Using Wavelets for the Detection of Discrete Events in Time Series of Hybrid Systems

Abstract

This contribution deals with the use of wavelets for the analysis of time series of systems which are hybrid in the sense that they contain discrete and continuous dynamics. We focus on the detection of discrete events which is an important step in the identification of hybrid systems. A brief overview of the characteristics of the wavelet transform is given, which shows that the wavelet transform is an appropriate method for the analysis of time series of hybrid systems. By the combination of two wavelet-based analysis techniques, a two-step procedure is obtained which allows the detection of switching points in the presence of weak noise. In this context, emphasis is given to the problems which arise when the theoretical results are used to detect discrete events in real time series. The procedure is demonstrated for a time series obtained from the simulation of a nonlinear laboratory plant.