基于贝叶斯深度学习的复杂结构爆炸载荷的快速估计

潘美霖; 彭卫文; 冷春江; 邱玖禄; 钟巍

doi:10.11883/bzycj-2024-0191

基于贝叶斯深度学习的复杂结构爆炸载荷的快速估计

doi: 10.11883/bzycj-2024-0191

1.
中山大学智能工程学院，广东广州 510275
2.
西北核技术研究所强脉冲辐射环境模拟与效应全国重点实验室，陕西西安 710024

详细信息

作者简介:
潘美霖（1999－　），女，硕士研究生，panmlin@mail2.sysu.edu.cn

通讯作者:
钟　巍（1986－　），男，博士，副研究员，zhongwei@nint.ac.cn

中图分类号: O382.1
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- 文章访问数: 110
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- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2024-06-18
- 修回日期: 2024-10-09
- 网络出版日期: 2024-11-05

Fast estimation of blast loading in complex structures based on Bayesian deep learning

1.
School of Intelligent System Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, China
2.
National Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

摘要

摘要: 对于复杂结构的爆炸载荷估计，传统数值模拟方法计算耗时长，而基于神经网络的快速估计仅能进行点估计，无法给出结果的置信度。为此，结合贝叶斯理论和深度学习，构建了复杂结构爆炸载荷快速估计的贝叶斯深度学习方法。通过开源数值模拟软件，计算了爆炸当量、位置、速度等参数大范围变化下复杂结构的爆炸载荷数据，基于贝叶斯理论将深度学习模型参数视为随机变量，利用变分贝叶斯推断高效训练模型，在保证爆炸载荷快速估计精度的同时，赋予模型不确定性量化的能力。结果表明，该方法对训练数据以外的爆炸载荷快速估计的误差约为12.2%，置信区间涵盖真实值的百分比超过81.6%，单点爆炸载荷估计时间不超过20 ms。该方法是实现复杂结构爆炸载荷快速、可信估计的新方法。
- 复杂结构 /
- 爆炸载荷 /
- 贝叶斯深度学习 /
- 不确定性量化
Abstract: For the estimation of blast loading in complex structures, traditional numerical simulation methods were computationally intensive whereas rapid estimation methods based on neural networks can only provide estimates at local points without providing confidence intervals for the predicted results. To achieve fast and reliable estimation of the blast loading in complex structures, Bayesian theory was combined with deep learning to develop a Bayesian deep learning approach for rapid estimation of blast loading in complex structures. The approach initially utilized open-source numerical simulation software to generate a dataset of blast loading in complex structures, encompassing a wide range of parameters such as explosion equivalents, locations, and velocities. During this process, mesh sizes that balanced computational accuracy and speed were determined through mesh sensitivity analysis and the verification of the numerical simulation accuracy. Then, the deep learning model was extended into a Bayesian deep learning model based on Bayesian theory. By introducing probability distributions over the weights of the neural network, the model parameters were treated as random variables. Variational Bayesian inference was then employed to efficiently train the model, ensuring the accuracy of rapid blast loading estimation while also equipping the model with the ability to quantify uncertainty. Finally, metrics such as mean absolute percentage error (MAPE), normalized mean prediction interval width (NMPIW) and prediction interval coverage probability (PICP) were adopted to quantitatively assess the model's estimated accuracy and the precision of the uncertainty quantification. Additionally, an error decomposition of the estimation results was conducted to analyze model’s performance based on target parameters and scaled distance. The results indicate that the proposed method achieved an estimation error of 12.2% on the test set, with a confidence interval covering over 81.6% of true values, and less than 20 milliseconds of the estimation time for a single sample point. This method provides a novel approach for fast and accurate estimation of blast loading in complex structures with sufficient confidence for the estimation results.
- complex structures /
- blast loading /
- Bayesian deep learning /
- quantization of uncertainty

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图 1 复杂结构模型及压力监测点分布

Figure 1. Complex structure model and distribution of pressure monitoring points

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图 2 网格尺寸不同时数值模拟与经验公式计算的结果对比

Figure 2. Comparison of numerical simulation results with empirical formulas under different grid settings

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图 3 模型训练过程中损失与训练迭代次数的关系

Figure 3. Relationship between iteration times and loss during model training

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图 4 超压峰值的估计结果

Figure 4. The estimated result of the peak overpressure

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图 5 超压峰值的真实值与估计值

Figure 5. The true value and estimated value of the peak overpressure

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图 6 范围不同时超压峰值的真实值与估计值

Figure 6. The true value and estimated value of the peak overpressure for different ranges

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表 1 爆源参数的范围

Table 1. The range of explosion source parameters

爆源参数	符号	单位	参数范围
当量	Q	kg	(200, 2000)
爆心距	R	m	(40, 100)
起爆速度	U	m/s	(0, 1020)

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表 2 经验常数的取值

Table 2. The value of empirical constant

A/TPa	B/TPa	R₁	R₂	λ₁	e/(TJ·m⁻³)	ρ₀/(kg·m⁻³)
609.77	12.95	4.50	0.9	0.25	9.0	1 630

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表 3 不同背景网格设置下数值模拟所需的计算时间

Table 3. Calculation time required for numerical simulation with different background grid settings

背景网格尺寸/m	5.0	7.5	10.0
计算时间/h	10	2	1

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表 4 待调节的超参数及其取值范围

Table 4. The hyperparameter to be adjusted and the corresponding range

神经网络层数	每层神经元数	激活函数	学习率
2～8	16, 32, 64, 128, 256	ReLU, Leaky ReLU	0.001, 0.005, 0.010

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表 5 模拟平台的参数

Table 5. Parameters of the simulation platform

平台	处理器	内存	操作系统
天河二号超级计算中心	2×12 Intel Xeon E5-2692 v2/单节点	128 GB/单节点	Linux lon26 3.10.0-514.el7.x86_64
本地台式机	AMD Ryzen7 3700x8-Core八核	32 GB	Windows10

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表 6 超压峰值的估计精度和不确定性

Table 6. The estimation accuracy and uncertainty of the peak overpressure

估计精度				不确定性
δ_mape		R²		p_picp		w_nmpiw
训练集	测试集	训练集	测试集	训练集	测试集	训练集	测试集
0.104	0.122	0.834	0.830	0.921	0.816	0.041	0.057

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表 7 基于目标范围的误差分解

Table 7. Error decomposition based on target range

超压峰值/kPa	样本数量	δ_mape/%	φ/%
超压峰值/kPa	样本数量	δ_mape/%	0 < δ_mape ≤ 10	10 < δ_mape ≤ 20	20 < δ_mape ≤ 30	30 < δ_mape ≤ 50	δ_mape ≤ 50
[0, 50]	1927	10.173	66.27	21.33	7.16	3.68	98.44
(50, 100]	282	20.492	37.94	24.82	15.60	16.67	95.03
(100, 150]	124	17.714	41.13	20.97	18.55	14.52	95.15
(150, 400]	83	25.008	18.07	18.07	26.51	32.53	95.18

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表 8 基于比例距离的误差分解

Table 8. Error decomposition based on scaled distance

比例距离/$ (\mathrm{m}\mathrm{\cdot kg}^{-\frac{1}{3}}) $	样本数量	δ_mape/%	φ_d/%
比例距离/$ (\mathrm{m}\mathrm{\cdot kg}^{-\frac{1}{3}}) $	样本数量	δ_mape/%	0 < δ_mape ≤ 10	10 < δ_mape ≤ 20	20 < δ_mape ≤ 30	30 < δ_mape ≤ 50	δ_mape ≤ 50
(3, 5]	388	21.114	34.79	23.97	16.75	18.04	93.55
(5, 7]	963	13.091	57.22	23.88	8.72	7.79	97.61
(7, 10]	949	8.389	71.97	18.12	6.43	2.85	99.37

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