Historical masonry constructions represent the most widespread architectural and cultural heritage of our territory. Due to the high vulnerability to damage, masonry constructions must be preserved and safeguarded over time. Appropriate conservation and restoration interventions require suitable investigation procedures (Binda et al., 2000), which mainly involves non-destructive techniques (Carpinteri et al., 2007; Ramos et al., 2010a; Castellano et al., 2015; Castellano et al., 2016; Camassa et al., 2019; Camassa et al., 2020; Pallarés et al., 2021). Among them, modal testing has the very appealing feature of monitoring the global response of a structure. This experimental technique provides the modal properties of a structure (natural frequencies, mode shapes, modal damping ratios) by measuring and analyzing structural vibration due to the external load (Salawu and Williams, 1995; Peeters and Ventura, 2003; Ivorra and Pallarés, 2006; Ramos et al., 2010b; Bartoli et al., 2013).

Structural vibration is generally measured through contact sensors (e.g., accelerometers). Despite the high measurement accuracy of these sensors, their installation on the structure is time consuming and require the full access to the structure. These issues often hinder the application of modal testing on masonry constructions and encourage the development of contactless sensing techniques. A promising and increasingly popular technique is the ground-based radar interferometry, or more briefly radar interferometry.

Radar interferometry exploits phase information of back-reflected microwave signals for detecting small displacement and vibration of structures at great distance. Its working principles have been thoroughly described in several works (Gocał et al., 2013; Pieraccini, 2013; Pieraccini and Miccinesi, 2019). Radar interferometry stems from space technology, which encouraged the development of portable sensors for remotely monitoring civil structures. After pioneering works (Tarchi et al., 1997; 1999; Farrar et al., 1999; Pieraccini et al., 2000; 2003), commercial systems have been properly designed for static and dynamic testing of structures (Gentile and Bernardini, 2010; Diaferio et al., 2017). The main applications concern bridges, towers, wind turbines, dams, and buildings. Compared with accelerometers, the interferometric radar is quick and easy to install and requires no access to the structure. However, it still shows some drawbacks mainly related to atmospheric influence, presence of clutters, phase jumps, broadband noise, and projection of displacement along the line-of-sight directions (Michel and Keller, 2021).

Some researchers have explored the possibility of using interferometric radar systems for monitoring the dynamic behavior of masonry constructions. The main applications concern modal testing of masonry towers and bridges. Furthermore, a recent promising application concerns the dynamic identification of tensile force in tie rods (Gioffré et al., 2017; Camassa et al., 2021).

Here we discuss some meaningful works studying the employment of the radar interferometry technique for modal testing of masonry constructions. In particular, we explore the capability of estimating natural frequencies and mode shapes highlighting the promising effectiveness for Structural Health Monitoring (SHM) of masonry constructions and the main experimental and theoretical issues, also outlining possible research directions to enhance this application.

In SHM of masonry constructions, the estimation of natural frequencies is of great importance both for the calibration of structural models and for the damage assessment. Natural frequencies are global properties of a structure that, in principle, do not depend on the measured point (except for nodal points), but only on the measurement accuracy. The interferometric radar is a device that could provide a good accuracy of displacement determination without the distinct location of the observed point (Gocał et al., 2013); consequently, it is particularly suitable for identifying natural frequencies of structures.

Several researchers have explored the capability of identifying natural frequencies of masonry towers (i.e., bell towers and civic towers) and masonry bridges by radar interferometry. In (Fratini et al., 2011) the natural frequencies of the dome of the Baptistery of San Giovanni (Firenze, Italy) were characterized. As for towers, the estimation of natural frequencies has proved to be as accurate as conventional accelerometers; nevertheless, a slight frequency shift has been observed (Castagnetti et al., 2019). As shown in Table 1, the frequencies associated with the first two bending modes (along orthogonal directions) are generally detected. Five frequencies were only estimated in (Calcina et al., 2016). As for bridges, in (Pieraccini et al., 2019) five natural frequencies of a very slender bridge were determined. To our knowledge, there are no articles in the literature on the topic that demonstrate the possibility of estimating higher frequencies.

The reliability of frequency identification primarily depends on the Signal-to-Noise Ratio (SNR) of the acquired displacement signals, which is related to both the measurement accuracy of the interferometric radar and the magnitude of the radar line-of-sight component of displacements of the observed point. Furthermore, the identification algorithm may play a fundamental role in the estimation of natural frequencies. Here, we discuss some fundamental key concepts on these aspects focusing on the dynamic excitation and the identification algorithm.

The accuracy of the interferometric radar mainly depends on the SNR of the echoes received by the surveyed targets (Thermal SNR). The higher is the Thermal SNR, the better is the measurement accuracy. Masonry constructions, however, poorly reflect electromagnetic waves due to the low reflectivity and the limited presence of “corner zones” (Gentile and Saisi, 2012; 2014). To improve the Thermal SNR, short-range measurements should be preferred (Pieraccini et al., 2009). Another possible strategy concerns the installation of corner reflectors on the structure (Pepi et al., 2017). However, this solution requires the access to the structure and reduces the very appealing feature of contactless monitoring of radar interferometry.

The magnitude of the displacement of an observed point could be increased either by properly setting the geometry of acquisition or enhancing the dynamic excitation. The relation between the geometry of acquisition and the magnitude of the line-of-sight displacement can be found by simple projection operations (Michel and Keller, 2021). The discussion about dynamic excitation requires deeper considerations.

Contrary to natural frequencies, a full reconstruction of mode shapes of masonry constructions requires information about both the position of the measured points and the measurement of the whole three-dimensional displacement vector of the observed points. The interferometric radar does not provide the exact position of the observed points nor the component of displacement orthogonal to the line-of-sight direction. Therefore, radar interferometry has inherent limitations in determining three-dimensional displacement vectors and full three-dimensional mode shapes of masonry structures. Nevertheless, information about mode shapes is of utmost importance both for the calibration of structural models and the identification of damage.

A first study for assessing the operating deflection shape of a masonry tower under the oscillation of its own bells is shown in (Pieraccini et al., 2005). The application of a more standard approach for identifying the mode shapes of the Leaning Tower of Pisa was explored in (Atzeni et al., 2010). The authors were able to identify two closely spaced bending modes in the orthogonal planes of the tower by applying the FDD method.

Since the interferometric radar only provide the line-of-sight displacement of a target, these studies are based on kinematic assumptions about the possible displacements of the monitored structure. Without such assumptions, only the projection of mode shapes along the line-of-sight directions can be achieved. However, kinematic assumptions can only be applied to few types of constructions because, in general, the effective motion of a structure is unknown.

Some authors have proposed a number of solutions for reconstructing the whole displacement vector of a target. Except for a method able to detect both vertical and torsional movements of the sections of a bridge using an interferometric radar (Dei et al., 2009), other solutions are all based on the use of multiple interferometric radar sensors or bistatic radar systems (Michelini and Coppi, 2017; Monti-Guarnieri et al., 2018; Miccinesi et al., 2021; Michel and Keller, 2021; Olaszek et al., 2021).

The capability of estimating the displacement vector, however, does not directly imply the ability to reconstruct full three-dimensional mode shapes of large and complex masonry structures. In fact, it would be necessary to measure the vibration of the structure with multiple interferometric radar sensors from different points of view and, consequently, in different acquisitions (Figure 1). By applying OMA methods, it is possible to obtain partial three-dimensional mode shapes from each acquisition (i.e., mode shapes related to the degrees of freedom of the structure that are monitored in that acquisition), as shown in (Castellano et al., 2022). However, since OMA methods provide unscaled mode shapes (Rainieri and Fabbrocino, 2014), partial mode shapes estimated in different acquisition cannot be assembled in full mode shapes of the structure. This is a major limit of the use of radar interferometry for dynamic testing of masonry constructions. Further research to develop ad hoc methods for reconstructing mode shapes of masonry structures could lead to a great improvement in this application.

Starting from the previous literature review, here we evaluate the advantages that radar interferometry can bring to the SHM of masonry constructions. We discuss the possibility of using modal properties estimated from interferometric radar measurements for the calibration of structural models (model updating) and the structural assessment.

Regarding the estimation of modal properties, the interferometric radar measurements make it possible to estimate the natural frequencies of the first bending modes and the projection of mode shapes along the line-of-sight directions. In general, neither higher natural frequencies nor full three-dimensional mode shapes can be obtained. The estimation of modal damping ratios is not explored in the literature, albeit information about the energy dissipation could be useful for damage detection (Ivorra et al., 2020).

In model updating, uncertain mechanical parameters are generally identified by minimizing the difference between theoretical and experimental modal behavior. A good updating may be obtained by just considering lower natural frequencies (Calcina et al., 2016; Castellano et al., 2018). More accurate results could be achieved by also considering mode shapes (Gentile and Saisi, 2007), which however cannot be completely estimated by radar interferometry.

As for structural assessment, it should be firstly noticed that, in general, structural damage is a local phenomenon. Therefore, the most useful modal properties for damage characterization are higher frequencies and mode shapes since they contain local information (Doebling et al., 1998; Fan and Qiao, 2011). Quite the opposite, lower frequencies are not very sensitive to localized damage because they are global properties of structures. Nevertheless, information about the fundamental frequency can still be used to detect damage that affects the whole structure, such as damage caused by seismic events (Calcina et al., 2013) or by foundation settlements (Castellano et al., 2021).

Finally, these considerations suggest that the interferometric radar can be effectively used to perform prompt dynamic tests on masonry constructions, especially in emergency conditions such as controls after seismic events (Saisi et al., 2016; Saisi and Gentile, 2020). In this vein, expeditious and no-contact approaches, as proposed in (Pieraccini et al., 2014), can provide pre-diagnostic information that may suggest deeper investigation with conventional contact sensors. Nevertheless, it emerged that, to date, the interferometric radar does not provide enough information to perform comprehensive structural monitoring of masonry constructions.

To enhance this application, in our opinion, future studies should be oriented toward two possible directions. One research line should be aimed at overcoming the limitations that emerged from this mini review, with a special focus on the identification of higher frequencies and the reconstruction of full mode shapes. Another research direction could involve the integration of radar interferometry with both Internet of Things (IoT) devices and satellite InSAR data (Selvakumaran et al., 2020; Scuro et al., 2021).