Modelagem paramétrica de sistemas dinâmicos não-estacionários

Abstract

In this work, the identification and analysis of time-varying systems are investigated. The problem of non-stationarity is addressed in the context of time-varying, parametric and discrete dynamical system identification. The necessary theoretical background for the understanding of system identification and non-stationarity is given. Three different methods used to analyze time series generated by dynamical time-varying systems were studied. The first method, TV-OPS, deals with the problem of structure selection and tracks the changes in the coefficients of a polynomial model by expanding them into two different basis functions: Walsh and Legendre. In the case of the two other methods, RLSVFF and VLSWBLS, the change in dynamics is tracked by inspecting the model coefficients calculated using the recursive and ordinary least squares methods respectively. Linear and nonlinear systems, polynomial models were used in this work as a basis for system identification. Using simulated time series, the hypothesis that changes in the model coefficients could explain the dynamical changes in the system behavior was investigated. As a by-product, the location in time where these changes occurred was found. Issues such as sensitivity to measurement noise, choice of free-parameters in the aforementioned methods and the effect of the parameters in each other were also addressed. The caveats of the above methods were addressed. Several conclusions on how to analyze the results of applying such methods were drawn. One of them is that the correct model structure is essential to all methods. The main ideas and methods were also applied to real data.