accuracy improvement of the prestressed concrete

16th International Multidisciplinary Scientific GeoConference SGEM 2016, www.sgem.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-59-9 / ISSN 1314-2704, June 28 - July 6, 2016, Book2 Vol. 2, 799-806 pp, DOI: 10.5593/SGEM2016/B22/S10.102

ACCURACY IMPROVEMENT OF THE PRESTRESSED CONCRETE STRUCTURES PRECISE GEOMETRY ASSESSMENT BY USE OF BUBBLE MICRO-SAMPLING ALGORITHM

Krystyna Nagrodzka-Godycka1 Jakub Szulwic2 Patryk Ziółkowski1 1

Department of Concrete Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Poland 2 Department of Geodesy, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Poland

ABSTRACT Prestressed concrete structures are well-known technology for a vast period, but nevertheless, this very technology is a leading solution, currently used in construction industry. Prestressed concrete structures have a huge advantage over conventional methods because it uses the properties of concrete in a very efficient way. The main idea behind this technology is to introduce into the cross-section of the structure, the internal forces which are opposed to external loads effects. Authors have proposed a method to improve the accuracy of the geometry measurement in prestressed concrete structures using Terrestrial Laser Scanning (TLS). The method raised by the authors is based on Spheres Translation Method, which was developed to study geometry deformation of concrete elements subjected to failure. The new solution, prepared by the authors, enhanced Spheres Translation Method with the generation of additional points in the cloud using a Monte Carlo simulation. Monte Carlo simulation used in point cloud generation gives a better estimation of the marker position which leads to a better motion tracking for the geometry of the object being scanned. Geometry assessment of prestressed reinforced concrete beam has been performed by use of TLS. Prestressed reinforced concrete beam has been subjected to failure and scanned by Terrestrial Laser Scanner. Obtained data has been post-processed in dedicated software. Failure test was carried out in a Regional Laboratory of Civil Engineering by Concrete Structures Department at the Gdansk University of Technology, as a part of research focused on optical methods development for the diagnosis of concrete structures. Keywords: terrestrial laser scanning, concrete structure, concrete elements diagnostic, teledetection, remote sensing INTRODUCTION In recent years, there was substantial progress in the development of contactless threedimensional measuring methods. Among the others contactless measurement techniques use visible light or a coherent light, as an information carrier [2, 5, 11]. Due to the rapid

16th International Multidisciplinary Scientific GeoConference SGEM 2016

development of computers computational power, contemporary measurement systems allows conducting an advanced operation on collected data. Modern optic contactless systems based on measurement of reflection or light scattering from the surface of the object. Numerous of optical methods decreasing and become more various, which are divided into two groups passive and active. Passive and active methods mean that passive do not require artificial light source and on the contrary active does. Laser scanning and structural light method involve light emission, coherent in a case of laser scanning and incoherent in a structural light method. In details, active methods involve projection a numerous of light formation on the scanned object, such as grids, lines, strips, and points. Additional light sources are sometimes used in the measurement of passive exposure to the characteristic points, in order to accelerate the process of measuring, light lamps in Aramis system, developed by GOM. Terrestrial Laser Scanning (TLS) is a popular method of contactless measurement method used mainly in surveying sciences. The new field of application, which relatively recently occurred is the use of TLS in non-destructive diagnostics of concrete structures. The weak spot of TLS is its adequacy in a measurement of small objects, or measurement fields, which include a precise tracking of changes on the scanned surface, which has been described in the literature [1, 4, 5]. However, research conducted by the authors within the previous project indicated that accuracy of TLS data might be increased in the postprocessing stage [6, 10]. The accuracy of measuring geometrical deformation is particularly essential in the analysis of prestressed concrete elements. In this paper, authors proposed a solution that may improve the accuracy of TLS usage, by increasing the accuracy of markers position estimation during post-processing stage. The algorithm developed by the authors involves a use of Monte Carlo method [3, 8, 9] to enhance the density of the point cloud. The algorithm framework has been created as a continuation of a research project conducted at the Gdansk University of Technology. TERRESTRIAL LASER SCANNING IN BRIEF DEFINITION Terrestrial laser scanning, which is used to research presented in this article is a method based on the time of flight. Due to the fact that light travels at a constant speed, measuring the time shift between the pulse emission of the light and returning it offers a very convenient way to gauge the distance of a point on the object surface of the source optical signal. The method is based on the time of the return pulse is also known as light detection and ranging (LIDAR). Scanners using this approach and high-speed rotating mirrors to scan the beam along the object so that it can be measured by a series of points. In order to generate additional textures, the survey must be performed along with photo capture. The accuracy of the measurement depends on the accuracy of the measurement time, early detection pulse, the distance from the measured object, drift and fluctuations in consumer electronics and weather conditions affecting the visibility. Another system, that base phase shift of laser light might also distinguish among these systems. BUBBLE SAMPLING ALGHORITM IN GENERAL THEORY The principle of operation is based on bubble sort algorithm. The algorithm uses cycles of comparing pairs of adjacent elements and swap their order in case of the nonstandard set of ordinal. This operation is performed until the entire collection is sorted. The exact specification of the problem is illustrated Tab. 1 and Fig. 1. The bubble sort algorithm is well described in the literature.


Table 1: Output, input and auxiliary variables.

𝑛

- The number of elements in the sorted set, 𝑛 ∈ 𝑁

𝑑[]

- A set of n-element which will be sorted. Are elements of the set of indices 1 𝑡𝑜 𝑛. - A sorted set of n-element. Are elements of the set of indices 1 𝑡𝑜 𝑁.

𝑑[]

Auxiliary variables

𝑖, 𝑗

List of steps

Output data

Input data

Variable/Array

- Loop control variables 𝑖, 𝑗 ∈ 𝑁

1. 𝑓𝑜𝑟 𝑗 = 1,2, . . . , 𝑛 − 1: 𝑒𝑥𝑒𝑐𝑢𝑡𝑒 2 2. 𝑓𝑜𝑟 𝑖 = 1,2, . . . , 𝑛 − 1: 𝑖𝑓 𝑑[𝑖] > 𝑑[𝑖 + 1], 𝑡𝑜 𝑑[𝑖] ↔ 𝑑[𝑖 + 1] 3. End

Figure 1: Flowchart of bubble sort algorithm. BUBBLE MICRO-SAMPLING ALGORITHM IN GEOMETRY ASSESMENT As a part of the research focused on the development of the methods for precise geometry assessment of prestressed concrete structures. The authors proposed the algorithm, which may improve measurements and increase accuracy. Prestressed concrete beam has been properly prepared before the test. Rectangular grid has been superimposed on the surface along with the degree of signal tags (round plates on the surface), the beam is shown in Fig. 2.


Figure 2: Prestressed concrete beams in the test set-up. The beam in the course of loading underwent the deformation, until failure. The deformation caused by the load resulted in the displacement and rotation of rectangular fields, which has been superimposed on the lateral surface of the beam, which has been shown in Tab. 2. Table 2: Displacement and rotation of rectangular on the surface of the beam. The view before the load has been applied

The view after the load has been applied

The individual scans have been performed for each increment of the load force. In the course of the excessive loading the displacement and rotation of the characteristic rectangles has increased. In order to determine changes on the surface of the beam, the authors proposed Bubble Micro-Sampling Algorithm, which is based on bubble sort algorithm, described in the previous chapter. The method has boundary conditions and limitations, mainly arising out of very nature point cloud post-processing.


Figure 3: Terrestrial Laser Scanner - reproduction of the environment in the form of the dense cluster of points, called point cloud. Terrestrial Laser Scanner in the course of measurement, illuminates the surrounding objects by generated laser beam and reproduce the existing state of the environment in the form of the dense cluster composed of a vast number of closely spaced points (Fig. 3). During the device operation, the laser beam goes from the top to the bottom. Depending on the adopted resolution creates long vertical strings of points with the characteristic structure shown in Tab. 3. The model spaces for every considered state of the object must have identical coordination system. Therefore, the use of signal tags registration is inexpedient. Table 3: “Chains” of points in Point Cloud cluster.

Steady distribution

Chaotic distribution

By use of these vertical sequences and the micro-sampling bubble algorithm, changes might be identified. The framework assumes checking the vertical strings on points and the corresponding points in the horizontal direction. However, evenly distributed points may become distorted corresponding to a various angle of the laser beam. The laser beams that pursuing the object undergo interference, which leads to chaotic distribution on points (Tab. 3). Because of such unpredictability in points distribution and obstacles to get even points location pattern in the whole point cloud, the authors decided to divide the surface of analysed objects into Micro-Clusters. The role of the Monte Carlo algorithm is based on increasing the point clouds density, to better define the intensity character of the Micro-Cluster. Monte Carlo sampling creates a new layer populated with a point sampling of the current mesh. Samples are generated in a randomly uniform way, or with a distribution biased by the per-vertex quality values of the mesh. Monte Carlo sampling has as essential meaning, without it some spots are well-dense


and the others very poorly dense, which may interfere the local map intensity value. Notwithstanding to handle a complex matter of Monte Carlo sampling, one of the computation methodologies must be considered. Computing expectation problem with the use of Monte Carlo has been described [3, 8, 9]. 𝑝(𝑥)

∫ 𝑓(𝑥) 𝑝(𝑥) 𝑑𝑥 = ∫ 𝑓(𝑥) 𝑞

𝑔(𝑥) 𝑑𝑥 ≈ 1⁄𝑛 ∑𝑛𝑖=1

(𝑥)

𝑝(𝑥𝑖 ) 𝑞(𝑥)

𝑓(𝑥𝑖 )

(1)

In order to reduce a bias introduced by sampling from the improper distribution, the use of 𝑞(𝑥) , with importance weights showed as followed 𝑝(𝑥𝑖 ) ⁄𝑞(𝑥𝑖 ) has been conducted. Where 𝑝(𝑥𝑖 ) = 𝑝̃(𝑥) ⁄𝑧𝑝 and 𝑞(𝑥𝑖 ) = 𝑞̃(𝑥) ⁄𝑧𝑞 . Importance sampling might be used during approximation of 𝑧𝑝 and 𝑧𝑞 , while 𝑟𝑖 = 𝑝̃(𝑥) ⁄𝑞̃(𝑥) . 𝑝̃(𝑥)

𝑧𝑞

∫ 𝑓(𝑥) 𝑝(𝑥) 𝑑𝑥 = 𝑧 ∫ 𝑓(𝑥) 𝑞̃ 𝑝

𝑧𝑞 𝑧𝑝

1

𝑝̃(𝑥)

𝑝

(𝑥)

= 𝑧 ∫ 𝑝̃(𝑥) 𝑑𝑥 = ∫ 𝑞̃

𝑝̃(𝑥) 𝑧𝑞 𝑧𝑞 𝑞(𝑥) 𝑑𝑥 ≈ 𝑧 1⁄𝑛 ∑𝑛𝑖=1 𝑞̃ 𝑓(𝑥𝑖 ) = 𝑧 1⁄𝑛 ∑𝑛𝑖=1 𝑟̃𝑖 𝑓(𝑥𝑖 ) (2) 𝑝 𝑝 (𝑥) (𝑥)

𝑞(𝑥) 𝑑𝑥 ≈ 1⁄𝑛 ∑𝑛𝑖=1 𝑟̃𝑖

(3)

̃ (𝑥) 𝑝

∫ 𝑓(𝑥) 𝑝(𝑥) 𝑑𝑥 = ∑𝑖

̃ (𝑥) 𝑞

∑𝑖

̃ (𝑥) 𝑝

𝑓(𝑥𝑖 )

(4)

̃ (𝑥) 𝑞

Probability might be described as followed

𝑝̃(𝑥)

𝑝̃(𝑥)

(𝑥)

(𝑥)

𝑤𝑖 = 𝑞̃ ⁄∑𝑖 𝑞̃ , where 𝑥𝑖 has been

sampled from 𝑞(𝑥) . Good match between 𝑞(𝑥) and 𝑝(𝑥) is desirable, otherwise, a base of generated samples should be increased. Micro-Clusters divides analysed surface into the even grid of parallelograms while each parallelogram comprises an unspecified number of points forming a point cloud model of the analysed element arranged at random in the grid area (Fig. 4). It is assumed that each parallelogram has a certain amount of points, which averaged intensity value (gathered from maps on intensity) from each point, represent the character of considered Micro-Cluster area.

Figure 4: Micro-Clusters samples of points in the point cloud The bubble micro-sampling algorithm is designed to reverse the process of deformation virtually. The idea of tracing the imperceptible elements has been derived from the Translation Spheres Method described by the authors in previous works. While knowing


the steps that led to the particular type of deformation, the displacement and rotation object after deformation might be identified. Concerning the operation of the algorithm proposed by the authors, the following analysis has been illustrated in Tab. 4. The grid is shown in Tab. 4 represents a grid of Micro-Clusters. Table 4: The two states of the considered surface divided on Micro-Clusters at a time.

a.

b.

c.

d.

a. The element before deformation. b. The element after deformation. c. The element before the deformation imposed on the image after deformation. d. Directions of the points movement during execution of the algorithm. LEGEND - The position of the object before deformation. - The position of the object before deformation. - Fields with the same Intensity value, which overlapping on each other. CONCLUSION Structural analysis using the Terrestrial Laser Scanning is a new scientific field, which evolves is a very fast rate. Laser scanners, year by year, become quicker and more accurate. Modern laser scanners, unlike its predecessors, allow scanning with high resolution in a very short time. However, despite the enormous progress in the development of hardware, currently, the biggest challenge a stage of point cloud postprocessing. The framework of the algorithm presented by the authors focused on improving an accuracy of the element position estimation and also lays the groundwork for automated computation of point cloud. The method tabled by the authors might have significant value is prestressed concrete deformation measurement. The solution proposed by the authors involves the equalization of the point cloud density, by use of Monte Carlo sampling. Unified point cloud has to be divided into Micro-Clusters, which contains the information of average intensity value of the area fenced by the cluster. The division is executed for both object states, deformed and not deformed. The


model spaces for every considered state of the object must have identical coordination system, use of signal tags registration is inadvisable. Undeformed object state is treated as a model reference space. The aim of the bubble sort of every Micro-Cluster (which represent average intensity value of fenced area) it to reverse the transition from deformed state to the reference one. Due to retrogression caused by bubble sort, every move of the Micro-Cluster is registered, which gives information about local displacement and rotation. Displacement and rotation of objects superimposed on the lateral surface of the prestressed concrete element allows assessing certain deformation state. The analysis has been carried out as a part of the research focused on the development of contactless optical techniques with application in concrete structures studies, conducted at the Gdansk University of Technology. REFERENCES [1] Bencardino F., Condello A.: Experimental study and numerical investigation of behavior of RC beams strengthened with steel reinforced grout. Computers and Concrete, Vol. 14, Iss. 6, pp. 711-725, 2014, DOI:10.12989/cac.2014.14.6.711 [2] Bobkowska K., Janowski A., Przyborski M.: Image correlation as a tool for tracking facial changes causing by external stimuli. Book Series: International Multidisciplinary Scientific GeoConference SGEM, ISSN 1314-2704, Book 2, Vol. 1, 2015, pp. 1089-1096, 2015, DOI:10.5593/SGEM2015/B21/S10.139; [3] Glover J., Bradski G., Rusu R.B.: Monte Carlo Pose Estimation with Quaternion Kernels and the Bingham Distribution. Robotics: Science and Systems. The MIT Press, Cambridge-Massachusetts, 2012 [4] Gordon S., Lichti D.: Modeling terrestrial laser scanner data for precise structural deformation measurement. Journal of Surveying Engineering, Vol. 133, Iss. 2, pp. 72-80, 2007, DOI:10.1061/(ASCE)0733- 9453(2007)133:2(72) [5] Hejmanowska B., Kaminski W., Przyborski M., Pyka K., Pyrchla J.: Modern remote sensing and the challenges facing education systems in terms of its teaching. EDULEARN15 Proceedings, ISBN 978-84-606-8243-1, ISSN 2340-1117, 7th International Conference on Education and New Learning Technologies, Barcelona, Spain, pp. 6549-6558, 2015 [6] Janowski A., Nagrodzka-Godycka, K., Szulwic, J., Ziółkowski, P.: Remote sensing and photogrammetry techniques in diagnostics of concrete structures. Computers & Concrete, 2016 [7] Kowalska E., Rutkiewicz E., Szumiło M.: The digital image correlation system in experimental tests of bended beam. 2016 Baltic Geodetic Congress (Geomatics), 23.06.2016, Gdansk, Poland, 2016 [8] Kulis, B., Ashari, A.: Monte Carlo Sampling Methods, CSE 788.04: Topics in Machine Learning, Ohio, 2012. [9] Metropolis N., Ulam S.: The Monte Carlo method. Journal of the American Statistical Association, Vol. 44, Iss. 247, pp. 335-341, 1949, DOI:10.2307/2280232 [10] Nagrodzka-Godycka, K., Szulwic, J., Ziółkowski, P., The method of analysis of damage reinforced concrete beams using terrestrial laser scanning, 14th SGEM GeoConference on Informatics, Geoinformatics and Remote Sensing, Vol. 3, pp. 335342, Bulgaria, 2014, DOI:10.5593/SGEM2014/B23/S10.042 [11] Rucka M., Wilde K.: Experimental Study on Ultrasonic Monitoring of Splitting Failure in Reinforced Concrete. Journal of Nondestructive Evaluation, Vol. 32, Iss. 4, pp. 372-383, 2013,DOI:10.1007/s10921-013-0191-y.