| This work presents a two-part study on the development of modeling and on-line system identification tools for nonlinear structural health monitoring.; First, a multi-rate Kalman filtering and smoothing approach is proposed to estimate the velocity and displacement from noise contaminated measurements of acceleration and low sampling displacement. The availability of acceleration response measurements as well as the displacement and velocity is crucial for the damage detection and on-line system identification. This is particularly important in the context of nonlinear system identification, because the nonlinear restoring forces are often modeled as nonlinear functions of velocity and displacement. In civil and mechanical structural modeling accelerometers are most often used, however displacement sensors, such as non-contact optical techniques as well as GPS-based methods for civil structures are becoming more common. A common feature of displacement based sensing is that relatively low sampling rates are used. In contrast, accelerometers are often more accurate for higher frequencies and higher sampling rates are often available. The fusion of these two data types must therefore combine data sampled at different frequencies.; Secondly, the application of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) to nonlinear structural system identification problems has been explored and compared in this study. The unscented Kalman filter has also been developed to identify the structural parameters of extended differential model of hysteresis which can capture most hysteretic characteristics including degradation and pinching. It has been shown through the simulation studies that with only the measurements of acceleration responses and excitations the unscented Kalman filter is capable of tracking on-line system states and parameters of the extended hysteretic systems accurately. |
