MEASUREMENT AND ESTIMATION OF SYSTEM NONLINEARITY VIA A NEURAL-NETWORK

This paper defines the degree of nonlinearity as a measure for the non linearity of the system. A method for estimating the nonlinearity is p roposed based on the input and the output time-series signals under th e actual condition that the additive observation noise is included. Th e degree of nonlinearity of the system takes a value between 0 and 1. It approaches 1 when the part of the variational power that cannot be represented by the linear combination of the input increases in the ou tput variation depending on 0-input in the linear system. A multilayer perceptron is introduced as a parametric function which represents th e wide class of nonlinear functions needed in the estimation. An examp le is shown of the family of memoryless and nonlinear systems where th e degree of nonlinearity changes from 0 to 1 by the change of the syst em parameter. An example also is shown of the system with a finite mem ory having a degree of nonlinearity of 1. By a computer simulation, th e validity of the nonlinearity estimation proposed in this paper is de monstrated. The method will be applied effectively to the modeling of the system based on the observed input and output signals.