  Detection and identification of nonlinearity is a task of high importance for
structural dynamics. Detecting nonlinearity in a structure, which has been
designed to operate in its linear region, might indicate the existence of
damage. Therefore, it is important, even for safety reasons, to detect when a
structure exhibits nonlinear behaviour. In the current work, a method to detect
nonlinearity is proposed, based on the distribution of the gradients of a
data-driven model, which is fitted on data acquired from the structure of
interest. The data-driven model herein is a neural network. The selection of
such a type of model was done in order to not allow the user to decide how
linear or nonlinear the model shall be, but to let the training algorithm of
the neural network shape the level of nonlinearity according to the training
data. The neural network is trained to predict the accelerations of the
structure for a time-instant using as inputs accelerations of previous
time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of
the output of the neural network with respect to its inputs are calculated.
Given that the structure is linear, the distribution of the aforementioned
gradients should be quite peaked, while in the case of a structure with
nonlinearities, the distribution of the gradients shall be more spread and,
potentially, multimodal. To test the above assumption, data from an
experimental structure are considered. The structure is tested under different
scenarios, some of which are linear and some nonlinear. The statistics of the
distributions of the gradients for the different scenarios can be used to
identify cases where nonlinearity is present. Moreover, via the proposed method
one is able to quantify the nonlinearity by observing higher values of standard
deviation of the distribution of the gradients for "more nonlinear" scenarios.
