Assessing fire safety using complex numerical models with a Bayesian multi-fidelity approach

Abstract

Nowadays, fire safety engineers are increasingly relying on sophisticated numerical simulators, typically based on Computational Fluid Dynamics (CFD) solvers, to conduct their analyses. However, the complexity of these numerical models often limits drastically the number of simulations that can be afforded, making traditional methods of safety analysis difficult or impossible to apply. This paper proposes a statistical method to evaluate a quantity of interest with an expensive simulator while saving computation time. The method is based on Bayesian statistics and multi-fidelity. We use Gaussian process regression to construct a Bayesian model of the complex simulator. This model is based on a multi-fidelity approach, which consists in simulating at different levels of accuracy, for instance by varying the spatial discretization in a CFD solver. We illustrate the method on an example of fire safety analysis, where the quantity of interest is the probability of exceeding a tenability threshold in a building on fire.