PSI - Issue 78

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

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structures. While visual inspections as well as destructive and non-destructive investigations are typically applied for damage detection, the local nature of tests, the subjectivity of the expert judgment, and the costs and very limited frequency of inspections have solicited strong research efforts, over the last decades, to change the paradigm towards more efficient approaches. Structural Health Monitoring (SHM) is nowadays a well-established technology for remote structural health and performance assessment of civil structures (UNI 2016). The main objective of continuous SHM systems is damage detection at an early stage, so that timely countermeasures can be taken. In this perspective, it has been often successfully applied for timely assessment of structures hit by seismic events (Giordano et al. 2022, Rainieri et al. 2011). Damage identification can be accomplished at different levels -a. detection; b. localization; c. identification of damage type; d. quantification of damage severity; e. prognosis- (Rytter 1993) resulting in analysis procedures of increasing complexity. Modal based damage detection (Sohn et al. 2001) is probably one of the most popular approaches in civil SHM, exploiting the development of several robust automated Operational Modal Analysis (OMA) algorithms in the last decades. The interested reader can refer to Rainieri and Fabbrocino (2010) and Rainieri and Fabbrocino (2015) for an extensive review. Modal based damage detection is very simple in principle. It starts from referring to as damage any change of the structure that adversely affects its functionality or load bearing capacity (Farrar and Worden 2012). Damage can be, for instance, associated with changes of stiffness due to cracking in concrete or masonry structures, of external (soil settlements) and/or internal restraints (loosening of tightening force in bolts of steel structures), or of mass. The relationship between the physical properties of the structure (i.e. mass, stiffness, damping) and its modal parameters is therefore exploited for damage detection. In fact, considering that changes in the physical properties induced by damage yield changes in the modal properties, the analysis of the variations of damage-sensitive features, defined in terms of modal parameters, can support remote detection of damage. Several damage-sensitive features based on modal parameters have been defined and tested over the years, the most common of which being natural frequencies, mode shapes, and mode shape curvature (Farrar and Worden 2012, Carden and Fanning 2004). The possibility of getting accurate estimates even in the presence of a few installed sensors (Ubertini et al. 2017) makes the use of natural frequencies as damage features particularly attractive. Monitoring the changes of natural frequencies allows detecting the occurrence of damage; however, they usually provide limited information for damage location and quantification. When locating damage is of interest, mode shapes and mode shape curvatures are more informative (Deraemaeker et al. 2008). Advantages and limitations of modal based SHM are currently well established. Among the latter, the most relevant is the sensitivity of natural frequency estimates to environmental and operational variables (EOVs) (Moser and Moaveni 2011). Changes in natural frequency estimates due to EOVs are often of the same order of magnitude of those caused by damage. If the effect of EOVs is not taken in due consideration, type I (false identification) and type II (missed identification) errors can occur, seriously affecting the reliability of damage detection. An effective compensation of the influence of EOVs on natural frequency estimates is therefore critical in view of the development of SHM systems. Temperature is often the dominant factor influencing the dynamic response of the monitored structure, even if a number of studies documented the importance of additional factors (Cross et al. 2013, Ubertini et al. 2017). Whenever explicit measurements of relevant EOVs affecting the modal properties are available, a mathematical model mapping the changes of the features with the EOVs can be set. Linear regression models represent the simplest approach to model the effect of EOVs on dynamic properties. Data normalization methods not requiring measurements of the EOVs (Jin et al. 2015) are an attracting alternative to the previous ones. Since the selection of the EOVs to measure is often not straightforward, because the factors influencing the estimates cannot be clearly identified or they cannot be measured, this class of methods looks for a subspace in which the environmental effects lie, so that they can be removed by the projection of the damage features in the subspace orthogonal to the identified one. In other words, these methods are effective in removing the influence of EOVs as long as the variations in the features due to damage are in some way orthogonal or uncorrelated to those caused by the environmental variability (Deraemaeker et al. 2008). In any case, an effective SHM system cannot skip a data normalization phase aimed at compensating the influence of EOVs on modal parameter variability. Whenever the environmental and operational influence is properly considered, modal-based SHM systems show high reliability and they give the opportunity to identify response anomalies without any prior information about damage, provided that reference monitoring data associated with the healthy condition of the structure are available (Farrar and Worden 2012).