عنوان مقاله [English]
This article proposes a new approach for identifying damage in structures through model updating. The approach is based on principal component analysis (PCA) of strain-based power spectral density (PSD) data. The proposed method detects damage, identifies damage location, and quantifies damage severity using an innovative sensitivity equation of strain-based data on a least square optimization. The data is obtained from incomplete measured structural responses, and the approach utilizes frequency domain data where changes in stiffness matrix of elements model damage. One of the crucial components for successful model updating is evaluating an accurate sensitivity relation. Highly sensitive structural indices such as PSD data require a valid sensitivity relation to yield satisfactory results. The PCA technique provides an advantage by transforming PSD data to PCs with the most significant changes and ignoring PCs that correspond to low changes caused by measurement errors. The presented approach embeds the PCA of incomplete PSD data and measured strain data for a damaged structure into a mathematical formulation to obtain an appropriate sensitivity equation. To prevent weakening the sensitivity equation, the proposed formulation does not employ derivatives of the PCs. The proposed method is applied to two steel structures, a 2-D truss and a 2-D two-story two-bay frame, to demonstrate its performance as a strong damage identification algorithm, even in the presence of measurement errors. Comparative observations indicate that the results obtained by the provided sensitivity equation and strain-based PSD data are more appropriate than the results of other strain-based methods such as PCA-FRF or using only PSD data.