title: A new class of wavelet networks for nonlinear system identification.
abstract: A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.
authors.affiliation: Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UK. s.billings@sheffield.ac.uk
authors.forename: Stephen A
authors.initials: SA
authors.lastname: Billings
authors.forename: Hua-Liang
authors.initials: HL
authors.lastname: Wei
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003205:Computing Methodologies; D017143:Fuzzy Logic; D008954:Models, Biological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes