Reliability Updating in the Presence of Spatial Variability

During the construction and operation of engineering systems, information on their properties and performance becomes available through monitoring and other means of observation. Such information can be used to update predictions of the system’s reliability through a Bayesian analysis. We present Bayesian analysis and updating of the reliability of engineering systems that depend on physical quantities that vary randomly in space, which are modelled by means of random fields. The numerical treatment of random fields requires their discretization with a finite number of random variables. To this end, we employ the Expansion Optimal Linear Estimation (EOLE) method, which is shown to be especially efficient in obtaining an approximation of a second-order random field. This property is beneficial for Bayesian analysis in cases where the moment function depends on hyperparameters, such as the correlation length of a random field. We discuss the application of EOLE in the context of BUS, which is a recently proposed framework for Bayesian updating of parameters of engineering systems and the resulting system reliability. In BUS, monitoring data is expressed in terms of an equivalent limit state function such that Bayesian updating can be performed with structural reliability methods. We apply BUS with EOLE to update the reliability of the stability of a foundation resting on spatially variable soil with deformation measurements obtained at an intermediate construction stage.