Professor Stephen A. Billings

Photo of Professor S A BillingsAddress:
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

Stephen A Billings is a leading authority on nonlinear system identification, signal processing and analysis in the time, frequency, and spatio-temporal domains. As an original member of the list of the most Highly Cited Researchers in the world his work has been cited over 15,085 times with a h-index of 58, and he is ranked as the UK’s fourth most cited researcher across all engineering disciplines, based on information from the Web of Science. Google Scholar gives over 25,280 citations and an h-index of 72.

Research interests
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.

Centre for Signal Processing and Complex Systems

[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 30.06.2014, £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 30.06.2015, £1,205,632

BBSRC, D Coca, M Juusola, S A Billings, 'Reverse Engineering Drosophila's Retinal Networks' 01.08.2010 to 01.01.2014, £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

The Ryder Briggs Charity, PG Sarrigiannis, Y Zhao, H L Wei, F He, S A Billings, "The thalamic clock and the cortical focus theory in childhood absence epilepsy—an insight with a new approach of quantitative EEG analysis in the time domain: the error reduction ratio method”, 01.04.2013 to 30.03.2014, £8,378

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

EPSRC Frontier Engineering Award, M J Hounslow, D Lacroix, M Viceconti, S A Billings, V Kadirkamanathan, A Pavic, E McCloskey, T Skerry, 'Modelling Complex and Partially Identified Engineering Problems — Application to the Individualised Multi-scale Simulation of the Musculoskeletal System', 01.09.2013 to 31.08 2018, £6.7M

EU Horizon 2020, R Von Fay-Siebenburgen, S N Walker, M A Balikhin, S A Billings, H L Wei, V Fedun et al, 'Prediction of Grespace Radiation Environment and Solar Wind Parameters (PROGRESS)', 02.01.2015 to 01.01 2018, 2,358,232

Alzheimer's Research UK, D Blackburn, P Sarrigiannis, S A Billings, 'Developing a new biomarker for the early diagnosis of dementia; a novel nonlinear signal processing approach using resting state EEG', 01.10.2014 to 31.09.2015, £29,805

Professional activities and recognition

  • Member of the EPSRC College
  • Referee for several international funding bodies
  • Referee for many journals
  • International Program Committees
  • External Examiner for higher degrees
  • Advisor and consultant to several companies both in the UK and internationally

A small Selection of Recent Publications

Nonlinear System Identification book coverBillings, S. A, Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains, John Wiley & Sons Ltd, 2013, ISBN: 978-1-119-94359-4

Brief description and contents

Download Addendum to Chapter 3 - The Latest FROLS Algorithm

Billings S. A., Wei H. L., A new class of wavelet networks for nonlinear system identification, IEEE Trans Neural Networks, 2005, 16, 862-874

Lang Z. Q., Billings S. A., Energy transfer properties of nonlinear systems in the frequency domain, Int J Control, 2005, 78, 345-362

Wei H., Billings S. A., Long term prediction of nonlinear time series using multiresolution wavelet models, Int J Control, 2006, 79, 569-580

Lang Z Q, Billings S. A., Yue R., Li J., Output frequency response function of nonlinear Volterra systems, Automatica, 2007, 43, 805-816

Wei H. , Billings S. A., Feature subset selection and ranking for data dimensionality reduction, IEEE Trans Pattern Analysis and Machine Intelligence, 2007, 29, 162-166

Guo L. Z., Billings S. A., State space reconstruction and spatio-temporal prediction of lattice dynamical systems, IEEE Trans on Automatic Control, 2007, 52, 622-632

Wei H. L., Billings S. A., Model structure selection using an integrated forward orthogonal search algorithm interfered with squared correlation and mutual information, Int J Modelling, Identification and Control, 2008, 3, 341-356

Zhang B., Billings S. A., Lang Z. Q., Tomlinson G. R., A novel nonlinear approach to suppress resonant oscillations, J Sound and Vibration, 2008, 317, 918-936

Guo Y., Billings, S. A., Coca D., Identification of n-state spatio-temporal dynamical systems using a polynomial model, Int J Bifurcation and Chaos, 2008, 18, 2049-2057

Wei H. L., Billings S.A., Zhao Y., Guo L., Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification, IEEE Trans Neural Networks, 2009, 20, 181-185

Wei H. L., Zheng Y, Pan Y., Coca D, Li L., Mayhew J E W, Billings S. A., Model estimation of cerebral hemodynamics between blood flow and volume changes; A data based modelling approach, IEEE Trans Biomedical Eng, 2009, 56, 1606-1616

Zhao Y., Billings S. A., Coca D. Ristic R. I., DeMatos L., Identification of the transition rule in a modified cellular automata model; The case of dendritic NH4Br crystal growth, Int J Bifurcation and Chaos, 2009, 19, 2295-2305

Zhang B., Billings S. A., Lang Z. Q., Tomlinson G. R., Suppressing resonant vibrations using nonlinear springs and dampers, J Vibration and Control, 2009, 15, 1731-1744

Wei H. L., Billings, S. A., Zhao Y., Guo L. Z., An adaptive wavelet neural network for spatio-temporal system identification, J Neural Networks, 2010, 23, 1286-1299

Nehmzow, U., Akanyeti O., Billings, S. A., Towards modelling complex robot training tasks through system identification, Int J Robotics and Autonomous Systems, 2010, 58, 265-275

Zheng Y., Pan Y., Harris S., Billings S. A., Coca D., Berwick J., Jones M., Kennerley A., Johnston D., Martin C. I., Devonshire M., Mayhew J. E. W., A dynamic model of neurovascular coupling: implications for blood vessel dilation and constriction, NeuroImage special issue: Computational Models of the Brain, 2010, 52, 1135-1147

Zhao Y., Coca D., Billings S. A., Ristic R. I., DeMatos L., Identification of geometrical models of interface evolution for dendritic crystal growth, Physics Letters A, 2011, 375, 1084-1091

Li L. M., Billings S. A., Analysis of nonlinear oscillators using Volterra series in the frequency domain, J Sound and Vibration, 2011, 330, 337-355

Boynton R. J., Balikhin M., Billings S. A., Wei H. L., Ganuskkina N., Using the narmax OLS-ERR algorithm to obtain the most influential coupling functions that affect the evolution of magnetosphere, J Geophysical Research-Space Physics, 2011, 116, 1-8

Kadirkamanathan V, Andersen S, Billings S A, Zhang X L, Holmes G R, Reyes-Aldasoro C C, Elks P M, Renshaw S A., The neutrophils eye view: inference and visualisation of the chemoattractant field driving cell chemotaxis in vivo, Plos One, 2012, 7, 1-10

Zhao Y., Wei H. L., Billings S. A., A new fast Cellular Automata neighbourhood detection and rule identification algorithm, IEEE Trans Systems, Man and Cybernetics Part B, 2012, 42, 1283-1287

Li L. M., Billings S. A., A new frequency domain representation and analysis for sub-harmonic oscillations, J Nonlinear Dynamics, 2012, 70, 1485-1497

Zhao Y., Billings S. A., Wei H. L., Sarrigiannis P. G., Tracking time varying causality and directionality of information flow using an error reduction ratio test with applications to EEG data, Physical Review E, 2012, 86, 1-11

Zhao Y., Billings S. A., Wei H. L., He F, Sarrigiannis P. G., A new NARX based Granger linear and nonlinear causal influence detection method with application to EEG data , J Neuroscience Methods, 2013, 212, 79-86

Guo L. Z., Guo Y. Z., Billings S. A., Coca D., Lang Z. Q., A Volterra series representation for a class of nonlinear infinite dimensional systems with periodic boundary conditions, Systems and Control Letters, 2013, 62, 115-123

Zhao Y., Billings S. A., Wei H. L., Sarrigiannis P. G., A parametric method to measure time varying linear and nonlinear causality method with applications to EEG data, IEEE Trans Biomedical Eng, 2013, 60, 3141-3148

Sarrigiannis P. G., Zhao Y., Wei H. L., Billings S. A., Qualitative EEG analysis using error reduction ratio causality test; validation on simulated and real EEG data, Clinical Neurophysiology, 2014, 125, 32-46

Vidal Rosas E. E., Billings S. A., Zheng Y., Mayhew J. E. W., Johnston D., Kennerley A., Coca D.,  Reduced order modelling of light transport in tissue for real time monitoring of brain haemodynamics using diffuse optical tomography, J Biomedical Optics, 2014, 19, 1-14

Guo L. Z., Guo Y. Z., Zhao Y, Billings S A., Coca D., Lang Z Q., Spatio temporal and frequency domain identification and analysis of the Belousov Zhabotinsky reaction, Int J Bifurcation and Chaos, 2014, 24, 1-14

Bigg G. R., Wei H. L., Wilton D. J., Zhao Y., Billings S. A., Hanna E., Kadirkamanathan V., A century of variation in the dependence of Greenland iceberg calving on ice sheet surface mass balance and regional climate change, Proc Royal Society A, 2014, 470, 1-14