**1. Introduction**

Among the technical parameters for assessing the structural health, the displacements are probably the most relevant. The structural suitability is verified by loading a structure with known loads and comparing the actual displacements with those expected in the design phase.

As for bridges, some trucks of known weight, arranged in one or more rows, are positioned on the deck in predetermined positions. Levels or total stations are used to measure beam deflections; additional dynamic tests are performed, depending on the importance of the structure [1].

For Structural Health Monitoring (SHM), along with the deformations, di fferent physical and mechanical parameters are measured. A broad overview of the methodologies used can be found in [2]. Below is a short list of noteworthy techniques: (a) The structural vibration data are increasingly used; a review of vibration-based methods can be found in [3], where natural frequency-based, mode shape-based and curvature/strain mode shape-base methods are described; (b) Instrumented vehicles are more and more used for indirect bridge monitoring. This technique allows measurements without the need to place sensors on the deck or on the piers; references can be found in [4]; (c) Acustic Emission (AE) is an e ffective technique, used since several decades [5]; this method, as the X-ray methods, requires to roughly know the position of damages, along with the accessibility for performing tests; (d) Magnetic sensing is used in particular in structures that contain ferrous elements such as reinforced concrete [6]; (e) Ground Penetrating Radar (GPR) is increasingly adopted both to identify hidden lesions and to find discontinuities in structural materials [7].

For detecting and monitoring structural displacements, both conventional and innovative methods are used; below are some of the most used, with their pros and cons. (1) Digital levels are still among the most used tools, thanks to their high accuracy. Their main limit is the need to measure one target at a time, so they cannot be used to dynamically monitor multiple points; (2) Total robotic stations are characterized by high precision and measurement automation. Thanks to the capability to transfer data even via the Internet and be managed remotely, they are used to monitor slopes and large structures [8,9]. The sampling frequency up to 7 Hz allows its use for dynamic measurements [10,11], but it is not possible to track more points at the same time; (3) GNSS satellite surveying is often used for tall buildings and large span bridges [12–14]. It is possible to obtain an accuracy of a few millimeters, while the acquisition frequency reaches 20 Hz. The main limitation lies in the need to place an antenna on each point one must monitor; (4) The increase in the resolution of digital cameras facilitated the development of computer vision based systems. Among the techniques used, digital image correlation (DIC) has proved to be e ffective for measurements of bridge deflection [15–20]; (5) Dial gauges, widely employed for measurements of floor slabs deflections, are used for bridges with limited height and in absence of water; (6) The use of inclination parameters obtained from microelectromechanical systems (MEMS) has been proposed to derive the deflection [21]. The high S/N ratio, typical of these devices, strongly influences the results of dynamic tests; (7) Currently, the measurement of deflections by using laser beams is widespread. Some systems for the measurement of deflections and displacements with the use of laser beams are described in [22,23]; (8) An e ffective methodology for measuring displacements of large structures is o ffered by Ground-Based Synthetic Aperture Radar (GB-SAR).Used in RAR mode (Real Aperture Radar) it allows measurements of vibration frequency and displacements associated with dynamic loads. In SAR mode (Synthetic Aperture Radar) the instrument is mounted on a slide and allows to obtain the mapping of the area investigated at di fferent times and to ge<sup>t</sup> the deflection of each point. In both cases the precision of the displacement measurements is about 0.1 mm. This technique is increasingly used, but is still limited by the high cost of the instrumentation [24,25].

Nowadays TLS is a widespread and reliable technique for monitoring bridges in static conditions [26]. Comparing the scans acquired in di fferent epochs, we can get, e.g., the maps of deviations between the surface points of a bridge subject to various conditions (loads, temperature, etc.). As for dynamic monitoring, it is possible to take advantage of the high sampling rate of TLS; specifically, we can measure the deflections of a bridge superstructure dynamically. In this regard a point-surface based method has been proposed in [27].

We can see that, even if the coordinates of the single points obtained by a TLS are of low precision (±2 mm to ±20 mm), a 2D/3D model of the entire point cloud can be e ffective for detecting the shape of a structure and its changes. Therefore, if the goal of a TLS survey is to model a line or a surface starting from a number of points, we can observe that the best interpolating line/surface has generally a rather better precision than any single point; for this reason, the reconstructed lines/surfaces show a better precision than the one declared by the manufacturers. In other words, a modeled surface will represent an object more precisely than the unmodeled observations.

Starting from this remark, Gordon and Lichti [26] have developed a methodology devoted to the measurement of the deformation of structures. At the basis of the method are theoretical elements of mechanics of beam. For its implementation, least-squares are used. This method is based on obtaining analytical models that represent the physical bending of a structure and, in particular, of a beam.

The models, derived from the governing di fferential equation for the elastic curve, are represented, in the case of simple static schemes, by low order polynomials. The coe fficients, treated as unknown parameters, are estimated by solving a least squares procedure. Such a method is e ffectively applicable when two conditions are satisfied: (a) the theoretical model and the real structure are really similar and

(b) the structure had not experienced events such as yielding of foundation or phenomena such as relaxation and creep.

In this paper, in light of all the above considerations, a methodology has been developed that allows to obtain the displacements and, consequently, the elastic curve of a structure using a TLS. The instrument must be configured as a line scanner and able to provide line scans, along with the timestamp for the detected points [28]. The displacements at time *t* are given by the di fference between the best fitting line of the points acquired at the same time for a bridge with a loaded deck, and the fitting line obtained for the unloaded bridge. These displacements provide the instant elastic curve of the structure subject to the mobile load present at the time *t*.

The procedure can also be used for vertical structures subjected to loads with a horizontal component (tall buildings, pylons, etc.). The main characteristics of the method are: (1) Ease of installation; (2) The accuracy required to monitor the deflection of the bridges; and (3) High acquisition rate (up to 120 lines per second) useful for monitoring phenomena characterized by rapid changes.

The methodology for dynamic monitoring of displacements and the elastic curves of the structures presented below, is characterized by high precision, is easily implementable and can be e ffectively used within the SHM. It is worth mentioning that the steps of Structural Health Monitoring are: (1) Determination of damage existence; (2) Determination of damage's geometric location; (3) Quantification of damage severity and (4) Prediction of remaining life of the structure. The methodology presented concerns the first and third steps. To perform the others, it is generally necessary to integrate various information, coming from di fferent types of sensors, with an accurate model of the structure to be analyzed. We should stress that TLS is a non-destructive technique performed remotely. Such techniques usually require a priori knowledge of the damaged region. As for the first and the third phases, the determination of damage existence and its quantification can be obtained by comparing the deflections measured with those expected in a design phase or obtained by previous measurements.

One of the main features of this methodology lies in the synchronization of measurement of deflections and positioning of mobile loads. Three experimental tests performed on as many bridges demonstrated its e ffectiveness and precision.

The topics covered in this paper are: (1) the methodology description; (2) the hardware components (Terrestrial Laser Scanner, Total Station, Digital Camera, GNSS receiver, Computer); (3) the software implemented, (4) the in-field tests; and (5) the discussion of results.
