Uncertainty propagation in FE modelling of a fire resistance test using fractional factorial design based model reduction and deterministic sampling

Abstract

In this paper, fractional factorial design (FFD) and deterministic sampling (DS) are applied to a finite element (FE) model of a fire resistance test of a loaded steel beam, to investigate how uncertainties are propagated through the FE model. The sought quantity was the time when the deflection of the beam exceeded 225mm. The FFD method was used as a model reduction technique which reduced the number of uncertain parameters from 5 to 3. The DS method was compared to a reference Monte Carlo (MC) method of 1000 simulations from all 5 uncertain parameters, which was the minimum number of simulations in order for the statistical moments to converge. The combined FFD and DS method successfully computed the propagation of the mean and standard deviation in the model, compared to the MC method. Given the uncertainties in the FE model, the fractional factorial design reduced the number of simulations required in the DS method by 82%. The combined method of FFD and DS reduced the number of required simulations by 96% compared to the MC method. The DS method did not capture the tails of the probability distribution and is therefore not a suitable candidate for probabilistic evaluation of the time of failure at the edges of the domain of possible failure times. Future research could very well be on improving the tails in DS. However, the DS method provides a conservative 95% coverage interval of 6min for the time to failure of the steel beam.