PSI - Issue 62

Laura Ierimonti et al. / Procedia Structural Integrity 62 (2024) 832–839 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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attributes: G (1-5), indicating the significance of the defects, which is pre-defined; K1 (0.2-0.5-1), denoting the extent or spread of the defect; K2 (0.2-0.5-1), reflecting the intensity or severity of the defect. In this context, according to LLGG (2020) and to the document on post-tensioned bridges special inspections (FABRE, 2022), the deteriorating defects related to the prestressing system can be categorized into two macro groups: apparent defects and latent defects. An example of common apparent defects is the degradation of sheaths, and the oxidation of wires. Cracks exhibiting a longitudinal pattern along the beam serve as a classic example of latent defects. To determine the level of defects within structural components and the overall structure, all the attributes are combined, resulting in the following tags: (i) low, (ii) medium, (iii) high. Subsequently, in conjunction with defining the defectiveness level, it is crucial to correlate the inspected defects with the monitored damage scenarios, leveraging expertise knowledge. 2.2. SHM-based bridge deflection reconstruction Ensuring the robust health of a bridge and implementing timely maintenance measures are essential actions to mitigate latent risks in bridge safety and prevent potential safety issues. Given that deflection serves as an informative indicator reflecting prestress losses, the measurement of deflection stands as a pivotal task in the comprehensive ever- evolving realm of bridge health monitoring. Experimentally, the bridge deflection can be reconstructed from monitoring data (Lan etal., 2019) by means of measured rotations ∗ at selected positions along the bridge, by means of an appropriate calibrated polynomial function: ሺ ǡ ሻ ൌ ሺ ሻሾ ͳ ሺ ሻ ͵ ൅ ʹ ሺ ሻ ʹ ൅ ͵ ሺ ሻ ൅ Ͷ ሺ ሻሿ (1) where ሺ ሻ is a function that respects the boundary conditions, in the present case of a simply supported beam, defined as ሺ ሻ ൌ ሺ − ሻ ; the terms ሺ ሻ are the unknown coefficients to be calibrated through experimental data at each time step according to the following equation: ∗ ሺ ǡ ሻ ൌ ሺ ǡ ሻȀ (2) where represents the partial derivative function and w ( x , t ) is the vertical deflection of the beam. The optimal solutions for coefficients ሺ ሻ can be obtained by using the least square method (Lan etal., 2019). A minimum of 5 inclinometers should be used to find out accurate solutions (Hou etal., 2005). 2.3. Novelty detection Novelty detection is here performed by using Hotelling’s Control charts involving monitoring structural properties or sensor measurements over time (Hotelling, 1947). The Hotelling’s Control T -squared (T²) chart is a statistical tool that helps to identify deviations from the expected behaviour in multivariate data. In the context of SHM, Hotelling's T² assesses whether the mean vector of a multivariate dataset is significantly different from a reference or baseline mean vector and it can be evaluated as follows: ʹ ൌ ሺ − ሻ Σ − ͳ ሺ − ሻ (3) where is the analyzed data set; is the mean value of the residual error R between the deflection time series and the predicted values evaluated within the range ; and Σ are the mean value and the covariance matrix of R evaluated in the training period (typically one year of measurements), respectively. The chart's space is divided vertically into two sub-regions using a specific upper control limit (UCL). The separation into these sub-regions is guided by statistical considerations, and the chosen UCL serves as a threshold to identify and distinguish normal behaviour from potential anomalies in the monitored data. The Hotelling Control chart provides a way to visually and quantitatively assess whether the observed data points fall within the expected range, highlighting potential anomalies that warrant further investigation in the monitored structure.