Uncertainty quantification of shock to detonation experiment of PBX 9502 based on probability learning on manifold

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.