10.02 Bayesian Updating Of Engineering Models with Spatially Variable Properties (BAYES)

Research

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.

Illustration of Bayes rule. Available knowledge (e.g., expert knowledge) about an uncertain parameter \theta is formulated as a prior probability distribution. Information from measurements or any other observed data is expressed in terms of a likelihood function. By combining the information from both, we can update our state of knowledge about \theta - which is referred to as the posterior distribution.
In the IGSSE project BAYES we apply Bayes' rule to reduce uncertainty in random fields through observations. The random fields we work with are used as input to engineering models. Observations are typically the response of the engineering system of interest. We try to develop more efficient updating strategies to tackle the Bayesian inference problem on random fields, as well as study the influence of assumptions in the prior random field and likelihood on the posterior random field and the posterior engineering model.

Publications

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.

Team

Project team leader

Wolfgang Betz
Engineering Risk Analysis Group

Doctoral researcher

Elizabeth Bismut
Engineering Risk Analysis Group

Doctoral researcher

Ionut Farcas
Scientific Computing in Computer Science

Doctoral researcher

Felipe Uribe
Engineering Risk Analysis Group

Doctoral researcher

Jonas Latz
Chair of Numerical Analysis

Principal investigator

Professor Daniel Straub
Engineering Risk Analysis Group

Principal investigator

Professor Elisabeth Ullmann
Chair of Numerical Analysis

Principal investigator

Dr. Iason Papaioannou
Engineering Risk Analysis Group