Nonlinearity Detection using Zeroed Early-Time FFTs

Nonlinearity detection scheme for free response based on FFTs

Nonlinearity detection scheme based on zeroing the initial time response over various intervals and computing the FFT of each, as described in: M. S. Allen and R. L. Mayes, "Estimating the Degree of Nonlinearity in Transient Responses with Zeroed Early-Time Fast Fourier Transforms," in International Modal Analysis Conference Orlando, Florida, 2009.

It works by deleting the beginning of the time history up to some zero crossing and then taking the FFT. In this way one can see when certain features in the frequency domain drop out in time. This is quite different than most time-frequency methods such as wavelets because the initial response is zeroed rather than nullified using a window. ZEFFTs are especially effective if nonlinear events occur very early and decay in only a few cycles, such as macroslip of a joint due to impulsive loading.

This Zip file contains everything you need to compute and plot a set of ZEFFTs from the response of one or multiple sensors. An example file generates simulated data from a 7-DOF system and applies the algorithm. The package also contains the ability to curve fit the ZEFFTs and extrapolate them to different times, as described in the paper, but those capabilities require additional toolboxes that will shortly be available on Matlab Central.