The Concept of Accuracy Analysis of the Vertical Displacements Gained from the Hydrostatic Levelling Systems’ Measurements

Abstract

Nowadays, hydrostatic levelling is a widely used method for the vertical displacements’ determinations of objects such as bridges, viaducts, wharfs, tunnels, high buildings, historical buildings, special engineering objects (e.g., synchrotron), sports and entertainment halls. The measurements’ sensors implemented in the hydrostatic levelling systems (HLSs) consist of the reference sensor (RS) and sensors located on the controlled points (CPs). The reference sensor is the one that is placed at the point that (in theoretical assumptions) is not a subject to vertical displacements and the displacements of controlled points are determined according to its height. The hydrostatic levelling rule comes from the Bernoulli’s law. While using the Bernoulli’s principle in hydrostatic levelling, the following components have to be taken into account: atmospheric pressure, force of gravity, density of liquid used in sensors places at CPs. The parameters mentioned above are determined with some mean errors that influence on the accuracy assessment of vertical displacements. In the subject’s literature, there are some works describing the individual accuracy analyses of the components mentioned above. In this paper, the author proposes the concept of comprehensive determination of mean error of vertical displacement (of each CPs), calculated from the mean errors’ values of components dedicated for specific HLS. The formulas of covariances’ matrix were derived and they enable to make the accuracy assessment of the calculations’ results. The author also presented the subject of modelling of vertical displacements’ gained values. The dependences, enabling to conduct the statistic tests of received model’s parameters, were implemented. The conducted tests make it possible to verify the correctness of used theoretical models of the examined object treated as the rigid body. The practical analyses were conducted for two simulated variants of sensors’ connections in HLS. Variant no. I is the sensors’ serial connection. Variant no. II relies on the connection of each CPs with the reference sensor. The calculations’ results show that more detailed value estimations of the vertical displacements can be obtained using variant no. II.

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