With advances in computation and monitoring technologies, there is a large number of possibilities for enhanced probabilistic predictions of engineering systems. It is becoming increasingly recognized that accurate predictions of such systems often require models that account for the random spatial variability of parameters. This holds in particular if monitoring and other observational data is to be used to learn the models and update predictions. In this project, the focus is on learning engineering models with spatially variable properties using Bayesian analysis. The Bayesian framework enables the combination of uncertain and incomplete information with sophisticated probabilistic models and it provides probabilistic information on the accuracy of the updated model. This project has two main goals: Firstly, we want to provide the first systematic investigation of the effect of different model choices on the posterior predictions, and provide recommendations for engineering practice. Secondly, we want to identify and further enhance efficient computational methods for Bayesian analysis of engineering models with discretized random fields. The engineering PIs have been very successful recently with new methods for Bayesian analysis in the field of engineering risk. To now bring them to the next level, and to possibly extend their application to other fields, their collaboration with the mathematical sciences is essential.
Diego A. Alvarez, Felipe Uribe, Jorge E. Hurtado: "Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory", 2018.
Elizabeth Bismut, Jesus Luque and Daniel Straub: "Optimal prioritization of inspections in structural systems considering component interactions and interdependence", 2017.
Felipe Uribe, Iason Papaioannou, Wolfgang Betz, Jonas Latz, Daniel Straub : "Bayesian model inference of random fields represented with the Karhunen-Loève expansion", 2017.
Felipe Uribe, Iason Papaioannou, Wolfgang Betz, Elisabeth Ullmann, Daniel Straub : "Random fields in Bayesian inference: effects of the random field discretization", 2017.
Betz, W., Papaioannou, I., Straub, D.: "Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion", 2014.
Betz, W., Papaioannou, I., Straub, D.: "Adaptive variant of the BUS approach to Bayesian updating", 2014.
Betz, W., Papaioannou, I., Straub, D.: "Assessment of methods for the numerical solution of the Fredholm integral eigenvalue problem”, 2013.
Betz, W., Papaioannou, I., Straub, D.: "A finite cell approach for discretization of random fields”, 2012.