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A Bayesian system identification approach to modelling stochastic linear dynamical systems involving multiple scales is proposed, where multiscale means that the output of the system is observed at one (coarse) resolution whilst the input of the system can only be observed at another (fine) resolution. The proposed method identifies linear models at different levels of resolution, where the link between the two resolutions is realised via a non-overlapping averaging process. The averaged data at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables model at the coarse level of resolution. By using a Bayesian inference and Markov chain Monte Carlo method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. Simulation examples are provided to show the efficiency of the new method. Furthermore, an application to the analysis of the relativistic electron intensity at the geosynchronous orbit is also included. [ABSTRACT FROM AUTHOR]

In this article, the identification of a class of multiscale spatio-temporal dynamical systems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a B-spline wavelet multi-resolution analysis. The resulting identified models of the spatio-temporal evolution form a system of partial differential equations with different spatial scales. Examples are provided to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward least-squares algorithm. This model can then be converted between different scales to produce predictions of the system outputs at different scales. The method can be applied to both multiscale and conventional spatio-temporal dynamical systems. For multiscale systems, the method can generate a parsimonious and effective model at a coarser scale while considering the effects from finer scales. Additionally, the proposed method can be used to improve the performance of the identification when the measurements are noisy. Numerical examples are provided to demonstrate the application of the proposed new approach. [ABSTRACT FROM AUTHOR]

It is known that the least-squares (LS) class of algorithms produce unbiased estimates providing certain assumptions are met. There are many practical problems, however, where the required assumptions are violated. Typical examples include non-linear dynamical system identification problems, where the input and output observations are affected by measurement uncertainty and possibly correlated noise. This will result in biased LS estimates and the identified model will exhibit poor generalisation properties. Model estimation for this type of error-in-variables problem is investigated in this study, and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non-linear dynamical system identification. [ABSTRACT FROM AUTHOR]

This article introduces a new residual-based recursive parameter estimation algorithm for linear partial differential equations. The main idea is to replace the unmeasurable noise variables by estimates of the noise and to compute recursively both the model parameters and the noise estimates. It is proven that under some mild assumptions the estimated parameters converge to the true values with probability one. Numerical examples that demonstrate the effectiveness of the proposed approach are also provided. [ABSTRACT FROM AUTHOR]

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance. [ABSTRACT FROM AUTHOR]

New results for model order reduction, for weakly non-linear systems in the frequency domain, are derived based on a parametric modelling approach. [ABSTRACT FROM AUTHOR]

A new adaptive orthogonal search (AOS) algorithm is proposed for model subset selection and non-linear system identification. Model structure detection is a key step in any system identification problem. This consists of selecting significant model terms from a redundant dictionary of candidate model terms, and determining the model complexity (model length or model size). The final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system. In the new AOS algorithm, a modified generalized cross-validation criterion, called the adjustable prediction error sum of squares (APRESS), is introduced and incorporated into a forward orthogonal search procedure. The main advantage of the new AOS algorithm is that the mechanism is simple and the implementation is direct and easy, and more importantly it can produce efficient model subsets for most non-linear identification problems. [ABSTRACT FROM AUTHOR]

In this paper, a fast identification algorithm for non-linear dynamic stochastic system identification is presented. The algorithm extends the classical orthogonal forward regression (OFR) algorithm so that instead of using the error reduction ratio (ERR) for term selection, a new optimality criterion, Shannon's entropy power reduction ratio (EPRR), is introduced to deal with both Gaussian and non-Gaussian signals. It is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

In this article, the identification and analysis of spatio-temporal dynamical systems is presented. An approximated B-spline wavelet representation of spatio-temporal dynamical systems is identified using an orthogonal least-squares algorithm from measured data. Control variables are incorporated to represent controlled external inputs and/or some system parameters for the purpose of analysis. The identified system models can be used to evaluate how the external inputs or system parameters affect the evolution of the spatio-temporal dynamics and pattern formation. Two examples are used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

For non-linear Volterra systems which include a non-linear state equation and a general non-linear output function, the system frequency response functions and some related frequency response characteristics are developed and discussed in this study. These new results establish the frequency response functions for this general form of non-linear systems by extending some existing theory, and provide an analytical insight into the relationship between model parameters and frequency response functions, and the relationship between model parameters and the magnitude bound of frequency response functions. Several examples are given to illustrate the new results. [ABSTRACT FROM AUTHOR]

This paper is concerned with extending the energy transfer filters (ETFs) designs to a more general case where the design requirement is to focus signal energy from different input frequency bands into a desired output frequency range. ETFs are a class of non-linear filters recently proposed by the authors to employ non-linear effects to transfer signal energy from one frequency band to a different frequency location. The new ETF designs considered in the present study involve the development of an algorithm for determining output frequencies of non-linear systems subject to an input the frequency components of which are located in two separate frequency intervals and a new procedure for the implementation of the filter design. The results achieved provide an effective approach to the solution to a more general ETF design problem. [ABSTRACT FROM AUTHOR]

The concept of non-linear output frequency response functions (NOFRFs) is extended to the non-linear systems that can be described by a multi-input Volterra series model. A new algorithm is also developed to determine the output frequency range of non-linear systems from the frequency range of the inputs. These results allow the concept of NOFRFs to be applied to a wide range of engineering systems. The phenomenon of the energy transfer in a two degree of freedom non-linear system is studied using the new concepts to demonstrate the significance of the new results. [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]

A novel approach to the determination of the neighbourhood and the identification of spatio-temporal dynamical systems is investigated. It is shown that thresholding to convert the pattern to a binary pattern and then applying cellular automata (CA) neighbourhood detection methods can provide an initial estimate of the neighbourhood. A coupled map lattice model can then be identified using the CA detected neighbourhood as the initial conditions. This provides a coarse-to-fine approach for neighbourhood detection and identification of coupled map lattice models. Three examples are used to demonstrate the application of the new approach. [ABSTRACT FROM AUTHOR]

New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Non-linear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique for the magnitude based analysis of nonlinear systems in the frequency domain, for example, evaluation of the truncation error in a volterra series expression of non-linear systems and the highest order needed in the volterra series approximation. A numerical example is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Wavelet based non-parametric additive NARX models are proposed for nonlinear input-output system identification. By expanding each functional component of the non-parametric NARX model into wavelet multiresolution expansions, the non-parametric estimation problem becomes a linear-in-the-parameters problem, and least-squares-based methods such as the orthogonal forward regression (OFR) approach, coupled with model size determination criteria, can be used to select the model terms and estimate the parameters. Wavelet based additive models, combined with model order determination and variable selection approaches, are capable of handling problems of high dimensionality. [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]

A new approach for the estimation of spatial derivatives and the identification of a class of continuous spatio-temporal dynamical systems from experimental data is presented in this study. The proposed identification approach is a combination of implicit Adams integration and an orthogonal forward regression algorithm (OFR), in which the operators are expanded using polynomials as basis functions. The noisy experimental data are de-noised by using biorthogonal spline wavelet filters and the spatial derivatives are estimated using a multiresolution analysis method. Finally, a bootstrap method is applied to refine the identified parameters from the OFR algorithm. The resulting identified models of the spatio-temporal evolution form a system of partial differential equations. Examples are provided to demonstrate the efficiency of the proposed method. [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]

The long term prediction of non-linear dynamical time series, based on identified multiresolution wavelet models, from historically observed data sets is investigated and a new direct prediction approach is introduced. Prediction results based on the new direct scheme are compared with those from iterative methods and it is shown that improved predictions can be obtained using the new approach. [ABSTRACT FROM AUTHOR]

The generation of generalized frequency response functions for multi-imput–multi-output non-linear system models is investigated with particular emphasis on the cross-kernel transforms. A unified framework for the output response of non-linear systems in the frequency domain is also introduced. [ABSTRACT FROM AUTHOR]

Traditionally the Volterra time and frequency domain analysis tools cannot be applied to severely non-linear systems. In this paper, a new method of building a time-domain NARX MISO model for a class of severely SISO non-linear systems that exhibit subharmonics is introduced and it is shown how this allows the Volterra time and frequency domain analysis to be extended to this class of non-linear systems. The new approach is based on decomposing the original single input based on a Fourier analysis to provide a set of modified input signals which have the same period as the output signal. A MISO NARX model can then be constructed from the decomposed multiple inputs and the single output signal. The resulting MISO model is shown to meet the basic requirement for the existence of a Volterra series representation from which important frequency domain properties can be derived, explained and discussed. This is done by first introducing the derivation of generalized frequency response functions (GFRFs) from time domain MISO NARX models. The steady state response synthesis problem using the input spectrum and the MISO GFRFs is then investigated in order to verify the effectiveness and accuracy of the MISO modelling approach for severely non-linear systems. Finally a new frequency domain analysis method is introduced for systems that exhibit subharmonic oscillations. [ABSTRACT FROM AUTHOR]

In Part 1 of this paper the concepts of input and output frequency subdomains were introduced to give insight into the relation between one dimensional and multi-dimensional frequency spaces. The visualisation of both magnitude and phase responses of third order generalized frequency response functions was also presented. In this, the second part, symbolic expansion techniques are introduced and together with the results achieved in Part 1, yield new methods for analysing the properties of generalized frequency response functions. Case studies are included to illustrate the application of the new methods. [ABSTRACT FROM AUTHOR]

The characteristics of generalized frequency response functions (GFRFs) of non-linear systems in higher dimensional space are investigated using a combination of graphical and symbolic decomposition techniques. It is shown how a systematic analysis can be achieved for a wide class of non-linear systems in the frequency domain using the proposed methods. The paper is divided into two parts. In Part 1, the concepts of input and output frequency subdomains are introduced to give insight into the relationship between one dimensional and multi-dimensional frequency spaces. The visualization of both magnitude and phase responses of third order generalized frequency response functions is presented for the first time. In Part 2 symbolic expansion techniques are introduced and new methods are developed to analyse the properties of generalized frequency response functions of non-linear systems described by the NARMAX class of models. Case studies are included in Part 2 to illustrate the application of the new methods. [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]

In this paper, an analysis of the energy transfer properties of non-linear systems in the frequency domain is studied based on a new concept known as non-linear output frequency response functions (NOFRFs). The new concept allows the analysis to be implemented in a manner similar to the analysis of linear systems in the frequency domain, and provides great insight into the mechanisms which dominate the non-linear behaviour. The new analysis is also helpful for the design of non-linear systems in the frequency domain. [ABSTRACT FROM AUTHOR]

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilize the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least-squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for the local reconstruction of coupled map lattice (CML) models of stochastic spatio-temporal dynamics 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 significant terms from wavelet functions to form an accurate representation of the nonlinear spatio-temporal dynamics. Two examples are used to demonstrate the application of the proposed new approach. [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]

The purpose of variable selection is to pre-select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection. It is required that the selected significant variables alone should sufficiently represent the system. Generally, not all the model terms, which are produced by combining different variables, make an equal contribution to the system output and terms, which make little contribution, can be omitted. A parsimonious representation, which contains only the significant terms, can often be obtained without the loss of representational accuracy by eliminating the redundant terms. Based on these observations, a new variable and term selection algorithm is proposed in this paper. The term detection algorithm can be applied to the general class of non-linear modelling problems which can be expressed as a linear-in-the-parameters form. The variable selection procedure is based on locally linear and cross-bilinear models, which are used together with the forward orthogonal least squares (OLS) and error reduction ratio (ERR) approach to determine the significant terms and to pre-select the important variables for both time series and input-output systems. Several numerical examples are provided to illustrate the applicability and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

A new direct approach of computing multi-step ahead predictions for non-linear time series is introduced. The covariance of the parameter estimates associated with, and the mean squared k-step ahead prediction errors of the new direct approach are smaller than those obtained using the conventional direct approach. Numerical examples are included to illustrate the application of the new direct approach. [ABSTRACT FROM AUTHOR]

An enhanced frequency analysis method is introduced, using a phase shift wavelet representation, to analyse individual frequency components and to reveal features of a given signal. The frequency representation provides details at each time location without the loss, caused by local orthogonality between the wavelet basis functions and the given signal, which occurs when a normal wavelet decomposition is employed. Movement of the local orthogonality locations, corresponding to the phase shift of the wavelet basis functions, are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain, such as continuities, smoothness, and trends. Several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach. [ABSTRACT FROM AUTHOR]

The analysis of non-linear systems in the frequency domain is studied and a new class of filters, called energy transfer filters, is introduced. While conventional linear filter design procedures are based on the principle of attenuating unwanted effects the new energy transfer filter design concept exploits non-linearity to allow energy to be moved to new frequency locations. The ability to design non-linear filters that can move energy to designed locations in the frequency domain introduces new degrees of freedom into filter design and offers new solution possibilities to many filtering problems. [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]

This paper introduces a novel approach to the identification of Coupled Map Lattice (CML) models of linear and nonlinear infinite-dimensional systems from discrete observations. The method exploits the regularity of the CML model so that only a finite number of spatial measurements are required. The measurement system associated with a CML is discussed and some necessary conditions for the input/output equations to form a CML are presented. Numerical simulations illustrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

The effects of overparametrization in non-linear system identification and neural networks are often presented as overfitting to a particular data set. An overparametrized model tends to interpolate the data set and can fail to capture the underlying dynamics represented by the data. Past studies have usually concentrated on overparametrisation in the number of model terms or the number of hidden layer nodes. In the present study, the effects of several forms of overparametrization on the model dynamics are compared using qualitative validation methods. The dynamic properties of the identified model or the trained network are graphically displayed and compared with those of the real system. It is shown that overparametrization in the number of time lags or input nodes has the worst effect on the dynamic properties of the resulting model. [ABSTRACT FROM AUTHOR]

A new methodology for identifying non-linear NARMAX models, from noise corrupted data, is introduced based on semi-orthogonal wavelet multiresolution approximations. An adaptive model sequencing strategy is introduced to infer model complexity from the data while reducing computational costs. This is used in conjunction with an iterative orthogonal-forward-regression routine coupled with model validity tests to identify sparse but accurate wavelet series representations of non-linear processes. Experimental data from two real systems, a liquid level system and from a civil engineering structure are used to illustrate the effectiveness of the new identification procedure. [ABSTRACT FROM AUTHOR]

Community health nurse practitioners are often the major contraceptive counselors who may use anticipatory guidance to help clients' use behaviors. Because pregnancy rates during typical use are much higher than during 'perfect' use, more effective anticipatory guidance could help improve use behaviors. Principles of cognitive theory were used to explore the implications of specific words and approaches associated with discussing young adults' contraceptive use. Qualitative results are reported here, and potential implications are made for nurse practitioners' anticipatory guidance related to contraceptive use. [ABSTRACT FROM AUTHOR]

A new algorithm, for identifying non-linear differential equation models, is introduced. The algorithm avoids the computation of derivatives by using the generalized frequency response functions to reconstruct the model. It is shown that the model can be constructed sequentially by building in first the linear terms, then the quadratic terms and so on and provides unbiased estimates in the presence of noise. A simulated example and the identification of a model relating the action of waveforces on an offshore structure are included to demonstrate the procedure. [ABSTRACT FROM AUTHOR]

Recursive algorithms are derived to compute the generalized frequency response function matrix of multi-input multioutput (MIMO) non-linear systems as an analytical map from both non-linear differential equation models and NARX (Non-linear Auto Regressive Models with eXogenous inputs) models of the system. The algorithm is computationally compact and exposes the explicit relationship between the model parameters and the elements of the generalized frequency response function matrix and can thus provide important insights into the behaviour of non-linear systems. [ABSTRACT FROM AUTHOR]

A new instrumental-variable-based identification procedure is introduced to estimate linear and nonlinear continuous-time models using a shifted Chebyshev basis in the presence of noise. [ABSTRACT FROM AUTHOR]

A novel identification scheme using wavelet networks is presented for nonlinear dynamical systems. Based on fixed wavelet networks, parameter adaptation laws are developed using a Lyapunov synthesis approach. This guarantees the stability of the overall identification scheme and the convergence of both the parameters and the state errors, even in the presence of modelling errors. Using the decomposition and reconstruction techniques of multiresolution decompositions, variable wavelet networks are introduced to achieve a desired estimation accuracy and a suitable sized network, and to adapt to variations of the characteristics and operating points in nonlinear systems. B-spline wavelets are used to form the wavelet networks and the identification scheme is illustrated using a simulated example. [ABSTRACT FROM AUTHOR]

New multi-directional model validation tests are derived to provide improved statistical validation test procedures for a wide class of non-linear modelling methods. [ABSTRACT FROM AUTHOR]

A new direct approach to identifying the parameters of distributed parameter systems from noise-corrupted data is introduced. The model of the system which takes the form of a set of linear or nonlinear partial differential equations is assumed known with the exception of a set of constant parameters. Using finite-difference approximations of the spatial derivatives the original equation is transformed into a set of ordinary differential equations. The identification approach involves smoothing the measured data and estimating the temporal derivatives using a fixed interval smoother. A least-squares method is then employed to estimate the unknown parameters. Three examples that illustrate the applicability of the proposed approach are presented and discussed. [ABSTRACT FROM AUTHOR]

A regularized rational model estimator is formulated for the estimation of nonlinear dynamic rational models. Theoretical analysis and numerical simulations demonstrate that the regularized algorithm provides improved estimates compared with previously developed rational model estimators. [ABSTRACT FROM AUTHOR]

A sequential fuzzy clustering algorithm is proposed based on a modification to the objective function used in the fuzzy competitive learning algorithm. The new learning algorithm can be used to enhance the excitation on the non-winning centroids and to reduce the excitation on the winning centroid when the fuzziness parameter is close to unit. The excitation on the winning centroid can be further reduced when the input pattern is far away from the winning centroid. An excitationinhibition mechanism can also be introduced into the learning such that the non-winning centroids move towards the input pattern while the winning centroid moves away from the input pattern when the winning centroid is far away from the input pattern. The new algorithm overcomes the problem of underutilization of centroids found in the k -means or related clustering algorithms and in the fuzzy competitive learning algorithm when the fuzziness parameter is close to unity. The performance of the new algorithm is demonstrated on the IRIS data set. [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]

Neural network-based variable structure control is proposed for the design of nonlinear discrete systems. Sliding mode control is used to provide good stability and robustness performance for nonlinear systems. An affine nonlinear neural predictor is introduced to predict the outputs of the nonlinear process, and to make the variable structure control algorithm simple and easy to implement. When the predictor model is inaccurate, variable structure control with sliding modes is used to improve the stability of the system. A recursive weight learning algorithm for the neural networks based affine nonlinear predictor is also developed, and the convergence of both the weights and the estimation error is analysed. [ABSTRACT FROM AUTHOR]