PSI - Issue 62

1064 S. Anastasia et al. / Procedia Structural Integrity 62 (2024) 1061–1068 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 caused by variations in environmental operating conditions (EOC). This is accomplished by training a statistical model a set of with samples from a baseline control population , often referred to as the training period. This basic data set statistically represents the health of the facility considering all possible EOCs. Once trained, the model predictions ̂ can be used to gradually eliminate the variance due to EOC from by forming the so-called residual error matrix ∈ℝ × . Matrix ̂ produces the portion of the variance of the EOC-driven features when the system is still healthy, whereas E merely contains the residual variance due to modeling errors. On the other hand, if damage occurs, it will solely impact the data inside, matrix ̂ remaining unaltered. As a result, matrix is appropriate for use in damage identification since it concentrates the damage-induced variation. In this work, Principal Components Analysis (PCA) is adopted for the data normalization phase. PCA is a dimensionality reduction technique, which can be defined as an orthogonal linear transformation that orients the data into a new co-ordinate system, where the first principal components (PCs) hold the maximum variance (Henrion, 1994). PCs are obtained through the eigenvalue decomposition of the covariance matrix of the original data, forming an orthogonal basis of uncorrelated components. In the context of SHM, the first PCs hold the most significant contributions to variance, while noise-related variations are contained in the last components. The normalised data matrix ̂ is obtained by projecting the original data on the space occupied by the PCs. The loading matrix is determined by the training data and remains constant in the prediction phase. The choice of the number of PCs stored ( ) is crucial and it is common to retain the PCs that explain more than 80 per cent of the cumulative variance. The prediction of the normalised data matrix ̂ is done by mapping a reduced subset of PCs onto the original data space. The formula is given by: ̂ = ( ̂ ̂ T ) . (8) where ̂ represents a reduced matrix of the first columns of the loading matrix . The choice of affects the effectiveness of PCA as a data normalisation technique in the SHM model. 2.3. Anomaly detection using statistical pattern recognition end Control chart definition Once the vector of residuals is estimated, the appearance of anomalies induced by damage can be appraised through statistical quality control charts. Among the various control charts available in the literature, the Hotelling's control chart (Hotelling, 1947) is the most widely utilized approach in the realm of SHM. The definition of the statistic is defined as follows: = ( ̅ − ̿ ) ∑ ( ̅ − ̿ ) − . (9) where ∈ is the subgroup size, ̅ is the mean of the residuals in the subgroup, and ̿ and ∑ 0 are the mean values and the covariance matrix of the residuals estimated in the training period. 3. Numerical Results and Discussion 3.1. Description of the structure The Santa Ana viaduct, in the Quisi ravine, was built between 1913 and 1915. It has a six-span structure connected by Pratt-type metal trusses on metal profile piers. The viaduct is currently used as a crossing for tram line 9 between the cities of Benidorm and Denia, in Alicante (Spain) (Fig. 1a). The structure is made of steel, is approximately 170 m long and consists of six spans, with the central spans (S3 and S4) being 42 m long and having a continuous hyperstatic structural scheme, while the four lateral spans (S1, S2, S5 and S6) are isostatic. (as in Fig. 1b). The substructure consists of two masonry abutments and five pillars. 4