Mode shape area difference method for sparse damage detection in beam‐like structures

Abstract This article develops the mode shape area difference (MSAD) method for detecting sparse damage in beam‐like structures under serviceability conditions. MSAD enhances the static deformation area difference (DAD) damage detection method by extending its application to the modal domain. MSAD leverages the sensitivity of mode shapes to the damage, enabling damage detection and localization through the quantification of area differences between functions of modal displacements and their derivatives. To test the applicability of the method to real modal data that is affected by measurement noise resulting in different accuracies on which the modal displacements are estimated, method is evaluated under different levels of artificial noise added to the theoretical mode shapes derived from numerical model of a simply supported reinforced concrete beam. The noise level is defined by a maximum noise amplitude representing the maximal permutation in each component of normalized mode shape. Additionally, the threshold value of noise level from within the reliable estimation of damage based on MSAD method is determined. It is confirmed that MSAD method requires mode shapes with exceptionally low noise levels and demands precise estimation of all mode shape components, thereby reducing its applicability to real experimental data.