Fusion of Modal Strain Energy Differences for Localization of Damage
The fusion of multiple modal strain energy differences is proposed for the detection of damage at single and multiple locations. The approaches assume the existence of several modal shapes of the structure in the undamaged and damaged states. Modal curvatures obtained through iterative high- order spline fits of the shapes permit the determination of the modal strain energy content of the structure in both states. Locations with increases in the modal strain energy between the undamaged and damaged structure are indicative of possible damage. The damage indications resulting from multiple modes are fused according to three rules: (1) an Average Standard Norm, (2) a union of probability mass functions and (3) a weighted intersection of the probabilities that the strain energy are greater than zero. the third rule requires knowledge of the statistics of the modal shape measurements. While not strictly adhering to the classical data fusion methodologies such as, Dempster-Shafer or Bayesian, the combination of information at the probabilistic level yields result that are consistent with those expected in a formal data fusion formulation. The fusion algorithms for the location of damage are tested using five modal shapes obtained from aluminum beams in undamaged and damaged states. One and two locations at different damage magnitudes are considered. The results indicate that the last two approaches are superior to the standard norm method.