The University of Sheffield
Automatic Control and Systems Engineering

Professor Stephen A. Billings
Director of the Signal Processing and Complex Systems Research Team

Signal Processing and Complex Systems Research Team

Photo of Professor S A Billings

 
Address:
Professor Stephen A. Billings, BEng, PhD, DEng, CEng, CMath, CSci, FIEE, FIMA
Department of Automatic Control and Systems Engineering
University of Sheffield
Sheffield
S1 3JD
Tel: (+44) (0)114 222 5232
Fax: (+44) (0)114 222 5683
Email: s.billings @ sheffield.ac.uk
Room: B15, Amy Johnson Building

Research interests
Grants
Professional activities and recognition
Key publications since 2001

Research interests

Identification of nonlinear systems, NARMAX methods, signal and information processing for nonlinear systems, model validation, spectral analysis for nonlinear systems, nonlinear time series analysis and forecasting, machine learning and neural networks, wavelets, fractals, nonlinear filtering and smoothing, analysis and control of nonlinear and chaotic systems, self tuning, fault detection, dynamic modelling of nonlinear continuous time processes, adaptive noise cancellation, machine vision, mobile robots, cellular automata, spatio-temporal systems, neuro-imaging including fMRI and diffuse optical tomography, bio-imaging, financial modelling, modelling for biology, systems and synthetic biology, stem cell population dynamics, reaction-diffusion systems and crystal growth.

See the Signal Processing and Complex Systems Research Team website for more details.

Signal Processing and Complex Systems Research Team website

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Grants
[From 2000 onwards]

EPSRC, S A Billings and G R Tomlinson, `Estimation, Analysis and Synthesis of Nonlinear Systems´, 1.2.97 to 31.1.02, £131,535

EPSRC, Y Zheng, S A Billings, J E W Mayhew, P J Coffey, `Identification and Analysis of Spatio-Temporal Systems with Applications to Brain Imaging´, 1.7.97 to 30.6.02, £272,620

EPSRC, S A Billings, `Wavelet Modelling of Nonlinear Systems´, 22.02.99 to 21.02 2002, £134,156

EPSRC, S A Billings and G R Tomlinson, `Frequency Domain Estimation and Filtering for Nonlinear Systems´, 01.02.2000 to 31.01.2003, £167,637

EPSRC, S A Billings, `Identification of Spatio-Temporal Dynamical Systems´, 01.07.00 to 30.06.03, £212,573

EPSRC ROPA Award, G R Tomlinson, S A Billings and Z Q Lang, `A Novel Approach to Vibration Attenuation Exploiting Nonlinear Energy Transfer Concepts´, 01.10.02 to 31.09.04, £136,931

EPSRC, Y Zheng, S A Billings, and J E W Mayhew, `Identification and Modelling of Haemodynamic Response and Oxygen Delivery Brain´, 01.03.02 to 31.08.05, £223,788

EPSRC, S A Billings, `Identification of Engineering Systems that Exhibit Sub Harmonics´, 01.10.02 to 31.09.05, £208,476

EPSRC, S A Billings, `Identification and Analysis of Spatio Temporal Systems´, 01.08.03 to 31.07.06, £244,255

EPSRC, U Nehmzow and S A Billings, `Robot MODIC: Modelling Identification and Characterisation of Robot Environment Interaction´, 01.01.04 to 31.12.06, £193,722

SRIF Funding, J E W Mayhew et al, S A Billings, 'Neuroscience Imaging Initiative', 2005 to 2006, £1.08M

EPSRC Platform Grant, S A Billings, V Kadirkamanathan, Z Q Lang, D Coca, M Balikhin, `System Identification and Signal Processing for Complex Systems´, 03.01.05 to 02.01.10, £422,571

EPSRC, S A Billings, `Identification and Analysis of Nonlinear Systems in the Time and the Frequency Domain´, 01.10.05 to 31.03.09, £256,875

EPSRC, S A Billings, Y Zheng, J Martingdale, D Coca and J E W Mayhew, `System Identification and Signal Processing for Neuro-Imaging data Analysis´, 02.01.06 to 01.11.09, £264,277

EPSRC, S A Billings, D Coca, `System Identification and Model validation for Spatio-Temporal Dynamical Systems´, 01.08.06 to 31.07.09, £295,373

The Leverhulme Trust, U Nehmzow and S A Billings, `System Identification for Rapid Generation of Transparent, Analysable Control Code for Autonomous Mobile Robots´, 1.07.07 to 1.04.2011, £129,887

EPSRC, Z Q Lang, S A Billings, G R Tomlinson, 'New Generation Damping Technologies', 01.05.08 to 30.04.2011, £378,519

BBSRC, P Wright et al including S A Billings, 'Microbial Applications to Tissue Engineering: An Exemplar Network for Synthetic Biology', 01.06.08 to 31.05.2011, £135,520

BBSRC, S McNeil et al including ACSE staff S A Billings, V Kadirkamanathan, D Coca, 'Doctoral Training Grant for ten four-year PhD studentships at the interface between Medicine, the Life Sciences, Engineering and Chemistry', 2009-2013, £763,459

Advanced Investigator Grant of the European Research Council, S A Billings, 'Nonlinear Systems Identification and Analysis in the Time, Frequency, and Spatio-Temporal Domains', 1.04.2009 to 31.03.2014, €1,947,104

EPSRC, S A Billings, D Coca, 'Spatio-Temporal Systems Estimation, Modelling and Analysis', 02.02.2010 to 01.02.2014, £499,542

EPSRC Platform Grant, S A Billings, V Kadirkamanathan, Z Q Lang, D Coca, M Balikhin, H L Wei, `System Identification and Information Processing for Complex Systems´, 04.01.2010 to 03.01.2015, £1,205,632

BBSRC, D Coca, M Juusola, S A Billings, 'Reverse Engineering Drosophila's Retinal Networks' 01.08.2010 to 31.07.2013, £532,115

NERC, G R Bigg, E Hanna, V Kadirkamanathan, S A Billings, 'A century of variability in Greenland melting and iceberg calving' 02.01.2011 to 01.01.2014, £311,959

BBSRC, Y Zheng, J Berwick, A J Kennerley, M Jones, S A Billings, D Coca, E Milne and P Redgrave, 'Understanding neural excitation and inhibition: Implications for the interpretation of extracellular field potentials and neurovascular coupling', 01.05.2013 to 31.04.2016, £615,105

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Professional activities and recognition

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Key publications since 2001

  Details of Publication Brief description of contribution
1 Guo L.Z., Billings S.A.: `State space reconstruction and spatio-temporal prediction of lattice dynamical systems´, IEEE Transactions on Automatic Control, 2007, 52, 622-632 This paper derives an embedding theory for spatio-temporal systems. This is a key fundamental development that has remained unsolved for many years. The results are fundamental to spatio-temporal system identification, modelling, and prediction since they prove the existence of a class of models.
2 Billings S.A., Wei H. L. : ´A new class of wavelet networks for nonlinear system identification´ IEEE Trans Neural Networks, 2005, 16, 862-874 This paper introduces a new and important class of wavelet networks as an alternative to standard neural network architectures. The new wavelet architecture and the associated training algorithms that are derived, provide significantly improved performance compared with existing methods and solve the problem of nonlinear system identification in high dimensions.
3 Boaghe O., Billings S.A., : ´Subharmonic oscillation modelling and MISO Volterra series´, IEEE Trans Circuits and Systems I, 2003, 50, 877-884 This paper introduces two important advancements. The response spectrum map [RSM], which is the frequency domain equivalent to the bifurcation diagram for nonlinear systems, is defined. Based on the RSM, the first systematic frequency domain approach to studying complex nonlinear systems that exhibit sub-harmonics is derived.
4 Wei H., Billings S.A., Lui J: ´Term and variable selection for nonlinear models´ Int J Control, 77, 2004, 86-110 This paper solves the very important and core problem of selecting the variables and terms for nonlinear modelling. This is a fundamental paper in the field of model selection with applications to narmax modelling, neural networks, fuzzy logic and pattern recognition.
5 Billings S. A., Yang Y. X.: ´Identification of probabilistic CA´, IEEE Trans Man systems and Cybernetics, Part B, 33, 2003, 225-236 This paper describes a major new development in the identification of probabilistic cellular automata. Algorithms, which can be used to identify CA rules from noisy observations, are derived for the first time.
6 Billings S. A., Yang Y. X.: ´Identification of the neighbourhood and CA rules from spatio-temporal CA patterns´, IEEE Trans Systems Man and Cybernetics, Part B, 33, 2003, 332-339 This paper introduces a new class of algorithms that determine the neighbourhood and parsimonious models from observed multi-dimensional binary cellular automata patterns. These results overcome many long-standing problems associated with finding the cellular automata rule from observed patterns.
7 Coca D., Billings S. A.: `Identification of finite dimensional models of infinite dimensional dynamic systems´; Automatica, 38, 2002, 1851-1865 This paper introduces fundamentally new and important results to show how finite dimensional models can be reconstructed for infinite dimensional dynamical systems.
8 Billings S.A., Lang Z Q: ´Nonlinear systems in the frequency domain: Energy transfer filters´ Int J Control, 75, 2002, 1066-1081 A new class of filters that allow energy, in unwanted frequency bands, to be moved to other frequency locations are introduced for the first time.
9 Wei H., Billings S.A.: ´Long term prediction of nonlinear time series using multiresolution wavelet models´ Int J Control, 2006, 79, 569-580 A new direct prediction algorithm is introduced in this paper using multiresolution wavelet models.
10 Li L. M., Billings S.A.,: ´Generalised frequency response functions and output response synthesis for mimo nonlinear systems´ Int J Control, 2006, 79, 53-62 The analytic map from parametric mimo nonlinear models to the generalised frequency response functions is derived.

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