New techniques for nonlinear system analysis and identification from random data

Abstract

Direct and reverse MI/SO (multiple-input/single-output) techniques are new frequency-domain techniques that provide accurate practical methods to analyze and identify the dynamic properties of nonlinear systems. The Dirac MI/SO technique is applicable to nonlinear systems with specified parallel linear and nonlinear transformations. The reverse MI/SO technique is applicable to nonlinear systems that can be reasonably modeled by nonlinear integrodifferential equations of motion. Nonlinear systems are included where the coefficients can be constants or frequency dependent. Simulated or measured data can have arbitrary probability and spectral features. Each of the identified nonlinear components can be evaluated at any desired frequency with separate coherence functions. Thus these techniques represent a significant advance in using real-world data to help improve the design and understanding of nonlinear systems. This presentation will review the analytical basis of these new techniques and illustrate their application from material in the latest book by J. S. Bendat [Nonlinear System Techniques and Applications (Wiley-Interscience, New York, 1998)].