An Unbiased Method for Probabilistic Fire Safety Engineering, Requiring a Limited Number of Model Evaluations

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well.