A Discontinuous class of filtering methods for the identification of non-smooth dynamical systems

Engineering problems often arise in relation to phenomena such as plasticity, friction or impact. A common factor in these aforementioned cases lies in that the behavior of the system may vary substantially depending on the realization of its states. Mathematically, this can be attributed to the fact that for the corresponding models the corresponding state-space equations of the system or their derivatives are discontinuous. This discontinuity in turn affects the observability and identifiability properties of such systems, which is a major topic within the context of system identification and structural health monitoring. A notable effect lies in response intervals during which one or more parameters of the system may be unidentifiable, i.e., their value may not be inferred on the basis of the measured signals regardless of the efficiency of the identification algorithm used, while the same parameters may become identifiable in a subsequent time window. As a direct consequence, online system identification algorithms, such as the popularly employed Kalman filter methods, are also affected by the discontinuous nature of the system. In this work, the authors introduce an enhancement to the widely adopted Extended Kalman Filter in order to account for dynamic systems comprising discontinuous governing equations. The corresponding effect on the observability and identifiability properties of the systems will further be assessed. This enhanced variant is in this work referred to as the Discontinuous Extended Kalman Filter. An illustrative example is offered for demonstrating the robustness of the Discontinuous Extended Kalman Filter for physical problems involving discontinuous behavior