Neural detection of parameter changes in a dynamic system using time-frequency transforms

Abstract

In this paper a neural detector of internal parameter changes in a stationary, nonlinear SISO dynamic system, represented by a discrete model of the NARX type, is considered. The system analysed in this paper is described by the nonlinear difference equation y(n) = f(y(k-1), ..., y(k-p), u(k), ..., u(k-q), Θ), where f is a non-linear function, y(k), ..., y(k-p) are the output samples, u(k), ..., u(k-q) are the input samples and Θ is a vector of internal parameters of the system. The values of the vector Θ can be changed in random moments of time, but these values belong to the finite set, so that detection of parameter changes can be considered as classification of signals acquired for different values of changeable parameters. Such a formulation of the problem can be suitable in industrial applications where the change of parameters can model selected faults (or changes of an operating point) of an industrial dynamic system. To decrease dimensionality of classified data, extraction of specific characteristics from a time-frequency transform of an output signal, produces a vector of features Φ, which constitutes the decision space for classification. As the intelligent approach to such a complex problem is justified, the extracted signal features are the inputs of a neural network. The LVQ (Learning Vector Quantisation) neural network has been chosen because of its ability of learning data classification, where the similar input vectors are grouped into a region represented by a socalled coded vector (CV). Such an approach corresponds to pointing out the most probable values of the vector Θ. The detection ability of the LVQ network, both in a non-noisy and noisy environment, has been examined in detail in the paper.