Extended Kalman filtering for the detection of damage in linear mechanical structures

This paper addresses the problem of assessing the location and extent of damage in a vibrating structure by means of vibration measurements. Frequency domain identification methods (e.g. finite element model updating) have been widely used in this area while time domain methods such as the extended Kalman filter (EKF) method, are more sparsely represented. The difficulty of applying EKF in mechanical system damage identification and localisation lies in: the high computational cost, the dependence of estimation results on the initial estimation error covariance matrix P_ex (0), the initial value of parameters to be estimated, and on the statistics of measurement noise R_ex and process noise Q_ex. To resolve these problems in the EKF, a multiple model adaptive estimator consisting of a bank of EKF in modal domain was designed, each filter in the bank is based on different P_ex (0). The algorithm was iterated by using the weighted global iteration method. A fuzzy logic model was incorporated in each filter to estimate the variance of the measurement noise R_ex. The application of the method is illustrated by simulated and real examples.