Propagation of Uncertainty in a Thermal Analysis Model Using Polynomial Chaos Expansion

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Computational fire models are a valuable tool for engineers, investigators, and researchers, but the governing equations and solution approaches typically are too complicated, and the models rely on too many variables to allow for direct uncertainty analysis and error propagation. Without these necessary steps in hypothesis testing and model validation, the true accuracy of predictions cannot be completely quantified. Additionally, there is no standard accepted methodology to determine the kinetics of thermal degradation of a material, which can further complicate uncertainty quantification, validation, and interlaboratory studies. Recently, the polynomial chaos expansion method has emerged as a means to conduct uncertainty quantification on complicated models with relatively low computational cost. A method is presented in this work to determine the kinetics of pyrolysis for polycarbonate and to quantify the uncertainty in the mass loss rate prediction. Using this methodology, predictions of mass loss rate measured in themogravimetric experiments showed relative standard deviations of the peak value ranging from 16% to 23% for heating rates ranging from 30 to 3 K/min. The experimental data were within the bounds of uncertainty of the mass loss rate predictions. This study demonstrated a successful parameterization methodology and validated the use of generalized polynomial chaos to inexpensively quantify uncertainty in pyrolysis model predictions.