Examining structural dynamics using information flow

In this work, two different information-theoretic approaches are presented for exploring coupling in structural dynamics. Specifically, both the time delayed mutual information and the transfer entropy are used to compute the amount of information transmitted between points on a structure. The resulting “information flow” is a probabilistic quantity that makes no assumptions about the underlying model and is therefore an appropriate tool for studying both linear and nonlinear coupling mechanisms. Both metrics can be used to quantify information transport, however they stem from fundamentally different assumptions. Time-delayed mutual information may be appropriately viewed as a nonlinear cross-correlation function, while transfer entropy incorporates the information provided by one dynamical process about another’s transition probabilities. For a linear, two-degree-of-freedom structure subjected to Gaussian excitation, the exact formula for both quantities is derived. An algorithm is then presented for computing these measures from time series data and is shown to be in agreement with theory. Nonlinearity is then introduced into the system in the form of a bi-linear stiffness term between the system’s masses. As the coupling changes from linear to nonlinear, the mutual information and transfer entropy curves exhibit characteristics that clearly identify the presence and degree of nonlinearity when compared with their “linearized” versions. Possible applications of this approach include structural health monitoring, where nonlinearity is often associated with structural damage.