Uncertainty quantification of shock to detonation experiment of PBX9502 based on probability learning on manifold

To address the challenges posed by insufficient statistical sampling density and inherent irreducible uncertainties in multi-physical property detonation experiments, probability learning on manifold (PLoM) involving diffusion map and Itô projection sampling are used to generate sufficient dataset satisfying the detonation physical mechanism and therefore, to fulfill the uncertainty quantification of experiment. Firstly, scale transformation is implemented on the experimental data with multi-physical asset of insensitive high explosive PBX9502. The training set is obtained through the normalization of the scale matrix by means of principal component analysis. Secondly, an improved high-dimensional Gaussian kernel density estimation is utilized to calibrate the probability measure of the random matrix associated with the training dataset. 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. Finally, the learning set is obtained via inverse transformation. The result shows that the Gaussian statistics obtained from random numbers generated by PLoM coincide with the statistical information of density of PBX9502 calibrated in the literature. 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 result in literature, however the cost is negligible. More accurate digital test result is obtained through the learning and processing of existing experimental data via PLoM. The PLoM method demonstrates strong generalization capability, enabling its extension to detonation experiments with various types of explosive.