Fast estimation of blast loading of complex structures based on Bayesian deep learning
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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却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,该方法在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。Abstract: For the estimation of blast loading on complex structures, traditional numerical simulation methods were computationally intensive, while rapid estimation methods based on neural networks could only provide point estimates without offering confidence intervals for the results. To achieve fast and reliable estimation of blast loading on complex structures during explosions, Bayesian theory was integrated with deep learning to develop a Bayesian deep learning approach for rapid estimation of blast loading on complex structures. The approach initially utilized open-source numerical simulation software to generate a dataset of blast loading on 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 numerical simulation accuracy verification. On this foundation, 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 uncertainty quantification precision. Additionally, an error decomposition of the estimation results was conducted, analyzing model performance based on target parameters and scaled distance. The results indicate that the proposed method achieved an estimation error of approximately 12.2% on the test set, with a confidence interval covering over 81.6% of true values, and the estimation time for a single sample point did not exceed 20 milliseconds. This method enables fast and accurate estimation of blast loading on complex structures while providing confidence information for the estimation results, representing a novel approach for achieving rapid and reliable estimation of blast loading on complex structures.
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Key words:
- complex structures /
- blast loading /
- Bayesian deep learning /
- quantization of uncertainty
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表 1 爆源参数的范围
Table 1. The range of explosion source parameter
爆源相关参数 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 )表 2 经验常数的取值
Table 2. The value of empirical constant
A/TPa B/TPa R1 R2 λ e/(TJ·m−3) ρ0/(kg·m−3) 609.77 12.95 4.50 0.9 0.25 9.0 1 630 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 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 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 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 δmape R2 ppicp wnmpiw 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 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 δmape/% φ/% 0 < δmape ≤ 10 10 < δmape ≤ 20 20 < δmape ≤ 30 30 < δmape ≤ 50 δmape ≤ 50 Δp0 ≤ 50 1927 10.173 66.27 21.33 7.16 3.68 98.44 50 < Δp0 ≤ 100 282 20.492 37.94 24.82 15.60 16.67 95.03 100 < Δp0 ≤ 150 124 17.714 41.13 20.97 18.55 14.52 95.15 150 < Δp0 ≤ 400 83 25.008 18.07 18.07 26.51 32.53 95.18 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/$ (m{\cdot kg}^{-\frac{1}{3}}) $ 样本数量 δmape/% φd/% 0 < δmape ≤ 10 10 < δmape ≤ 20 20 < δmape ≤ 30 30 < δmape ≤ 50 δmape ≤ 50 3 < d ≤ 5 388 21.114 34.79 23.97 16.75 18.04 93.55 5 < d ≤ 7 963 13.091 57.22 23.88 8.72 7.79 97.61 7 < d ≤ 10 949 8.389 71.97 18.12 6.43 2.85 99.37 -
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