A novel two-stage method is proposed to properly identify the location and severity of damage in plate structures. In the first stage, a superposition of modal flexibility curvature (SMFC) is adopted to locate the damage accurately, and the identification index of modal flexibility matrix is improved. The low-order modal parameters are used and a new column matrix is formed based on the modal flexibility matrix before and after the structure is damaged. The difference of modal flexibility matrix is obtained, which is used as a damage identification index. Meanwhile, based on SMFC, a method of weakening the “vicinity effect” is proposed to eliminate the impact of the surrounding elements to the damaged elements when damage identification is carried out for the plate-type structure. In the second stage, the objective function based on the flexibility matrix is constructed, and according to the damage location identified in the first stage, the actual damage severity is determined by the enhanced whale optimization algorithm (EWOA). In addition, the effects of 3% and 10% noise on damage location and severity estimation are also studied. By taking a simply supported beam and a four-side simply supported plate as examples, the results show that the method can accurately estimate the damage location and quantify the damage severity without noise. When considering noise, the increase of noise level will not affect the assessment of damage location, but the error of quantifying damage severity will increase. In addition, damage identification of a steel-concrete composite bridge (I-40 Bridge) under four damage cases is carried out, and the results show that the modified method can evaluate the damage location and quantify 5%–92% of the damage severity.
Placement and sizing of EESS bundled with uncertainty modeling by two-stage stochastic search based on improved shark smell optimization algorithm in micro-grids
