Treatment of Design Fire Uncertainty using Quadrature Method of Moments
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Date
02/2008Author
Upadhyay, Rochan
Ezekoye, Ofodike A
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Abstract
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 bound in distributions. In
QMOM one solves for only the moments of a relevant uncertain parameter. The
cumulative distribution function (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 4-parameter
Generalized Lambda Distribution (GLD) give accurate results at a significantly smaller
computational cost.
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