Study of a fixed-lag Kalman smoother for input and state estimation in vibrating structures

ABSTRACT This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration measurements. Two numerical examples are examined in order to study the influence of model errors and measurement noise on the estimate quality. From simulations of a simply supported beam, it is shown that estimates from the smoother are superior to those of a conventional Kalman filter, both when the level of model error and measurement noise are increased. By studying simulations of a truck component, the improvement due to smoothing over a conventional Kalman filter is shown to be even greater when the model error is present in both the eigenfrequencies and the mode shapes. In addition, a sensitivity analysis of a tuning methodology with the assumption of constant noise covariance matrices is performed. The result indicates that the proposed tuning methodology results in stable estimates with a good trade-off between estimator adaptability and noise sensitivity. The presented approach of tuning and evaluating the estimates is therefore suggested as a guideline for using the fixed-lag smoother when solving input and state estimation problems in vibrating structures.