Final Report Summary - NSYS (Nonlinear System Identification and Analysis in the Time, Frequency, and Spatio-Temporal Domains)
Considerable progress relating to system identification, information processing, and the analysis of nonlinear dynamic systems has been made during the course of this ERC Advanced Investigator Grant.
New methods for the analysis of nonlinear dynamic systems in the frequency domain have been derived so that a wide class of either discrete nonlinear or continuous time nonlinear differential equation models can be mapped directly to the generalised frequency response functions. The output frequency response function, output spectrum and a new class of filters called energy transfer filters have all been studied and analysed.
Severely nonlinear systems have been studied by developing a completely new framework that allows models with sub-harmonic effects to be studied in both the time and frequency domains. This allows complex time domain effects such as sub-harmonics and the cascade to chaos to be studied in the nonlinear frequency domain to provide considerable insight into these complicated dynamic behaviours.
Spatio-temporal systems, or systems that evolve over both space and time, have been extensively studied. Many new results have been derived including algorithms for the identification of nonlinear partial differential equation, coupled map lattice, cellular automata and n-state system models. The first results which map spatio-temporal models to the nonlinear frequency domain have also been derived to provide an analysis of this class of systems as invariant frequency domain features.
The modelling, identification and analysis of space data systems for example modelling the magnetosphere and space weather have been investigated. New methods of identifying nonlinear differential equation models without any direct differentiation have been introduced, and a completely new class of wavelet models have been derived that allow tracking of very rapid time variations in nonlinear models. One of the models developed as part of the space weather studies is run daily by NASA and currently provides the most accurate forecasts.
We have also made significant advances in related fields and applications. Some examples include: The derivation of important new results in the design of nonlinear damping systems, for example cubic dampers which we can prove are always stable and which offer significant benefits compared to classical linear dampers or active damping devices. The identification and consequent understanding of the visual processing system of Drosophila, a type of fruit fly. The identification of simple intuitive models of crystal growth, the Belouisov Zhabotinskey reaction and other related complex chemical systems. The analysis of EEG data. We are currently working with clinicians at a local hospital who are routinely applying our algorithms to children with absence epilepsy. This project also includes rapid nonlinear frequency response analysis and is being extended to study myoclonus or twitching. Another application in a completely different field has involved the modelling and forecasting of the number of icebergs passing Greenland at 480N and has produced some significant new results relating to the effects of changing climate on the rise in sea levels. We have also derived a new algorithm for solving the Diffuse Optical Tomography (DOT) problem for neuro imaging and we plan to try and implement this so that this can be used as a very cheap and portable non invasive imaging technique in medicine. Other new results include important new developments in the identification and modelling of coronary artery disease, irritable bowel syndrome, metal rubber damping devices which exhibit hysteresis effects, modelling bio-parts for synthetic biology, modelling neutrophil and many other real systems.
New methods for the analysis of nonlinear dynamic systems in the frequency domain have been derived so that a wide class of either discrete nonlinear or continuous time nonlinear differential equation models can be mapped directly to the generalised frequency response functions. The output frequency response function, output spectrum and a new class of filters called energy transfer filters have all been studied and analysed.
Severely nonlinear systems have been studied by developing a completely new framework that allows models with sub-harmonic effects to be studied in both the time and frequency domains. This allows complex time domain effects such as sub-harmonics and the cascade to chaos to be studied in the nonlinear frequency domain to provide considerable insight into these complicated dynamic behaviours.
Spatio-temporal systems, or systems that evolve over both space and time, have been extensively studied. Many new results have been derived including algorithms for the identification of nonlinear partial differential equation, coupled map lattice, cellular automata and n-state system models. The first results which map spatio-temporal models to the nonlinear frequency domain have also been derived to provide an analysis of this class of systems as invariant frequency domain features.
The modelling, identification and analysis of space data systems for example modelling the magnetosphere and space weather have been investigated. New methods of identifying nonlinear differential equation models without any direct differentiation have been introduced, and a completely new class of wavelet models have been derived that allow tracking of very rapid time variations in nonlinear models. One of the models developed as part of the space weather studies is run daily by NASA and currently provides the most accurate forecasts.
We have also made significant advances in related fields and applications. Some examples include: The derivation of important new results in the design of nonlinear damping systems, for example cubic dampers which we can prove are always stable and which offer significant benefits compared to classical linear dampers or active damping devices. The identification and consequent understanding of the visual processing system of Drosophila, a type of fruit fly. The identification of simple intuitive models of crystal growth, the Belouisov Zhabotinskey reaction and other related complex chemical systems. The analysis of EEG data. We are currently working with clinicians at a local hospital who are routinely applying our algorithms to children with absence epilepsy. This project also includes rapid nonlinear frequency response analysis and is being extended to study myoclonus or twitching. Another application in a completely different field has involved the modelling and forecasting of the number of icebergs passing Greenland at 480N and has produced some significant new results relating to the effects of changing climate on the rise in sea levels. We have also derived a new algorithm for solving the Diffuse Optical Tomography (DOT) problem for neuro imaging and we plan to try and implement this so that this can be used as a very cheap and portable non invasive imaging technique in medicine. Other new results include important new developments in the identification and modelling of coronary artery disease, irritable bowel syndrome, metal rubber damping devices which exhibit hysteresis effects, modelling bio-parts for synthetic biology, modelling neutrophil and many other real systems.