Treatment of evacuation time uncertainty using polynomial chaos expansion

Abstract

In order to deal with uncertainties in evacuation time associated with the uncertainty in input parameters at a reasonable computational cost, a probabilistic method based on polynomial chaos expansion is proposed that combines evacuation models with Latin hypercube sampling. Evacuation models enable the prediction of evacuation time; polynomial chaos expansion is used to construct a surrogate model of evacuation time; Latin hypercube sampling is adopted as post-processing of the surrogate model to predict numerically the distribution of evacuation times. Additionally, an Uncertainty Factor is defined to quantify the total effect of the uncertainty of input parameters on evacuation time. To illustrate the proposed probabilistic method, evacuation of a simplified fire compartment typical of large commercial buildings is analyzed while considering uncertain input parameters including occupant density, child-occupant load ratio and exit width. This case study indicates that when exit width is small, the Uncertainty Factor is almost constant with respect to exit width but increases with an increase in specified (acceptable) reliability level. Furthermore, if exit width exceeds a certain critical value, the Uncertainty Factor will decrease with an increase in exit width and its sensitivity to reliability level will become smaller. Finally, the case study shows that compared with the conventional Monte Carlo simulation, the proposed method can give similar estimations of evacuation time uncertainty at a significantly reduced computational cost.

An Arbitrary Polynomial Chaos-Based Approach to Analyzing the Impacts of Design Parameters on Evacuation Time under Uncertainty

“…However, the uncertainty of evacuation time is affected by many factors such as occupancy type, exit width, and the characteristics of evacuees, which makes safety factors random. Thus, the effect of exit width on uncertainty factor [26], which is defined as the ratio of evacuation time under uncertainty to the base case evacuation time, is investigated, as shown in Fig. 6.…”

An optimization method for the distance between exits of buildings considering uncertainties based on arbitrary polynomial chaos expansion

“…Moreover, Averill et al [7] employed a Modified-Markov Modeling approach to propose a grid-based evacuation model, which can be used to deal with uncertainty in the number of occupants. Additionally, Xie et al [8] utilized the polynomial chaos expansion to solve uncertainties in input parameters with the purpose of reducing the computational cost of uncertainty analysis of evacuation time. Besides, in order to address the randomness of occupant characteristics, distributions of stochastic variables (e.g.…”