Dynamic system change detection using a modification of the transfer entropy

Recent work has validated the use of transfer entropy for exploring coupling in structural dynamics. Transfer entropy is a measure of information flow between Markov processes. Using transitional probabilities, one can get a quantification of the degree of influence one process has on the dynamics of another. Previous research included a time lag to assess information exchanges at various time scales without resulting in tremendously burdensome computations. However, it is more informative to view the transfer entropy using two separate time lags to assess transitional probabilities between both processes. This work introduces a second time delay into a linearized version of the transfer entropy to produce a transfer entropy surface. This surface allows for a fuller assessment of dynamical coupling between measurements. Analytical and low-order-correlation-based measures of the transfer entropy were formed and compared to common modal analysis methods to assess their ability to detect linear dynamical changes in structures. Investigations were conducted on a computational linear oscillator and a simple experimental system. The transfer entropy is a much better indicator of dynamical changes than the modal techniques. For the structural systems studied, the plane of greatest sensitivity in the time-delayed transfer entropy surface is along the diagonal and not along one coordinate as was utilized in previous work.