Adaptive constrained unscented Kalman filtering for real-time nonlinear structural system identification

Abstract

Summary The unscented Kalman filter (UKF) is often used for nonlinear system identification in civil engineering; nevertheless, the application of the UKF to highly nonlinear structures could not provide accurate results. In this paper, an improvement of the UKF algorithm has been adopted. This methodology can consider state constraints, and it can estimate the measurement noise covariance matrix. The results obtained adopting a modified UKF have been compared to the ones obtained using the UKF for parameter estimation of a single degree of freedom nonlinear hysteretic system. The second part of this work shows results of an experimental activity on a base‐isolated prototype structure. Both numerical and experimental results underline that the adopted algorithm produces better state estimation and parameter identification than the UKF, being capable of taking into account parameter boundaries. The adopted algorithm is more robust than the standard UKF in the case of measuring noise variation.

Experimental verification of constrained minimum variance unbiased estimator for simultaneous input and state estimation of Bounded Input and Bounded Output (BIBO) type Bouc–Wen hysteretic structural system

“…However, numerical optimization in this approach is computationally expensive. Likewise, to take into account non‐linear equality/inequality constraints in sigma point‐based predictor‐corrector framework, unscented recursive non‐linear dynamic data reconciliation (URNDDR) 3,48 is developed. In this technique, sigma points lying outside the constraint region are projected back to the constraint boundary and weights are assigned accordingly.…”

“…1 Consequently, numerous attempts have been made to model the hysteretic behaviour of a system and to identify its properties from the measured time histories. [1][2][3][4][5] Among different identification algorithms, the recursive time-domain estimation techniques are found to be more efficient in incorporating measurements. Commonly used time-domain methods for non-linear system identification are least-square estimation (LSE), [6][7][8] extended Kalman filter (EKF) [9][10][11][12] and particle filter (PF).…”

“…Besides health monitoring, real‐time identification of the restoring force is an inevitable part of any close loop structural control algorithm 1 . Consequently, numerous attempts have been made to model the hysteretic behaviour of a system and to identify its properties from the measured time histories 1‐5 …”

Online estimation of the friction coefficient in sliding isolators

“…On the other hand, online estimation algorithms, such as EKF and UKF, perform real‐time identification by means of a recursive algorithm which uses the current measurements and previous parameter estimates to update the parameter and the states of the model when new data is available, and therefore are computationally effective. As a result, these procedures have been widely adopted in SHM …”

Damage quantification in moment resisting frame using phase space reconstructed from independent component sources

“…In the literature, several structural health monitoring techniques have evolved to detect the local and global damage in the structure. The popular and widely accepted structural health monitoring techniques in the time domain are Hilbert–Huang transform, empirical mode decomposition, wavelet transform, singular spectrum analysis, frequency domain decomposition, auto‐regressive (AR) model, auto‐regressive moving average model, time‐varying auto‐regressive, unscented Kalman filter, and extended Kalman filter‐weighted global iteration techniques . These techniques perform satisfactorily for the linear dynamic system to identify the system parameters.…”