Nonlinear Dynamics

The focus of the work on nonlinearity is the identification and modelling of the type of nonlinear systems which commonly occur in Mechanical and Structural Engineering. There is interest in all aspects of the problem: theoretical, computational and experimental. Methods investigated recently include: time-series methods (based on the NARMAX models developed by Professor Billings in the Department of Automatic Control and Systems Engineering and AVD models, Hilbert transforms and restoring force surfaces. A long-standing area of research is concerned with the use of functional series for the study of nonlinear systems. The Volterra series in particular, has proved effective in extending the classical ides of a Frequency Response Function (FRF) from linear to nonlinear systems.

Recent applications to wave forces of offshore structures have proved to be useful. The Volterra series was also essential in developing the pseudo-fault method which should ultimately allow the validation of in situ fault detection systems. The dynamics of Artificial Neural Networks (ANNs) can also be studied using Volterra series techniques and the computation of higher-order FRFs (HFRFs) has recently been possible; applications in the validity of ANN systems are anticipated. The Dynamics Research Group network software MLP is currently in use at many industrial and academic sites. A long-standing concern of the group has been with the modelling of automotive hydromounts - notoriously nonlinear systems. Current experimental work allows the computation of restoring force surfaces and HFRFs. New techniques are being developed for piecewise linear and hysteretic systems, which work when traditional methods fail. One of these approaches is based on Genetic Algorithms (GAs).

In the area of nonstationarity or time-varying systems and signals, extensive software for the production of time-scale (Wavelet) and time-frequency distributions has been produced. This is used in machinery diagnostics and the analysis of nonlinear systems. The wavelet analysis also has a potential in image compression problems and this approach is currently being pursued to analyse video records of dynamical systems.