A Discontinuous Extended Kalman Filter for non-smooth dynamic problems

Chatzis, M. N.; Chatzi, E. N.; Triantafyllou, Savvas P.

Abstract

Problems that result into locally non-differentiable and hence non-smooth state-space equations are often encountered in engineering. Examples include problems involving material laws pertaining to plasticity, impact and highly non-linear phenomena. Estimating the parameters of such systems poses a challenge, particularly since the majority of system identification algorithms are formulated on the basis of smooth systems under the assumption of observability, identifiability and time invariance. For a smooth system, an observable state remains observable throughout the system evolution with the exception of few selected realizations of the state vector. However, for a non-smooth system the observable set of states and parameters may vary during the evolution of the system throughout a dynamic analysis. This may cause standard identification (ID) methods, such as the Extended Kalman Filter, to temporarily diverge and ultimately fail in accurately identifying the parameters of the system. In this work, the influence of observability of non-smooth systems to the performance of the Extended and Unscented Kalman Filters is discussed and a novel algorithm particularly suited for this purpose, termed the Discontinuous Extended Kalman Filter (DEKF), is proposed.

Citation

Chatzis, M. N., Chatzi, E. N., & Triantafyllou, S. P. (2017). A Discontinuous Extended Kalman Filter for non-smooth dynamic problems. Mechanical Systems and Signal Processing, 92, 13-29. https://doi.org/10.1016/j.ymssp.2017.01.021

• Journal Article Type: Article
• Acceptance Date: Jan 18, 2017
• Online Publication Date: Jan 29, 2017
• Publication Date: 2017-08
• Deposit Date: Feb 1, 2017
• Publicly Available Date: Feb 1, 2017
• Journal: Mechanical Systems and Signal Processing
• Print ISSN: 0888-3270
• Electronic ISSN: 1096-1216
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 92
• Pages: 13-29
• DOI: https://doi.org/10.1016/j.ymssp.2017.01.021
• Keywords: System identification; Plasticity; Impacts; Non-smooth systems; Non-linearities; Kalman filters
• Public URL: https://nottingham-repository.worktribe.com/output/967052
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0888327017300298