ABSTRACT
This chapter discusses the main application of the Hilbert transform to the detection and identification of nonlinearity. The theory can be derived by two independent approaches. The first approach relies on the decomposition of a function into odd and even parts and the behaviour of this decomposition under Fourier transformation. The Hilbert transform and Fourier transform also differ in their interpretation. The Fourier transform is considered to map functions of time to functions of frequency and vice versa. There are essentially five methods of correcting Hilbert transforms for truncation errors: conversion to receptance; the Fei correction term; the Haoui correction term; the Simon correction method; and the Ahmed correction term. The Hilbert transform clearly shows the effect of the nonlinearity, particularly in the Nyquist plot. In the case of Coulomb friction, the nonlinearity is only visible if the level of excitation is low. The Hilbert transform operations give a diagnosis of nonlinearity with a little qualitative information.
