Uncertainty Propagation Analysis of Detonation Pressure Based on Active Subspace

Uncertainty cannot be eliminated in the indirect calibration of the detonation pressure, and the predictability and credibility of the model can be enhanced through uncertainty quantification of the detonation pressure. However, the indirect calibration function of the detonation pressure exhibits complex nonlinearity coupled with multiple inputs, making the study of uncertainty propagation of detonation pressure prone to issues such as the “curse of dimensionality”. Active subspace is proven to be an effective tool for handling uncertainty quantification of the detonation pressure model. The specific steps are as follows: to begin with, the covariance matrix is derived based on gradient of the system response quantity (SRQ). Then an active variable is deduced through the Monte Carlo method, which is the direction whose perturbations produce the greatest change in SRQ. A single derived active subspace is used as the input uncertainty instead of the six parameters. The “curse of dimensionality” can be relieved in this case. Finally, a fourth-order polynomial response surface model is established based on a one-dimensional active variable. The results show that the effects of input uncertainty on SRQ are successfully characterized using the means of the active subspace technique. The test data fall within the confidence interval of the predicted values from the surrogate model, and the predictive capability of the detonation pressure model is validated. The study also reveals that there is a significant degree of dispersion in detonation pressure, which is consistent with the viewpoint of Prof. Chengwei Sun. Furthermore, a new detonation pressure model is constructed in this paper. This model is a composite operation between an affine transformation and a polynomial function. It retains the characteristic of a concise form, sufficient smoothness, strong robustness, and fast computation. The input of the model is a random variable rather than a fixed value, and the polynomial coefficients remain unchangeable when it confronts the variability of input uncertainty. The research is an extension and development of previous scholars. Moreover, the research methodology is systematic, which can be applied to detonation pressure prediction for other types of explosives.