A new adaptive multiple modelling approach for non-linear and non-stationary systems

Abstract

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

Keywords:

• online modelling
• non-stationary
• non-linear
• multiple model
• time series

Acknowledgement

This research is sponsored by the UK Engineering and Physical Sciences Research Council and DSTL under the grant number EP/H012516/1.

Notes

1. The noise has little effect on the time consumption.

Additional information

Notes on contributors

Hao Chen

Dr Hao Chen received the B.Eng. degree in Automatic Control from National University of Defense Technology, P. R. China in 2006, the M.Sc.degree in Control Systems with distinction from The University of Sheffield, UK in 2009. In 2014, he received his Ph.D degree in Cybernetics with the School of Systems Engineering, University of Reading, U.K., sponsored by the Engineering and Physical Sciences Research Council (EPSRC) and Defence Science and Technology Laboratory (Dstl) from the British Government. He is currently working as a Postdoctoral Fellow in University of Alberta/Syncrude Canada Ltd, Canada. His research interest are in online learning, soft sensors, system identification, artificial neural networks, machine learning and signal processing. He was a recipient of the Chinese Government Award for Outstanding Self-financed Students Abroad in 2012.

Yu Gong

Dr Yu Gong is with School of Electronic, Electrical and Systems Engineering, Loughborough University, UK, in July 2012. Dr Gong obtained his BEng and MEng in electronic engineering in 1992 and 1995 respectively, both at the University of Electronics and Science Technology of China. In 2002, he received his PhD in communications from the National University of Singapore. After PhD graduation, he took several research positions in Institute of Inforcomm Research in Singapore and Queen's University of Belfast in the UK respectively. From 2006 and 2012, Dr Gong had been an academic member in the School of Systems Engineering, University of Reading, UK. His research interests are in the area of signal processing and communications including wireless communications, cooperative networks, non-linear and non-stationary system identification and adaptive filters.

Xia Hong

Prof Xia Hong received the B.Sc. and M.Sc. degree from the National University of Defense Technology, P.R. China, in 1984 and 1987, respectively, and the Ph.D. degree from the University of Sheffield, U.K. in 1998, all in automatic control. She worked as a research assistant in Beijing Institute of Systems Engineering, Beijing, China from 1987–1993. She worked as a research fellow in the Department of Electronics and Computer Science at University of Southampton from 1997–2001. She is currently a Professor at School of Systems Engineering, University of Reading, U.K. She is actively engaged in research into nonlinear systems identification, data modelling, estimation and intelligent control, neural networks, pattern recognition, learning theory and their applications. She has published over 150 research papers, and coauthored a research book. Professor Hong was awarded a Donald Julius Groen Prize by IMechE in 1999.