PSI - Issue 64

Marco Pirrò et al. / Procedia Structural Integrity 64 (2024) 669–676 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction

In recent years, Structural Health Monitoring (SHM) of Civil structures has seen an increasing interest, mainly due to a continuous exposition to deterioration caused by increased service loads and climate changes, that jeopardize the integrity of structures such as bridges and dams. A well-assessed SHM methodology, based on Operational Modal Analysis (OMA), aims to extract a set of modal parameters from the dynamic responses of the structure under ambient (unknown) excitations. Since the modal characteristics, such as natural frequencies and mode shapes, are related to stiffness and mass properties of the structure, their variation in time can be inspected to assess the structural integrity through Statistical Pattern Recognition (SPR) paradigm (Sohn et al., 2001): in particular, the evolution of modal parameters remains stationary as long as the structure behaves in normal conditions, otherwise it loses its stationarity when a structural anomaly occurs (Magalhães et al., 2012). However, in real monitoring activities, modal parameters are generally subjected not only to structural anomalies or changes, but also to environmental and operational variability (EOV). In bridges’ applications, for example, EOV is mainly due to temperature and traffic loads (Magalhães et al. 2012, Gentile and Saisi 2015, Cross et al. 2013, Peeters and De Roeck 2001, Borlenghi et al. 2023), while for dams EOV is mainly due to temperature and reservoir’s water level (Pereira et al. 2022). Consequently, changes on modal characteristics due to EOV could mask variations associated to structural variations, so that a minimization of the EOV effects is required before applying SPR paradigm for anomaly detection. Within this purpose, a diffused technique to account for EOVs is represented by the Principal Component Analysis (PCA) (Sharma, 1995), which is a multi-variate statistical technique that can be used to identify and discard the amount of variability mainly due to EOVs from the monitored natural frequencies. The PCA model has to be trained during a period in which the structure is supposed to behave in normal conditions: generally, the training period should be sufficiently long to cover a wide range of EOV and should not include any structural anomaly. As long as the structure maintains its normal behavior, the PCA regression model correctly predicts the natural frequencies: conversely, if a deviation from the normal structural condition appears, the PCA model would not be able to predict the frequencies. The residual between the identified and predicted natural frequencies can be used to assess the structural integrity through multi-variate control-charts, such as the T 2 -Hotelling control chart (Hotelling, 1947). A completely different procedure is proposed with Cointegration, which is a statistical technique inherited from Econometrics (Stock and Watson, 1988) and recently adapted to SHM applications (Cross et al. 2011, Cross et al. 2013, Tomè et al. 2020, Turrisi et al. 2022). Within the context of OMA, given a set of non-stationary natural frequencies, the Cointegration builds a stationary linear combination of them, namely the cointegration residual, with this latter function being purged from the common trends present in the monitored features and mainly related to EOVs. The parameters of the linear combination are determined through a maximum-likelihood multivariate algorithm, referred to as Johansen procedure (Johansen, 1988), during a training period: if the training period does not include any structural anomaly, the linear combination will maintain its stationarity as long as the structure behaves in normal condition. Compared to the traditional method based on PCA + T 2 -Hotelling control chart, the Cointegration technique does not make any prediction of the monitored features, but it relies on more general operations, such as the construction of a linear combination given a set of non-stationary features. The application of the proposed methodology deals with a 2-years continuous monitoring of the Baixo Sabor dam (Portugal). In this context, the PCA and Cointegration models are used and compared for structural assessment purposes, both of them trained with the natural frequencies collected when the dam is in normal condition under typical EOVs (i.e., under normal water level variation and temperature). 2. Description of the dam and monitoring system Baixo Sabor dam is a concrete double-curvature arch dam that crosses the Sabor River (Fig. 1) in the northeast of Portugal. The dam, operating since early 2016, hosts six horizontal visit galleries and a spillway of four floodgates, each of them being 6 m long. The arch is 123 m high and has a crest 505 m long, which is composed by 32 vertical