Data-Driven Dimensional Analysis of the Dynamic Response of Low-Carbon Steel Circular Plates under Uniform Impulsive Loading

doi:10.12382/bgxb.2025.0424

Abstract

Abstract:

Under explosive loading, the key to predicting a structure’s response is to accurately establish the relationship among the input load, material properties, and mechanical response. This study proposes a method that combines data-driven modeling with dimensional-invariance analysis to identify the key dimensionless parameters governing the dynamic plastic response of circular plates under impulsive loading, and to build a deflection-prediction model. An explicit dynamic model of a clamped circular plate is constructed in ABAQUS. Data are generated by varying the plate radius L, thickness H, density ρ, yield strength σ₀, and impulse I. An artificial neural network is used to fit the response surface and compute gradients; together with the exponent-matrix method and active subspace analysis, feature construction and dimensionality reduction are performed to identify the dominant dimensionless group(s). The results show that, after analysis in the principal subspace, the five original variables can ultimately be expressed as a combination of the Johnson damage number I²/(ρσ₀H²) and the geometric parameter H/L, thereby reducing a multivariable input to a single core variable. The identified dimensionless group effectively characterizes impact damage and dynamic response and exhibits good applicability. The findings provide an efficient data-driven analysis tool for impact-dynamics problems and demonstrate the potential of machine learning in engineering-physics applications.

Key words: Impulsive loading, data-driven, dimensional analysis, dynamic plastic response, finite-element simulation

GE Puxin, SONG Zihao, LI Zhiyang, WANG Hairen, LEI Jianyin, LIU Zhifang. Data-Driven Dimensional Analysis of the Dynamic Response of Low-Carbon Steel Circular Plates under Uniform Impulsive Loading[J]. Acta Armamentarii, 2025, 46(10): 250424-.

Figures/Tables 19

Table 1 Low-carbon steel parameters

ρ/(g·mm^-3)	E/MPa	ν	σ_o/MPa
0.007861	207×10³	0.3	233

Fig.1 Comparison of center deflection between experimental and simulated plates

Table 2 Parameter variation range for the dataset

参数	符号	下限	上限
半径	L/mm	27.03	36.57
厚度	H/mm	1.64	2.22
密度	ρ/(g·mm^-3)	0.00663	0.00897
脉冲载荷	I/(N·ms)	3150	7150
屈服强度	σ₀/MPa	189.55	256.45

Fig.2 Comparison of experimental and simulated data

Fig.3 Histogram of residuals

Fig.4 Schematic diagram of the data-driven dimensional analysis of the dynamic response of a low-carbon steel circular plate under uniform pulse load

Table 3 Dimensional vector in a circular plate under pulse loading

物理量	符号	量纲向量[M,L,T]
密度/(g·mm^-3)	ρ	[1,-3,0]
初始屈服强度/(N·mm^-2)	σ₀	[1,-1,-2]
半径/mm	L	[0,1,0]
厚度/mm	H	[0,1,0]
单位面积所受脉冲/(N·ms·mm^-2)	I	[1,-1,-1]

Fig.5 Schematic diagram of a neural network

Table 4 Neural network parameter

隐藏层	神经元数	激活函数	损失函数	优化器	批量大小
5	10	ReLU/Tanh	MAE	Adam	32

Fig.6 Training and validation loss versus iterations

Table 5 Comparison of training, validation, and test set performance

数据集	样本数	MSE	R²	MAE
训练集	700	0.021382	0.9981	0.073878
验证集	150	0.056340	0.9952	0.092583
测试集	150	0.037933	0.9974	0.089986

Fig.7 Comparison of neural network predictions with experimental results

Fig.8 Bar chart of dimensionless parameters for a low-carbon steel disk under uniform pulse loading

Fig.9 SHAP summary plot showing feature contributions

Table 6 Quality assessment of feature models based on different feature combinations

模型	输入特征	R²	MAE/%
FE-1	($\frac{{I}^{2}}{\rho {\sigma }_{0}{H}^{2}}$,$\frac{H}{L}$)	0.97	19.7
FE-2	($\frac{{I}^{2}}{\rho {\sigma }_{0}{L}^{2}}$,$\frac{H}{L}$)	0.88	33.3

Fig.10 Two dimensionless parameters characterizing a low-carbon steel circular plate subjected to a uniform impulsive load

Fig.11 Fitting relationship between the dimensionless parameter π and the central deflection-to-thickness ratio W/H

Table 7 Prediction formula for the deflection-to-thickness ratio at the center of the plate

方程	$\frac{W}{H}$=a(($\frac{{I}^{2}}{\rho {\sigma }_{0}{H}^{2}}$)⁰^.²⁰⁰($\frac{H}{L}$)^-0^.³⁸²)^b
参数	a	b	R²	MSE
数值	0.558	2.361	0.9703	0.249

Fig.12 Graph of the relationship between load intensity I and the deflection-to-thickness ratio in a low-carbon steel disc under uniform impulse loading

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