图学习驱动的爆炸冲击钢筋混凝土柱结构响应的建模与预测

潘刘娟; 张雍奇; 王祉乔; 王名川; 何勇; 胡杰; 吴威涛; 彭江舟

doi:10.11883/bzycj-2025-0179

图学习驱动的爆炸冲击钢筋混凝土柱结构响应的建模与预测

doi: 10.11883/bzycj-2025-0179

1.
南京理工大学机械工程学院，江苏南京 210094
2.
南京理工大学中法工程师学院，江苏南京 210094
3.
南京理工大学安全科学与工程学院，江苏南京 210094

基金项目: 中国博士后基金面上项目（2025M774265）；江苏省自然科学基金青年基金项目（BK20241439）

详细信息

作者简介:
潘刘娟（2001－　），女，博士研究生，panliujuan@njust.edu.cn

通讯作者:
彭江舟（1996－　），男，博士，博士后，pengjz@njust.edu.cn

中图分类号: O342
计量
- 文章访问数: 294
- HTML全文浏览量: 43
- PDF下载量: 100
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-17
- 修回日期: 2025-10-27
- 网络出版日期: 2025-11-04

Modeling and prediction of blast-Induced response in RC columns using graph neural networks

1.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
School of Sino-French Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
3.
School of Safety Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

摘要: 爆炸冲击下钢筋混凝土构件结构响应的高效准确预测对抢修决策、结构加固与防护设计具有关键意义。现有结构响应快速计算方法，例如解析模型、轻量级数据驱动方法，虽具备较高计算效率，但在三维结构响应场计算方面精度受限。本文提出一种基于图神经网络（graph neural networks，GNN）的钢筋混凝土柱毁伤快速预测模型，通过GNN中的领域节点聚合机制高效传递结构内部的力学关联信息，从而在爆炸荷载输入与三维构件结构响应之间建立端到端映射，实现对柱体毁伤状态的快速预测。进一步引入多工况特征耦合训练策略，使模型具备适应不同配筋率、爆炸当量和起爆位置等工况的预测能力，显著提升了模型的跨工况泛用性能。结果表明，该模型单次预测耗时仅55 ms，较传统方法速度提升4个数量级，预测误差低于3.33%，在多种爆炸工况下均实现高精度毁伤预测。该研究展示了GNN方法在爆炸毁伤预测中的应用潜力，为爆炸冲击结构毁伤的快速评估与防护优化提供创新技术路径。
- 爆炸荷载 /
- 钢筋混凝土构件 /
- 毁伤效应 /
- 深度学习 /
- 图神经网络
Abstract: The efficient and accurate prediction of structural responses in reinforced concrete components under blast loading plays a critical role in emergency repair decision, structural strengthening, and protective design. Existing rapid methods for calculating structural response, such as analytical models and lightweight data-driven approaches, are computationally efficient. However, they are limited in accurately resolving three-dimensional structural response fields. A Graph Neural Network (GNN)-based model for the rapid prediction of damage in reinforced concrete (RC) columns was proposed in this paper. By leveraging the neighborhood node aggregation mechanism of GNNs, the model efficiently transmits mechanical correlation information within the structure. This allows the model to establish an end-to-end mapping between blast load inputs and the 3D structural response of the component, enabling rapid prediction of the column's damage state. Furthermore, a multi-scenario feature coupling training strategy is introduced to significantly enhance the model's generalization capability. This strategy enables the GNN model to effectively adapt to variations in key design and loading parameters, including reinforcement ratios, explosive charge weights, and blast locations. The results demonstrate that the proposed model achieves a prediction time of merely 55 milliseconds per instance, representing a computational speed improvement of four orders of magnitude over conventional methods; meanwhile, the prediction error remains below 3.33%. Furthermore, it delivers high-precision damage predictions across various blast scenarios. The proposed study successfully highlights the significant potential of GNN-based approaches in predicting blast-induced damage and offers an innovative, data-driven solution for rapid structural assessment and protective design in the field of blast engineering.
- explosive load /
- RC member /
- damage effect /
- deep learning /
- graph neural networks

HTML全文

图 1 混凝土与钢筋结构示意图

Figure 1. Diagram of concrete and steel structure

下载: 全尺寸图片幻灯片

图 2 仿真结果与实验结果对比

Figure 2. Comparison between simulation results and experimental results

下载: 全尺寸图片幻灯片

图 3 数据结构比较

Figure 3. The Comparison of the two representation methods on a small scale

下载: 全尺寸图片幻灯片

图 4 代理模型的框架图.

Figure 4. The framework diagram of the GNN-based RC column damage prediction model

下载: 全尺寸图片幻灯片

图 5 训练数据集工况设计

Figure 5. Configuration of the Training Dataset

下载: 全尺寸图片幻灯片

图 6 数据集设计与额外特征

Figure 6. The dataset design and the additional feature

下载: 全尺寸图片幻灯片

图 7 接触爆炸下GNN模型与Abaqus仿真可视化结果对比

Figure 7. Visualization comparison between GNN model and Abaqus simulation under contact explosion conditions

下载: 全尺寸图片幻灯片

图 8 非接触爆炸下GNN模型与Abaqus仿真可视化结果对比

Figure 8. Visualization comparison between GNN model and Abaqus simulation under non-contact explosion

下载: 全尺寸图片幻灯片

图 9 接触爆炸与非接触爆炸误差指标柱状图

Figure 9. Contact explosion and non-contact explosion error index histogram

下载: 全尺寸图片幻灯片

图 10 RC柱单元损失百分比随当量的变化趋势

Figure 10. Change trend of RC column element percentage with equivalent change

下载: 全尺寸图片幻灯片

图 11 RC柱单元损失百分比随配筋率的变化趋势

Figure 11. Change trend of RC column unit percentage with reinforcement ratio

下载: 全尺寸图片幻灯片

图 12 钢筋单元损失百分比随配筋率的变化趋势

Figure 12. Change trend of reinforcement unit percentage with reinforcement ratio

下载: 全尺寸图片幻灯片

图 13 模型影响因素分析

Figure 13. Analysis of model influencing factors

下载: 全尺寸图片幻灯片

图 14 模型多案例稳定性

Figure 14. Stability of model in multi-case

下载: 全尺寸图片幻灯片

表 1 混凝土材料参数

Table 1. Material parameters for concrete

密度/(kg·m⁻³)	杨氏模量/GPa	泊松比	膨胀角	偏心率	初始等双向压缩屈服应力与初始单向压缩屈服应力的比值	拉伸子午线与压缩子午线上第二应力不变量的比值
2500	30	0.2	30	0.1	1.16	0.6667

压缩屈服应力/MPa	压缩强度/MPa	压缩断裂应变	拉伸屈服应力/MPa	拉伸强度/MPa	拉伸断裂应变
1.71	20.13	0.007	0.24	2.01	0.0005

下载: 导出CSV

表 2 钢筋材料参数

Table 2. Material parameters for steel

密度/(kg·m⁻³)	杨氏模量/GPa	泊松比	屈服应力/MPa	极限强度/MPa	极限强度对应应变
7850	205	0.3	450	600	0.5

下载: 导出CSV

表 3 炸药材料参数

Table 3. Material parameters for the explosive

密度/ (kg·m⁻³)	爆轰波速度/ (m·s⁻¹)	爆炸物常数A/ GPa	爆炸物常数B/ MPa	爆炸物常数ω	爆炸物常数R₁	爆炸物常数R₂	爆轰能量密度/ (MJ·g⁻¹)	爆轰前体积模量/MPa
1 630	6 930	373.77	3 747.1	0.37	4.15	0.95	4.29	1 290

下载: 导出CSV

表 4 训练超参数与代理模型结构

Table 4. The structure of the GNN model and training hyperparameters

MLP隐藏层层数	隐藏层大小	消息传递步数	连接半径(k)	节点特征数	激活函数	批量大小	p_beta	学习率
2	128	8	7	3	ReLU	2	1	1×10⁻⁴

下载: 导出CSV

表 5 接触爆炸下GNN模型预测与Abaqus仿真结果的误差

Table 5. The error between GNN model prediction and Abaqus simulation results under contact explosion

工况	爆炸位置 (x, y, z)	MAE/%		RMSE/%
工况	爆炸位置 (x, y, z)	混凝土	钢筋	混凝土	钢筋
1	(2.68, 0, 16)	3.02	1.97	9.87	4.98
2	(2.68, 0, 13)	3.18	2.22	10.96	4.62
3	(2.68, 0, 10)	2.66	2.48	9.01	4.56
4	(2.68, 0, 7)	2.75	1.98	9.75	3.54
5	(2.68, 0, 4)	2.33	1.37	8.67	2.96
方差		0.0870	0.1354	0.6289	0.5729

下载: 导出CSV

表 6 非接触爆炸下GNN模型预测与Abaqus仿真结果误差

Table 6. The error between GNN model prediction and Abaqus simulation results under non-contact explosion

工况	爆炸位置 (x, y, z)	MAE/%		RMSE/%
工况	爆炸位置 (x, y, z)	混凝土	钢筋	混凝土	钢筋
2-1	(6, 4, 2)	2.13	1.44	5.87	2.63
2-2	(6, 10, 6)	1.29	0.47	4.79	0.64
2-3	(6, 10, 2)	2.32	1.67	5.91	3.05
2-4	(10, 7, 0)	1.62	1.33	3.55	1.93
方差		0.1664	0.2063	0.9320	0.8346

下载: 导出CSV

表 7 GNN模型与Abaqus数值仿真耗时对比

Table 7. Comparison of time-consuming between GNN model and Abaqus numerical simulation

模型	时间/s
模型	工况1	工况2	工况3	工况4	工况5
GNN	0.055	0.054	0.055	0.054	0.054
Abaqus	2100	2220	2160	2220	2520

下载: 导出CSV

参考文献(26)

[1]	马春茂, 孙卫平, 李炎, 等. 武器装备毁伤评估研究进展 [J]. 火炮发射与控制学报, 2019, 40(4): 96–101. DOI: 10.19323/j.issn.1673-6524.2019.04.020. MA C M, SUN W P, LI Y, et al. Research progress in damage assessment of weapon equipment [J]. Journal of Gun Launch & Control, 2019, 40(4): 96–101. DOI: 10.19323/j.issn.1673-6524.2019.04.020.
[2]	CHAI C X, REN C X, YIN C C, et al. A multifeature fusion short‐term traffic flow prediction model based on deep learnings [J]. Journal of Advanced Transportation, 2022, 2022(1): 1702766. DOI: 10.1155/2022/1702766.
[3]	WEYN J A, DURRAN D R, CARUANA R. Improving data‐driven global weather prediction using deep convolutional neural networks on a cubed sphere [J]. Journal of Advances in Modeling Earth Systems, 2020, 12(9): e2020MS002109. DOI: 10.1029/2020MS002109.
[4]	张帆, 张恒, 李卓越, 等. 基于深度学习方法的圆柱绕流实验缺失数据重构 [J]. 物理学报, 2025, 74(7): 074701. DOI: 10.7498/aps.74.20241689. ZHANG F, ZHANG H, LI Z Y, et al. Reconstruction of gappy data in cylindrical flow experiments based on deep learning method [J]. Acta Physica Sinica, 2025, 74(7): 074701. DOI: 10.7498/aps.74.20241689.
[5]	LIU H, ZHANG G H. Enhancing efficiency and energy optimization: data-driven solutions in process industrial manufacturing [J]. EAI Endorsed Transactions on Energy Web, 2024, 11(1): 1–11. DOI: 10.4108/ew.6098.
[6]	UNNO K, MIKAMI A, SHIMIZU M. Damage detection of truss structures by applying machine learning algorithms [J]. International Journal of GEOMATE, 2019, 16(54): 62–67. DOI: 10.21660/2019.54.4840.
[7]	BANG H, LEE T H, LEE G C, et al. Strain-based fault detection of bolted truss structures using machine learning [J]. Advances in Mechanical Engineering, 2020, 12(11): 1–8. DOI: 10.1177/1687814020971890.
[8]	MAI H T, KANG J, LEE J. A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior [J]. Finite Elements in Analysis and Design, 2021, 196: 103572. DOI: 10.1016/j.finel.2021.103572.
[9]	ALMUSTAFA M K, NEHDI M L. Machine learning model for predicting structural response of RC columns subjected to blast loading [J]. International Journal of Impact Engineering, 2022, 162: 104145. DOI: 10.1016/j.ijimpeng.2021.104145.
[10]	ALMUSTAFA M K, NEHDI M L. Novel hybrid machine learning approach for predicting structural response of RC beams under blast loading [J]. Structures, 2022, 39: 1092–1106. DOI: 10.1016/j.istruc.2022.04.007.
[11]	ALMUSTAFA M K, NEHDI M L. Machine learning prediction of structural response of steel fiber-reinforced concrete beams subjected to far-field blast loading [J]. Cement and Concrete Composites, 2022, 126: 104378. DOI: 10.1016/j.cemconcomp.2021.104378.
[12]	ALMUSTAFA M K, NEHDI M L. Machine learning prediction of structural response for FRP retrofitted RC slabs subjected to blast loading [J]. Engineering Structures, 2021, 244: 112752. DOI: 10.1016/j.engstruct.2021.112752.
[13]	ALMUSTAFA M K, BALOMENOS G P, NEHDI M L. Data-driven reliability framework for qualitative damage states of reinforced concrete beams under blast loading [J]. Engineering Structures, 2023, 294: 116803. DOI: 10.1016/j.engstruct.2023.116803.
[14]	ZHOU X Q, HUANG B G, WANG X Y, et al. Deep learning-based rapid damage assessment of RC columns under blast loading [J]. Engineering Structures, 2022, 271: 114949. DOI: 10.1016/j.engstruct.2022.114949.
[15]	ABD-ELHAMED A, ALKHATIB S, ABDELFATTAH A M H. Prediction of blast-induced structural response and associated damage using machine learning [J]. Buildings, 2022, 12(12): 2093. DOI: 10.3390/buildings12122093.
[16]	TRAN P L, TRAN V L, KIM J K. Mid-span displacement and damage degree predictions of RC beams under blast loading using machine learning-based models [J]. Structures, 2024, 65: 106702. DOI: 10.1016/j.istruc.2024.106702.
[17]	AHMED B, PARK T, JEON J S. Blast response and damage assessment of reinforced concrete slabs using convolutional neural networks [J]. International Journal of Damage Mechanics, 2025, 34(5): 771–797. DOI: 10.1177/10567895231204640.
[18]	LUBLINER J, OLIVER J, OLLER S, et al. A plastic-damage model for concrete [J]. International Journal of solids and structures, 1989, 25(3): 299–326. DOI: 10.1016/0020-7683(89)90050-4.
[19]	LEE J, FENVES G L. Plastic-damage model for cyclic loading of concrete structures [J]. Journal of Engineering Mechanics, 1998, 124(8): 892–900. DOI: 10.1061/(ASCE)0733-9399(1998)124:8(892).
[20]	HILLERBORG A, MODÉER M, PETERSSON P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements [J]. Cement and Concrete Research, 1976, 6(6): 773–781. DOI: 10.1016/0008-8846(76)90007-7.
[21]	武伟超, 夏柳, 潘艾刚, 等. 多点同时爆炸对钢筋混凝土方柱构件的毁伤特性 [J]. 爆炸与冲击, 2023, 43(12): 125101. DOI: 10.11883/bzycj-2023-0025. WU W C, XIA L, PAN A G, et al. Damage characteristics of reinforced concrete square column components under multi-point simultaneous initiating [J]. Explosion and Shock Waves, 2023, 43(12): 125101. DOI: 10.11883/bzycj-2023-0025.
[22]	WU Z H, PAN S R, CHEN F W, et al. A comprehensive survey on graph neural networks [J]. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(1): 4–24. DOI: 10.1109/TNNLS.2020.2978386.
[23]	SUJON K M, HASSAN R B, TOWSHI Z T, et al. When to use standardization and normalization: empirical evidence from machine learning models and XAI [J]. IEEE Access, 2024, 12: 135300–135314. DOI: 10.1109/ACCESS.2024.3462434.
[24]	GAL M S, RUBINFELD D L. Data standardization [J]. New York University Law Review, 2019, 94: 737–770. DOI: 10.1007/springerreference_64724.
[25]	NGOC T T, VAN DAI L, MINH L B. Effects of data standardization on hyperparameter optimization with the grid search algorithm based on deep learning: a case study of electric load forecasting [J]. Advances in Technology Innovation, 2022, 7(4): 258–269. DOI: 10.46604/aiti.2022.9227.
[26]	KINGMA D P, BA J. Adam: a method for stochastic optimization [C]//Proceedings of the 3rd International Conference on Learning Representations. San Diego: ICLR, 2015: 1–15.