An arbitrary polynomial chaos-based approach to analyzing the impacts of design parameters on evacuation time under uncertainty

In performance-based fire protection 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 effect of design parameters on evacuation time under uncertainty. To determine the suitable values of 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 complex evacuation models. Afterwards, simple analytical method can be adopted to calculate the mean and standard deviation of evacuation time as well as Sobol sensitivity indices based on the arbitrary polynomial chaos coefficients. Meanwhile, the distribution of evacuation time can be generated by coupling Latin hypercube sampling (LHS) to the surrogate model. To demonstrate the proposed method, a case in accordance with the Chinese code GB50016-2012 is presented, evaluating the impact of exit width on evacuation time under arbitrary uncertainty caused by occupant density and child-occupant load ratio in a single-storey fire compartment with two exits. And the results of this case show that the proposed method can achieve the distribution of evacuation time close to those from MCS while dramatically reducing the number of evacuation simulations. When exit width per 100 persons is designed in the range of 0.1m and 0.5m, evacuation time uncertainty is severely affected by exit width and is more significant in exit with smaller width. However, exit width has little effect on Sobol sensitivity indices, the reliability level of a certain safety factor, and safety factor at a certain reliability level.