An Iterative Augmented Unscented Kalman Particle Filter for Simultaneous State-Parameter-Input Estimation for Structural Systems Subjected to Gamma-Distribution Noise

Abstract

Simultaneous estimations of the states, parameters and unknown inputs of nonlinear structural systems subjected to non-Gaussian noise are essential, because the inputs are not always available and the system noise is not always Gaussian. However, filters developed for this task require the inter-story drift measurements to be “fused” with the acceleration measurements to avoid the “drift phenomenon”. Because inter-story drifts may be inconvenient to obtain in practice, it is more desirable to use acceleration measurements only. To this end, this study develops a novel iterative augmented unscented Kalman particle filter (IAUKPF) for the simultaneous state-parameter-input estimation for systems subjected to non-Gaussian noise. The iterative strategy proposed in this study effectively corrects the “drift phenomenon” when only acceleration measurements are incorporated, so that the accuracies of the estimated unknown inputs are promoted. The importance density of the particle filter at each time step is provided by the augmented unscented Kalman filter so that the filter takes the best known information into consideration. Numerical examples of nonlinear structural systems affected by non-Gaussian noise are adopted to examine the effectiveness of the proposed IAUKPF.