Detecting nonlinearity in structural systems using the transfer entropy

The transfer entropy was recently proposed as a means of exploring coupling in dynamical systems. Transfer entropy is an information theoretic that quantifies the degree to which one dynamical process affects the transition probabilities (dynamics) of another. Here we demonstrate how this metric may be utilized to detect the presence of nonlinearity in a system. Using the method of surrogate data, the transfer entropy computed at various lag times are compared to values computed from linearized surrogates. The transfer entropy is shown to be a more sensitive indicator of nonlinearity than is the mutual information for both simulated and experimental data. This technique is particularly applicable to the field of structural health monitoring, where damage is often equated with the presence of a nonlinearity in an otherwise linear system.