Modal Identification by Cross-Time-Frequency Estimators

The aim of this work is to show that time-frequency and cross-time-frequency based techniques can be used effectively in system identification in nonstationary conditions, under unknown excitation. In some sectors, including civil structures, the use of techniques that exploit environmental excitation may avoid problems such as breaks in roadway traffic or production activities. The method here proposed uses a number of two-dimensional estimators defined in the time-frequency plane. Since they are derived directly from two-dimensional functions of the time and frequency variables, they retain their dependence on time variables and are punctual estimators. They make it possible to determine the time evolution of the modal shape associated with a given frequency component and hence to establish "a posteriori", i.e. at the end of the process, whether a given frequency value may or may not be a structural vibration mode. In linear systems, in fact, modal signals are characterised by the fact that amplitude and phase relationships are constant and therefore the modal shape to which they give rise is characterised by stability over time. The transforms being considered are those in Cohen's class which, in addition to possessing valuable properties for the analysis of mechanical signals, lend themselves to a clear interpretation in energy terms. In the second part of the paper it is proved that the cross-correlation based estimators are more effective, also thanks to their external noise filtering properties. In this connection, an improved version of the method for an accurate estimation of modal shapes, which avoids auto-correlation, is proposed. The accuracy and consistency of the procedure was tested by resorting to numerical simulations.