Uncertainty Quantification of Cylinder Test Based on Probability Learning on Manifold

Detonation research often suffers small size of computational and experimental datasets due to high risk of test implementation and substantial computational burden. Limited samples hinders the construction of probability distribution of quantity of interest(QoI). Probability learning on manifold (PLoM) conjoins diffusion maps and projected Ito sampling, which can generate a large number of realizations of physical quantity reconcilable with physical mechanism. It can also determine the probability measure of empirical parameters in equation of state. So PLoM is utilized to tackle uncertainty quantification of cylinder test with small computational and experimental samples. To begin with, the scaling transformation is conducted on the computational datasets of insensitive high explosive JOB-9003 with multi-physics attributes. Then the principal component analysis is utilized to normalize the scaling matrix, and the normalization matrix is regarded as training set. To make it further, an altered multi-dimensional Gaussian kernel density estimation is applied for estimating the probability of random matrix corresponding to training set. Moreover, diffusion maps is used to extract nonlinear manifold based on the training set. At last, additional realizations of learning dataset is fulfilled through the inversion transformation. The result shows that random number of QoI generated from PLoM satisfies the requirement of industrial needs. The probability density distribution of JWL parameters is also obtained from the learning set. The running time is only two orders of magnitude lower than that of classical parameter calibration method based on high fidelity detonation modeling. And PLoM is robust to the external noise.