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Jones-Wilkins-Lee (JWL)状态方程是一种不显含化学反应、由实验方法确定参数的半经验状态方程, 能比较精确地描述爆轰产物的膨胀驱动做功过程. 在JWL状态方程中有多个未知(不确定)参数需要确定. 传统的确定JWL状态方程参数的方法是调参数, 人为因素影响较大, 无法给出参数的不确定性信息. 本文利用贝叶斯分析方法研究了炸药的不确定参数, 该方法能够基于以往的认识、实验和模拟数据标定(calibration)不确定参数. 在本文结果中, 不确定参数的后验分布均值与文献结果相符合, 基于参数标定结果的数值模拟90%置信区间完全包含实验数据. 数值标定结果说明贝叶斯参数标定适用于确定样品炸药的JWL状态方程参数. 特别是, 在本文JWL状态方程参数标定过程中极大地减少了人为因素的影响.
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关键词:
- 炸药爆轰产物 /
- Jones-Wilkins-Lee状态方程 /
- 不确定参数 /
- 贝叶斯分析
Equation of state of detonation products possesses various types of mathematical expressions which describe the relation between pressure and volume. Jones-Wilkin-Lee (JWL) equation of state is a widely used equation of state of detonation products because of its simplicity in hydrodynamic calculations. The JWL equation of state may accurately describe the process of expansion drive of detonation products. The JWL equation of state contains parameters, and describe the relation among the volume, energy and pressure of detonation products. These parameters may be determined by detonation experimental data and numerical method. Traditional numerical method is adjusting parameters based on experimental data and numerical experience. Obviously, artificial ingredient may affect the calibrating result in traditional method. This paper uses the Bayesian method to determine the unknown (uncertain) parameter of JWL equation of state for detonation products. The method can calibrate the uncertain parameters based on the known parameter information, the experimental and simulating data. The results of the paper are consistent with those in the reference papers. By theoretical analysis the calibration result accords with the physical signification of the parameters of JWL equation of state. The epistemic uncertainty is slightly reduced. The calibration result collects all the parameter information in the prior parameter information, experimental data and numerical results. The experimental data are totally included in a 90% confidence interval of simulation. The numerical result shows that this method can be used to study the uncertain parameter of JWL equation of state for some sample explosives. Especially, the method reduces the artificial ingredient in the parameter calibration.-
Keywords:
- detonation products /
- Jones-Wilkin-Lee equation of state /
- uncertain parameters /
- Bayesian inference
[1] Green L, Lee E, Mitchell A, Tipton R, van Thiel M, Finger M 1993 UCRL-89664 CA: Lawrence Livemore National Laboratory
[2] Ralph M 2015 LA-UR-15-29536 Los Alamos National Laboratory
[3] Kury J W, Hornig H C, Lee E L, Mcdonnel J L, Ornellas D L, Finger M, Strangl F M, Wilkins M L 1966 Proceedings of the 4th International Symposium on Detonation White Oak, Maryland, October 12-15, 1965 p3
[4] Sun C W, Wei Y Z, Zhou Z K 2000 Applied Detonation Physics (Beijing: national defence Publication Company) p286 (in Chinese) [孙承伟, 卫玉章, 周之奎 2000 应用爆轰物理 (北京：国防工业出版社) 第286页]
[5] Zhou Z, Nie J, Guo X, Wang Q 2015 Chin. Phys. Lett. 32 016401
[6] Jiang H M, Zhang R Q 1998 Journal of Ballistics 10 25 (in Chinese) [江厚满, 张若棋 1998 弹道学报 10 25]
[7] Kennedy M, OHagan A 2001 J. Roy. Stat. Soc. B 68 425
[8] Yu D S, Zhao F, Tan D W, Peng Q X, Fang Q 2006 Explosion And Shock Waves 26 140 (in Chinese) [虞德水, 赵锋, 谭多望, 彭其先, 方青 2006 爆炸与冲击 26 140]
[9] Lee E L, Hormig H C, Kury J W 1968 UCRL-50422 CA: Lawrence Livemore National Laboratory
[10] Souers P C, Wu B, Haselman L C 1994 Detonation equation of state at LLNL CA: Lawrence Livermore National Laboratory.
[11] Ling Y, Mullins J, Mahadevan S 2014 J. Comput. Phys. 276 665
[12] Zhang S D, Zhou H B, Liu W T 2005 GF Report No. GF-A0091252 (in Chinese) [张树道, 周海兵, 刘文韬 2005 GF 报告, 编号: GF-A0091252]
[13] Zhang S W, Hua J S, Liu C L, Han C S, Wang D S, Sun X L, Zhang Z T 2004 Explosion and Shock Waves 24 219 (in Chinese) [张世文, 华劲松, 刘仓理, 韩长生, 王德生, 孙学林, 张振涛 2004 爆炸与冲击 24 219]
[14] Hallqui J O 1993 UCRL-MA-110630 CA: Lawrence Livermore National Laboratory, p148
[15] Liu Q, Wang R L, Lin Z, Wen W Z 2013 Explosion and Shock Waves 33 647 (in Chinese) [刘全, 王瑞利, 林忠, 温万治 爆炸与冲击 33 647]
[16] Wang R L, Liu Q, Wen W Z 2015 Explosion and Shock Waves 35 9 (in Chinese) [王瑞利, 刘全, 温万治 2015 爆炸与冲击 35 9]
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[1] Green L, Lee E, Mitchell A, Tipton R, van Thiel M, Finger M 1993 UCRL-89664 CA: Lawrence Livemore National Laboratory
[2] Ralph M 2015 LA-UR-15-29536 Los Alamos National Laboratory
[3] Kury J W, Hornig H C, Lee E L, Mcdonnel J L, Ornellas D L, Finger M, Strangl F M, Wilkins M L 1966 Proceedings of the 4th International Symposium on Detonation White Oak, Maryland, October 12-15, 1965 p3
[4] Sun C W, Wei Y Z, Zhou Z K 2000 Applied Detonation Physics (Beijing: national defence Publication Company) p286 (in Chinese) [孙承伟, 卫玉章, 周之奎 2000 应用爆轰物理 (北京：国防工业出版社) 第286页]
[5] Zhou Z, Nie J, Guo X, Wang Q 2015 Chin. Phys. Lett. 32 016401
[6] Jiang H M, Zhang R Q 1998 Journal of Ballistics 10 25 (in Chinese) [江厚满, 张若棋 1998 弹道学报 10 25]
[7] Kennedy M, OHagan A 2001 J. Roy. Stat. Soc. B 68 425
[8] Yu D S, Zhao F, Tan D W, Peng Q X, Fang Q 2006 Explosion And Shock Waves 26 140 (in Chinese) [虞德水, 赵锋, 谭多望, 彭其先, 方青 2006 爆炸与冲击 26 140]
[9] Lee E L, Hormig H C, Kury J W 1968 UCRL-50422 CA: Lawrence Livemore National Laboratory
[10] Souers P C, Wu B, Haselman L C 1994 Detonation equation of state at LLNL CA: Lawrence Livermore National Laboratory.
[11] Ling Y, Mullins J, Mahadevan S 2014 J. Comput. Phys. 276 665
[12] Zhang S D, Zhou H B, Liu W T 2005 GF Report No. GF-A0091252 (in Chinese) [张树道, 周海兵, 刘文韬 2005 GF 报告, 编号: GF-A0091252]
[13] Zhang S W, Hua J S, Liu C L, Han C S, Wang D S, Sun X L, Zhang Z T 2004 Explosion and Shock Waves 24 219 (in Chinese) [张世文, 华劲松, 刘仓理, 韩长生, 王德生, 孙学林, 张振涛 2004 爆炸与冲击 24 219]
[14] Hallqui J O 1993 UCRL-MA-110630 CA: Lawrence Livermore National Laboratory, p148
[15] Liu Q, Wang R L, Lin Z, Wen W Z 2013 Explosion and Shock Waves 33 647 (in Chinese) [刘全, 王瑞利, 林忠, 温万治 爆炸与冲击 33 647]
[16] Wang R L, Liu Q, Wen W Z 2015 Explosion and Shock Waves 35 9 (in Chinese) [王瑞利, 刘全, 温万治 2015 爆炸与冲击 35 9]
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