PSI - Issue 78

Carlo Rainieri et al. / Procedia Structural Integrity 78 (2026) 426–432

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compensate for the EOV effects in the absence of explicit measurements of such variables, and by analyzing the residue pattern in order to detect possible anomalies in the structural response.

Mode I

Mode II

Mode III

Fig. 2. Natural frequency and modal damping ratio time series for the first three modes of the building (from top) with indication of the seismic events occurred in the considered monitoring period.

PCA is a linear technique for SHM data normalization mapping data from their original space into a new set of coordinates called principal components scores. PCA aims at projecting the original data Z in the principal components space and then remap only the principal components associated with the largest variability within the data back to the original space, as follows: " = ( " ) " ! (1) where the transformation matrix, P ∈ℝ "×" , holds the singular vectors of the covariance matrix of X , which correspond to a reference structural condition. By retaining the first d columns of P , a rectangular transformation matrix " ∈ℝ "×$ is obtained. A common criterion for defining d involves retaining a given percentage of the total variance (Giglioni et al. 2021). The reverse projection allows computing the difference between the original data and the test matrix reconstructed by means of the selected principal components, according to Eq. (2).