Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold
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摘要: 样本容量稀疏和不确定度无法消除是制约多物理属性爆轰试验研究的障碍。流形上的概率学习(probability learning on manifold, PLoM)方法通过结合耗散映射与Itô投影采样技术,生成满足爆轰机理的丰富样本,进而实现试验不确定度量化。首先,对具有多物理属性的高能钝感炸药PBX9502的试验样本进行尺度变换。接着利用主成分分析对尺度矩阵规范化处理,构造训练集。然后,采用改进的多维Gauss核密度估计法,标定训练集对应的随机矩阵的概率测度。同时,利用耗散映射提取基于训练集的非线性流形。Wiener过程驱动的耗散Hamilton系统定义的Itô-MCMC随机生成器用于在流形上采样。最后,使用逆变换导出学习集的样本。结果表明,PLoM生成的随机数的Gauss统计量与Los Alamos国家实验室(LANL)及孙承纬院士标定的PBX9502的密度的统计信息相吻合。此外,该方法成功导出爆轰距离和爆轰时间与冲击应力服从双对数模型关系,曲线拟合的精度与LANL的成果相当,成本可以忽略不计。PLoM通过对已有试验数据的学习与处理,获得更高精度的数字试验结果。PLoM方法泛化能力强,可推广到其他类型炸药的爆轰试验。
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Abstract: Small sample size and unavoidable uncertainty seriously hinders the research of detonation experiments with multi-physical attributes. Probability learning on manifold (PLoM) involves diffusion map and Ito projection sampling, which can generate sufficient dataset satisfying the detonation physical mechanism. And uncertainty quantification of experiment can be fulfilled through PLoM. To begin with, scale transformation is implemented on the experimental data with multi-physical asset of insensitive high explosive PBX 9502. The training set is then obtained through the normalization of the scale matrix by means of principal component analysis. To make it further, an altered high-dimensional Gaussian kernel density estimation is utilized to derive the probability measure of the random matrix associated with the training dataset. Meanwhile, diffusion map is used to deduce the nonlinear manifold based on the training dataset. Sampling on the manifold is fulfilled through Itô-MCMC generator defined by a dissipative Hamilton system driven by the Wiener process. At last, the learning set is obtained via inverse transformation. The result shows that the Gaussian statistics obtained from random numbers generated from PLoM coincide with the statistical information of density of PBX 9502 calibrated by Los Alamos National Laboratory (LANL) and Prof. Chengwei Sun. Furthermore, the double logarithm model related to the distance to detonation and initial impact stress is constructed through the data generated. It also holds for the relationship between the time of detonation and initial shock stress. Fitting precision of the curve is almost equivalent to the accuracy of LANL, however the cost is negligible. More accurate digital test result is obtained through the learning and processing of existing experimental data via PLoM. PLoM is general enough to extend to detonation experiment of other type of explosives. -
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