Adaptive unscented Kalman filter methods for identifying time‐variant parameters via state covariance re‐updating

Abstract

The conventional parameter identification process generally assumes that parameters remain constant. However, under extreme loading conditions, structures may exhibit nonlinear behavior, and parameters could demonstrate time‐variant characteristics. The unscented Kalman filter (UKF), as an efficient online recursive estimator, is widely used for identifying parameters of nonlinear systems. Nevertheless, it exhibits limitations when attempting to identify time‐variant parameters. To address this issue, this paper proposes a covariance matching technique that produces an array of adaptive UKF algorithms. Firstly, the sensitivity parameter η is defined to identify the instant when the parameter change occurs, and its threshold is calculated based on the sensitivity parameter time history curve. Secondly, an adaptive forgetting factor is introduced to simultaneously update the innovation, cross, and state covariance matrices when the kth‐step sensitive parameter surpasses the threshold. Finally, a secondary correction forgetting factor (SCFF) is employed to further re‐update the state covariance values at the identified damage locations. This creative step enhances the adaptive capability and optimizes the identification accuracy of the proposed algorithms. Both the numerical simulations and shaking table test demonstrate that the proposed adaptive algorithms can efficiently identify the time‐variant stiffness‐type parameters, and accurately capture their time‐variant characteristics.