Measurement and Estimation of System Nonlinearity Via a Neural Network.

This paper defines the degree of nonlinearity as a measure for the nonlinearity of the system. A method for estimating the nonlinearity is proposed based on the input and the output time-series signals under the actual condition that the additive observation noise is included. The degree of nonlinearity of the system takes a value between 0 and 1. It approaches 1 when the part of the variational power that carmot be represented by the linear combination of the input increases in the output variation depending on 0-input in the linear system. A multilayer perceptron is introduced as a parametric function which represents the wide class of nonlinear functions needed in the estimation. An example is shown of the family of memoryless and nonlinear systems where the degree of nonlinearity changes from 0 to 1 by the change of the system parameter. An example also is shown of the system with a finite memory having a degree of nonlinearity of 1. By a computer simulation, the validity of the nonlinearity estimation proposed in this paper is demonstrated. The method will be applied effectively to the modeling of the system based on the observed input and output signals. [ABSTRACT FROM AUTHOR]