Damage Detection in Double Layer Grids with Modal Strain Energy Method and Dempster-Shafer Theory

Change in modal strain energy is one of the indicators used to detect damage in structures. However, in structures with high degrees of freedom, such as double-layer grids, this method requires a relatively large number of mode shapes which in practice is difficult to determine. Therefore, it is necessary to reduce the number of required mode shapes. In this study, a damage detection technique based on modal strain energy and Dempster-Shafer evidence theory is presented for locating damage in double layer grids using only a few number of mode shapes. First, by calculating mode shapes of the grid in undamaged and damaged states, the modal strain energy based index for each mode shape is determined. Then, the results obtained from separate mode shapes are combined using Dempster-Shafer theory to achieve better results. In order to investigate the effect of noise on damage detection, 3% random noise is added to mode shapes. To demonstrate the performance of the proposed method, different single and multiple damage cases with different damage intensities are considered. Numerical results show that using 5 mode shapes, the presented technique can detect up to 3 damaged elements with different damage intensities in different parts of the grid with good accuracy (probability of 92.3%). Considering the fact that the classical modal strain energy method fails to distinguish even 1 damaged element in the double layer grid, the result shows significant improvement.