1996 Volume 9 Issue 8 Pages 366-374
This paper discusses a method for parameter estimation in the NARMAX (non-linear autoregressive moving average with exogenous inputs) model using neural computation. The primary aim of the method is to examine the structure of biological systems, utilizing the fact that the NARMAX model contains a relatively few parameters. A three-layered feedforward neural network is trained to describe a system. The actual input of the system and the computed output of the network are used as the input data set of the network for training, and values of weights and thresholds in the network are determined to minimize the prediction error between the actual and computed output. Parameters in the NARMAX model are calculated from the values of weights by expanding the sigmoid functions in neural units using Maclaurin's formula. The structure of the NARMAX model is finally determined by information criteria. The proposed method, therefore, requires no prior knowledge of the structure of the NARMAX model. Some numerical examples are presented to illustrate that the propised method can work well for noisy data.