A transmittance-based methodology for damage detection under uncertainty: An application to a set of composite beams with manufacturing variability subject to impact damage and varying operating conditions

Oftentimes, the complexity in manufacturing composite materials leads to corresponding structures which although they may have the same design specifications they are not identical. Thus, composite parts manufactured in the same production line present differences in their dynamics which combined with additional uncertainties due to different operating conditions may lead to the complete concealment of effects caused by small, incipient, damages making their detection highly challenging. This damage detection problem in nominally identical composite structures is pursued in this study through a novel data-based response-only methodology that is founded on the autoregressive with exogenous (ARX) excitation parametric representation of the transmittance function between vibration measurements at two different locations on the structure. This is a statistical time series methodology within which two schemes are formulated. In the first, a single-reference transmittance model representing the healthy structure is employed, while multiple transmittance models from a sample of available healthy structures are used in the second. The model residual signal constitutes for both schemes the damage detection characteristic quantity that is used in appropriate hypothesis testing procedures with the likelihood ratio test. The methodology is experimentally assessed via damage detection for a population of composite beams which are manufactured in the same production line representing the half of the tail of a twin-boom unmanned aerial vehicle. The damage detection results demonstrate the superiority of the multiple transmittance models based scheme that may effectively detect damages under significant manufacturing variability and varying boundary conditions.