Dynamic state estimation in nonlinear stiff systems using implicit state space models

The problem of dynamic state estimation in vibrating systems displaying stiff behavior is considered. This behavior is characterized by the coexistence of response components with widely separated decay rates and/or frequencies or temporal slow and rapid variations. Explicit methods of discretization of the governing equations here fail to provide satisfactory solutions. We note that existing methods for dynamic state estimation generally assume explicit forms of process equations, which could hinder solutions to problems involving stiff systems. We address this difficulty and employ implicit schemes to discretize governing process equations and develop modifications needed to the existing unscented Kalman filtering, sequential importance sampling, and bootstrap filtering algorithms to account for the implicit nature of process equations. The benefits of the proposed formulations are illustrated by considering systems characterized by inelasticity, limit cycle oscillations, and geometric nonlinearities. An earthquake shake table study on an instrumented nonlinear building frame model is also reported.

Automated summary

This paper examines the problem of dynamic state estimation in vibrating systems displaying stiff behavior. The authors propose implicit methods and modifications to existing filtering algorithms to address the difficulties posed by the explicit forms of process equations. They demonstrate the benefits of these approaches using examples of systems with inelasticity, limit cycle oscillations, and geometric nonlinearities.