| System identification deals with the problem of building mathematical models of dynamical systems based on the observed data. Most contemporary studies in this field have a fundamental assumption: the observed data are stationary, which means that statistical characteristics of the data do not change with time. The thesis is motivated by an "ambitious" thought: is it possible to remove or weaken this assumption so that the knowledge in the field can be advanced? The answer is positive by introducing cyclo-stationary signals, which exhibit periodicity in their mean, correlation, and spectral descriptions.; The thesis consists of two parts. The first part studies cyclo-stationary signal analysis, including cyclo-period estimation, cyclo-statistic estimation and cyclo-spectral theory; they provide the second part with powerful computational tools and build up a solid theoretical background. The second part is to exploit cyclo-stationarity in system identification, including finite-impulse-response modeling for errors-in-variables/closed-loop systems, and blind identification of Hammerstein nonlinear systems. The main contributions achieved are briefly described as follows: (1) Cyclo-period estimation: A new method, named as the variability method, is proposed to estimate the cyclo-period of a discrete-time cyclo-stationary signal. Properties of the variability method are analyzed and compared with three existing cyclo-period estimation methods via simulation and real-life examples. (2) Cyclo-statistic estimation: We summarize the existing estimators of the time-varying mean/correlation and cyclic correlation/spectrum, and supplement a new cyclic spectrum estimator: the blocking-based estimator, and discuss implementation issues of these estimators. (3) Cyclo-spectral theory: Two problems in the spectral theory of discrete-time cyclo-stationary signals are studied: (i) four types of the cyclospectrum representation are presented and their interrelationships are explored; (ii) the problem of the cyclospectrum transformation is attacked in the framework of multirate systems using the blocking technique as a systematic solution. (4) Finite-impulse-response modeling for errors-in-variables/closed-loop systems: A complete study of the cyclic correlation analysis, which consistently estimates finite-impulse-response models, is developed including the time- and frequency-domain statistical performance of the models. (5) Blind identification of Hammerstein nonlinear systems: A new blind approach is proposed for identification of Hammerstein nonlinear systems by exploiting input's piece-wise constant property. In a real-time laboratory experiment, the proposed approach is successfully applied to modeling of a magneto-rheological damper. |
