Comparison of methods for model uncertainty quantification

Model uncertainties are included in reliability assessments to account for the uncertainty introduced by the use of computational models to obtain e.g. resistances and load effects. Often, the model uncertainty is modeled as a lognormal variable and is quantified using a dataset consisting of measured outcomes from experiments and corresponding outcomes of the computational model. Unless the dataset is very large, statistical uncertainty also needs to be included. Approaches for model uncertainty quantification include the Bayesian analytical approach, Markov Chain Monte Carlo (MCMC) sampling, the maximum likelihood method, and the method in EN1990:2002 Annex D. In this paper, the methods are compared from a theoretical point of view, and a quantitative comparison is made based on specific examples and using simulated data. It is concluded that the Bayesian analytical approach is most correct and efficient and that the MCMC converges to the same results, but only if the appropriate conjugate priors are used. In the maximum likelihood method, the estimated parameters are assumed to follow normal distributions as commonly done, and the parameter uncertainties are estimated based on the Hessian matrix. Because the maximum likelihood method identifies the mode value of the parameters instead of the mean, and because the standard deviation does not follow a normal distribution, this approach consistently leads to slightly non-conservative results. The method in EN1990:2002 estimates the coefficient of variation of the model uncertainty in correspondence with a Bayesian approach implicitly assuming a lognormal distribution for the error term. However, the mean value correction factor is found using the least squares best-fit, which is inconsistent with the lognormal assumption. The quantitative analysis reveals that the current method in EN1990:2002 does not systematically lead to a higher or lower estimated 5% quantile compared to the Bayesian approach, but it leads to a higher variation of the estimate. Since the Bayesian analytical approach is equally simple and more consistent, this work has motivated a proposal for changing the method in EN1990 annex D, which is included in the current draft PrEN1990:2022.