Non-parametric characterization of blast loads

Mathematical analysis of blast pressures has typically involved the empirical fitting of parametric models, which assumes a specific function shape. In reality, the true shape of the blast pressure is unknown and may lack a parametric form, particularly in the negative phase following arrival of the secondary shock. In this work, we develop a non-parametric (NP) representation that makes few assumptions and relies on the observed experimental data to fit a unique and previously unknown model. This differs from traditional approaches by not arbitrarily selecting a single, restrictive class of functions and estimating a minimal set of parameters, but rather estimating the underlying function class for which the blast pressure is generated; learning the model directly from the observed data. The method was applied to experimental blast measurements and the NP estimates matched the experimental data with a high degree of accuracy, both qualitatively and quantitatively. The NP approach was shown to significantly outperform other commonly used approaches, near-perfectly track the entire pressure and specific impulse history and predicting experimental peak specific impulse to within ±0.5% in all cases (compared to ±5.0% for a trained artificial neural network (ANN) and ±7.5% for the UFC semi-empirical approach). The NP approach predicts experimental net specific impulses (positive and negative phases combined) with a maximum variation of 2.7%, compared to maximum variations of −116% and 55% for the UFC and ANN approaches, respectively. Since the framework is probabilistic in nature, it can naturally account for random noise in sensor measurements, which are typically more pronounced in blast experiments than many other machine learning applications.