基于冲击Hugoniot关系的爆压性质和不确定度量化

doi:10.12382/bgxb.2022.1207

摘要/Abstract

摘要：

精确评估炸药冲击Hugoniot参数的可信区间,有效量化冲击起爆、状态方程等唯象模型的不确定度,提高模型的鲁棒性和可靠性,会极大地降低爆压标定的成本。利用线性回归拟合方法得到冲击Hugoniot参数,采用参数估计法推导出Hugoniot参数的置信区间,使用国内试验数据确认方法的有效性。在合理假设的基础上,结合Chapman-Jouguet理论和冲击Hugoniot关系,导出爆压与装药厚度、冲击波走时、初始密度、Hugoniot斜率和0-压声速之间的函数关系式。分别用对数正态分布和Beta分布表征输入不确定度,通过Rosenblatt变换将输入不确定度转化成相互独立的标准正态分布,使用自适应基函数多项式混沌不确定度传播量化方法,给出了爆压的概率密度函数和置信区间。研究结果表明,爆压与样品厚度、爆轰走时、爆速具有拟单调性,在特殊前提下证实了前人的判断。应用于PBX9502炸药,发现给出的置信区间较宽,与试验专家的先验论断吻合。该研究发展了一套有效量化爆轰不确定度的传播量化方法,为发展可信、强预测能力爆轰模拟软件提供了技术支撑。

关键词: 冲击Hugoniot关系, 不确定度量化, 爆压, Chapman-Jouguet理论, 自适应基函数多项式混沌, 拟单调性

Abstract:

The confidential interval of explosive shock Hugoniot parameters is exactly assessed and the uncertainties associated with shock ignition and equation of state are efficiently quantified to improve the robustness and reliability of the model and enormously reduce the calibration cost of detonation pressure. The linear regression method is utilized to calibrate the shock Hugoniot parameters, and the confidential interval of Hugoniot parameters are also deduced from parameter estimation. Moreover, the availability of Hugoniot model is validated through domestic experiment data. On the basis of reasonable assumptions, Chapman-Jouguet theory and shock Hugoniot relationship are combined to the functional relationships among detonation pressure. sample thickness, shock passing time, initial density, Hugoniot slope and 0-presure sound speed are deduced. The input uncertainty is characterized by log-normal distribution and Beta distribution, and it is transformed into independent standard normal random variables by Rosenblatt transformation. Polynomial chaos with basis adaptation is applied to implement uncertainty propagation, and the probability density function and confidential interval of detonation pressure is obtained. The results show that the detonation pressure satisfies the quasi-monotonicity with respect to sample thickness, passing time and detonation speed. The assertion of previous studies is confirmed in specific conditions. The confidence interval is much wider when it is used in PBX9502, which coincides with the prior judgment given by experimental expert. This study develops an efficient uncertainty quantification and propagation method. The result can provide technique support for developing highly predictable and confidential software.

Key words: shock Hugoniot relationship, uncertainty quantification, detonation pressure, Chapman-Jouguet theory, polynomial chaos with basis adaptation, quasi-monotonicity

中图分类号:

O381

梁霄, 王瑞利. 基于冲击Hugoniot关系的爆压性质和不确定度量化[J]. 兵工学报, 2024, 45(5): 1673-1680.

LIANG Xiao, WANG Ruili. Property and Uncertainty Quantification of Detonation Pressure Based on Shock Hugoniot Relationship[J]. Acta Armamentarii, 2024, 45(5): 1673-1680.

图/表 7

表1 冲击Hugoniot试验数据[21]

Table 1 Data of shock Hugoniot experiment[21]

编号	u_p/(mm·μs^-1)	D_s/(mm·μs^-1)
1	0.618	3.788
2	0.779	4.028
3	0.48	3.433
4	0.963	4.502

图1 PBX9502炸药试验数据与冲击Hugoniot曲线

Fig.1 Experimental data and shock Hugoniot curve of PBX9502

图2 PBX9502炸药初始密度的直方图和概率密度函数

Fig.2 Histogram and PDF of initial density of PBX9502

图3 PBX9502炸药厚度的直方图和概率密度函数

Fig.3 Histogram and PDF of thickness of PBX9502

图4 PBX9502炸药冲击波走时的直方图和概率密度函数

Fig.4 Histogram and PDF of passing time of shock wave

图5 冲击Hugoniot参数的概率密度函数

Fig.5 PDF of shock Hugoniot parameters

图6 爆压的概率密度函数

Fig.6 PDF of detonation pressure

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