An iterated IRS technique for cross-sectional damage modelling and identification in beams using limited sensors measurement

This paper presents an effective method for cross-sectional damage localization and quantification in beams. First, a new strategy is suggested for cross-sectional damage modelling by means of Iterated Improved Reduction System (IIRS) approach. Then, a novel damage localization index is proposed employing Grey System Theory (GST) as a geometrical criterion for quantifying the amount of correlation between vectors of the calculated curvatures for the diagonal members of the flexibility matrices in the damaged and undamaged states. Since the method employs only the modal data of the translational degrees of freedom, it can be interpreted as damage identification method by utilizing incomplete modal data or installing a limited number of sensors. After detecting the damage location, to estimate the exact parameters of the cross-sectional damage, the problem is defined as a finite element model-updating problem which is solved with a new evolutionary optimization approach named Imperialist Competitive Algorithm (ICA). The applicability of the method is demonstrated by studying different damage patterns on two numerical examples of beams. In addition, its robustness is investigated in the presence of random noises and modelling errors. Obtained results emphasize the high accuracy and promising performance of the method, especially when noisy incomplete modal data are used.