An adaptive unscented Kalman filter for tracking sudden stiffness changes

• We show that the unscented Kalman filter cannot track sudden stiffness changes.
• We develop a new scheme which allows the UKF to track sudden changes.
• The effectiveness of this scheme is demonstrated through numerical simulations.
• The effect of measurement noise on this scheme is studied.

The paper presents an approach to track sudden changes in stiffness of structural systems exposed to earthquake induced base excitations. Such sudden changes in the stiffness could be caused by abrupt damage of one or more structural members. To track such changes through a Kalman filter approach, the stiffness and damping coefficients of structural members to be tracked need to be a part of the state vector of a state space model. However, such state equations become nonlinear even for an otherwise linear system. The use of the unscented transform-based Kalman filter approach has been considered to effectively deal with such nonlinearities in state estimation. But this approach not intended to track sudden changes is unable to achieve this. Herein, an adaptive Kalman filter scheme is proposed for efficient detection as well as tracking of sudden changes in stiffness values. The approach first identifies the instant of a sudden change, followed by appropriate adjustment of the state covariance matrix for efficient tracking of the states. Numerical examples of structural models with several earthquake inputs with different characteristics are used to show that the proposed scheme can effectively track multiple events of sudden stiffness changes in several structural members occurring at different time instances.