**5. Periodic Diagnostics of the Bridge One Year after It Was Built**

The next part of the research was focused on the periodic diagnostics of the bridge. In 2017 a scan of the whole unloaded steel shell had been made, which was repeated one year later. This enabled to check not only short-term elastic displacements, caused by real traffic conditions during final-acceptance and inspection, but also the eventual permanent displacement of the analyzed soil-steel structure. The periodic diagnostics is done to learn about the order of the bridge permanent displacements, whose occurrence is typical for this type of structures, during their exploitation. Here, great accuracy of measurements is not so important, as we expect that the displacements, that could have occurred, can be as big as a dozen or so mm. Therefore, additional improvement of scanning accuracy, as done for the purpose of short-term tests, presented in the Section 4, is not done.

In 2017, after short-term static tests were completed, the bridge was unloaded and scanning control points were stabilized in order to prepare for additional measurements. After that, full image of the bridge was registered. Because of the large dimensions of the structure, position of the scanner during the measurement process was changed 12 times. This process was repeated in the year 2018.

It needs to be emphasized that the surveying in 2018 was done at weather conditions similar to the ones observed the year before. Therefore, the results of periodic diagnostics are not affected by temperature variations.

As new scanning required new alignment of the device, the TLS accuracy could have been additionally checked. The Iterative Closest Points (ICP) algorithm was used to align scan positions correctly, besides of reference points that were stabilized outside of the structure. The positions of elements, which were used for the algorithm processing, were not changed during this time period and they have not been influenced by any external factors. The results of this alignment are presented in the form of histogram in Figure 15.

**Figure 15.** Histogram of residues which shows the precision of scan alignment.

The standard deviation resulting from the alignment was σ = 1.6 mm. Therefore, in order to reliably estimate the accuracy of the measurement, in accordance with the principles of normal distribution, we assumed that it is 3 × σ = ~5 mm. In consequence, the accuracy of computed deformation differences (registered in the period between 2017–2018) should have not exceeded this value.

As usual, the noise reduction was done during the process of point cloud data filtration. The noise reduction algorithm described in [55] was used here, which locally fits a surface into the point cloud and then remove points that are too far from that surface. In the end, it was possible to exclude points lying outside the possible deformation shape that had a negative impact on the final results and to retain only the ones maintaining reasonable accuracy.

After the noise reduction had been done, it was possible to calculate the periodic diagnostics displacements of the steel shell that occurred between the years 2017 and 2018. The method described in paper [56] (available in CloudCompare software) was used for this purpose. This particular approach was chosen because most of the available comparative methods are based on the determination of the closest distance from a point or require 3D modelling of the compared surface. Thereby, they eliminate the problem of roughness, which cannot be eliminated here, as the corrugation of the steel sheets is an important feature of the whole structure and cannot be omitted. To find the distances between two point clouds, two main steps were done. First, normal surface and its orientation in 3D was estimated on a scale consistent with local surface roughness. Then, the mean surface change was measured along the surface normal direction and the local confidence interval was determined. This, in our opinion, allowed to obtain reliable information about the structure, which has varying roughness, as evidenced by the observed noise in the cloud of points and terrain diversity. The roughness is also reflected by the average change along the surface normal direction, as it was done in the second major calculation step of this procedure. In effect the distances between two point clouds were obtained and the deformations contours (magnitudes of displacements) are shown in Figure 16.

The results of the calculations presented in Figure 16 reveal that the upper part of the bridge has moved to the south up to 7 mm, while the shell in the vicinity of foundation remained undeformed. To check the accuracy of the obtained deformations a series of statistical tests, based on the Gaussian normal distribution, were run. Figure 17 presents the statistics of the Gauss function corresponding to the calculated distance uncertainties. On this basis it can be stated that the results were correctly determined in relation to the reference shown in Figure 15.

**Figure 16.** Periodic diagnostics of bridge deformations (displacement magnitude) measured one year after the final acceptance and inspection.

**Figure 17.** Distance uncertainty statistic.

Owing to the above, the uncertainty of the measured deformations (Figure 16) equals approximately 2 mm (within the computed σ from alignment). This means that the laser scanning enabled to register all of the points characterizing the largest geometric changes. Nevertheless, this uncertainty suggests that some discrepancies of the measurements occurred during the scanning. These resulted possibly from the standard issues connected with stabilization of points, their indication, and establishment. However, because of the fact that the measurements were repeated one year after the final acceptance tests and during this period of time the construction works were still ongoing, such an accuracy of measurements is to a large extent satisfactory. For example in paper [51] laser scans of an external system were done using other techniques and the resulting precision and accuracy was not as good as here.

Periodic diagnostic deformation images were created also in sections 2-2 and 4-4, that were previously tested during static tests in 2017. This enabled to additionally cross-check calculations of deformations of the whole bridge, presented in Figure 16. To create them it was required to perform a number of computational operations, enabling interpretation of deformation changes of the bridge. The results obtained from scanning during short-term tests, were quite helpful in achieving this goal. Displacements of the unloaded steel shell one year after the final acceptance and inspection tests is shown in Figure 18 for the 2-2 section and in Figure 19 for the 4-4 section. The directions of the extreme values of displacements are also shown in Figures 18 and 19.

**Figure 18.** Displacements of the unloaded steel shell 2-2 section one year after the final acceptance and inspection tests.

**Figure 19.** Displacements of the unloaded steel shell 4-4 section one year after the final acceptance and inspection tests.

The aforesaid results reveal, that during one-year period of time, the bridge did not exhibit deformations below the black border line, marked in the figures and named as "displacement boundary". In view of that, we noticed a certain negative feature of the computed periodic diagnostics deformations (see Figures 16, 18 and 19). Despite attaining satisfactory result of calculations, the displacements were not obtained in the lower parts of the steel shell. However, because of the measurement accuracy, their exact values are not so certain and may rather indicate the displacement tendency. Similarly, this could have resulted from the properties of the algorithm used. On the other hand, what also is interesting, the "displacement boundary" intersects the shell approximately at the same height at which bolt connections were done (refer to Figure 3). As one year passed since the date of final acceptance tests, slippage of this connections could have occurred and some rotations of the shell have become possible in this areas. This may explain why displacements of the upper part of the shell are only observed. Hence, a research gap has been identified here. These aspects will be analyzed and addressed in further studies.

Finally, it can be concluded that the periodic diagnostics displacements measured one year after the final acceptance tests are relatively small, 7 mm ± 2 mm. Here, we would like to emphasize that the extreme values of permanent displacements are observed above the aforesaid "displacement boundary." Therefore, maximum and certain displacement of the bridge did not exceed 9 mm. This is a very important information as the order of the permanent displacement was identified. Occurrence of deformation of this order is typical for soil-steel structures. Thus, the bridge experienced a change of its shape, which however does not affect its response and load-bearing capacity.
