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

Abstract

In performance-based design of buildings, much attention is paid to design parameters by fire engineers or experts. However, due to the time-consuming evacuation models, it is computationally prohibitive to adopt the conventional Monte Carlo simulation (MCS) to examine the effects of design parameters on evacuation time under uncertainty. To determine suitable design parameters under uncertainty with the reduced significantly computational cost, an arbitrary polynomial chaos-based method is presented in this paper. Arbitrary polynomial chaos expansion is used to construct surrogate models of evacuation time based on complex evacuation models. Afterwards, simple analytical method can be adapted to calculate the mean, standard deviation of evacuation time and Sobol sensitivity indices based on the arbitrary polynomial chaos coefficients. Moreover, the distribution of evacuation time can be generated by combining Latin hypercube sampling (LHS) with the obtained surrogate model. To demonstrate the proposed method, a hypothetical single-storey fire compartment with two exits is presented as a case in accordance with the Chinese code GB50016-2012, evaluating the impact of exit width on evacuation time under uncertain occupant density and child-occupant load ratio. And results show that the proposed method can achieve the distribution of evacuation time close to that from the MCS while dramatically reducing the number of evacuation simulations. When exit width per 100 persons is designed between 0.1 m and 0.5 m, the uncertainty of evacuation time is severely affected by exit width, which is more significant in smaller exit width. However, exit width has a small effect on Sobol sensitivity indices, the reliability level of a certain safety factor, and safety factor at a certain reliability level.