| dc.description.abstract | This thesis reports on combined experimental and computational investigations conducted on problems of state and combined state and parameter estimation applied to vibrating engineering structures. The standard dynamic state space modeling framework is adopted for this purpose, and the analysis is carried out using the Kalman filter (and its variants), particle filters, and Markov chain Monte Carlo (MCMC) samplers. A review of the relevant literature has revealed that these tools have not been applied to situations where the system under study and its numerical representation via the discretized process equation displays numerical stiff behaviour. This numerical stiffness is characterized by the presence of response components with widely separated decay rates and (or) frequencies of oscillations. A computationally efficient treatment of such systems calls for the application of implicit discretization schemes to deduce the discrete process equations from the governing semi-discretized equations of motion resulting from the application of the finite element method. The implicit nature of the process equation, however, poses several challenges in the analysis of the resulting dynamic state space model since most existing methods for this purpose assume explicit process equation models. The present thesis investigates the modifications needed to some of the existing Bayesian filters, such as the Kalman filter, extended Kalman filter, unscented Kalman filter, bootstrap filter, and sequential importance sampling particle filters so that the methods can be employed to allow for implicit process equation models. Some of these tools are then combined with MCMC samplers to tackle problems of combined state and parameter estimation problems. The thesis covers linear and nonlinear dynamical systems and allows for the identification of not only the dynamical system parameters but also the parameters associated with models for the process and measurement noises. The tools developed are applied to a suite of laboratory experimental models, which include shear building frame models containing an inerter element and piecewise geometrical nonlinear features and one-storey and five-storey asymmetric, bending-torsion coupled building frames. These frames are tested on a multi-axes earthquake simulator. Also studied are typical nonlinear dynamical systems such as a limit cycle oscillator, a multi-degree of freedom degrading inelastic frame model, and an elastically mounted pendulum undergoing large amplitude oscillations. The thesis is organized into an introductory chapter, a chapter that provides a review of literature, four contributing chapters, and a chapter that summarizes contributions made and makes a few suggestions for future research. The contributing chapters are sequenced as follows:
(a) Chapter 3 considers problems of state estimation in stiff linear state space model and discusses the application of an implicit Kalman filtering strategy,
(b) Chapter 4 presents the details of the modifications made to the extended Kalman filter, unscented Kalman filter, bootstrap filter, and sequential importance sampling filter and discusses the application of resulting algorithms to tackle problems of state estimation in a set of nonlinear dynamical systems,
(c) Chapter 5 considers the problem of combined state and parameter estimation in linear stiff systems by combining implicit Kalman filter with the general adaptive metropolis algorithm, an MCMC sampler, and
(d) Chapter 6 presents the formulations for the combined state and parameter estimation in nonlinear stiff systems using implicit unscented Kalman filter along with general adaptive Metropolis algorithm. The thesis has around 230 references covering a time window of 1964-2023. | en_US |
