Bayesian techniques – widely used to update the distributions of involved uncertain system variables based on new observations at different points in space and time – can be highly demanding and prohibitive in cases of sophisticated computational models. Here, we propose a highly efficient Bayesian updating framework that is integrated with multivariate Kriging surrogate modeling to quantify heteroscedastic uncertainties in the entire space of uncertain system variables and capture spatial and temporal dependencies among the responses using non-separable covariance structure. The advantages of the proposed framework are demonstrated on three geological and geotechnical examples, since geological properties are often highly uncertain and responses in these systems are frequently multivariate in nature. Results indicate that the developed framework is able to accurately and efficiently update uncertainties of system variables compared to existing Bayesian updating methods that are based on surrogate models. Moreover, considering the often-neglected spatiotemporal dependencies between responses is observed to noticeably enhance the accuracy of predictions. The proposed approach serves as an efficient tool to optimally utilize monitoring data from geological and geotechnical systems to arrive at reliable predictions of future responses.
Rahimi, M., Shafieezadeh, A., Wood, D., Kubatko, E.J., & Dormady, N. (2019). Bayesian Calibration of Multi-Response Systems via Multivariate Kriging: Methodology & Geological & Geotechnical Case Studies. Engineering Geology, 260(3): 105248.