Unscented Kalman filtering for nonlinear structural dynamics

Abstract

Joint estimation of unknown model parameters and unobserved state components for stochastic, nonlinear dynamic systems is customarily pursued via the extended Kalman filter (EKF). However, in the presence of severe nonlinearities in the equations governing system evolution, the EKF can become unstable and accuracy of the estimates gets poor. To improve the results, in this paper we account for recent developments in the field of statistical linearization and propose an unscented Kalman filtering procedure. In the case of softening single degree-of-freedom structural systems, we show that the performance of the unscented Kalman filter (UKF), in terms of state tracking and model calibration, is significantly superior to that of the EKF.

Structural Parameters Uncertainties Effect on Structural Responses

“…Herein due to the space limitation detail formulation of the UKF is ignored. However, interested reader may obtain detail formulation from [4], [7], [10], [11], [14].…”

Model Updating of a Nonlinear Experimental Vehicle Using Substructuring and Unscented Kalman Filtering

“…The main objective of this study is to establish a computational framework for identifying and adjusting these parameters, while estimating the structural states, in a problem that is referred to as joint state and parameter estimation (JS&PE) [6][7]. To achieve this, the Unscented Kalman Filter (UKF) is utilized [8], due to its efficient performance of in real-time nonlinear system identification problems [9][10][11][12][13].…”

Kalman Randomized Joint UKF Algorithm for Dual Estimation of States and Parameters in a Nonlinear System

“…It uses a minimal set of determinate sample points (Sigma points) to completely assess the true mean and covariance of the states via UT. Studies show that UT is more accurate than linearization for propagating mean and covariance [7][8][9][10][11][12].…”