Effects of noise on transfer entropy estimation for damage detection

Recent research has shown that transfer entropy can be effectively employed as a feature for nonlinearity detection and linear damage identification. However, computation of transfer entropy requires the estimation of non-parametric one-, two-, and three-dimensional probability density functions. Therefore, small random perturbations caused by noise could lead to large variances in transfer entropy estimates. In this paper, we evaluate the effect of input and output noise on estimation of transfer entropy, and how noise, in turn, affects the capability of transfer entropy as a damage detector in a structural health monitoring (SHM) application. A damage index from the transfer entropy is computed from the response of a simulated multi-degree-of-freedom oscillator subject to linear and nonlinear stiffness changes in the presence of various noise influences. Damage indices are also evaluated for an experimental frame structure. Based on the computational study, we find that input noise lessens the sensitivity of the damage feature by diminishing the ability of the non-parametric density estimators to produce low variance transfer entropy estimations. Despite this reduced capability, an input that has no deterministic component can still detect a 25% stiffness loss in the computational example employed. Output noise has a greater impact on the feature's ability to accurately estimate the transfer entropy, such that a signal-to-noise threshold of approximately 30 dB leads to a greatly diminished ability to detect damage. Despite these noise effects, all damage cases tested on an experimental frame structure were detectable using the transfer entropy damage index.