A method for detecting damage-induced nonlinearities in structures using information theory

Abstract

In this work a new approach is presented for detecting the presence of damage-induced nonlinearities in structures from measurements of structural dynamics. Two different information-theoretic (IT) measures, the time-delayed mutual information and the time-delayed transfer entropy are used to provide a probabilistic measure of the coupling between structural components. These measures may be used to capture both linear and nonlinear relationships among time-series data. The formula for both quantities is derived for a linear, five degree-of-freedom system subject to Gaussian excitation. An algorithm is then described for computing the IT metrics from time-series data and results are shown to agree with theory. We then show that as the coupling between the structure's components changes from linear to nonlinear the “information flow” can be used to indicate the degree of nonlinearity. Deviations from a linear model are quantified statistically by generating surrogate data sets that, by construction, possess only linear (second-order) correlations. We then apply the proposed algorithms to both the original data and the surrogates. Differences in the results are shown to be proportional to the degree of nonlinearity. This result is shown to be independent of global changes in stiffness and is therefore unaffected by certain models of environmental variability. Furthermore, the method provides an absolute measure of nonlinearity and therefore does not require a baseline data set for making comparisons. This approach is discussed in the context of structural health monitoring where damage is often associated with structural nonlinearity.