神经网络状态方程在强爆炸冲击波数值模拟中的应用

李秦超; 姚成宝; 程帅; 张德志; 刘文祥

doi:10.11883/bzycj-2022-0222

神经网络状态方程在强爆炸冲击波数值模拟中的应用

doi: 10.11883/bzycj-2022-0222

西北核技术研究所，陕西西安 710024

详细信息

作者简介:
李秦超（1998－　），男，硕士研究生，liqinchao@nint.ac.cn

通讯作者:
刘文祥（1982－　），男，博士，研究员，liuwenxiang@nint.ac.cn

中图分类号: O382.1
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-24
- 修回日期: 2022-10-24
- 网络出版日期: 2022-10-25
- 刊出日期: 2023-04-05

Application of the neural network equation of state in numerical simulation of intense blast wave

Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

摘要

摘要: 强爆炸数值模拟的主要挑战在于如何准确地描述爆炸产物状态方程。利用BP神经网络和强爆炸产物状态数据对神经网络产物状态方程进行训练，并将得到的状态方程植入自编的一维球对称数值模拟程序，对强爆炸冲击波参数进行了计算。结果显示，计算得到的冲击波峰值超压、冲击波到时、正压时间与标准值吻合较好，证明将神经网络状态方程应用于强爆炸冲击波数值模拟是可行的。研究结果对确定强爆炸数值模拟方法具有很好的借鉴意义。
- 爆炸冲击波 /
- 神经网络 /
- 状态方程 /
- 数值模拟 /
- 芝麻数据库
Abstract: The main challenge of numerical simulation of intense explosion is how to accurately determine the equations of state for the explosive products. The traditional equations of state are mostly empirical or semi-empirical formulas, which can just deal with ordinary explosions, but the treatment of intense explosions is of great limitation. The parameters of intense explosive products span an extremely wide range, which often exceeds the scope of empirical formula. Neural network has an excellent nonlinear fitting function and can realize the function of the equations of state. At the same time, there are a lot of state parameters of material in the sesame library, and the material parameters suitable for intense explosive products were selected as training data of neural network. The tabulated data of intensive explosive product samples were pretreated to make them better used in neural networks, then the data was adopted as training set to train the BP neural network and a one-dimensional spherical numerical code embedded with neural network equation of state was used to calculate the blast wave parameters of the explosion of fission device. In the process of neural network construction, the structure of neural network was optimized by enumeration experiment, and the structure of multi-layer neural network with a simple structure and good precision was obtained. In the process of numerical calculation, the code called the embedded neural network equations of state module, calculated the pressure of the explosive product through the density and the specific internal energy, and the flow field parameters of the whole explosive blast wave were finally obtained. The numerical results show that the calculated peak overpressure, arrival time and positive pressure duration coincide with the standard values, which proves the feasibility of the application of the neural network equation of states in the intense blast wave calculations. The results are of great significance to the numerical simulation of intense explosion.
- blast wave /
- neural network /
- equation of state /
- numerical simulation /
- sesame EOS data base

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图 1 神经网络状态方程概念

Figure 1. Conceptual sketch of equation of state using neural network

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图 2 数据样本散点图

Figure 2. Data sample scatter plot

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图 3 神经网络参数结构

Figure 3. Neural network parameter structure

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图 4 神经网络状态方程建立过程

Figure 4. Establishment process of equation of state using neural network

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图 5 神经网络结构

Figure 5. Neural network structure

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图 6 神经网络训练表现

Figure 6. Neural network training performance

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图 7 神经网络整体运算结构

Figure 7. The overall operational structure of neural network

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图 8 隐含层运算结构

Figure 8. Hidden layer operation structure

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图 9 训练集检测拟合精度

Figure 9. Fitting accuracy of training set

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图 10 神经网络压力输出相对误差

Figure 10. Relative error of pressure output value of neural network

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图 11 测试集检测是否过拟合

Figure 11. Test set detecting over-fitting

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图 12 爆后166 ms爆炸流场分布

Figure 12. Explosive flow field distribution at 166 ms after the explosion

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图 13 爆炸流场历程曲线

Figure 13. Explosive flow field history curve

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图 14 数值计算结果对比

Figure 14. Comparison of numerical results

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表 1 芝麻数据库中铁蒸气数据（部分）

Table 1. Iron steam data in sesame data(part)

密度/(kg·m⁻³)	比内能/(MJ·kg ⁻¹)	压力/GPa	密度/(kg·m⁻³)	比内能/(MJ·kg ⁻¹)	压力/GPa
61.328	25.062	384.18	117.01	21.508	704.39
61.328	83.371	1600.9	117.01	77.821	2937.6
61.328	255.24	3982.1	117.01	241.89	7347.0
61.328	848.09	12766	117.01	757.22	22873
61.328	3368.3	54259	117.01	3055.8	97777

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表 2 不同隐含层数量对应的理论单层最大节点数

Table 2. The number of the maximum nodes of single layer

隐含层总数	1	2	3	4	5	6	7	8
理论最大节点	275	30	22	18	15	13	12	11

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表 3 神经网络结构测试均方误差

Table 3. Mean squared error of different Neural network structure

L	N	δ₁/10⁻⁵	δ₂/10⁻⁵	δ₃/10⁻⁵	δ₄/10⁻⁵	δ/10⁻⁵
2	5	16.7	2.8	2.0	1.4	5.725
	10	13.2	28.5	12.1	2.9	14.175
	15	2.6	0.9	1.0	1.6	1.525
	20	1.5	1.2	0.9	1.4	1.25
	25	1.4	1.8	14.6	2.5	5.075
	30*	11.2	5.8	16.9	11.6	11.375
3	5	1.1	5.2	1.8	1.1	2.3
	10	0.3	10.1	0.8	0.2	2.85
	15	3.8	0.9	0.2	2.1	1.75
	20	0.4	0.5	0.9	4.2	1.5
	22*	1.1	5.6	0.6	2.7	2.5
4	5	2.6	4.0	0.9	15.6	5.775
	10	0.6	1.0	1.1	0.5	0.8**
	15	0.7	4.5	1.1	1.0	1.825
	18*	2.6	0.7	3.8	24.3	7.85
5	5	7.5	14.3	2.0	1.4	6.3
	10	1.4	0.5	0.6	2.0	1.125**
	15*	0.7	0.2	1.1	10.0	3
6	5	1.2	0.9	1.7	1.8	1.4
	10	0.5	0.5	1.0	0.5	0.625**
	13*	0.5	0.5	0.8	0.4	0.55**
7	5	4.1	19.1	1.4	0.9	6.375
	9	1.2	2.2	3.3	1.9	2.15
	12*	0.4	0.5	0.7	1.3	0.725**
注: * 理论最大节点数；** 平均δ小于1.2×10⁻⁵。

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表 4 神经网络参数组成

Table 4. Neural network parameter composition

层	节点	权值	阈值	激活函数
输入层	2	−	−	−
隐含层1	10	10×2	10×1	y=tanhx
隐含层2	10	10×10	10×1	y=tanhx
隐含层3	10	10×10	10×1	y=tanhx
隐含层4	10	10×10	10×1	y=tanhx
输出层	1	1×10	1	y = x
元素总和	43	330	41	−

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表 5 装置初始参数

Table 5. Initial device parameter

TNT当量/kt	质量/kg	半径/m	平均密度/(g·cm⁻³)	比内能/(GJ·kg⁻¹)
15	50	0.2	1.492	1067

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表 6 数值计算误差

Table 6. Error of numerical simulation

爆心距/m	峰值超压/GPa		到时/ms		正压作用时间/ms		误差/%
爆心距/m	计算值	参考值	计算值	参考值	计算值	参考值	峰值超压	到时	正压作用时间
50	53.57	46.48	2.592	2.944	372.3	405.7	15.3	12.0	8.2
100	7.264	6.139	15.10	16.65	360.2	403.7	18.3	9.3	10.8
200	1.097	0.8511	82.10	88.22	299.1	353.2	28.9	6.9	15.3
300	0.4524	0.3095	207.4	219.8	284.1	320.7	46.2	5.6	11.4

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