A comparative assessment of nonlinear state estimation methods for structural health monitoring

Researchers have been studying the uncertainties unique to civil infrastructure such as redundancy; nonlinearity; interaction with surrounding; heterogeneity; boundaries and support conditions; structural continuity, stability, integrity; life cycle performance expectations and so on. For incorporating such uncertainties, filtering techniques accounting for stochasticity can be implemented employing collected data from the structures. In this paper, an Iterated Square Root Unscented Kalman Filter (ISRUKF) method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems, idealized herein for simplified spring-mass-dashpot. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the Unscented Kalman Filter (UKF), the Square-Root Unscented Kalman Filter (SRUKF), the Iterated Unscented Kalman Filter (IUKF) and the Iterated Square Root Unscented Kalman Filter (ISRUKF) methods. The comparison reveals that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state.