Application of the Msplit Estimation Method in the Detection and Dimensioning of the Displacement of Adjacent Planes

Abstract

Building constructions are exposed to various forces and natural phenomena. Some of them are sudden and violent, e.g., an earthquake or heavy rains, causing a displacement of the ground. Other phenomena affect objects on a longer-term, e.g., vibrations caused by daily road traffic. Sometimes, building structures may have defects due to incorrect construction. In any case, if an engineering object shows changes in the relation to its correct geometry or position, deformation and displacement measurements are required. Engineering objects are also monitored during their construction. Nowadays, it is important to perform measurements quickly and with high accuracy. The use of a Terrestrial Laser Scanning (TLS) allows for the required measurement speed and accuracy. This measurement technology allows a large dataset, which can be arbitrarily elaborated, to be obtained. The structure of building objects can include vertices, lines, planes, and other shapes and can be described using mathematical functions. This allows data processing to be automated. In this article, we present the Msplit method as an effective approach to the processing of data obtained as a result of TLS measurements. The proposed approach is new because until now, the Msplit estimation method has not been used to detect adjacent planes in one-point cloud obtained from TLS. The Msplit estimation method allows a functional model to be split into two or more competitive models and thus two or more entities in a point cloud to be estimated simultaneously. Four different objects measured using TLS are presented: two objects representing vertical displacements and two objects representing horizontal displacements. The test results and analysis confirm that the Msplit estimation method can be successfully applied in the detection of adjacent planes.

Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

“…This paper presents an application of two variants of M split estimation, i.e., the SMS and AMS estimation, in the context of the determination of profiles of the terrain surface based on TLS data. Let us recall that up to now, the SMS estimation was applied in several problems of the laser scanning data analysis [1,15,22,31]. It was proved that the method in question could provide satisfactory results in the context mentioned.…”

“…As mentioned earlier, one of the variants of M split estimation, namely SMS estimation, was applied in several laser scanning data analyses [1,15,22,31]. We will discuss them in chronological order.…”

“…The SMS estimation's newest application in the context of laser scanning data processing is the detection and dimensioning of the displacement of adjacent planes in a point cloud acquired from TLS [15]. The paper presents tests which concerned the objects representing vertical planes (namely the fragment of the precast concrete wall and the fragment of the concrete slabs of a retaining wall) as well as the objects representing horizontal planes (namely the segment of the asphalt road and the fragment of the pavement).…”

“…Depending on the type of platform, there is airborne laser scanning (ALS), terrestrial laser scanning (TLS), satellite laser scanning (SLS) and mobile laser scanning (MLS) [1,2]. All types of laser scanning have a wide range of applications, e.g., terrain surface and vegetation cover measurements and digital terrain model (DTM) generation [3][4][5][6][7], building detection and their condition diagnosis [8][9][10][11][12], displacement detection [13][14][15], modeling of cultural heritage sites or object structures [2,13,16], registration roads, railways or power lines [17,18], monitoring coastal zones [19], mining damages and ground disasters [20,21].…”

“…Applications of M split estimation concerned so far not only processing of TLS data (presented in [1,15,22,31]) but also deformation analyses [29,30,[32][33][34][35][36], direct identification of gross errors [37], linear regression analyses [30,34], robust coordinate transformation [38], S-transformation [39] and marine navigation [40]. Most of these applications applied only the squared M split estimation (SMS), of which the objective functions stem from the assumption that observation errors are normally distributed.…”