基于人工神经网络算法的多相云雾爆轰毁伤效应预测模型

doi:10.12382/bgxb.2023.0094

摘要/Abstract

摘要：

云雾爆轰毁伤范围的预测是云爆武器造成大规模毁伤的研究基础,但云雾爆轰后超压场分布规律与燃料浓度的依赖关系未知,制约了对于云爆毁伤范围的预测。因此,针对2种最为常用的多相云雾燃料,采用最小自由能法计算得到了液相燃料完全以液滴或蒸汽形式存在的多相云雾发生理想爆轰的CJ参数,并通过拟合,得到体JWL状态方程参数。在此基础上计算得到了不同浓度和状态的多相云雾理想爆轰造成的超压场,并借助人工神经网络获得了浓度范围在0.03~0.30kg/m³的气固两相和气液固三相云雾场爆轰峰值超压随比例距离衰减规律的代理模型并预测不同毁伤等级对应的毁伤比例半径随燃料浓度的变化,得到毁伤比例半径最大的最优浓度。研究结果表明:云雾区中液相燃料以液滴或蒸汽形式存在对云雾爆轰参数,产物JWL状态方程参数,与云爆爆轰后超压场分布规律的影响都比较微弱(<1.5%);在0.03~0.18kg/m³的燃料浓度范围内,Ⅰ级~Ⅲ级毁伤比例半径的最大和最小值分别相差21%、19%、6%,因此大装药结构形成的云雾场爆轰后,Ⅰ级和Ⅱ级毁伤半径与燃料浓度的依赖性更强。

关键词: 云雾爆轰, 燃料浓度, 超压毁伤, 人工神经网络

Abstract:

The prediction of damage range caused by Fuel-air Explosive is fundamental to the study of large-scale damage caused by Fuel-air Explosive weapons. However, the distribution pattern of shock waves after detonation and its dependence on fuel concentration are unknown, which limits the prediction accuracy of damage range. In this study, the minimum free energy method is used to calculate the CJ parameters for the ideal detonation of biphasic cloud fog with liquid fuel present in either droplet or vapor form. The JWL equation of state parameters are obtained through fitting. Subsequently, the peak overpressure caused by ideal detonation of biphasic cloud fog with different concentrations and states is calculated. A proxy model is developed by utilizing an artificial neural network. The proposed model is used to predict the decay law of peak overpressure with respect to the scaled distance for biphasic gas-solid and gas-liquid-solid cloud detonations with concentrations ranging from 0.03 to 0.30kg/m³. The model is also used to predict the variation of damage proportion radius with fuel concentration for different damage levels, obtaining the optimal concentration with the maximum damage proportion radius. The study reveals that the influences of liquid fuel in droplet or vapor form on cloud detonation parameters, JWL equation of state parameters, and shock wave distribution after cloud detonation are relatively weak (<1.5%). Within the fuel concentrations ranging from 0.03 to 0.18kg/m³, the maximum and minimum values of damage proportion radius for damage levels Ⅰ-Ⅲ are differed by 21%, 19%, and 6%, respectively. Thus, the dependence of damage radii on fuel concentration is stronger for damage levels Ⅰ and Ⅱ after cloud burst caused by large explosive structures.

Key words: cloud detonation, fuel concentration, overpressure damage, artificial neural network

中图分类号:

TQ560.1

徐永康, 薛琨. 基于人工神经网络算法的多相云雾爆轰毁伤效应预测模型[J]. 兵工学报, 2024, 45(6): 1889-1905.

XU Yongkang, XUE Kun. Artificial Neural Network-based Prediction Model for Damage Effect of Fuel-air Explosive[J]. Acta Armamentarii, 2024, 45(6): 1889-1905.

图/表 25

表1 配方A和B的多相云爆燃料各组分构成,其中ρfuel为燃料整体密度

Table 1 The components of multiphase cloud explosion fuel of Formulae A and B

燃料配方	液相组分	固相组分	ω_m	ρ_fuel/(kg·m^-3)
A	乙醚(C₄H₁₀O)	铝粉(Al)	1.47	1230
B	环氧丙烷(C₃H₆O)		1	1640

表2 多相云爆燃料的液相和固相组分物化参数

Table 2 Physicochemical parameters of liquid and solid components of multiphase cloud explosion fuels

组分	ρ/(kg·m^-3)	M/(g·mol^-1)	$ν O 2 Ⅰ$	q/(MJ·g^-1)	$q ¯$ /(MJ·mol^-1)	P_CJ/MPa	D_CJ/(m·s^-1)	Q_CJ/(kJ·m^-3)
乙醚	0.713	74	6	36.78	2.73	1.15	1374	1463
环氧丙烷	0.830	58	4	45.8	2.66	1.4	1522	1980
铝粉	2.700	27	3/4	31.05	0.84	1.58	1513	2213

表2 多相云爆燃料的液相和固相组分物化参数

Table 2 Physicochemical parameters of liquid and solid components of multiphase cloud explosion fuels

组分	ρ/(kg·m^-3)	M/(g·mol^-1)	$ν O 2 Ⅰ$	q/(MJ·g^-1)	$q ¯$ /(MJ·mol^-1)	P_CJ/MPa	D_CJ/(m·s^-1)	Q_CJ/(kJ·m^-3)
乙醚	0.713	74	6	36.78	2.73	1.15	1374	1463
环氧丙烷	0.830	58	4	45.8	2.66	1.4	1522	1980
铝粉	2.700	27	3/4	31.05	0.84	1.58	1513	2213

图1 多相云团混合物密度和当量比随燃料浓度的变化

Fig.1 Change of the density ρmix and equivalent ratio of multiphase cloud with the fuel concentration

表3 不同多相含能体系的CJ爆轰参数的计算值与文献[22]值对比

Table 3 Comparison of calculated and literature values[22] of CJ detonation parameters for different multiphase energetic systems

燃料	燃料质量浓度/%	P_CJ/MPa			D/(km·s^-1)
燃料	燃料质量浓度/%	计算值	文献值	误差/%	计算值	文献值	误差/%
甲烷	7.25	1.652	1.780	-7.19	1.814	1.837	-1.25
庚烯	6.26	1.913	2.014	-5.01	1.811	1.800	0.61
环氧丙烷	9.62	2.037	2.106	-3.28	1.835	1.826	0.49
0.9庚烯+0.1环氧丙烷	6.49	1.921	2.018	-4.81	1.813	1.801	0.67
0.8庚烯+0.2环氧丙烷	6.73	1.930	2.023	-4.60	1.814	1.803	0.61
0.9庚烯+0.1硝酸丁酯	6.71	1.931	2.027	-4.74	1.815	1.806	0.50
0.8庚烯+0.2硝酸丁酯	7.23	1.951	2.042	-4.46	1.820	1.802	1.00
铝粉	20.87	2.432	2.562	-5.07	1.854	1.847	0.38

图2 CJ爆压PCJ,爆速DCJ,(单位体积)爆热 q ˙和爆温TCJ随燃料浓度 ρ f u e l *的变化

Fig.2 Change of CJ detonation pressure PCJ, detonation velocity DCJ, (unit volume) detonation heat q ˙ and explosion temperature TCJ with the fuel concentration ρ f u e l *

表4 2种燃料配方的多相云团在状态Ⅰ和Ⅱ下等当量比下的爆轰参数

Table 4 Detonation parameters of multiphase clouds with two fuel formulae at the same equivalent ratio in States Ⅰ and Ⅱ

燃料配方	云团状态	P_CJ/ MPa	D_CJ/ (km·s^-1)	$q ˙ C J$ / (kJ·m³)	T_CJ/ K
A	Ⅰ 147	2.136	1873	4414	3309
A	Ⅱ 144	2.161	1862	4483	3243
B	Ⅰ 146	2.063	1842	4388	3249
B	Ⅱ 142	2.066	1821	4359	3203

表4 2种燃料配方的多相云团在状态Ⅰ和Ⅱ下等当量比下的爆轰参数

Table 4 Detonation parameters of multiphase clouds with two fuel formulae at the same equivalent ratio in States Ⅰ and Ⅱ

燃料配方	云团状态	P_CJ/ MPa	D_CJ/ (km·s^-1)	$q ˙ C J$ / (kJ·m³)	T_CJ/ K
A	Ⅰ 147	2.136	1873	4414	3309
A	Ⅱ 144	2.161	1862	4483	3243
B	Ⅰ 146	2.063	1842	4388	3249
B	Ⅱ 142	2.066	1821	4359	3203

图3 不同燃料浓度下云雾爆轰后产物的等熵膨胀线

Fig.3 Isentropic expansion curves of the products at different fuel concentrations after cloud detonation

表5 A燃料Ⅰ、Ⅱ状态爆轰参数表

Table 5 Detonation parameters of Formula A in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.03	1.210	0.21	359.40	1.42	325.54	0.397	1216	950	824	Ⅰ
	1.203	0.21	418.08	1.55	321.29	0.388	1220	954	825	Ⅱ
0.05	1.230	0.34	197.18	0.78	500.79	0.359	1442	1610	1175	Ⅰ
	1.219	0.34	419.08	0.62	499.76	0.366	1448	1617	1174	Ⅱ
0.07	1.250	0.48	176.35	0.55	630.66	0.322	1587	2270	1455	Ⅰ
	1.234	0.49	173.63	0.53	629.25	0.321	1595	2280	1452	Ⅱ
0.11	1.290	0.75	208.45	0.47	831.43	0.265	1776	3583	1912	Ⅰ
	1.264	0.63	203.37	0.46	825.22	0.262	1784	3597	1894	Ⅱ
0.15	1.330	1.03	195.40	0.47	974.32	0.239	1870	4531	2189	Ⅰ
	1.295	1.06	189.99	0.44	955.98	0.242	1879	4422	2151	Ⅱ
0.19	1.370	1.3	215.54	0.46	1043.52	0.256	1922	4585	2363	Ⅰ
	1.326	1.35	206.38	0.44	1018.64	0.258	1929	4449	2303	Ⅱ
0.23	1.410	1.58	188.14	0.46	1106.02	0.264	1944	4663	2464	Ⅰ
	1.356	1.65	173.98	0.45	1074.01	0.265	1950	4504	2383	Ⅱ
0.27	1.450	1.85	161.26	0.42	1152.93	0.269	1953	4757	2540	Ⅰ
	1.387	1.95	152.17	0.41	1110.69	0.270	1958	4573	2443	Ⅱ

表5 A燃料Ⅰ、Ⅱ状态爆轰参数表

Table 5 Detonation parameters of Formula A in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.03	1.210	0.21	359.40	1.42	325.54	0.397	1216	950	824	Ⅰ
	1.203	0.21	418.08	1.55	321.29	0.388	1220	954	825	Ⅱ
0.05	1.230	0.34	197.18	0.78	500.79	0.359	1442	1610	1175	Ⅰ
	1.219	0.34	419.08	0.62	499.76	0.366	1448	1617	1174	Ⅱ
0.07	1.250	0.48	176.35	0.55	630.66	0.322	1587	2270	1455	Ⅰ
	1.234	0.49	173.63	0.53	629.25	0.321	1595	2280	1452	Ⅱ
0.11	1.290	0.75	208.45	0.47	831.43	0.265	1776	3583	1912	Ⅰ
	1.264	0.63	203.37	0.46	825.22	0.262	1784	3597	1894	Ⅱ
0.15	1.330	1.03	195.40	0.47	974.32	0.239	1870	4531	2189	Ⅰ
	1.295	1.06	189.99	0.44	955.98	0.242	1879	4422	2151	Ⅱ
0.19	1.370	1.3	215.54	0.46	1043.52	0.256	1922	4585	2363	Ⅰ
	1.326	1.35	206.38	0.44	1018.64	0.258	1929	4449	2303	Ⅱ
0.23	1.410	1.58	188.14	0.46	1106.02	0.264	1944	4663	2464	Ⅰ
	1.356	1.65	173.98	0.45	1074.01	0.265	1950	4504	2383	Ⅱ
0.27	1.450	1.85	161.26	0.42	1152.93	0.269	1953	4757	2540	Ⅰ
	1.387	1.95	152.17	0.41	1110.69	0.270	1958	4573	2443	Ⅱ

表6 B燃料Ⅰ、Ⅱ状态爆轰参数表

Table 6 Detonation parameters of Formula B in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.07	1.25	0.39	941.26	1.23	460.11	0.259	1550	2136	1504	Ⅰ
	1.233	0.39	284.07	0.78	574.73	0.309	1554	2153	1403	Ⅱ
0.11	1.290	0.61	190.84	0.45	795.94	0.270	1735	3377	1822	Ⅰ
	1.263	0.61	190.51	0.47	792.25	0.265	1746	3402	1809	Ⅱ
0.15	1.330	0.84	157.22	0.39	956.22	0.231	1838	4599	2117	Ⅰ
	1.293	0.84	154.35	0.47	949.38	0.224	1850	4626	2086	Ⅱ
0.20	1.380	1.11	158.02	0.39	1089.22	0.222	1919	5391	2391	Ⅰ
	1.330	1.11	156.06	0.40	1065.49	0.223	1934	5252	2340	Ⅱ
0.24	1.420	0.79	183.81	0.39	1158.82	0.229	1963	5605	2568	Ⅰ
	1.360	0.79	211.06	0.61	1127.95	0.224	1978	5444	2498	Ⅱ
0.29	1.470	1.62	193.81	0.40	1238.10	0.232	1998	5898	2744	Ⅰ
	1.398	1.62	193.14	0.41	1192.6	0.231	2011	5710	2648	Ⅱ

表6 B燃料Ⅰ、Ⅱ状态爆轰参数表

Table 6 Detonation parameters of Formula B in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.07	1.25	0.39	941.26	1.23	460.11	0.259	1550	2136	1504	Ⅰ
	1.233	0.39	284.07	0.78	574.73	0.309	1554	2153	1403	Ⅱ
0.11	1.290	0.61	190.84	0.45	795.94	0.270	1735	3377	1822	Ⅰ
	1.263	0.61	190.51	0.47	792.25	0.265	1746	3402	1809	Ⅱ
0.15	1.330	0.84	157.22	0.39	956.22	0.231	1838	4599	2117	Ⅰ
	1.293	0.84	154.35	0.47	949.38	0.224	1850	4626	2086	Ⅱ
0.20	1.380	1.11	158.02	0.39	1089.22	0.222	1919	5391	2391	Ⅰ
	1.330	1.11	156.06	0.40	1065.49	0.223	1934	5252	2340	Ⅱ
0.24	1.420	0.79	183.81	0.39	1158.82	0.229	1963	5605	2568	Ⅰ
	1.360	0.79	211.06	0.61	1127.95	0.224	1978	5444	2498	Ⅱ
0.29	1.470	1.62	193.81	0.40	1238.10	0.232	1998	5898	2744	Ⅰ
	1.398	1.62	193.14	0.41	1192.6	0.231	2011	5710	2648	Ⅱ

图4 实验云雾场图片和计算模型

Fig.4 Experimental cloud and fog field image and computational model

图5 实验和模拟得到的超压时程曲线

Fig.5 Experimental and simulated overpressures

图6 不同位置处的峰值超压实验模拟对比

Fig.6 Comparison of experimental and simulated peak overpressures at different positions

图7 球形云爆区爆轰超压场的一维楔形计算构型

Fig.7 One-dimensional wedge shaped computational configuration of detonation overpressure field in spherical cloud explosion zone

图8 球形云雾区爆轰后的流场压力和速度云图

Fig.8 R-t diagram of ΔPmax (a) and u(b)

图9 不同位置超压时程曲线

Fig.9 P-t diagram at different positions

图10 ΔPmax($\widetilde{R}$) of fuels with different qualities in Formula A

Fig.10 Variation curves of steady-state swerve response phase shift angle at different elevation angles

表7 A配方燃料云雾区(状态Ⅱ)爆轰后峰值超压随比例距离的衰减规律,ΔPmax( R ˙),进行拟合得到的拟合参数

Table 7 Attenuation law of peak overpressure with proportional distance after detonation in the cloud region (State Ⅱ) of fuel in Formula A

$ρ f u e l *$ / (kg· m^-3)	A₁/ (kPa·m·kg^-1/3)	A₂/ (kPa·m·kg^-1/3)	A₃/ (kPa·m·kg^-1/3)	R²
0.03	62	703	1596	0.997
0.07	138	725	853	1.000
0.11	120	991	281	0.999
0.15	93	1114	-102	0.999
0.19	69	1160	-330	0.999
0.23	51	1145	-469	0.999
0.27	39	1141	-569	0.999

表7 A配方燃料云雾区(状态Ⅱ)爆轰后峰值超压随比例距离的衰减规律,ΔPmax( R ˙),进行拟合得到的拟合参数

Table 7 Attenuation law of peak overpressure with proportional distance after detonation in the cloud region (State Ⅱ) of fuel in Formula A

$ρ f u e l *$ / (kg· m^-3)	A₁/ (kPa·m·kg^-1/3)	A₂/ (kPa·m·kg^-1/3)	A₃/ (kPa·m·kg^-1/3)	R²
0.03	62	703	1596	0.997
0.07	138	725	853	1.000
0.11	120	991	281	0.999
0.15	93	1114	-102	0.999
0.19	69	1160	-330	0.999
0.23	51	1145	-469	0.999
0.27	39	1141	-569	0.999

图11 MLP网络结构示意图

Fig.11 Schematic diagram of MLP network structure

图12 总样本数据集在二维参数空间{ ρ f u e l *, R ˙}内的分布

Fig.12 Total sample data set in two-dimensional parameter space { ρ f u e l *, R ˙}

图13 MSE随训练子集样本量占总样本量比例和迭代步数的变化

Fig.13 Change of MSE with the proportion of training subset sample size to total sample size and the number of iteration steps S

图14 ANN代理模型 f m a x A N N( ρ f u e l *, R ˙)预测的A和B配方燃料爆轰超压峰值

Fig.14 Peak values of detonation overpressure in cloud region (state Ⅱ) of fuels in Formulae A and fuel B predicted by ANN model f m a x A N N( ρ f u e l *, R ˙)

图15 爆轰超压峰值的预测值Δ P m a x p r e在{ ρ f u e l *, R ˙}空间内的等值线分布

Fig.15 Contour distribution of Δ P m a x p r e in { ρ f u e l *, R ˙}

图16 基于Δ P m a x p r e得到的云雾爆轰的三级比例毁伤半径 R ˙ i(i=1,2,3)随燃料浓度 ρ f u e l *的变化

Fig.16 R ˙ i (i=1,2,3) of different ρ f u e l * based on Δ P m a x p r e

表8 2种燃料配方在不同状态下发生云雾爆轰的三级比例毁伤半径的最大值$\widetilde{R}_{i}$,对应的燃料浓度 ρ f u e l , i *和当量比ϕi,i=1,2,3

Table 8 Maximum value $\widetilde{R}_{i}$ of the third-order proportional damage radius of cloud and mist detonation for two fuel formulae under different conditions ρ f u e l , i * and ϕi

毁伤参数	燃料配方A		燃料配方B
毁伤参数	状态Ⅰ	状态Ⅱ	状态Ⅰ	状态Ⅱ
$\widetilde{R}_{1,max}$/(m·kg^-1^/³)	8.4	8.5	8.1	8.2
$\widetilde{R}_{2,max}$/(m·kg^-1^/³)	6.2	6.2	6.0	6.0
$\widetilde{R}_{3,max}$/(m·kg^-1^/³)	3.9	3.9	3.8	3.8
$ρ f u e l, 1 *$ /(kg·m^-3)	0.096	0.097	0.101	0.104
$ρ f u e l, 2 *$ /(kg·m^-3)	0.107	0.108	0.116	0.118
$ρ f u e l, 3 *$ /(kg·m^-3)	0.112	0.112	0.117	0.117
ϕ₁	0.67	0.63	0.56	0.77
ϕ₂	0.73	0.61	0.65	0.71
ϕ₃	0.77	0.52	0.65	0.59
χ₁	20%	21%	21%	22%
χ₂	19%	19%	19%	20%
χ₃	6%	6%	8%	9%

表8 2种燃料配方在不同状态下发生云雾爆轰的三级比例毁伤半径的最大值$\widetilde{R}_{i}$,对应的燃料浓度 ρ f u e l , i *和当量比ϕi,i=1,2,3

Table 8 Maximum value $\widetilde{R}_{i}$ of the third-order proportional damage radius of cloud and mist detonation for two fuel formulae under different conditions ρ f u e l , i * and ϕi

毁伤参数	燃料配方A		燃料配方B
毁伤参数	状态Ⅰ	状态Ⅱ	状态Ⅰ	状态Ⅱ
$\widetilde{R}_{1,max}$/(m·kg^-1^/³)	8.4	8.5	8.1	8.2
$\widetilde{R}_{2,max}$/(m·kg^-1^/³)	6.2	6.2	6.0	6.0
$\widetilde{R}_{3,max}$/(m·kg^-1^/³)	3.9	3.9	3.8	3.8
$ρ f u e l, 1 *$ /(kg·m^-3)	0.096	0.097	0.101	0.104
$ρ f u e l, 2 *$ /(kg·m^-3)	0.107	0.108	0.116	0.118
$ρ f u e l, 3 *$ /(kg·m^-3)	0.112	0.112	0.117	0.117
ϕ₁	0.67	0.63	0.56	0.77
ϕ₂	0.73	0.61	0.65	0.71
ϕ₃	0.77	0.52	0.65	0.59
χ₁	20%	21%	21%	22%
χ₂	19%	19%	19%	20%
χ₃	6%	6%	8%	9%

图17 不同燃料质量三级毁伤对应最大毁伤半径和最大毁伤面积

Fig.17 Maximum damage radius and maximum damage area for different fuel qualities

参考文献 26

[1]	姚金侠, 胥会祥, 于海江, 等. 燃料空气炸药的发展现状及展望[J]. 飞航导弹, 2014(2):85-89.
	YAO J X, XU H X, YU H J, et al. Development status and prospect of fuel-air explosives[J]. Aeronautical Missile Journal, 2014(2): 85-89. (in Chinese)
[2]	LAVOIE L. Fuel-air explosives, weapons and effects[J]. Winged Missiles Journal, 1990, 23(5):814-816.
[3]	刘想炎, 黄振贵, 陈秋元, 等. 云爆弹对地面人员综合杀伤的仿真评估研究[J]. 兵器装备工程学报, 2020, 41(8):103-106, 147.
	LIU X Y, HUANG Z G, CHEN Q Y, et al. Simulation evaluation of comprehensive killing effect of FAE on ground personnel targets[J]. Journal of Ordnance Equipment Engineering, 2020, 41(8): 103-106, 147. (in Chinese)
[4]	陈学文. 爆炸冲击波毁伤威力快速评估测试系统设计[D]. 太原: 中北大学, 2022
	CHEN X W. Design of rapid evaluation and test system for damage power of explosion shock wave[D]. Taiyuan: North University of China, 2022. (in Chinese)
[5]	仲倩. 燃料空气炸药爆炸参数测量及毁伤效应评估[D]. 南京: 南京理工大学, 2012.
	ZHONG Q. Research on measurement of explosion parameters and evaluation of damage effect of Fuel Air Explosive[D]. Nanjing: Nanjing University of Science and Technology, 2012. (in Chinese)
[6]	ZHANG Q, BAI C H, LIU Q M, et al. Study on near field dispersal of fuel air explosive[J]. Journal of Beijing Institute of Technology, 1999, 8(2):113-118.
[7]	方伟, 赵省向, 李文祥, 等. 爆炸抛撒过程中FAE云雾的运动特性[J]. 含能材料, 2015, 23(11):1061-1066.
	FANG W, ZHAO S X, LI W X, et al. Movement characteristics of fuel-air explosive (FAE) clouds in the explosion dispersal process[J]. Chinese Journal of Energetic Materials, 2015, 23(11):1061-1066. (in Chinese)
[8]	郭明儒, 娄文忠, 金鑫, 等. 燃料空气炸药固体燃料浓度动态分布试验研究[J]. 兵工学报, 2016, 37(2):226-231. doi: 10.3969/j.issn.1000-1093.2016.02.005
	GUO M R, LOU W Z, JIN X, et al. Experimental research on dynamic concentration distribution of FAE solid fuel[J]. Acta Armamentarii, 2016, 37(2):226-231. (in Chinese)
[9]	吉童安, 娄文忠, 付胜华, 等. 燃料空气炸药二次起爆引信与爆轰云雾动态交会浓度检测方法[J]. 兵工学报, 2021, 42(11):2327-2332. doi: 10.3969/j.issn.1000-1093.2021.11.005
	JI T A, LOU W H, FU S H, et al. Dynamic rendezvous concentration detection method for FAE secondary detonation fuze and blast cloud[J]. Acta Armamentarii, 2021, 42(11): 2327-2332. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.11.005
[10]	陈明生. 大体积燃料空气混合物爆轰基础问题研究[D]. 北京: 北京理工大学, 2015.
	CHEN M S. Research on Research on basic characteristics of large volume fuelair mixtures detonation[D]. Beijing: Beijing Institute of Technology, 2015. (in Chinese)
[11]	薛社生, 刘家骢, 彭金华. 液体燃料爆炸抛撒过程分析[J]. 南京理工大学学报, 1998, 22(1):34-38.
	XUE S S, LIU J C, PENG J H. Analysis of liquid fuel explosion and throwing process[J]. Journal of Nanjing University of Science and Technology, 1998, 22(1):34-38. (in Chinese)
[12]	BAI C H, ZHAO X Y, YAO J, et al. Numerical investigation of the shockwave overpressure fields of multi-sources FAE explosions[J]. Defence Technology, 2021, 17(4): 1168-1177. doi: 10.1016/j.dt.2020.06.020
[13]	白春华, 梁慧敏, 李建平, 等. 云雾爆轰[M]. 北京: 科学出版社,2012.
	BAI C H, LIANG H M, LI J P, et al. Cloud and mist detonation[M]. Beijing: Science Press, 2012. (in Chinese)
[14]	王德润, 沈兆武, 周听清. 液体燃料爆炸抛撒及云雾形成的实验研究[J]. 流体力学实验与测量, 2004, 18(4):15-19.
	WANG D R, SHEN Z W, ZHOU T Q. Experimental study on the explosion dispersion and cloud formation of liquid fuel[J]. Journal of Experiments in Fluid Mechanics, 2004, 18(4):15-19. (in Chinese)
[15]	赵衡阳, 欧育湘. 气体和粉尘爆炸原理[M]. 北京: 北京理工大学出版社,1996.
	ZHAO H Y, OU Y X. Principles of gas and dust explosion[M]. Beijing: Beijing Institute of Technology Press, 1996. (in Chinese)
[16]	刘庆明, 白春华, 张奇, 等. 多相云雾爆炸计算机仿真[J]. 兵工学报, 2002, 23(1): 19-22.
	LIU Q M, BAI C H, ZHANG Q, et al. Computer simulation of multiphase cloud explosion[J]. Acta Armamentarii, 2002, 23(1): 19-22. (in Chinese)
[17]	廉政. 云雾爆轰超压场及其破坏效应[D]. 北京: 北京理工大学, 2020.
	LIAN Z. Overpressure field of cloud detonation and their destructive effects[D]. Beijing: Beijing Institute of Technology, 2020. (in Chinese)
[18]	LEE E L, HORNIG H C, KURY J W. Adiabatic expansion of high explosive detonation products:UCRL-50422[R]. Livermore, CA, US: University of California Radiation Laboratory at Livermore, 1968.
[19]	CUDZILO S, TREBINSKI R, TRZCINSKI W. Determination of the effective exponent of isentrope for the detonation products of high explosives[J]. Chemical Physics Reports, 1997, 16(9):1719-1732.
[20]	GRYS S, TRZCINSKI W A. Calculation of combustion, explosion and detonation characteristics of energetic materials[J]. Central European Journal of Energetic Materials, 2010, 7(2): 97-113.
[21]	张宝平, 张庆明, 黄风雷. 爆轰物理学[M]. 北京: 兵器工业出版社, 2009.
	ZHANG B P, ZHANG Q M, HUANG F L. Detonation physics[M]. Beijing: Publishing House of Ordnance Industry, 2009. (in Chinese)
[22]	SEDGWICK R T, KRATZ H R. Fuel air explosives: a parametric investigation[C]∥Proceedings of the 10th Symposium on explosive and pyrotechnics. San Francisco. CA, US: Philadelphia Franklin Research Center, 1979.
[23]	赵星宇, 白春华, 姚箭. 燃料空气炸药爆轰产物JWL状态方程参数计算[J]. 兵工学报, 2020, 41(10): 1921-1929.
	ZHAO X Y, BAI C H, YAO J, et al. Parameters calculation of JWL EOS of FAE detonation products[J]. Acta Armamentarii, 2020, 41(10): 1921-1929. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.10.001
[24]	SUCESKA M, DOBRILOVIC M, BOHANEK V, et al. Estimation of explosive energy output by EXPLO5 thermochemical code[J]. Zeitschrift für anorganische und allgemeine Chemie, 2021, 647(4):231-238.
[25]	YAO Z, SUNG W J, MAVRIS D N. Application of convolutional neural network to predict airfoil lift coefficient[C]∥Proceedings of 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Kissimmee, FL, US:AIAA, 2018.
[26]	辛大钧, 薛琨. 基于人工神经网络的非球形破片阻力系数预测模型[J]. 兵工学报, 2022, 43(5): 1083-1092. doi: 10.12382/bgxb.2021.0121
	XIN D J, XUE K. Artificial neural network-based prediction model for the air drag coefficient of non-spherical fragments[J]. Acta Armamentarii, 2022, 43(5):1083-1092. (in Chinese) doi: 10.12382/bgxb.2021.0121