Treatment of design fire uncertainty using Quadrature Method of Moments

The use of a single-design fire in a performance-based fire design code typically fails to account for the inherent uncertainty in knowledge of the future use of the space. Uncertainties in knowledge of intended use and the implications in terms of fuel loading and potential heat release rate can be bounded using probabilistic methods. Use of a cumulative distribution function (CDF) and the related probability density function (PDF) specify the best available estimate of the probability (likelihood) of a fire of given size to take place in a compartment. Monte Carlo simulation is a widely used computational method for treating uncertainty that might be described by a PDF. In this technique, one samples the uncertain variables from their underlying PDFs and runs a fire model for each sample. For complex fire models, this approach may be computationally intractable. In this work we present a computationally efficient technique called the Quadrature Method of Moments (QMOM) for propagating uncertainty bounds in distributions. In QMOM one solves for only the moments of a relevant uncertain parameter. The CDF of the uncertain parameter provides all the statistical information required for risk assessments. We consider a simplified propagation of uncertainty problem. Results using both the ASET and CFAST fire models indicate that computation of the moments of the PDF using QMOM and the reconstruction of the CDF by matching the moments with those of a four-parameter Generalized Lambda Distribution (GLD) give accurate results at a significantly smaller computational cost.