基于活跃子空间的爆压不确定度传递分析

梁霄 范孟君 王言金 王瑞利

梁霄, 范孟君, 王言金, 王瑞利. 基于活跃子空间的爆压不确定度传递分析[J]. 高压物理学报. doi: 10.11858/gywlxb.20240862
引用本文: 梁霄, 范孟君, 王言金, 王瑞利. 基于活跃子空间的爆压不确定度传递分析[J]. 高压物理学报. doi: 10.11858/gywlxb.20240862
LIANG Xiao, FAN Mengjun, WANG Yanjin, WANG Ruili. Uncertainty Propagation Analysis of Detonation Pressure Based on Active Subspace[J]. Chinese Journal of High Pressure Physics. doi: 10.11858/gywlxb.20240862
Citation: LIANG Xiao, FAN Mengjun, WANG Yanjin, WANG Ruili. Uncertainty Propagation Analysis of Detonation Pressure Based on Active Subspace[J]. Chinese Journal of High Pressure Physics. doi: 10.11858/gywlxb.20240862

基于活跃子空间的爆压不确定度传递分析

doi: 10.11858/gywlxb.20240862
基金项目: 国家自然科学基金(12171047);国家自然科学基金委-中国工程物理研究院NSAF联合基金(U2230208); 山东省自然科学基金(ZR2021BA056);国家留学基金委公派访学项目(CSC202308370209)
详细信息
    作者简介:

    梁 霄(1984-),男,博士,副教授,主要从事爆轰不确定度量化研究. E-mail:mathlx@163.com

  • 中图分类号: O241; O521.3

Uncertainty Propagation Analysis of Detonation Pressure Based on Active Subspace

  • 摘要: 爆压间接标定中的不确定度无法消除,不确定度量化能提高模型的可信度和预测能力。然而,爆压间接标定函数具有复杂非线性结构耦合多输入变量等特征,使得爆压不确定度传播研究遇到“维数灾难”等问题。活跃子空间是处理爆压不确定度量化的有效工具。首先,导出系统响应量(system response quantity, SRQ)的梯度协方差矩阵;然后,基于Monte Carlo方法,寻找活跃变量,即SRQ变化最快的方向;接着,将高维输入不确定度转化成一维空间处理,避免了“维数灾难”;最后,建立基于一维活跃变量的四阶多项式响应面模型。结果表明,活跃子空间方法成功刻画了输入不确定度对SRQ的影响,且试验结果落在代理模型预测值的置信区间内,确认了爆压模型的预测能力。研究还发现,爆压的离散程度较大,与孙承纬的结论吻合。此外,建立了一种新的爆压模型。该模型是仿射变换与多项式函数的复合运算,具有形式简洁、光滑性好、鲁棒能力强、运算速度快的特点,且系统输入量是随机变量而非固定值,多项式拟合系数不因输入不确定度的变化而改变。该研究方法具备体系性,可以推广到其他类型的炸药爆压预测。

     

  • 图  基于AS的降维流程

    Figure  1.  Flow chart of dimensionality reduction based on active subspace

    图  输入不确定度的概率密度函数

    Figure  2.  PDF of the input uncertainty

    图  对数尺度下特征值的分布

    Figure  3.  Distribution of eigenvalues for the logarithmic scale

    图  活跃变量Y的概率密度函数

    Figure  4.  PDF of the active variable Y

    图  基于AS的爆压的概率密度函数

    Figure  5.  PDF of detonation pressure deduced from active subspace

    图  AS和Monte Carlo方法得到的爆压的概率密度函数

    Figure  6.  PDF of detonation pressure deduced from AS and Monte Carlo methods

    表  1  爆压的试验和统计结果

    Table  1.   Test and statistical results of the detonation pressure GPa

    Statistical resultsTest data[2]
    MeanStandard deviationUpper confidence limitLower confidence limit
    34.671.5136.0132.7534.41
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-07-26
  • 修回日期:  2024-08-24
  • 网络出版日期:  2024-11-01

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