Uncertainty quantification of magnetically driven quasi-isentropic compression experiments based on the Monte Carlo method
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摘要: 磁驱动准等熵压缩实验是研究材料偏离Hugoniot状态高压物性和动力学行为的重要实验技术之一，开展不确定量化评估具有重要意义和价值。基于Monte Carlo原理，结合磁驱动准等熵压缩实验过程分析、Lagrange分析和特征线正向数据处理方法建立了适用于此类实验的Monte Carlo不确定度量化评估方法，实现利用磁驱动准等熵压缩实验获取材料声速、应力、应变等物理量以及状态方程和本构关系等物理模型的不确定度量化评估。利用建立的不确定度评估方法，对文献中已开展的钽、铜和NiTi合金的磁驱动准等熵压缩实验结果进行不确定度量化评估与分析。结果表明，基于本文中方法的评估结果与国外文献以相同原理得到的评估结果一致。对基于CQ-4装置开展的NiTi合金磁驱动准等熵压缩实验的评估结果表明，设计的磁驱动准等熵压缩实验是一种可靠的精密物理实验。在此基础上，深入讨论了磁驱动准等熵压缩实验的误差相关性和敏感性。结果表明：台阶样品厚度和粒子速度的测量是影响实验精度的主要因素。
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关键词:
- 磁驱动准等熵压缩 /
- 不确定度 /
- Monte Carlo方法 /
- 量化评估
Abstract: Magnetically driven quasi-isentropic compression is one of the important experimental techniques to study high-pressure physics and dynamic behaviors of materials under off Hugoniot states. It is of great significance to carry out quantitative evaluation of experimental uncertainty. By combining with the process analysis of magnetically driven quasi-isentropic compression experiments and two forward data processing methods, an uncertainty quantitative evaluation method was established for such experiments based on the Monte Carlo method (MCM). The uncertainty quantification evaluations of physical quantities such as sound speed, stress, strain, and the parameters of equations of state and constitutive models were realized. Compared with the conventional method such as guide to the expression of uncertainty in measurement (GUM), the MCM uncertainty evaluation is more applicable to the cases in which the probability distribution of the input quantities is non-symmetric and the measurement model is non-linear. In fact, the uncertainty evaluation results obtained by the MCM is reasonable and not the ones under the maximum estimation condition. Employing the law of large numbers, nested cycle setting of the probability density functions (PDF) and nested loop construction of virtual samples makes the uncertainty evaluation results more accurate. By using the established MCM uncertainty evaluation method, the uncertainty evaluations of the experimental results of tantalum and copper samples under magnetically-driven quasi-isentropic compression were quantitatively analyzed firstly. The results are consistent with the data proposed in the literatures, which proves the correctness and reliability of our method. And then, the quantitative evaluation was conducted on magnetically-driven quasi-isentropic compression experiments of NiTi alloy carried out on a CQ-4 device. The results show that the experiments on the CQ-4 device are reliable and precise for high-pressure physics and material dynamics studies. Finally, the error correlation and sensitivity of magnetically-driven quasi-isentropic compression experiments were discussed in depth, and the results show that the measurements of step sample thickness and particle velocity are the main factors affecting the experimental accuracy but have different influence weights. This work has important guiding significance for studying high-pressure physics and dynamic behaviors of materials by using magnetically-driven quasi-isentropic compression experimental technology. -
超高速碰撞是指这样一类碰撞：碰撞所产生的冲击压强远远大于（弹靶）材料的强度。在超高速碰撞的最初阶段，材料的性态类似于可压缩流体，遵从流体力学定律。小天体对地球的撞击、空间碎片对航天器的撞击、动能武器对目标的撞击是典型的超高速碰撞现象。
超高速碰撞研究的兴起与航天工程、武器工程、地球及行星科学等领域的需求密不可分。20世纪50年代中期，由于航天安全和反弹道导弹技术的需要，世界主要军事和科技大国大力开展超高速碰撞研究。几十年来，在超高速加载与试验技术、高压状态方程、厚靶成坑、材料破碎与结构解体、碎片云膨胀规律、空间碎片防护结构、超高速碰撞数值计算等方面研究取得了较大进展。进入21世纪以来，超高速碰撞研究与力学、航空宇航科学与技术、兵器科学与技术、材料科学与工程、物理、天文学等相关学科领域进一步交叉融合，不仅在航天器空间碎片防护、反弹道导弹、装甲与反装甲、核反应堆安全防护设计、惯性约束聚变等工程领域发挥了重要作用，而且也促进了极端条件下材料的性质和状态方程、生命起源、陨石坑形成、高分辨诊断技术、多物理场多尺度数值模拟技术等基础研究的快速发展。
为促进我国在超高速碰撞领域最新研究成果的交流，探讨其发展趋势，推动该领域及相关学科的进一步发展，《爆炸与冲击》编辑部于2019年策划了“超高速碰撞”专题。专题征集了中国工程物理研究院、中国空间技术研究院、中国空气动力研究与发展中心、西北核技术研究院、哈尔滨工业大学、北京理工大学等单位提交的9篇论文，从不同侧面反映了近几年我国相关单位在该领域取得的最新成果。该专题在编辑、出版过程中得到了作者、审稿专家、编委和《爆炸与冲击》编辑部的大力支持，在此表示衷心的感谢。
北京理工大学教授、博士生导师 张庆明 《爆炸与冲击》副主编 -
图 1 磁驱动准等熵压缩实验原理图
Figure 1. A principle of magnetically-driven quasi-isentropic compression experiment
图 2 基于Monte Carlo原理评价不确定度的主要阶段
Figure 2. The main stages of evaluation uncertainty based on the Monte Carlo method
图 3 磁驱动准等熵压缩实验的Monte Carlo不确定度评价流程
Figure 3. Monte Carlo uncertainty evaluation process for magnetically-driven quasi-isentropic compression experiments
图 9 自由面速度历史曲线的虚拟样本构造结果
Figure 9. Band construction results of virtual samples for free surface velocity profiles
图 12 应力应变的不确定度评价结果及其极大估计
Figure 12. Uncertainty evaluations and their great estimates of stress and strain
图 14 两种数据处理方法的不确定度评价结果比较
Figure 14. Comparison of uncertainty evaluation results by two kinds of data processing methods
图 16 自由面速度历史曲线基于时序误差和速度误差的模拟带
Figure 16. Simulation bands of free surface velocity histories based on time deviation and velocity deviation
图 17 插值前后变量的映射关系
Figure 17. Mapping relationships of variables before and after interpolation
图 20 输出量误差与输入量误差的敏感系数
Figure 20. Sensitivity coefficients of the output deviation and input deviation
表 1 分布形式设置
Table 1. Settings of distribution form
设定形式名称 时间分布形式 自由面速度分布形式 A 正态分布 正态分布 B 正态分布 伽马分布 C 均匀分布 正态分布 D 均匀分布 伽马分布 
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