Estimating the limit state exceeding probability of a deteriorating structure using the Kalman filter, extended Kalman filter, unscented Kalman filter and the sequential Monte Carlo simulation - Garciano, Lessandro Estelito O. (Animo Repository, 2011)
This paper focuses on determining the limit state exceeding probability of a deteriorating model using optimal and sub-optimal Bayesian algorithms. Specifically the Kalman filter (for a linear system), extended Kalman filter, unscented Kalman filter and the sequential Monte Carlo simulation (for non-linear systems) are used to approximate the present state of a deteriorating system given measurements tainted with noise of the system output. In addition to the comprehensive discussion of the theory, numerical implementation and comparison of the results through numerical examples are shown.