Probabilistic Identification and Prognosis of Nonlinear Dynamic Systems with applications in Structural Control and Health Monitoring

A Bayesian approach to system identification for structural control and health monitoring contains three main levels of inference, namely model assessment, joint state/parameter estimation and noise estimation. All of them have individually, or as a whole, been studied extensively for offline applications. In an online setting, the middle level of inference (joint state/parameter estimation) is performed using various algorithms such as the Kalman filter (KF), the extended Kalman filter (EKF), the Unscented Kalman filter (UKF), or particle filter (PF) methods. This problem has been explored in depth for structural dynamics. This dissertation focuses on the other two levels of inference, in particular on developing methods to perform them online, simultaneously to the joint state/parameter estimation. The quality of structural parameter estimates depends heavily on the choice of noise characteristics involved in the aforementioned online inference algorithms, hence the need for simultaneous online noise estimation. Model assessment, on the other hand, is an integral part of many engineering applications, since any analytical or numerical mathematical model used for predictive purposes is only an approximation of the real system. An online implementation of model assessment is valuable, amongst others, for structural control applications, and for identifying several models in parallel, some of which might be of deteriorating nature, thus generating some sort of alert. The performance of the proposed online techniques is evaluated using simulated and experimental data sets generated by nonlinear hysteretic systems. Upon completion of the study of hierarchical online system identification (diagnostic phase/estimation), a system/damage prognostic analysis (prognostic phase/prediction) is attempted using a gamma deterioration process. Prognostic analysis is still at a relatively early stage of development in the field of structural dynamics, but it can potentially provide useful insights regarding the lifetime of a dynamically excited structural system. The technique is evaluated on a data set recorded during an experiment involving a full-scale bridge pier under base excitation, tested to impending collapse.