Development and optimization of a spline-based Hugoniot for unreacted equations of state

Parametric forms, such as linear and quadratic fits, are common for fitting a Hugoniot curve to shock data. However, these forms only admit certain shape features and may exclude a better fit. Thus, a semiparametric Hugoniot curve was developed with cubic b-splines to allow more flexibility in fitting the shock data. A genetic algorithm that respects convexity constraints performed the optimization to fit the model to experimental data. In two cases with artificial data, the spline Hugoniot model resulted in close agreement with the known truth. Finally, a spline Hugoniot was fit to existing shock, pop plot, and overdriven data for a triaminotrinitrobenzene (TATB)-based explosive LX-17 [92.5% TATB and 7.5% Kel-F (polychlorotrifluoroethylene) binder by weight] and obtained a close fit.

Automated summary

Parametric forms like linear and quadratic fits are common for fitting Hugoniot curve to shock data, but a semi-parametric Hugoniot curve with cubic b-splines was developed to allow more flexibility. A genetic algorithm respecting convexity constraints performed optimization to fit experimental data, resulting in close agreement with known truth in two cases with artificial data.