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This brief introduces a new parametric modelling and identification method for linear time-varying systems using a block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be applied to track rapidly or even sharply varying processes and is developed by combining wavelet approximation theory with a block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstationary processes. Application of the proposed approach to a real mechanical system indicates better tracking capability of the multi-wavelet basis function algorithm compared with the normalized least squares or recursive least squares routines. [ABSTRACT FROM PUBLISHER]

The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov–Zhabotinsky reaction are identified. The identified SCML models are shown to possess almost the same local dynamics as the original systems and are able to provide good long term predictions. [ABSTRACT FROM AUTHOR]

In this paper, a modified orthogonal forward regression (OFR) least-squares algorithm is presented for system identification and modelling from noisy regressors. Under the assumption that the energy and signal-to-noise ratio (SNR) of the signals are known or can be estimated, it is shown that unbiased estimates of the Error reduction ratios (ERRs) and the parameters can be obtained in each forward regression step. Examples are provided to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for the identification of coupled map lattice models of complex spatio-temporal patterns from measured data. The nonlinear functionals describing the evolution of the spatio-temporal patterns are constructed using B-spline wavelet and scaling functions. This provides a multiresolution approximation for the underlying spatio-temporal dynamics. An orthogonal least squares algorithm is used to determine the suitable terms from wavelet functions to form an accurate representation of the nonlinear spatio-temporal dynamics. Three examples are used to demonstrate the application of the proposed new approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development of a new method for the design of energy transfer filters (ETFs). ETFs are a new class of non-linear filters recently proposed by the authors, which employ non-linear effects to transfer signal energy from one frequency band to a different frequency location. The new method uses the powerful orthogonal least squares (OLS) algorithm to solve the least squares problem associated with the design and compared with previous methods achieves much better filtering performance. [ABSTRACT FROM AUTHOR]

A novel fast cellular automata orthogonal least squares (FCA-OLS) identification method is introduced by extending and developing the CA-OLS identification method presented in a previous study by Billings and Yang. Both one-dimensional CA and two-dimensional CA were identified with FCA-OLS as the simulation examples. The simulation results show that the new method significantly reduces the computational time compared with existing methods. [ABSTRACT FROM AUTHOR]

A new modelling framework for identifying and reconstructing chaotic systems is developed based on multir esolution wavelet decompositions. Qualitative model validation is used to compare the multir esolution wavelet models and it is shown that the dynamical features of chaotic systems can be captured by the identified models providing the wavelet basis functions are properly selected. Two basis selection algorithms, orthogonal least squares and a new matching pursuit orthogonal least squares, are considered and compared. Several examples are included to illustrate the results. [ABSTRACT FROM AUTHOR]

Generalization properties of support vector machines, orthogonal least squares and zero-order regularized orthogonal least squares algorithms are studied using simulation. For high signal-to-noise ratios (40 dB), mixed results are obtained, but for a low signal-to-noise ratio, the prediction performance of support vector machines is better than the orthogonal least squares algorithm in the examples considered. However, the latter can usually give a parsimonious model with very fast training and testing time. Two new algorithms are therefore proposed that combine the orthogonal least squares algorithm with support vector machines to give a parsimonious model with good prediction accuracy in the low signal-to-noise ratio case. [ABSTRACT FROM AUTHOR]

Cell to cell mapping for the global analysis of non-linear systems is adopted to enable the qualitative validation of identified non-linear systems. The method provides a framework for the global analysis of a diverse range of non-linear systems, including continuous and discrete time systems, and non-linear identified models, and can be used to benchtest the effectiveness of various identification procedures. In the present study, the method is used to reveal the dynamic properties of a non-linear system, including the fixed points, periodic or aperiodic solutions and the corresponding stability properties. The orthogonal least squares algorithm (OLS) is then used to identify a parametric NARMAX model of the system. The resulting model is analysed using the same framework and the dynamic properties of the model are qualitatively compared with those of the original system. Based on the results of the validation, a modified selection criterion for the OLS algorithm is proposed, which incorporates the non-linear degree of the terms in the model complexity. The effectiveness of the new algorithm is demonstrated using examples. [ABSTRACT FROM AUTHOR]