The University of Southampton
University of Southampton Institutional Repository

# Time-frequency characterisation of nonlinear systems

Adamopoulos, Panos Georgiou (1990) Time-frequency characterisation of nonlinear systems. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

## Abstract

Tentative suggestions for equivalencies between nonstationary and nonlinearity have hitherto been alluded to but not developed. This thesis is aimed at such a rapprochement where the problem on nonlinear (inclusive of Chaotic) system characterisation is addressed. A common assumption in the analysis and characterisation of a process is that the process is stationary but such an assumption, although it might be a satisfactory approximation in certain circumstances, is very questionable in many situations. In particular, many physical nonstationary processes exhibit a frequency and/or amplitude modulated structure which embody the nonstationary behaviour. An example of such a process is the response of a mass-spring-damper nonlinear system where a hardening (or softening) spring is incorporated. In this thesis the equivalencies between nonstationarity and nonlinearity will be incorporated in a pattern recognition approach'. In this approach the use of specific signal analysis tools will allow the responses of nonlinear systems to be mapped and examined on various (time and/or frequency, phase-space, etc.) planes. The effect of the system's residing nonlinearity on the system's nonstationary (mapped) response will provide a characterising signature for the system and/or the nonlinearity. The main tool for nonlinear system characterisation will be the conjoint time-frequency Wigner-Ville distribution, but in addition a number of classic' and `contemporary' methods will be highlighted and (sometimes) utilised, in particular when dealing with nonlinear systems which are capable of generating a chaotic response. The majority of the characterisations will be carried out from simulated results, but also some data acquired from experiments on nonlinear systems will be utilised and analysed for system and/or nonlinearity characterisation.

Published date: 1990

## Identifiers

Local EPrints ID: 460710
URI: http://eprints.soton.ac.uk/id/eprint/460710

## Catalogue record

Date deposited: 04 Jul 2022 18:28