Uncertainty assessment for the Bayesian updating process of concrete strength properties
Keywords:Bayesian updating, bootstrapping, burn-in, concrete compressive strength, Markov chain Monte Carlo, MCMC, Metropolis algorithm, Roding Bridge, structural reassessment
Reassessment of infrastructure buildings has become an essential approach to deal with increasing traffic loads on ageing infrastructure buildings and to verify the service-life of those structures. Good estimation of the actual material properties is highly relevant for reliable structural reassessment. Although this holds for all building materials, the importance of good parameter estimation is of special importance for concrete structures, where the strength properties show relatively high variation and where the nominal strength properties tend to be too conservative. Modern design guidelines allow to make use of scientific methods such as Bayesian Updating of material properties to enable a more realistic consideration of the actual material properties in the reassessment of existing structures. However, guidelines for application and experience with those methods are not yet reported much or are rather vague . The presented study focuses on the effect of the Bayesian Updating process for material parameters with special emphasis on the number and sampling location of test specimens as well as on the accuracy and confidence in the obtained posterior distribution, since sampling also includes a certain margin of uncertainty. The investigation on the methodological potential and on the uncertainty margin in the updating process in this contribution uses a batch of 14 test results on the concrete compressive strength obtained from drill cores along with the inherent measurement uncertainties from the testing procedure. After a short review of Bayes’ Theorem, the Markov Chain Monte Carlo Method (MCMC) and the bootstrap methodology, all combinations of subsamples of size 1, 3 and 5 specimens were built and provided to the Bayes’ updating procedure via MCMC to determine the posterior distributions. The series of obtained posterior distributions for a certain subsample was used to determine the uncertainty in the Bayesian Updating process by evaluation of the scatter in the expected value, the standard deviation and the 5 %-quantile of the updated distribution. The simulations show the importance of an adequate sample size and quantify the uncertainties arising from the limited number of observations.