Nonlinear System Identification and Information Processing
The group has pioneered the most advanced nonlinear system identification and information processing methodology, tools and algorithms available to date, which can be applied to a wide class of nonlinear complex dynamical systems, including chaotic, spatio-temporal and stochastic systems.
A wide class of nonlinear models is being investigated, including polynomial, radial basis function and wavelet multiresolution models. The focus of research is on model structure selection and the identification of models that a) capture the underlying dynamics rather than fit the data and b) provide insight into or predict fundamental properties of the system of interest.
The derivation of generic model validity test and model analysis methods for all classes of nonlinear models are also being studied.
The methods and tools developed by the group have been successfully used to develop the Sheffield online GEO forecast tool, providing the most accurate two-day-ahead forecast available of the electron flux. Forecasting the evolution of these fluxes enables mitigation of their effects on spacecraft.
The group is also carrying out research to reverse-engineer neural processes using a wide range of experimental data sets, including electrophysiological, EEG, MRI and DOT recordings. In collaboration with researchers in other disciplines we model the visual system of the fruit flies to understand how fly brains process information about the visual environment. In collaboration with NHS clinicians we developed causality detection and wavelet adaptive tracking algorithms to predict the onset of epileptic seizures.
Sheffield online GEO forecast tool
Frequency Domain Analysis of Nonlinear Systems
The group has developed a complete theory for the analysis of nonlinear systems in the frequency domain. This consists of analytic methods for mapping from nonlinear discrete and continuous time nonlinear differential equation models to the multi-dimensional generalised frequency response functions and vice versa. A new class of filters, called energy transfer filters, has recently been derived which allows energy to be moved to new frequency locations or spread over a band of frequencies.
The focus of current research is to extend the theory, methods and algorithms, developed for analysing and synthesising lumped nonlinear systems in the frequency domain, to spatio-temporal systems.
The higher-order frequency response analysis tool developed by the group has been successfully used to elucidate for the first time, as part of a BBSRC funded project, the nonlinear coding mechanisms implemented by fly photoreceptors to encode and enhance salient stimuli features that are behaviourally important.
Reverse Engineering Drosophila Retinal Networks
Complex, Spatio-Temporal Systems
Many biological, chemical and physical systems involve variables which depend on both space and time. Such systems, which often operate away from equilibrium, exhibit complex emergent behaviour such as pattern formation, self organization, turbulence, spatio-temporal chaos etc. The goal of this research is to use this data and extract informative structures, reconstruct the underlying spatio-temporal dynamics that govern these systems as well as analyse, understand and forecast their emerging properties.
The realisation, identification, prediction, analysis and control of this class of systems are being studied at theoretical level, with the aim to develop practical methodologies and tools that can help address big research challenges in energy, environment, life sciences etc.
The tools developed as part of this research have been applied successfully to study iceberg calving patterns and climate change in Greenland, model and control of crystal growth, fluid flows and wildfires.
The group is also carrying out research on the multiscale modelling of musculoskeletal system in biomedical system engineering and the differentially expressed gene modelling in biology.