عنوان مقاله [English]
A new model updating approach is proposed in this article duo to identify damage of structures. The approach is formulated based on principal component analysis (PCA) of strain-based power spectral density (PSD) data. Structural damage detection including identifying damage location and quantifying damage severity is applied by an innovative sensitivity equation of strain-based data on a least square optimization. The data is taken from the incomplete measured structural responses. The approach is based on using frequency domain data and damage is modeled by changes in stiffness matrix of elements. One of the key issues for successful model updating is evaluating accurate sensitivity relation. For some structural indices such as PSD data which are highly sensitive, the validity of sensitivity relation becomes a more main coefficient. The advantage of the using PCA technique is that with transforming PSD data to PCs with the most change and even by ignoring PCs corresponding to the low changes because of measurement errors, better results can be achieved. Finally, the PCA of the incomplete PSD data and measured strain data corresponding to the damaged structure are embedded in a formulation mathematically for obtaining an appropriate sensitivity equation. Also, in order to prevent the weakening of the sensitivity equation, derivatives of the PCs have not been employed in the proposed formulation. For illustrating the ability of the presented approach, the method is employed to two steel structures including a 2-D truss and a 2-D two-story two-bay frame. The results show the good performance of the approach as a strong damage identification algorithm, even in the presence of errors corresponding to measurement. Also, the comparative observations demonstrate that the results came by the provided sensitivity equation and strain-based PSD data are more appropriate than the results of other strain-based methods like PCA-FRF or using only PSD data.