Treatment of design fire uncertainty using Quadrature Method of Moments

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.

Quadrature-based moment closures for non-equilibrium flows: Hard-sphere collisions and approach to equilibrium

“…QMOM and its variants (e.g. Direct Quadrature Method of Moments, DQMOM) have been successfully extended and applied for different types of KEs and PDFs in many applications [35][36][37][38][39][40][41][42][43][44][45][46].…”

Predicting the Effects of Barrier Fabrics on Residential Upholstered Furniture Fire Hazard

“…Several papers have demonstrated methods for propagating uncertainty through fire models. Upadhyay and Ezekoye used the Quadrature Method of Moments (QMOM) to propagate HRR uncertainty through CFAST and an algebraic model for layer height [16]. Layer height cumulative distribution functions (CDFs) were reconstructed using a generalized lambda distribution.…”

“…It will typically take fewer samples to accurately estimate L than it will to approximate Pr (L = l). An more efficient alternative to Monte Carlo simulations is the quadrature method of moments (QMOM), which has been used to propagate uncertainty through fire models [16]. Although this procedure will not be used in the following, it is a potential tool for use in future extensions of this work.…”

An advanced fire estimation model for decentralized building control

“…The use of the sensor-data-based method does not allow any obstruction to block the smoke transport to the sensors, and its performance also relies heavily on the accuracy of sensor data. Another fire estimation method, which takes advantage of the output provided by fire and smoke propagation models, has been applied to reconstruct fire incidents Upadhyay and Ezekoye 2008). However, the uncertainty associated with model inputs and the computational complexity associated with the building structure have resulted in the fire-model-based method mainly being adopted after fires for fire investigations (Shu et al 2012).…”