高维参数不确定爆轰的不确定度量化

doi:10.3969/j.issn.1000-1093.2020.04.008

兵工学报 ›› 2020, Vol. 41 ›› Issue (4): 692-701.doi: 10.3969/j.issn.1000-1093.2020.04.008

高维参数不确定爆轰的不确定度量化

梁霄¹，陈江涛²，王瑞利³

(1.山东科技大学数学与系统科学学院, 山东青岛 266590; 2.中国空气动力研究与发展中心，四川绵阳 621000； 3.北京应用物理与计算数学研究所, 北京 100094)

收稿日期:2019-06-27 修回日期:2019-06-27 上线日期:2020-06-02
通讯作者: 王瑞利(1964—), 男, 研究员 E-mail:wang_ruili@iapcm.ac.cn
作者简介:梁霄(1984—), 男, 副教授，硕士生导师。E-mail: mathlx@163.com；
陈江涛（1983—），男，副研究员。E-mail: chenjiangtao@163.com
基金资助:
国家数值风洞工程项目（NNW2019ZT7-A13）；山东省自然科学基金项目(ZR2017BA014)；国家自然科学基金项目(61573008)；科学挑战专题项目(TZ2018001)

Uncertainty Quantification of Detonation with High-dimensional Parameter Uncertainty

LIANG Xiao¹, CHEN Jiangtao², WANG Ruili³

(1.School of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, China; 2.China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China; 3.Institute of Applied Physics and Computational Mathematics, Beijing 100094, China)

Received:2019-06-27 Revised:2019-06-27 Online:2020-06-02

摘要/Abstract

摘要： 由于测量技术等因素导致物理参数的随机波动，加上化学反应率方程、状态方程均是唯象建模，使得爆轰系统含有不同类型的高维相关不确定度。评估输入不确定度对输出结果的影响具有重要的理论意义和应用价值。针对参数敏感的绕爆问题拐角效应，使用基于回归方法的非嵌入多项式混沌方法研究此问题的不确定度量化。使用Rosenblatt变换将一列相关随机变量组转化成服从独立标准均匀分布的随机变量组。先用采样法将积分转化成欠定线性方程组，进而选择优化方法求解回归方程，再借助基追踪方法将优化问题转化成线性规划问题。给出拐角附近拉格朗日参考点的速度分量、压力、位置的期望和置信区间。结果表明：拐角处位置临近的两个拉格朗日参考点，轨迹差别很大；不确定度随着时间演化而逐渐增加，预测系统的长期动力行为难度加大；研究方法可推广到其他爆轰问题。

关键词: 爆轰, 不确定度量化, 基追踪, 非嵌入多项式混沌, 绕爆, 回归, Rosenblatt变换

Abstract: Different types of dependent uncertainties exist in detonation system since the random vibration of physical parameters in measurement technique, and the equation of state (EOS) and the reaction rate equation are empirical modeling. And these random variables are not independent and identically distributed. Assessing the impact of these input uncertainties on the output result of system has important theoretical significance and practical value. The corner effect in detonation diffraction is studied. The non-intrusive polynomial chaos based on regression method is used for uncertainty quantification. Rosenblatt transformation is used to transform the dependent random variables into independent random variables satisfying standard uniform distribution. Under-determined linear equations are derived from the sampling method. Optimization method is chosen to solve the regression equation. The basis pursuit is applied to change the optimization problem into linear programming. The expectation and confidence interval of velocity components, horizontal positions, and pressures of two Lagrangian reference points near the corner are given by using the method mentioned. The results show that the trajectories of two Lagrangian reference points are dramatically different although they are not far from each other. It is difficult to judge the long time dynamical behavior since the uncertainty is becoming large over time. The method can also be applied to other detonation problems. Key

Key words: detonation, uncertaintyquantification, basispursuit, non-intrusivepolynomialchaos, detonationdiffraction, regression, Rosenblatttransform

中图分类号:

O381

梁霄，陈江涛，王瑞利. 高维参数不确定爆轰的不确定度量化[J]. 兵工学报, 2020, 41(4): 692-701.

LIANG Xiao, CHEN Jiangtao, WANG Ruili. Uncertainty Quantification of Detonation with High-dimensional Parameter Uncertainty[J]. Acta Armamentarii, 2020, 41(4): 692-701.

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高维参数不确定爆轰的不确定度量化

Uncertainty Quantification of Detonation with High-dimensional Parameter Uncertainty

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