Identification of Linear and Nonlinear Systems using Signal Processing Techniques
Gaëtan Kerschen, Fabien Poncelet, Jean‐Claude Golinval, Alexander F. Vakakis, Lawrence A. Bergman · ORBi (University of Liège) · 2007
Recovering unobserved source signals from their observed mixtures is a generic problem in many domains and is referred to as blind source separation (BSS) in the literature [1]. One well-known example is the cocktail-party problem, the objective of which is to retrieve the speech signals emitted by several persons speaking simultaneously in a room using only the signals recorded by a set of microphones located in the room. BSS techniques proved useful for the analysis of multivariate data sets such as financial time series, astrophysical data sets, electrical and hemodynamic recordings from the human brain, and digitized natural images. In this presentation, we show that the SOBI method, which belongs to the class of BSS techniques, may be useful in linear structural dynamics. Specifically, for free and random vibrations, a one-to-one relationship between the vibration modes and the mixing matrix computed through SOBI is demonstrated using the concept of virtual source. Based on this theoretical link, a new method for the extraction of the mode shapes, natural frequencies and damping ratios directly from the measured system response (i.e., operational modal analysis) is proposed. The method is then validated using numerical and experimental applications. In particular, modal analysis of a compressor blade of a turbojet engine is carried out [2, 3].