Efficient uncertainty quantification method applied to structural fire engineering computations

Abstract

Probabilistic Risk Assessment methodologies are gaining traction in fire engineering practice as a (necessary) means to demonstrate adequate safety for uncommon buildings. This induces a need to apply uncertainty quantification to structural fire engineering problems. Yet, the combination of probabilistic methods and advanced numerical fire engineering tools has been limited due to the absence of a methodology which is both efficient (i.e. requires a limited number of model evaluations) and unbiased (i.e. without prior assumptions regarding the output distribution type). In this paper, the recently proposed MaxEnt method is combined with the dedicated structural fire engineering software SAFIR to evaluate the ability of the method to achieve efficient, unbiased assessments of structural fire performance. The case studies include the probability density function (PDF) of (i) the standard fire resistance of a composite column; (ii) the load bearing capacity of a composite floorplate exhibiting tensile membrane action, after 90 min of standard fire exposure; (iii) the load bearing capacity of the same composite floorplate, considering a parametric fire exposure including cooling phase; and (iv) the maximum temperature reached in a protected steel element under realistic fire exposure. In the first application, the MaxEnt PDF correctly and efficiently captures the distribution obtained using Monte Carlo Simulations. The floorplate example under parametric fire exposure shows the true strength of the MaxEnt method as an unbiased assessment, as different failure modes are observed in the cooling phase resulting in an irregular shape of the load-bearing capacity PDF. For this case, reliance on a traditional assumption of lognormality for the capacity would result in an overestimation of the capacity at lower quantiles. The last case study yields a bi-modal output due to the physics-based duality between localized (traveling) and post-flashover fire development. While the MaxEnt captures this bi-modality, it does not accurately reproduce the distribution obtained by Monte Carlo Simulation. Limitations of the MaxEnt method and needs for further research are discussed at the end of the paper.