	2~3	360~400	30.8	2 300	283.5~565.5	73.25~239.53
黄民荣^[22]	5	4.43	57	456.4	4	600~1200	35	2 450	340.2~590	310~625
李清献^[23]	5	0.241	27.3	220.7	8.54		24.1	2356	398~465	155~201
周宁等^[24]	5	25	100	666		3000	35		310~468	590~1190
邓佳杰^[25]	13	0.0655~0.541	14.5~30	87~180	4	1000	40.3~45.1		523.1~797.8	127~450

名称	具体公式内容
美国陆军工程兵(ACE)公式 (144m/s<v<310m/s 3≤h/d≤18)	$\frac{x}{d}$= $\frac{3.5\times {10}^{-4}}{\sqrt[　]{{f}_{c}}}\left(\frac{m}{{d}^{3}}\right)$d^0.2v^1.5+0.5
修正国防研究委员会(NDRC)公式 (152m/s<v<300m/s 0.6≤x/d≤2.0)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=2G^0.5	G≥1
修正国防研究委员会(NDRC)公式 (152m/s<v<300m/s 0.6≤x/d≤2.0)		$\frac{x}{d}$=G+1	G<1
弹道研究实验室(BRL)公式 (600m/s≤v≤800m/s)	$\frac{x}{d}$= $\frac{1.33\times {10}^{-3}}{\sqrt[　]{{f}_{c}}}\left(\frac{m}{{d}^{3}}\right)$d^0.2v^1.33
Kar公式 (20MPa≤f_c≤60MPa)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{E}{{E}_{s}}\right)}^{1.25}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=2G^0.5	G≥1
Kar公式 (20MPa≤f_c≤60MPa)		$\frac{x}{d}$=G+1	G<1
Haldar-Hamieh公式 (20MPa≤f_c≤35MPa) 300m/s≤v≤800m/s	$\frac{x}{d}$=0.2251I_a+0.0308	I_a= $\frac{mN{v}^{2}}{{f}_{c}{d}^{3}}$	0.3≤I_a≤4.0
	$\frac{x}{d}$=0.0567I_a+0.6740		4.0≤I_a≤21
	$\frac{x}{d}$=0.0299I_a+1.1875		21≤I_a≤455
Petry公式 (500m/s≤v≤2500m/s)	$\frac{x}{d}$=k $\frac{m}{{d}^{3}}$lg $\left(1+\frac{{v}^{2}}{19974}\right)$
英国原子能管理局(UKAEA)公式 (v<340m/s m<500kg)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=0.275-[0.0756-G]^0.5	G≤0.0726
		$\frac{x}{d}$=[4G-0.242]^0.5	0.0726≤G≤1.06
		$\frac{x}{d}$=G+0.9395	G≥1.06
Forrestal公式 (200m/s≤v≤600m/s m<500kg)	$\frac{x}{d}$=v ${\left(\frac{m}{c}\right)}^{0.5}$	${v}_{1}^{2}$= $\frac{2m{v}^{2}-64.3988\times {10}^{6}\pi {d}^{3}{f}_{c}^{0.5}}{2m+\pi {d}^{3}N{\rho }_{c}}$	x≤2d
Forrestal公式 (200m/s≤v≤600m/s m<500kg)	$\frac{x}{d}$= $\frac{2m}{\pi N{\rho }_{c}{d}^{3}}$ln $\left(1+\frac{N{\rho }_{c}{v}_{1}^{2}}{64.3988\times {10}^{6}f{ }_{c}^{0.5}}\right)$+2.0	c= $\frac{\pi d}{8}$(64.3988×10⁶ ${f}_{c}^{0.5}$+Nρ_c ${v}_{1}^{2}$)	x>2d
Chen公式 (200m/s≤v≤600m/s)	$\frac{x}{d}$= $\sqrt[　]{\frac{\left(1+\left(\frac{k\pi }{4N}\right)\right)}{1+\left(\frac{I}{N}\right)}\frac{4kI}{\pi }}$	I= $\frac{{I}^{*}}{S}$= $\frac{1}{S}\left(\frac{m{v}^{2}}{{f}_{c}{d}^{3}}\right)$	$\frac{x}{d}$≤5
		N= $\frac{\lambda }{N}$= $\frac{1}{N}\left(\frac{m}{{\rho }_{c}{d}^{3}}\right)$	$\frac{x}{d}$≤5
	$\frac{x}{d}$= $\frac{2}{\pi }$Nln $\left[\frac{1+\left(\frac{I}{N}\right)}{1+\left(\frac{k\pi }{4N}\right)}\right]$+k	S=72 ${{f}_{c}}^{-0.5}$	$\frac{x}{d}$>5
	$\frac{x}{d}$=1.628 ${\left(\frac{\left(1+\left(\frac{k\pi }{4N}\right)\right)}{1+\left(\frac{l}{N}\right)}\frac{4kI}{\pi }\right)}^{1.395}$	k= $\left(\begin{array}{c}0.707+\frac{h}{d}\end{array}\right)$	$\frac{x}{d}$<0.5

名称	具体公式内容
美国陆军工程兵(ACE)公式 (144m/s<v<310m/s 3≤h/d≤18)	$\frac{x}{d}$= $\frac{3.5\times {10}^{-4}}{\sqrt[　]{{f}_{c}}}\left(\frac{m}{{d}^{3}}\right)$d^0.2v^1.5+0.5
修正国防研究委员会(NDRC)公式 (152m/s<v<300m/s 0.6≤x/d≤2.0)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=2G^0.5	G≥1
修正国防研究委员会(NDRC)公式 (152m/s<v<300m/s 0.6≤x/d≤2.0)		$\frac{x}{d}$=G+1	G<1
弹道研究实验室(BRL)公式 (600m/s≤v≤800m/s)	$\frac{x}{d}$= $\frac{1.33\times {10}^{-3}}{\sqrt[　]{{f}_{c}}}\left(\frac{m}{{d}^{3}}\right)$d^0.2v^1.33
Kar公式 (20MPa≤f_c≤60MPa)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{E}{{E}_{s}}\right)}^{1.25}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=2G^0.5	G≥1
Kar公式 (20MPa≤f_c≤60MPa)		$\frac{x}{d}$=G+1	G<1
Haldar-Hamieh公式 (20MPa≤f_c≤35MPa) 300m/s≤v≤800m/s	$\frac{x}{d}$=0.2251I_a+0.0308	I_a= $\frac{mN{v}^{2}}{{f}_{c}{d}^{3}}$	0.3≤I_a≤4.0
	$\frac{x}{d}$=0.0567I_a+0.6740		4.0≤I_a≤21
	$\frac{x}{d}$=0.0299I_a+1.1875		21≤I_a≤455
Petry公式 (500m/s≤v≤2500m/s)	$\frac{x}{d}$=k $\frac{m}{{d}^{3}}$lg $\left(1+\frac{{v}^{2}}{19974}\right)$
英国原子能管理局(UKAEA)公式 (v<340m/s m<500kg)	G=3.8×10^-5 $\frac{Nm}{d\sqrt[　]{{f}_{c}}}{\left(\frac{v}{d}\right)}^{1.8}$	$\frac{x}{d}$=0.275-[0.0756-G]^0.5	G≤0.0726
		$\frac{x}{d}$=[4G-0.242]^0.5	0.0726≤G≤1.06
		$\frac{x}{d}$=G+0.9395	G≥1.06
Forrestal公式 (200m/s≤v≤600m/s m<500kg)	$\frac{x}{d}$=v ${\left(\frac{m}{c}\right)}^{0.5}$	${v}_{1}^{2}$= $\frac{2m{v}^{2}-64.3988\times {10}^{6}\pi {d}^{3}{f}_{c}^{0.5}}{2m+\pi {d}^{3}N{\rho }_{c}}$	x≤2d
Forrestal公式 (200m/s≤v≤600m/s m<500kg)	$\frac{x}{d}$= $\frac{2m}{\pi N{\rho }_{c}{d}^{3}}$ln $\left(1+\frac{N{\rho }_{c}{v}_{1}^{2}}{64.3988\times {10}^{6}f{ }_{c}^{0.5}}\right)$+2.0	c= $\frac{\pi d}{8}$(64.3988×10⁶ ${f}_{c}^{0.5}$+Nρ_c ${v}_{1}^{2}$)	x>2d
Chen公式 (200m/s≤v≤600m/s)	$\frac{x}{d}$= $\sqrt[　]{\frac{\left(1+\left(\frac{k\pi }{4N}\right)\right)}{1+\left(\frac{I}{N}\right)}\frac{4kI}{\pi }}$	I= $\frac{{I}^{*}}{S}$= $\frac{1}{S}\left(\frac{m{v}^{2}}{{f}_{c}{d}^{3}}\right)$	$\frac{x}{d}$≤5
		N= $\frac{\lambda }{N}$= $\frac{1}{N}\left(\frac{m}{{\rho }_{c}{d}^{3}}\right)$	$\frac{x}{d}$≤5
	$\frac{x}{d}$= $\frac{2}{\pi }$Nln $\left[\frac{1+\left(\frac{I}{N}\right)}{1+\left(\frac{k\pi }{4N}\right)}\right]$+k	S=72 ${{f}_{c}}^{-0.5}$	$\frac{x}{d}$>5
	$\frac{x}{d}$=1.628 ${\left(\frac{\left(1+\left(\frac{k\pi }{4N}\right)\right)}{1+\left(\frac{l}{N}\right)}\frac{4kI}{\pi }\right)}^{1.395}$	k= $\left(\begin{array}{c}0.707+\frac{h}{d}\end{array}\right)$	$\frac{x}{d}$<0.5

研究对象及冲击结果	参数	最小值	中位值	最大值	平均值	标准差
子弹	质量/kg	0.0144	1.16	25	2.36	3.83
	密度/(kg·m^-3)	7830	7830	8118	7895	115.94
	长度/mm	23.93	232.3	684	240.46	125.94
	直径	6.4	30	125	33.87	18.72
	CRH	2	3.66	8.54	3.61	0.90
	抗拉强度/MPa	550	1677	1730	1570.64	283.71
	屈服强度/MPa	1000	1500	1999	1519.72	363.28
靶板	厚度/mm	40	1019.3	3000	1070.64	497.42
	密度/(kg·m^-3)	2040.0	2303.5	2600.0	2344.91	92.93
	抗压强度/MPa	14.8	39.45	125.2	43.93	19.84
冲击	着靶速度/(m·s^-1)	63.2	569	859	518.32	190.93
结果	侵彻深度/mm	20.34	352.18	1418.72	430.50	318.28