A modified index for damage detection of structures using improved reduction system method

The modal strain energy method is one of the efficient methods for detecting damage in the structures. Due to existing some limitations in real-world structures, sensors can only be located on a limited number of degrees of freedom (DOFs) of a structure. Therefore, the mode shape values in all DOFs of structures cannot be measured. In this paper, a modified modal strain energy based index (MMSEBI) is introduced to locate damaged elements of structures when a limited number of sensors are used. The proposed MMSEBI is based on the reconstruction of mode shapes using Improved Reduction System (IRS) method. Therefore, in the first step by employing IRS method, mode shapes in slave degrees of freedom are estimated by those of master degrees of freedom. In the second step, the proposed MMSEBI is used to located damage elements. In order to evaluate the efficiency of the proposed method, two numerical examples are considered under different damage patterns considering the measurement noise. Moreover, the universal threshold based on statistical hypothesis testing principles is applied to damage index values. The results show the effectiveness of the proposed MMSEBI for the structural damage localization when comparing with the available damage index named MESBI. The results demonstrate that the presented method can be used as a practical strategy for structural damage identification, especially when a limited number of sensors are installed on the structure. Finally, the combination of MMSEBI and IRS method can provide a reliable tool to identify the location of damage accurately.