Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures

Abstract

In recent years, Global Navigation Satellite System (GNSS) technologies, which take full advantage of both real-time kinematic (RTK) and precise point positioning (PPP), managed to reach centimeter-level positioning accuracy with ambiguity resolution (AR) quick convergence techniques. One great advantage over traditional structural health monitoring (SHM) systems is that GNSS technologies will be functional in disaster management situations, when terrestrial communication links become unavailable. In this study, a multi-GNSS system, based on GPS and Galileo constellations and exploiting advanced RTK and PPP-AR technologies with update rate of 100 Hz is tested on two benchmark structures as an SHM system. The first case study served as a baseline to outline the methodology: first, a setup phase of the instrumentation, then a signal processing phase and last, the validation of the results. The methodology was then applied to a real-case scenario, in which the GNSS was tested on a road bridge. A comparative analysis with the results acquired by a set of accelerometers showed that the GNSS was able to identify the crossing of heavy vehicles. The work is paving the way for the development of an affordable and efficient multi-GNSS-based tool for the monitoring of civil infrastructures.

1. Introduction

The work presented herein was developed by the joint effort of the University Roma Tre (UNIROMA3), the Italian Department of Civil Protection (DPC) and the Italian ICT company SOGEI. The activities carried out were part of the European project GISCAD-OV (Galileo Improved Services for Cadastral Augmentation Development On-field Validation) and the main aim was to study the effectiveness of a multi-GNSS-based monitoring system for civil infrastructures [1,2]. The system is based on the integration of GPS and the Galileo High Accuracy System (HAS), exploiting advanced RTK and PPP-AR techniques, with an update rate up to 100 Hz.

The current state of the art shows that in the SHM field, accelerometers are widely used. By processing the acquired accelerations, the displacements and the frequency content can be evaluated and used to obtain parameters to assess the integrity of the monitored structure [3,4]. However, the great limitation is the numerical error that the process suffers from, induced by the experimental noise and the sampling frequency. Indeed, the displacements are calculated via the double numerical integration of the accelerations and the frequency content by applying a fast Fourier transform-based algorithm to the signal. A possible advantage of using a GNSS-based monitoring system is that it allows a direct measurement of the displacements and therefore improves the double integration conditioning. As an example, such kinds of measurement can be used to calculate the relative displacements and inter-floor drifts in order to obtain the parameters for the assessment of the state of the structure [3]. Current applications of the GNSS-based monitoring system (also exploiting advanced PPP technologies), with a sampling frequency up to 100 Hz, also allow us to fully cover the frequency range of interest in seismic applications, which is limited to between 0.1 Hz and 15 Hz [5,6,7,8,9]. Moreover, the proposed technology allows us to measure both static and dynamics displacements, contrary to terrestrial systems, which are distinct for the two types of measurements [10,11]. The system will be a cost-effective solution for monitoring structures that are not endowed with a terrestrial monitoring system [12,13]. The last great advantage is that it will be useful in case of the unavailability of terrestrial communication links as well as for continuous monitoring in infrastructure monitoring applications [14,15,16].

The current state of the art of GNSS-based SHM systems shows that is possible to exploit RTK and standard PPP techniques basically carried out in a post-processing mode on controlled infrastructures [17,18,19]. The work here presented focuses on the application of real-time GNSS PPP-RTK high-accuracy techniques for operative infrastructure monitoring (e.g., bridge monitoring), paving the way for the use of the Galileo HAS, a fully satellite-based positioning service. For this purpose, the GNSS monitoring system was tested on two benchmark structures of different natures, which represented the two case studies of the work. The first one, a small-scale benchmark structure, served as a baseline to outline the methodology of the work. The GNSS was then tested on a structure of civil interest, a large-scale benchmark structure, which represented the real-case scenario. The main difference between the two cases is that in the first scenario the displacements of interest were those in the plane tangent to the surface of the earth, the horizontal displacements from people point of view. For the real case scenario, the GNSS based structural monitoring was applied to a road bridge under normal traffic conditions. Hence, the displacements of interest were those in the plane orthogonal to the surface of the Earth, the vertical displacements from people point of view. In order to assess the accuracy of the GNSS, the structures were also monitored by means of accelerometers. The results acquired by the two types of monitoring systems were then compared. As it will be discussed in the conclusions, the GNSS managed to capture the displacements in both scenarios, showing, as expected from the literature, higher accuracy in the acquisition of horizontal displacements.

The text is divided into three main sections. The first one, divided into three subsections, explains the methodology that was outlined for the work. Therefore, it gives a description of the small-scale benchmark structure, the setup configuration of the monitoring system and the signal processing, and last, it shows the results of the comparative analysis. The second section, divided in two subsections, shows the application of the methodology to the real-case scenario, the road bridge. Hence, this section gives a description of the benchmark structure and the setup configuration of the GNSS monitoring system, after which the results are presented. A final section presents a discussion upon the results and the conclusion of the paper.

2. Materials and Methods

This section focuses on the methodology that was outlined to test the GNSS-based monitoring system. This consisted of three main steps, beginning with the setup configuration of the GNSS instrumentation, proceeding with the acquisition and the processing of the satellite signal and concluding with the validation of the results. The methodology was first tested on a small-scale benchmark structure. Since this part of the work was devoted to outlining the methodology, the structure under investigation needed to be easily accessible and simple to analyze through an appropriate configuration of the satellite system. The following subsection is meant to describe the monitored structure, the installed monitoring systems and the tests that were carried out. After that, a second subsection explains the signal processing phase, focusing on the analysis conducted on the acquired GNSS signal. Finally, the last subsection presents the validation process. This was achieved by means of a comparative analysis in the time and frequency domain between the results of the post-processed satellite signal and those obtained by an accelerometric monitoring system [15]. Moreover, the results in the frequency domain were compared with those obtained by a preliminary modal analysis conducted on a finite element model (FEM) of the structure.

2.1. Benchmark Structure and Test Configuration

In order to outline the methodology, a flexible steel structure was chosen as a small-scale benchmark. The structure, shown in Figure 1, is located on the top roof of one of SOGEI’s buildings in Rome and is composed of a steel frame paneled with a steel grillage. The beams are C-channels with flange width of 39 mm and web depth of 80 mm. The thickness of both flange and web is about 4 mm. The columns are hollow structural sections (HSS) with cross sections of 50 × 100 mm and 100 × 100 mm, the latter for the two corner columns. The beams and the grillage are connected to columns through bolts. Welding is partially used to connect beams and columns of the main entrance. All columns are fixed to the ground.

The structure was monitored through the GNSS instrumentation that was provided by the Canadian company NovAtel Inc. (Calgary, AB, Canada), which allows continuous monitoring with update rate of 100 Hz. Concerning the GNSS system, high accuracy positioning is foreseen through the application of real-time augmentation multiconstellation and multifrequency RTK and PPP-RTK services, provided by the RTCM NTRIPCaster GISCAD-OV Sogei Control Centre service managed by Sogei. The monitoring system consisted of an antenna, which was directly installed on the point of interest of the structure, cable connected to a receiver, which was fixed to the ground. The used receiver is the NovAtel PwrPak7, equipped with the NovAtel antenna model GNSS-850. This system is a multi-constellation and multi-frequency receiver, able to process latest GNSS signals, with particular reference to Galileo E6B (transmitting the Galileo HAS corrections). A topographic levelling base was employed to fix the antenna to the structure in order to reach an optimal levelling. Both have been fixed with a g-clamp to the benchmark structure. The setup of the monitoring system is shown in Figure 2. According to the number of sensors provided, five points of the structure were monitored. The fact that the points are part of a very restricted region of the structure is due to the nature of the dynamic tests conducted. Indeed, the tests were performed by manually exciting the structure in order to generate vibrations of high amplitude, which could therefore be measured by the GNSS monitoring system. Hence, the portion of structure being monitored, shown in Figure 2, is that part subjected to the excitation.

The validation of the results was carried out thanks to a set of five piezoelectric single axis accelerometers provided by the DPC. The accelerometers, model PCB 393A03 produced by PCB Piezotronics, are voltage-mode output sensors characterized by a high sensibility level, 1000 mV/g, and a measurement range equal to ±5 g with maximum error of 5% in a frequency range from 0.5 to 2000 Hz. Each accelerometer was connected to a 24-channels data logger, that is, LMS-SCADAS mobile hardware with 24-bit A/D for a dynamic range of 150 dB, with shielded cables of 3, 6 or 10 m. The installation was carried out by the DPC, making sure that the single axis accelerometers were aligned along the direction of the displacements of interest. Referring to Figure 2, the five accelerometers were installed so that the first two were aligned with the y-direction while the other three with the x-direction.

The tests consisted of four time series acquisitions. The first one was carried out to define the displacement’s baseline and to characterize the noise associated to the satellite signal. For this purpose, the first acquisition was performed under static conditions of the structure. The subsequent tests were carried out by performing a manual excitation on the structure. Specifically, for the second and the fourth tests, the manual excitation was performed along the y-axis, while for the third one, it was performed along the x-axis. The reference system that was taken into consideration is depicted in Figure 2. Throughout the dynamic tests, the manual excitation was applied twice, for about 10 s each time. The excitation was applied near the first monitored point for the second and the fourth tests and near the fifth monitored point for the third one. The manual excitation consisted of imparting a forced oscillation to the structure by grabbing it with one hand and moving it back and forward, as shown in Figure 3.

The acquisition time was about 150 s.

Table 1. Features of the four tests.

Test	Direction of Excitation	Point of Application 1
1	-	-
2	y	1
3	x	5
4	y	1

¹ Refer to the schematic representation in Figure 2a.

sums up the main features of the four tests.

2.2. Analysis of the GNSS Signal

The correct positioning data were obtained through the application in real-time of the PPP-RTK correction messages generated by the GISCAD-OV Control Center. Only the analysis of the results was carried out in post-processing. The acquired positioning data contain information about the positions in geodetic coordinates of the monitored points. On the other hand, the accelerometric system used for the validation process stores the positions in its local coordinate system. In order to proceed with the validation of the results, the two sets of data must be organized in a common coordinate system. It was decided to consider the local coordinate system of the tested structure as reference. Hence, before the comparative analysis, it was necessary to apply a series of coordinate transformations to the satellite data.

The customary reference for the GNSS is the Earth-Centered Earth-Fixed geodetic (ECEF-g) reference system [20]. Therefore, the coordinates for this frame are the geodetic latitude, longitude and height. Geodetic coordinates are defined relatively to a particular Earth geodetic datum, which is a means of representing the figure of the Earth [21]. The datum that the GNSS monitoring system considers is known as WGS84 (World Geodetic System 1984) and it consists of an ellipsoid with geometrical features, as reported in

Table 2. Features of the WGS84.

Name	Symbol	Value
Semimajor axis	a	6,378,137 m
Semiminor axis	b	6,356,752.31424518 m
Flatness	f	3.3528107 × 10−3
Eccentricity	e	81.8191908 × 10−3

.

The flatness and the eccentricity are defined by the following formulas:

$$f=\frac{a-b}{a},$$

(1)

$$e=\sqrt{f\left(2-f\right)}.$$

(2)

Figure 4 depicts the meridian plane of the ellipsoid, with its geometrical features highlighted. In particular, the normal radius of curvature N is graphically defined as the distance along the normal between the vertical projection of P, the point of interest, on the surface of the ellipsoid and the semiminor axis b. N can be evaluated by the following formula:

$$\mathrm{N}=\frac{a}{\sqrt{1-e^2{\sin }^2\left(\mathsf{\varphi }\right)}}.$$

(3)

The geodetic datum is obtained by considering a Cartesian reference system with origin O in the center of the ellipsoid. This is usually referred to as Earth-Centered Earth-Fixed rectangular (ECEF-r) reference system. The revolution of the ellipsoid is about the polar axis z while the axes x and y are positioned in order that the positive x-axis defines zero longitude while the positive y-axis is chosen to complete an orthogonal right-handed coordinate system [22]. Hence, the geodetic coordinates can be defined relatively to the ECEF-g reference system. Latitude ϕ is defined as the angle between the ellipsoidal normal through the point of interest and the equatorial plane. Longitude λ is defined as the angle between the meridian that contains the point of interest and the prime meridian, also known as Greenwich meridian. Finally, height h is defined as the elevation of the point of interest above the surface of the ellipsoid. Since the geodetic coordinates are measured relative to a fixed point on the surface of the earth, ECEF-g rotates at the Earth’s rate, i.e., it is a non-inertial frame. Figure 5 depicts the ellipsoid that was taken into consideration.

The straightforward method to convert the geodetic coordinates to local coordinates involves a three-step coordinate transformation. The first one serves the purpose of calculating the coordinates in the ECEF-r reference system. This can be performed through the following equations, explained in the work by Heiskanen and Moritz [23]:

$$x=\left(h+N\right)\cos \varphi \cos \lambda ,$$

(4)

$$y=\left(h+N\right)\cos \varphi \sin \lambda ,$$

(5)

$$z=\left(h+\left(1-e^2\right)N\right)\sin \varphi .$$

(6)

The second transformation is necessary to express the coordinates in a tangent plane reference system, known as the East-North-Up (ENU) reference system. It is a Cartesian system with the first two axes in the plane tangent to the surface of the ellipsoid, while the third one is aligned to the ellipsoidal normal through the origin of the system. An orthogonal transformation matrix, explained in the work by Heiskanen and Moritz [23], allows the coordinate transformation from ECEF-r to ENU:

$$\left(\begin{array}{}\\ E\\ \\ N\\ \\ U\\ \end{array}\right)=\left(\begin{array}{}\\ -\sin \left(\lambda \right)& \cos \left(\lambda \right)& 0\\ \\ -\cos \left(\lambda \right)\sin \left(\varphi \right)& -\sin \left(\lambda \right)\sin \left(\varphi \right)& \cos \left(\varphi \right)\\ \\ \cos \left(\varphi \right)\cos \left(\lambda \right)& \cos \left(\varphi \right)\sin \left(\lambda \right)& \sin \left(\varphi \right)\\ \end{array}\right)\left(\begin{array}{}\\ x-x_0\\ \\ y-y_0\\ \\ z-z_0\\ \end{array}\right).$$

(7)

In the above equation, x₀, y₀ and z₀ are the coordinates of the origin of the ENU reference system expressed in the ECEF-r coordinate system.

Lastly, coordinates must be expressed according to the reference system of the accelerometers. Since the structure lays on the plane tangent to the surface of the Earth, this last coordinate transformation involves only a 2D rotation about the vertical axis. The transformation matrix that is used for a clockwise rotation α is given by the following formula:

$$\left(\begin{array}{}\\ X_L\\ \\ Y_L\\ \\ Z_L\\ \end{array}\right)=\left(\begin{array}{}\\ \cos \left(\alpha \right)& -\sin \left(\alpha \right)& 0\\ \\ \sin \left(\alpha \right)& \cos \left(\alpha \right)& 0\\ \\ 0& 0& 1\\ \end{array}\right)\left(\begin{array}{}\\ E\\ \\ N\\ \\ U\\ \end{array}\right).$$

(8)

In conclusion, the straightforward method to convert the geodetic coordinates to local coordinates implies a three-step transformation process: a first conversion in ECEF-r, a second in ENU and the last in the local reference system. Figure 6 depicts the four coordinate systems involved in the transformation process.

As an example, the signal acquired by the GNSS-based monitoring system during the second test is showed in Figure 7. The plot depicts the positions in geodetic coordinates of the first monitored point. By means of the formulas previously shown, it was possible to transform the geodetic coordinates into local coordinates. Moreover, as shown in Figure 8, the displacements of the monitored point were calculated by simply subtracting the resting position, calculated as the mean position, from the acquired signal. As expected, the major displacements are along the y-axis, the same direction of the excitation. In order to improve the result by reducing the noise that affects the signal, a fourth order Butterworth band pass filter with lower cutoff frequency of 1 Hz and higher cutoff frequency of 15 HZ was implemented in a MATLAB script. Figure 9 depicts the post-processed signal that clearly shows the two time gaps in which the excitement was performed.

2.3. Validation

The validation process was carried out by means of a comparative analysis in both the time and frequency domain. The post-processed satellite signal was compared to the results obtained from the accelerometric monitoring system and from the FEM. In the time domain, the displacements obtained from the two monitoring systems were compared. In the frequency domain, the natural frequency of the structure obtained from the signals and from the numerical model were compared.

The results that follow refer only to the second test that was conducted. The other results are being omitted since they lead to the same results.

2.3.1. Time Domain

In order to carry out the comparison of the acquired displacements, the recorded accelerations were integrated twice, according to the Simpson’s rule for numerical integration and the application of a suitable fourth order Butterworth type band pass filter. In the integration process, a pass band filter with range 0.3–25 Hz was used. The higher bound was chosen in order to set the same conditions of the satellite receivers. Indeed, these sample at a rate of 50 Hz, which means they see frequencies from 0 Hz to 25 Hz.

Figure 10 shows the graphical comparison between the post-processed signals acquired with the two monitoring systems. The signals represent the displacements in time of the first monitored point during test 2.

Table 3. Comparison of the peak displacements acquired by the GNSS and the accelerometers. The peak displacements were caused by the first excitation during test 2.

Points	Peak Displacements [mm]
	GNSS [mm]	Accelerometer [mm]	Difference [mm]	Percentage Difference [%]
1	25.4	18.7	6.7	26.4
2	13.2	8.9	4.3	32.6
3	5.8	3.4	2.4	41.4
4	12.8	9.1	3.7	28.9
5	14.6	9.9	4.7	32.2
Mean values			4.4	32.3
Mean values without GNSS 3			4.9	30

reports the values of the peak displacements acquired by the two systems for each monitored point. It also shows the maximum differences and the mean difference between the two types of measurements.

As expected, the first signal showed the highest peak while the third one showed the lowest. Indeed, the first monitored point is the closest to the excitation point, while the third one is the closest to the corner of the structure, which is the stiffer part of the structure. As a result, the monitoring of the third point exhibited the highest difference between the two types of measurements. This is because the GNSS suffers from noise that has such a high order of magnitude that the measurement becomes difficult when the displacement being acquired is very small. Therefore, the table also shows the mean value of the differences when the acquisition inherent to the third monitored point is being omitted.

2.3.2. Frequency Domain

In order to proceed with the comparative analysis in the frequency domain, one has to evaluate the natural frequency of the structure from the acquired signals. For this purpose, a fast Fourier transform-based algorithm was applied to that part of the signal that describes the free oscillations of the structure, highlighted in Figure 11 [24]. This portion of signal was analyzed with MATLAB by using the CPSD function which estimates the cross power spectral density of two discrete-time signals, x and y, using Welch’s averaged, modified periodogram method of spectral estimation [25]. This procedure allowed us to calculate the natural frequency of the benchmark structure. Figure 12 shows the graphical comparison of the PSDs evaluated from the signals acquired by the two different monitoring systems.

Noticeably, the two monitoring systems identified almost the same peak frequencies. The mean peak frequency was considered as an estimation of the natural frequency of the structure.

Table 4. Comparison of the peak frequencies evaluated from the GNSS and the accelerometers. The peak frequencies were calculated by applying the PSD function to the first set of free oscillations acquired during test 2.

Points	Peak Frequencies
	GNSS [Hz]	Accelerometer [Hz]	Difference [Hz]	Percentage Difference [%]
1	4.6	4.6	0.0	0.0
2	4.6	4.6	0.0	0.0
3	3.3	4.3	1.0	23.3
4	4.3	4.6	0.3	6.5
5	4.6	4.6	0.0	0.0
Mean values	4.28	4.54	0.26	6.0
Mean values without GNSS 3	4.5	4.6	0.08	1.6

shows the values of the peak frequencies together with the mean values calculated with and without the third signal.

The natural frequency was then compared to the one obtained by a modal analysis conducted on the FEM. The model was implemented thanks to a 3D survey conducted on the structure by means of a laser scan. The portion of structure that is subjected to the displacements was modelled through an appropriate distribution of one-dimensional structural elements in SAP2000, the structural engineering software that was considered for this work. The remaining part of structure was taken into consideration through a system of suitably designed external constraints that could correctly describe the dynamic behavior of the entire structure. All the structural elements that create the steel frame are considered as beam elements with an assigned cross section. Since the axes of the structural elements do not always physically intersect in the model, a series of body constraints were necessary for recreating the continuity in the structure. A preliminary modal analysis was then conducted on the model, showing a natural frequency of 5.11 Hz. The difference between the natural frequency obtained from the GNSS signal analysis (4.5 Hz) and the FEM is about 11.9%. The quite high difference in the result suggests that the FEM needs further calibration. Beside the result of the comparison, the FEM represented an important aspect of the methodology since it allowed us to compare the motion measured by means of the GNSS with the global deformation obtained through the preliminary modal analysis conducted on the FEM.

3. Results on a Real Bridge

The methodology previously described was then applied to a real-case scenario that involved the monitoring of a structure for civil use, which is described in the following subsection. A second subsection is dedicated to the validation of the results through the comparative analysis between the GNSS and the accelerometric system. Unlike before, it was decided not to consider the FEM for the comparative analysis.

3.1. Benchmark Structure and Test Configuration

In order to study a real-case scenario, a road bridge, shown in Figure 13, was taken into consideration as a large-scale benchmark structure.

The main difference from the previous case is that the displacements being monitored belong to the vertical plane. Indeed, the road bridge was monitored with normal traffic conditions and the displacements that we were able to acquire were those caused by the crossing of the vehicles. The road bridge is located near the city of Orte (belongs to the county of Viterbo, localized in the center region of Italy, Lazio) and links the two-lane national road SS675 over the river Tiber. The structure consists of a multi-span road bridge (for a total of 33 spans) made of prestressed concrete, and its deck is composed of four box girders. Figure 14 shows the schematic cross section of the bridge deck in which the four box girders can be noted, with the cross section specified in Figure 15. Figure 16 shows a view of the deck from beneath the bridge.

The monitoring campaign was carried out thanks to ANAS s.p.a., the national company that is in charge the management of the structure, and consisted of mounting the GNSS system on the second span of the bridge and acquiring data continuously under normal traffic conditions. The static system that describes the behavior of the single span of the road bridge is composed of a simply supported beam, 40 m long, with a distributed load representing its weight. Figure 17 depicts the first two bending mode shapes of a single span of the road bridge, which were taken into consideration to choose the setup of the sensors. Figure 18 shows the second span of the bridge and the location of the sensors for the monitoring campaign.

The road was partially closed to traffic in order to secure the installation process of the monitoring systems. Due to the nature of the GNSS-based system, the antennas needed to be mounted on top of the guardrails. For this purpose, the DPC conducted a campaign of data acquisition via accelerometers to verify that the vertical displacements of the top and bottom parts of the guardrail, with the latter integrated to the bridge, were the same. This test was conducted by means of two temporary accelerometers, installed on the same vertical axis of the guardrail, being one mounted at the bottom of the guardrail and one at the top. The accelerations were acquired under normal traffic conditions. The results that are not reported for the sake of brevity show that there is no relative vertical motion of the guardrail. After this preliminary verification, a set of three antennas and one accelerometer were installed on the road bridge, precisely, on the lane in the direction of Viterbo. Two antennas were mounted at the centerline of the bridge, one on the right-side guardrail and one on the left-side one. A third antenna was mounted at a quarter of the span length on the right-side guardrail. Figure 19 shows a schematic representation of the plan view of the bridge in which the monitored points are highlighted. In this case, only one accelerometer was employed and was installed on point 2. Figure 20 depicts the installation process of the GNSS instrumentation. It is important to underline that, in this case, the accelerometer was of the force-balance type, with a measurement range from 0 to 200 Hz, and therefore was also able to measure the accelerations caused by quasi-static excitation.

The monitoring systems were mounted on the structure and left in position for about two weeks. In this period, the two monitoring systems acquired data continuously and organizing data in 1 h interval measurements. Data shown here refer to a 1 h interval measurement that was acquired from 1:31 AM to 2:31 AM on 24 September 2021.

3.2. Validation

In contrast to the case of the small-scale benchmark structure, the comparison was carried out only in the time domain. Indeed, the bridge dissipates the oscillations quickly due to the crossing of a vehicle. The free oscillations could not be identified via the GNSS signal and therefore, the natural frequency of the structure could not be calculated.

Moreover, due to the high order of magnitude of the noise when analyzing vertical displacements, the comparative analysis focused its attention on the displacements caused by the crossing of heavy vehicles that exhibited an order of magnitude higher than the threshold of the signal’s noise.

Focusing on the first 500 s of acquisition, a peak of almost 40 mm was identified by both the monitoring systems, as shown in Figure 21. The figure illustrates the three satellite signals and the one accelerometric. The latter was obtained by double numerical integration by applying a band pass filter from 0.03 to 25 Hz, in order to also capture the quasi-static component of the structural response.

Since the antennas were mounted on different spots of the bridge, it was reasonable to expect different amplitudes of the peak displacements. On the other hand, due to the impulsive nature of the excitation, we expected all three antennas to show the peak displacement at almost the same time.

4. Discussion

In the case that involved the monitoring of the small-scale benchmark structure, the five GNSS receivers managed to capture the dynamics of the structure during each test. As expected, the location chosen for the antennas turned out to be a key aspect for a successful acquisition. As an example, the signal that describes the position of the third monitored point, very close to the corner of the structure, did not allow a precise measuring of the point’s displacements and, moreover, a clear identification of the peak frequency of the structure. Overall, the receivers managed to correctly identify the displacements and the natural frequencies of the structure. The slight discrepancy between the results of the two monitoring systems could be due to the effects of both the error linked to the double numerical integration of the accelerations and the noise that typically affects a satellite signal. This latter effect was analyzed through a statistical analysis that was carried out on the signals acquired during the first static test. In the acquisition of the displacements that belonged to the plane tangent to the surface of the Earth, the noise exhibited a threshold of about +/− 2 mm, under which the identification of the displacement may be problematic. In the acquisition of the displacements that belonged to the vertical plane, the noise exhibited a higher threshold, according to the literature, of about +/− 4 mm. The analysis provided us with information about the minimal sensible displacement of the GNSS. This allowed us to assess the correctness of the GNSS application methodology by comparing the results with those of the literature [19]. The detailed results of the analysis are shown in the following section.

On the other hand, the monitoring of the road bridge was more complicated but managed to identify the crossing of heavy vehicles. The difficulties encountered in this case study were due to different aspects. First, the monitored structure is far more rigid than the steel structure from the previous case. Second, the normal traffic conditions under which the test was carried out caused, most of the time, small vertical displacements. Indeed, with the structure being old and in need of restoration, ANAS s.p.a. imposed a partial stopto heavy traffic in order to prevent risks to the structure and to the users of the infrastructure. Moreover, according to the literature, vertical displacements are more complicated to identify in respect to horizontal ones. Last, with the sensors mounted on the guardrails, the close passage of the vehicles may have caused a disturbance in the signal. For these reasons, the GNSS managed to identify only the crossing of heavy vehicles, merely in the time domain. The identification was possible since the excitation due to the crossing of heavy vehicles produced displacements bigger than the signal’s noise, which exhibited a threshold of about 10 mm in the vertical direction. The detailed results of the statistical analysis carried out on the signal’s noise are shown in the following section. Figure 22 shows a graphical comparison between the signals acquired by the two monitoring systems. Noticeably, displacements of amplitudes lower than 10 mm could be identified from their accelerometric signal but would get lost in the noise of the satellite signal.

The minimal sensible displacements of the GNSS were those greater than the threshold of the noise. Those displacements were caused by the crossing of heavy vehicles, such as fully loaded trucks, capable of imparting displacements of amplitude between 10 mm and 40 mm to the road bridge. A detailed discussion of the minimal sensible displacement is reported in Section 4.1.

In conclusion, the work carried out paves the way for the development of GNSS SHM systems independent from the terrestrial infrastructures (as needed locally for the implementation of RTK systems).

Galileo HAS, through the development in a second phase of the service of ionospheric and tropospheric errors, will be analysed in a future work.

4.1. Statistical Analysis of the Noise of the GNSS Signal

In order to characterize the minimal sensible displacement of the GNSS, a statistical analysis of the noise that affects the signal was carried out for both case studies.

4.1.1. Small Scale Benchmark Structure

The results of the static test were used to carry out the analysis. The analysis was carried out for the results of each receiver and helped to define a threshold of the noise, different between the cases of horizontal and vertical displacements that set the limit of the minimal sensible displacement of the GNSS. For the sake of brevity, the following results refer only to the GNSS installed in the first monitored point. Figure 23 depicts the the displacements along the local x, y and z directions. For each signal, the maximum, minimum and mean values were defined together with the variance and standard deviation of the data distribution. Moreover, due to the presence of outlier values, only the 99.9% of data were considered, ignoring the presence of the 0.1% of higher values. The limits are identified by the quantiles of order 99.95 and 0.05, respectively. These were considered as the thresholds of the minimal sensible displacements. Noticeably, the minimal sensible displacement changes significantly if horizontal or vertical displacements are considered.

According to the literature, Figure 24 shows that the data are perfectly described by the normal distribution. All distributions are symmetrical with respect to the mean value, which is always zero. Again, a big difference can be noticed in the normal distributions that describe the cases of horizontal and vertical displacements. Indeed, while the mean value is always zero, the variance increases quite significantly when vertical displacements are considered. In this case, the data appear to be spread out around the mean value, making the bell curve graph flatter and wider.

Figure 25 shows the position of the first monitored point in its local reference system. Noticeably, the oscillations due to the noise of the GNSS signal affect the results. The limits of the axes were fixed by the quantiles previously introduced, so that the data shown represent the 99.9% of all data. It is clear that the minimal sensible displacement of the GNSS depends on the noise’s order of magnitude. In the case of horizontal displacements, the minimal sensible displacement is about +/− 2 mm while in the case of vertical displacements it is about +/− 4 mm.

The results of the statistical analysis are shown in

Table 5. Results of statistical analysis on GNSS1.

	Max	Min	Mean	Variance	Standard Deviation	Percentile 99.95%	Percentile 0.05%	Threshold
	[mm]	[mm]	[mm]	[mm2]	[mm]	[mm]	[mm]	[mm]
x	4.41	−7.20	0.00	0.30	0.55	2.11	−2.11	+/−2.11
y	4.07	−6.35	0.00	0.24	0.48	1.94	−1.92	+/−1.93
z	7.30	−12.45	0.00	1.35	1.16	4.28	−4.40	+/−4.34

.

4.1.2. Road Bridge

The statistical analysis was also carried out for the second case study. Indeed, the nature of both the structure and the test carried out led to different results in respect to the previous case. Moreover, due to the presence of peak displacements caused by the crossing of vehicles, it was decided to consider data, in between the quantiles of order 99.5 and 0.05, as noise. For the sake of brevity, it was decided to show only the results referring to GNSS 2 during the 1 h interval measurement that was acquired from 1:31 AM to 2:31 AM on 24 September 2021. Figure 26 shows the results of the statistical analysis carried out on the x, y and z signal. Figure 27 shows the normal distribution for the three signals. Figure 28 shows the limits along the three axes of the minimal sensible displacement of the GNSS. Noticeably, the minimal horizontal sensible displacement is about +/− 5 mm while the vertical one is about +/− 10 mm.

The results of the statistical analysis are shown in

Table 6. Results of statistical analysis on GNSS2.

	Max	Min	Mean	Variance	Standard Deviation	Percentile 99.5%	Percentile 0.5%	Threshold
	[mm]	[mm]	[mm]	[mm2]	[mm]	[mm]	[mm]	[mm]
x	10.55	−6.52	0.06	2.87	1.70	5.04	−4.32	+/− 4.68
y	8.21	−7.80	−0.09	3.29	1.81	4.96	−4.89	+/− 4.93
z	22.84	−36.04	−0.17	11.06	3.33	9.26	−8.27	+/− 8.77

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