Abstract
In this paper, an iterated square-root central difference Kalman particle filter method (ISRCDKF-PF) is used for the estimation of the state variables and model parameters of nonlinear structural systems. In the current work, we propose to extend our previous work (Mansouri et al. in J Civil Struct Health Monit 5(4):493-508, 2015) to deal with non-parametric Monte Carlo sampling-based method and propose to use an enhanced PF technique which incorporates the latest observations into a prior updating scheme using the ISRCDKF algorithm. 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 central difference Kalman filter (SRCDKF), the iterated unscented Kalman filter (IUKF), the iterated square-root central difference Kalman filter (SRCDKF), the conventional particle filter (PF), the unscented Kalman particle filter (UKF-PF), the SRCDKF-PF, the iterated unscented Kalman particle filter (IUKF-PF) and the developed ISRCDKF-PF, in two comparative studies through two examples, one using synthetic data and the other using simulated three DOF damped system data. In the first comparative study, the state variables are estimated from noisy measurements of these variables, and the comparison of the different estimation techniques is performed by computing the root mean square error (RMSE) of the state with respect to the noise-free data. In the second comparative study, both the state variables and the model parameters are simultaneously estimated, and the impact of the used measurement noise, and number of estimated states/parameters on the performances of the estimation techniques are investigated. The ISRCDKF-PF algorithm consists of a PF based on ISRCDKF to obtain a better importance proposal distribution. This proposal is able to integrate the latest observation into the state density, then it can improve the posteriori density. The results of both comparative study show that PF, UKF-PF, SRCDKF-PF, IUKF-PF and ISRCDKF-PF provide improved estimation performance over the UKF, SRCDKF, IUKF, ISRCDKF. The results also show that ISRCDKF-PF provides improved estimation performance over IUKF-PF, even with abrupt changes in estimated states, and both of them provide better accuracy than the conventional PF, UKF-PF and SRCDKF-PF. These advantages of the ISRCDKF-PF are due to the fact that it uses an optimal proposal distribution which make efficient use of the latest observation by using the ISRCDKF algorithm.