S. A. Billings

Neural networks for nonlinear dynamic system modelling and identification

Many real-world systems exhibit complex nonlinear characteristics and cannot be treated satisfactorily using linear systems theory. A neural network which has the ability to learn sophisticated nonlinear relationships provides an ideal means of modelling complicated nonlinear systems. This paper addresses the issues related to the identification of nonlinear discrete-time dynamic systems using neural networks. Three network architectures, namely the multi-layer perceptron, the radial basis function network and the functional-link network, are presented and several learning or identification algorithms are derived. Advantages and disadvantages of these structures are discussed and illustrated using simulated and real data. Particular attention is given to the connections between existing techniques for nonlinear systems identification and some aspects of neural network methodology, and this demonstrates that certain techniques employed in the neural network context have long been developed by the control e...

Identification of MIMO non-linear systems using a forward-regression orthogonal estimator

Abstract An orthogonal least squares estimator, which was originally derived for single-input single-output systems, is extended to multi-input multi-output non-linear systems. The estimator can provide information about the structure, or which terms to include in the model, and final parameter estimates in a very simple and efficient manner. Multivariable non-linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included.

Properties of neural networks with applications to modelling non-linear dynamical systems

Properties of neural network performance are investigated by studying the modelling of non-linear dynamical systems. Network complexity, node selection, prediction and the effects of noise are studied and some new metrics of performance are introduced. The results are illustrated with both simulated and industrial examples.

Identification of non-linear output-affine systems using an orthogonal least-squares algorithm

Abstract The identification of a non-linear output-affine difference equation model is considered. An orthogonal least-squares algorithm is derived that can determine the term to regress upon, detect significant terms in the model expansion, and provide the final parameter estimates. It is shown that the orthogonal property of the algorithm results in a particularly simple estimation routine and simulated examples are included to illustrate the techniques.

Parallel recursive prediction error algorithm for training layered neural networks

A new recursive prediction error algorithm is derived for the training of feedforward layered neural networks. The algorithm enables the weights in each neuron of the network to be updated in an efficient parallel manner and has better convergence properties than the classical back propagation algorithm. The relationship between this new parallel algorithm and other existing learning algorithms is discussed. Examples taken from the fields of communication channel equalization and nonlinear systems modelling are used to demonstrate the superior performance of the new algorithm compared with the back propagation routine.

Nonlinear model validation using correlation tests

New higher order correlation tests which use model residuals combined with system inputs and outputs are presented to check the validity of a general class of nonlinear models. The new method is illustrated by testing both simple and complex nonlinear system models.

Mapping non-linear integro-differential equations into the frequency domain

A recursive algorithm is derived to compute the generalized frequency response functions for a large class of non-linear integro-differential equations. Applications to Duffings equation and a modified Van der Pol model are discussed.

Non-linear system identification using the Hammerstein model

An algorithm for the identification of non-linear systems which can be described by a Hammerstein model consisting of a single-valued non-linearity followed by a linear system is presented. Cross-correlation techniques are employed to decouple the identification of the linear dynamics from the characterization of the non-linear element. These results are extended to include the identification of the component subsystems of a feedforward process consisting of a Hammerstein model in parallel with another linear system.

Model validation tests for multivariable nonlinear models including neural networks

A fast and concise MTMO nonlinear model validity test procedure is derived, based on higher order correlation functions, to form a global-to-local hierarchical validation diagnosis of identified MEMO linear and nonlinear models. The new procedure is applied to four MIMO nonlinear system models including a neural network training example, to demonstrate the effectiveness of the tests.

Energy transfer properties of non-linear systems in the frequency domain

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.