Intrusive and non-intrusive uncertainty quantification methodologies for pyrolysis modeling

Abstract

In this work we discuss and compare multiple uncertainty analysis methodologies for pyrolysis modeling. Using Arrhenius equation as the pyrolysis model and kinetic parameters for PMMA material as uncertain variables, different approaches for stochastic uncertainty quantification and their computational effort are analyzed. First non-intrusive (NI) methods are compared through convergence analysis where the deterministic model can be used as is to ascertain the statistical moments, followed by an intrusive polynomial chaos (IPC) approach which requires reformulation of the deterministic model, but solution of the model only once. The applied NI methods include Monte Carlo based simulations, regression and projection based non-intrusive polynomial chaos (NIPC) methods. The uncertainty analysis and convergence comparison is performed for three materials including the effects of overlapping reactions and dependent parameters. In general for different uncertain parameters and materials, IPC gave accurate statistical information in a single model run compared to NIPC projection requiring runs ranging from tens to hundreds and NIPC regression requiring runs in range of thousands to generate converged statistics. However, in case of only a few uncertain parameters, presence of non-polynomial functions in the model and small-scale simulations, projection based NIPC outshines IPC in terms of simplicity and applicability.