MODIFICATION OF INTERSECTION TECHNIQUE IN MONITORING THE ENGINEERING STRUCTURES

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1 International ITRTIOL Journal of ivil ngineering JOURL and Technology OF IVIL (IJIT), GIRIG ISS D (rint), ISS (Online), Volume 5, Issue, December (04), pp IM TOLOG (IJIT) ISS (rint) ISS (Online) Volume 5, Issue, December (04), pp IM: Journal Impact Factor (04): (alculated by GISI) IJIT IM MODIFITIO OF ITRSTIO TIQU I MOITORIG T GIRIG STRUTURS ossam l-din Fawzy Lecturer, ivil ngineering Department, Faculty of ngineering, Kafr l-sheikh University, Kafr l-sheikh, GT STRT ost and accuracy required are the two important factors that decide on the appropriateness of intersection technique method for a certain setting out and deformation problems. In this paper, modification of intersection technique by three methods used to determine the coordinates of points and its associated accuracy during the process of setting out and structural deformation of engineering structures by three methods is presented. The main objective of this paper is tried to find the best location of two/three total stations with respect to the building facade under consideration. pplication of Genetic lgorithm for finding an ideal solution for the accuracy problem is presented also to make it possible for determining the optimum layout of the total station and also to determine the object accuracy, for any instrument set- up, right in the field. This paper gives also the sequence of the field operations and computational steps for this task. numerical example is included to reinforce the theoretical aspects. Keywords: Intersection, Total Station, ccuracy, Monitoring, Genetic lgorithm. - ITRODUTIO Deformation of structures is a problem that demands the engineer s attention. The intersection method has been widely used for determine the dimensional coordinates of any points. In this work, the three methods of intersection (angular, linear and multi stations) are modified to obtain a minimal error in coordinates of any point under monitoring system. The problem which faces the intersection is in determining the optimum positions of the total stations relative to the object in order to achieve the required accuracy. So far, there have been no satisfactory mathematical formulas, in the field of intersection, which allows determine the optimum layout of the total stations. 56

2 ISS (Online), Volume 5, Issue, December (04), pp IM - MODIFITIO OF GULR ITRSTIO FOR LULTIG T OIT OORDITS ngular intersection is a well known method used to determine the artesian coordinates of any point during the process of setting out and monitoring the deformation of engineering structures []. ngular intersection can be done practically by using Theodolite or total station. For achieving accurate results of observations of the process of setting out and structural deformation monitoring, the suggested geodetic technique recommend that each monitoring point must be observed from three occupied stations as shown in figure. The four horizontal angles to each object point i are α, β, α and β. These observations must be observed from three occupied known stations, and respectively (Fig. ). These observations can be done using advanced accurate theodolite or total station. Figure (): Geometry of observations using the suggested modified angular intersection The suggested modification technique can be summarized by determining the coordinates and associated accuracy of observed point from three occupied stations (oints, and, Fig. ). The coordinates of observed point will be calculated from each two individual points (from and then from and ) and its associated accuracy. y comparing the results values and accuracy, the corrected values can be determined. The horizontal coordinates (, ) of observed points can be calculated by using formulae of angular intersection in dependence on the two angular measurements α, β from two occupied known points as follows (Fig. ): cot β cot α ; ot α ot β cot β cot α. ot β ot α () The horizontal coordinates (, ) of observed points can be calculated by using formulae of angular intersection in dependence on the two azimuths line from two occupied known points as follows: 57

3 ISS (Online), Volume 5, Issue, December (04), pp IM Where: azimuth of line () azimuth of line () or disadvantage of this method of point positioning is that there is no check on the calculations []. In dependence on the errors of measuring horizontal angles, the error in point position M can be determined using the following formula: M // b mα // ρ sinγ sin sin α β. () Where: (b) ase line (the distance between the two occupied stations and can be calculated from the coordinates); (m // α ) mean square error of measuring horizontal angles (taken from specifications of applied instrument or from experimental study); ρ // 0665 //. So the coordinates and accuracy of point position can be determined from the two triangles and (Fig. ). This means that point has two values of coordinates and two values of position error (M and M ). For accepting the observations and resulted coordinates of point from the two triangles and, it is necessary that the coordinates must satisfy the following condition. () r M t, Where: ; and M t M M., - oordinates of point from first triangle ();, - oordinates from second triangle (); M, M rror in point position for the first and second triangles respectively. If the coordinates satisfy condition in equation (), the corrected coordinates of point can be determined by the arithmetic mean of two values. (4) ;. - MODIFITIO OF LIR ITRSTIO TO LULT T OIT OORDITS Linear intersection can be used also to determine the coordinates of observed points during setting out or structural deformation. For achieving accurate measurements, especially in monitoring the structural deformation, it is recommended that each observed point on the structure must be observed from three occupied known coordinates stations. The linear intersection observations can be done using the reflectorless total station. The coordinates of point (Fig. ) can be determined by two methods as follows: 58

4 ISS (Online), Volume 5, Issue, December (04), pp IM t first two distances (q and h) must be determined as following []: 0 q.5( h ) q (5) Then secondly, the coordinates of point can be determined []. q ) h ( ). q ) h ( ) (6) ( ( S S S (, ) (, ) (, ) Figure (): Geometry of observations using the suggested modified linear intersection In dependence on errors of measuring horizontal distances m position can be determined using the following formula m,, the error in point M m m sin, (7) y the same way for accepting the observations and the resulted coordinates of point from the two triangles and (Fig. ), it is necessary that the coordinates of point must satisfy the following condition: r M t, (8) Where: ; and M t M M. 59

5 ISS (Online), Volume 5, Issue, December (04), pp IM 4- MODIFITIO OF D OIT OORDITS USIG MULTI STTIOS OSRVLS ( I, I, Z I ) Target point ( O, O, Z O ) Figure (): Geometry of observed point in D space coordinates From Figure (), a local three-dimensional coordinates system is needed to calculate the spatial coordinates of any target point. Such a system, presumably, has -axis is chosen as a horizontal line, which the -axis is a horizontal line perpendicular to the -axis, the Z- axis is a vertical line determined by the vertical axis of the instrument at occupied station. The space coordinates (,, Z) of any point I (Figure ) can be determined mathematically as follows: I o S os β osθ S os β Sinθ I o Z Zo S Sinβ Where: S distance between point 0 and the point I. θ the bearing angle to point I. Β the vertical angle to point I. I (9) The multi stations technique can be summarized as follows: Let points, and be the location of the three-leveled total stations (Figure 4) and I be the observed point. Let (θ, θ, θ ) and (β, β, β ) be the bearing and vertical angles of point I from points, and, respectively. Then and are the horizontal distances in -direction between the total station centers ( and, and respectively) and and are the coordinate s differences in -direction between the total stations center and the other total stations centers and, respectively but h h are the height differences between the total station center and the other total stations centers and, respectively. Direction cosines of each total station pointing can be obtained as follows: Let the vertical angles be the following: earing I θ, earing I θ, earing I θ II β II β II β 60

6 ISS (Online), Volume 5, Issue, December (04), pp IM 6 Figure (4): Geometry of D intersection using multi stations technique The above observables enable us to calculate direction cosines of I, I and I: os β os θ, os β os θ, os β os θ, os β Sin θ, os β Sin θ, os β Sin θ, Sin β, Sin β, Sin β (0) So using the equations (9) and (0), the coordinates of point I can be determined as following: () The most probable value of, and can be obtained by solving equations (0) and () using the least square adjustment technique [5]. y substitution of and into quation (), two possible coordinates of I are obtained. Taking the mean of these two values, the most probable value of unknown coordinate point (I) is thus obtained. The shortest distance (d) between two directions can be determined directly from the following equation: () Where: Z D, D, D, 4 D The equation () assigns a numeric value to an arrangement of the total stations, for a given measurement. Z Z Z Z I I I 4 ) ( ) ( ) ( D D D D d

7 ISS (Online), Volume 5, Issue, December (04), pp IM 5- OTIMIZTIO OF T OFIGURTIO OF T ISTRUMT OSITIO USIG GTI LGORITM (G) Genetic lgorithms are computationally simple, powerful with probabilistic transition rules, and not limited by assumptions about the search space and are non-deterministic stochastic search/optimization methods that utilize the evolution theories to solve a problem within a complex solution space [6]. onsequently, constrained numerical optimization of this index over the set of all instrument positions will produce the optimal disposition of the total stations for that measurement. Genetic lgorithm will be used to perform this task. Genetic lgorithms are well suited for this problem. The suggested whole optimization process using Genetic lgorithm is outlined in Figure 5. The genetic algorithm loops over an iteration process to make the population evolve. ach iteration consists of the following steps: - The first step consists in selecting the total stations position parameters (positions { i & i & Z i }) for reproduction. This selection is done randomly with a probability depending on the relative fitness of the individuals so that best twos are often chosen for reproduction than poor twos. These are the only parameters that will be changed in the optimization process. This means that, each individual of the population will consist of the three coordinates (i & i & Z i ) of the three total stations, this means that we have 9 parameters. These 9 real parameters will be codified with a standard floating point based representation. Figure (5): Flow chart of the suggested optimization process using Genetic lgorithm - In the second step, offspring are bred by the selected total stations position parameters. For generating new chromosomes, the algorithm can use both recombination and mutation. 6

8 ISS (Online), Volume 5, Issue, December (04), pp IM - The fitness of the new chromosomes is evaluated [6]. - During the last step, individuals from the old total stations position parameters (population) are deleted and replaced by the new ones. The algorithm is stopped when the population converges toward the optimal solution. In this study, the stopping criteria were the minimum value of the trace of the variance covariance matrix [4]. 6- RIMTL WORKS D FILD STUD The accuracy of points coordinates (point positioning) that have been observed through the process of setting out or deformation monitoring using the presented geodetic techniques must be studied. It is necessary also to study the effect of the used instrument position distances and the observations angle on the accuracy of observed point positioning to get the optimum instrument positions. To achieve that goal, several observations were done on horizontal area. This section illustrates the results of practical measurements on area of land (8.0 m x.0 m) inside Kafr l- Sheikh University represented by an extensive number of well-distributed targets in Figure 6. Figure (6): Geometry of experimental study (layout of occupied and observed points) The test was carried out in the daytime when sunlight and temperature was 0. mesh of seventeen observed points on area (8.0 m x.0 m) is distributed for coordinating a building foundation (as shown in Table ). local three-dimensional rectangular coordinates system is needed to calculate the spatial coordinates of any target points on the mesh. Such a system, presumably, has -axis is chosen as a horizontal line parallel to the base direction (side 8m), which the -axis is a horizontal line perpendicular to the base direction and positive in the direction towards the object area, the Z- axis is a vertical line determined by the vertical axis of the instrument. 6

9 ISS (Online), Volume 5, Issue, December (04), pp IM Table (): The oordinate of test field points point no. Z point no. Z In this study, we applied the Genetic lgorithm. In this context, we used the same test field with the same conditions, specifications and instruments that have been used in the angular intersection, linear intersection and multi stations intersection. Table shows the parameters of the genetic algorithm. The coordinates of the positions of the total stations, the base distance ratio and the angle of triangle (φ) after the optimization process are shown in Table. Table (): Genetic algorithm parameters arameter Value opulation size 00 Tournament size rossover probability 5 70% Mutation probability 0.5% Table (): The oordinates of Total Stations (in m), base height ratio and the angle of triangle in different techniques of intersection using Genetic lgorithm optimization ase the eight of The method Z Distance ϕ station instrument ratio ngular Intersection Linear Intersection Multi-Station Intersection \.4 \\ \ 5. \\ \ \\ 64

10 ISS (Online), Volume 5, Issue, December (04), pp IM Table 4: The accuracy and standard deviations (Std.) for the test field coordinates (in mm) in different techniques of intersection after using Genetic lgorithm optimization ngular Intersection Linear Intersection Multi-Station Intersection Max. ( ) in mm Min. ( ) in mm verage ( ) in mm Std. ( ) in mm Max. ( ) in mm Min. ( ) in mm verage ( ) in mm Std. ( ) in mm Max. ( Z) in mm Min. ( Z) in mm verage ( Z) in mm Std. ( Z) in mm ositioning in mm In case of using the angular intersection, linear intersection and multi stations intersection with genetic algorithm optimization, the evaluated accuracy and standard deviations (SD) for the test field coordinates will also be presented in tabular form (see Table 4). It is to be mentioned that, the standard deviation (SD), as calculated from the least-squares adjustment will be considered as a measure of precision and the obtained results of the verage ( ), verage ( ), verage ( Z) and ositioning will be considered as a measure of accuracy [5]. 7- OLUSIOS In this paper, the uses of different intersection techniques are investigated. The multi station intersection technique to be very efficient for setting out and deformation problems in ngineering Structures. The achieved accuracy using multi station intersection technique is more accurate than that obtained by the conventional methods (angular and linear intersection). In the intersection techniques, the best estimated accuracy for the object space coordinate is achieved when the least squares adjustment technique was used. ased on experimental results, the genetic algorithm technique for determine the optimal total station placement in intersection (optimization problems) is efficient, easy to computerize and is considered more simple and economic than the other techniques. The best estimated accuracy is achieved when the genetic algorithm used for solving the optimization problem. 65

11 ISS (Online), Volume 5, Issue, December (04), pp IM 8- RFRS [] llan.., 996 Surveying uilding Surface by Theodolite Intersection Survey Review. [] eshr., 004 " ccurate surveying measurements for smart structural members", M.Sc. Thesis, Mansoura university, Mansoura gypt, 94 p. [] higiator R., hiorobo J., higiator O., eshr., 0 "Modification of Geodetic Methods for Determining The Monitoring Station oordinates on The Surface of ylindrical Oil Storage Tank" Research Journal in ngineering and pplied Sciences () [4] Matlab Online Support website, [5] Mittermayer,., 97. Zur usgleichung freier etze.zfv(97), S [6] Sivanandam, S.., Deepa, S.., 008 " Introduction to Genetic lgorithms" IS Springer erlin eidelberg ew ork. 66