Bayesian reliability assessment with spatially variable measurements: The spatial averaging approach

A large portion of the hydraulic structures in the German waterways network have been in service for over 70 years. Verification of these structures according to current standards is not always possible, as they were built according to the standards valid at the time of construction. The massive shape of large hydraulic structures can lead to spatially variable properties, which should be explicitly addressed in a reliability assessment through a random field modeling. Spatially distributed measurements of the concrete properties are available for many structures. These measurements can be used to update the random field model of the concrete properties through Bayesian analysis. In this contribution, we develop and investigate a simplified approach to model non-homogeneous spatial variability in Bayesian posterior random field models that is consistent with the common semi-probabilistic assessment format. The proposed method reduces the random field to a small number of random variables that correspond to local averages of the random field and, hence, generalizes the spatial averaging method originally developed for approximating homogeneous random fields. This should facilitate its application in engineering practice. We apply the proposed methodology to a numerical example and compare the results to those obtained with the random field approach.