Horizontal and vertical positions of points for the control assessment of crane rails are classically determined separately. The procedure is time consuming and causes non-homogenous accuracy of the horizontal and vertical position of control points. The proposed alternative approach is based on polar measurements using a high accuracy total station instrument and a special platform with two precise surveying prisms fixed on it. Measurements are carried out from a single station thus ensuring a common coordinate system and homogenous accuracy. The position of the characteristic point of a rail is derived from the measured positions of both prisms with known geometry of the platform. The influence of platform non-horizontality is defined, along with its elimination procedure. Accuracy assessment is ensured with redundant measurements. Result of the proposed procedure is a numerical and graphical presentation of characteristic points. The control parameters required in international Eurocode standards are easily determined from them.

This article presents a method for measuring the geometry of crane rails with terrestrial laser scanning (TLS). Two sets of crane rails were divided into segments, their planes were adjusted, and the characteristic rail lines were defined. We used their profiles to define the positional and altitude deviations of the rails, the span and height difference between the two rails, and we also verified that they complied with the Eurocode 3 standard. We tested the method on crane rails at the hydroelectric power plant in Krško and the thermal power plant in Brestanica. We used two scanning techniques: “pure” TLS (Riegel VZ-400) and “hybrid” TLS (Leica MS50) scanning. This article’s original contribution lies in the detailed presentation of the computations used to define the characteristic lines of the rails without using the numeric procedures from existing software packages. We also analysed the influence of segment length and point density on the rail geometry results, and compared the two laser scanning techniques. We also compared the results obtained by terrestrial laser scanning with the results obtained from the classic polar method, which served as a reference point for its precision.

TLS is nowadays often used for deformation monitoring. As it is not able to scan identical points in different time epochs, mathematical models of objects derived from point clouds have to be used. The most common geometric form to describe built objects is a plane, which can be described by four parameters. In this study, we aimed to find out how small changes in the parameters of the plane can be detected by TLS. We aimed to eliminate all possible factors that influence the scanning. Then, we shifted and tilted a finite physical representation of a plane in a controlled way. After each controlled change, the board was scanned several times and the parameters of the plane were calculated. We used two different types of scanning devices and compared their performance. The changes in the plane parameters were compared with the actual change values and statistically tested. The results show that TLS detects shifts in the millimetre range and tilts of 150″ (for a 1 m plane). A robotic total station can achieve twice the precision of TLS despite lower density and slower performance. For deformation monitoring, we strongly recommend repeating each scan several times (i) to check for gross errors and (ii) to obtain a realistic precision estimate.

This article deals with the characteristics of deformation of a body or a figure represented by discrete points of geodetic network. In each point of geodetic network kinematic quantities are considered normal strain, shear strain, and rotation. They are computed from strain and rotation tensors represented by displacement gradient matrix on the basis of known point displacement vector. Deformation analysis requires the appropriate treatment of kinematic quantities. Thus statistical properties of each quantity in a single point of geodetic network have to be known. Empirical results have shown that statistical properties are strongly related to the orientation in single point and local geometry of the geodetic network. Based on the known probability distribution of kinematic quantities the confidence areas for each quantity in a certain point can be defined. Based on this we can carry out appropriate statistical testing and decide whether the deformation of network in each point is statistically significa...

This article discusses the method of computing the values of the unknowns under the condition of the minimum sum of the squares of the residuals of the observations, also known as the least squares method, with the additional condition of taking into account the errors in the unknowns. The problem has already been treated by many authors, especially in the field of regression analysis and the computation of transformation parameters. We give an overview of the theoretical foundations of the least squares method and extensions of this method by considering the errors in the unknowns in the model matrix. So, the total least squares method is presented in this paper, fitting the regression line to a set of points and computing transformation parameters for the transition between the old and the new Slovenian national coordinate systems. Furthermore, for the first time, the method is also presented and tested in the S-transformation between different geodetic datum-dependent solutions. Also, for the first time, we systematically compare the results of the approach with conventional approaches in all three considered tasks. With the results based on relevant statistics, we confirm the suitability of the described method for dealing with the considered computational tasks.

Deformation analysis is a complex procedure where, based on several periodic geodetic measurements, displacements of points in the geodetic network are detected and determined. On this basis, movements and deformations of the built and natural environment are detected. The article discusses the Squared Msplit estimation, an extension of the maximum likelihood method, which is one of the procedures used in deformation analysis. The equations of the Squared Msplit estimation are derived and the method is presented on 2D geodetic network case study. The effectiveness of the presented method is compared with the results of other deformation analysis approaches performed with the same numerical example. The results obtained using the Squared Msplit estimation slightly differ from the simulated values, with the maximum discrepancy being 11.5 mm at unstable points and 10.4 mm at stable points, which are satisfactory results. The findings indicate that the Squared Msplit estimation provides results comparable to other methods. Therefore, it is considered suitable for deformation analysis and can be regarded as one of the applicable procedures in this field.