Practical applications for nonlinear system identification using discrete-time Volterra series

Abstract

Volterra series is a helpful integral approach to represent the output of nonlinear systems using multiple convolutions. However, its extensive application in actual structures is limited due to convergence, stability, and overparameterization issues. In particular, the Volterra series’ discrete-time version can be efficiently applied, with a set of orthonormal Kautz functions, to overcome these limitations using a nonparametric model. The present paper illustrates this method and introduces a simple criterion to detect the level of nonlinearity based on the contribution of linear and nonlinear Volterra kernels. This criterion also allows qualitatively classifying the type and mechanism responsible for the nonlinear phenomenon presented in the data. Two representative nonlinear systems subjected to traditional modal testing: a magneto-elastic beam with a bistable behavior, and an F-16 aircraft, are used to demonstrate the method’s applicability. The nonlinearity detection is also compared with the conventional approaches using frequency response functions and time-frequency analysis. Based on input-output measured data, the identification results adequately predict the nonlinear operation of the systems.