Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls

Iglesias, Marco; Sawlan, Zaid; Scavino, Marco; Tempone, Raul; Woodard, Christopher

Abstract

In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analo- gous to our previously proposed approach [1, 2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add in- flation, and converges to the mean field posterior using 50% or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.

Citation

Iglesias, M., Sawlan, Z., Scavino, M., Tempone, R., & Woodard, C. (2018). Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls. Inverse Problems, 34(7), https://doi.org/10.1088/1361-6420/aac224

• Journal Article Type: Article
• Acceptance Date: May 2, 2018
• Online Publication Date: May 3, 2018
• Publication Date: May 22, 2018
• Deposit Date: May 4, 2018
• Publicly Available Date: May 4, 2019
• Journal: Inverse Problems
• Print ISSN: 0266-5611
• Electronic ISSN: 0266-5611
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 7
• DOI: https://doi.org/10.1088/1361-6420/aac224
• Public URL: https://nottingham-repository.worktribe.com/output/933329
• Publisher URL: http://iopscience.iop.org/article/10.1088/1361-6420/aac224
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6420/aac224