Double exponential transform and generalized Hopfield network for modelling dynamic non-linear circuits

Abstract

In this paper a new tool, i.e. the double exponential transform, is introduced for characterizing a non-linear dynamic circuit directly on the basis of its elements. The resulting characterization aims to improve the computational cost connected with the analysis and to add flexibility to the identification procedure of unknown elements in a circuit of this type. The identification is performed by using a generalized Hopfield network with modifiable activation functions. The proposed neural network deserves attention for two reasons, (i) It represents the model of the physical mechanism which maps input excitations to output responses via a circuit description of an electrical context. From this point of view it can be considered as a macromodel, in contrast with other neural networks yielding a micromodel of this context. (ii) It allows the identification of a device present in the circuit using what is known and focusing attention only on the unknown elements. The training of the network is carried out on its feedforward version by using the classical back-propagation rule. Afterwards the parameters are frozen and the recurrent operation is resumed. A simple circuit illustrates in detail all the aspects of the proposed method. In order to reduce the computational cost, the fast version of Fourier transform is used in connection with the double exponential transform. This requires one to know the ranges of values spanned by electrical quantities applied to the non-linear elements. These ranges are directly defined by the training set. © 1997 by John Wiley & Sons, Ltd.