Mahalanobis distance among the phase portraits as damage feature

A number of damage-sensitive features have been proposed based on the damage-induced changes in the phase portrait, reconstructed from the measured dynamic responses of structure. Of a number of alternatives, the change in phase space topology is the most widely acclaimed for assessment of structural health. In this study, a damage feature is proposed by contrasting the damaged phase portrait with the pristine one. The contrast is expressed using the Mahalanobis distance measure, which is remarkably simpler than the change in phase space topology in algorithmic aspect. The feature is referred as Mahalanobis distance among the phase portraits. The performance of the feature is demonstrated by its sensitivity and localization of damage. The noise immunity study reveals reasonable tolerance to the measurement noise. The feature is numerically illustrated on a shear building subjected to Lorentz chaotic excitations and natural wind excitations. The feature is experimentally verified in a railway bridge model subjected to moving wheel load of a model train. The results show the effectiveness of the feature for localizing both the support damage (as in bearing) and damage in the span. Simple analytical argument is also provided to link the phase portrait distortion with the extent and localization of damage(s).