Study on Vertical Alignment Maintenance Technique using GNSS in Skyscraper

Transcription

1 Study on Vertical Alignment Maintenance echnique using GNSS in Skyscraper Eunchurn Park 1, Yu-Seung Kim 1, Joong-Yub Lee 1, Jun-Sung Choi 1* and Yeon-Back Jung 2, Won-Kyun Seok 2, Kwang-Soo Jung 2, Soon-Jeon Park 2, Joo-Ho Lee 2 1 Korea Maintenance Co., LD., Seoul, South Korea (el: , eunchurn@kmbest.co.kr, yuseungkim@kmctech.co.kr, joongyup@kmctech.co.kr, eunchurn@kmbest.co.kr, kimchan@kmbest.co.kr, ceo@kmctech.co.kr * ) 2 Lotte Engineering & Construction, Seoul, South Korea (el: , jung61@lottenc.com, archief@lottenc.com, ksjung716@lottenc.com, soon1026@lottenc.com, joo7777@lottenc.com) Abstract: In this study, vertical alignment maintenance technique of building form was implemented by using GNSS(global navigation satellite system) in skyscraper. An example test building was chosen as apartment building named as Lotte Castle Firenze which is under construction in Pusan, Korea. For the faster construction term of works, RK-DGPS was chosen and for insuring the data set accuracy of RK- DGPS measurements, the network adjustment method was used. his method is data processing which has compensating and differential process by using multi-reference point data sets except survey point. he standard deviation of survey point can be reduced by optimizing the reference network. he optimization method was chosen as the Procrustes analysis which involves matching shape configuration, through translation, rotations, and possibly scaling, to minimize the Euclidean distance between them. his technique effectively assumes that the coordinate have an isotropic covariance structure. he four point reference sites were chosen for Procrustes analysis. he network adjustment result showed that the standard deviation of survey point could be reasonably minimized. Keywords: skyscraper, real-time kinematic, DGPS, network adjustment, Procrustes analysis, form adjustment 1. Introduction In recent years there has been considerable interest in the construction of super high-rise buildings. o keep pace with the recent high-rise construction techniques, GNSS technology has been developed tremendously with effort in architectural and civil engineering measurement and survey field each year. From the prior art, various procedures and devices for surveys during and after the phase of erection of a high-rise building are known. High-rise buildings are subject to strong external tilt effects caused, for instance, by wind pressures, unilateral thermal effects by exposure to sunlight, and unilateral loads. Such effects are a particular challenge in the phase of construction of a high-rise building, inasmuch as the high-rise building under construction is also subject to tilt effects, and will at least temporarily lose its as a rule exactly vertical alignment. Yet construction should progress in such a way that the building is aligned as planned, and particularly so in the vertical, when returning into an untilted basic state. his paper has been implicated in a GNSS system into our skyscraper project that maintains a construction by a mechanized system in each development. With this research, a system that mechanically control and maintain the skyscraper s verticalalignment was developed and arranged. he GNSS system on the field was applied by creating an accurate vertical-alignment data and send to the central station. With this data set, the central station creates the system of structure and attitude and applies to the field condition to confirm the system s possibilities. here are several structures in architecture and civil engineering cases that apply a GNSS system, but it has limitation of use in measurement. But with advance development of GNSS technology and its accuracy, a measurement system has gotten close to more accurate and precise operating system. In addition, these types of measurement research are evaluated with the accelerometer in safety of structure and usability during wind load. But if we implicate a GNSS system in the on-going construction field, it would be difficult to measure the displacement at the present due to vibrations, a short measuring time and the other noise problems. o secure our accuracy of the system, three RK reading stations were used with real-time network adjustment reference coordinate, which lead to adjust the structure coordinate. 2. Elements of the theory In this chapter, the theoretical frameworks describing the processes were summarized. First, the post processing DGPS method which has taken a long time to calculate and convince coordinates. It is not proper to apply to construction processes of building, because reducing times of the each term of works is very important element in the construction processes of a highrise building. In order to overcome the accuracy and precision of RK-DGPS, the real-time network adjustment using multipoint controlling and displacement compensation using accelerometers were applied to proposed method. 2.1 Real-time Procrustes analysis network adjustment Basic concept of network adjustment

2 Reference 2 F = 2A A 2A B + ( L + L ) = 0 (5) where ( A A ) and ( + ) L L are symmetric matrices. Multiplying Eq. (5) on the left side by, Survey point 1 Reference 3 Survey point 2 Reference 1 Figure 1. Basic conceptual diagram of network adjustment For insuring the data set accuracy of RK-DGPS measurements, the network adjustment method was used. his method is data processing which has compensating and differential process by using multi-reference point data sets except survey point. As the coordinates of reference points were measured by the postprocessing DGPS method, it could be assumed as convincible reference coordinates. he standard deviation of survey point can be reduced by optimizing the reference network. he optimization method was chosen as the Procrustes analysis method. In order to transform the WGS84 coordination to M coordination, the translation matrix which was Geodetic to ECEF and ECEF to ENU transformation was needed Applied Procrustes analysis We suppose that A is the set of floating points surveyed from RK-fixed mode data. B is the set of reference points surveyed from the post-processed DGPS data. A = {( x, y ), i = 1,, k}, B = {( x, y ), i = 1,, k} (1) i i i i Orthogonal Procrustes problem [Schoenemann, 1970] is the least squares solution of the problem that is the transformation of a given matrix A into a given matrix B by an orthogonal transformation matrix in such a way to minimize the sum of squares of the residual matrix E=A-B. Matrices A and B are (p k) dimensional, in which contain p corresponding points in the k-dimensional space. A least squares solution must satisfy the following condition, minimize to : tr { E E} = tr {( A B) ( A B )} he problem also has another condition, which is the orthogonal transformation matrix, = = I Both of the conditions can be combined in a Lagrangian function, F = tr{ } + tr{ ( )} {( ) ( )} { ( )} tr{ A A A B B A B B} tr { L( I) } E E L I (2) F = tr A B A B + tr L I (3) F = + (4) + where L is a matrix of Lagrangian multipliers, and tr{ } stands for trace of the matrix. he derivation of this function with respect to unknown matrix must be set to zero. ( L + L ) 2 L + L AA AB + = 0 (6) 2 ( ) ( ) ( ) = A B A B A A (7) ( L + L ) = 2 Since ( A B) is symmetric, ( ) symmetric. Remind that ( + ) A B must also be L L is also symmetric. herefore, the following condition must be satisfied. ( ) = ( ) A B A B (8) Multiplying Eq.(8) on the left side by, ( ) = ( ) A B A B (9) and on the right side by, ( ) = ( ) A B A B (10) Finally, we have the following equation using Eq.(9) and (10), ( )( ) = ( ) ( ) A B A B A B A B (11) A B A B are symmetric. Both of them have same eigenvalues. Matrices ( A B )( A B ) and ( ) ( ) svd {( )( ) } = svd ( ) ( ) { } A B A B A B A B (12) where svd { } stands for Singular Value Decomposition, namely Eckart-Young Decomposition. he result is, his means that, s = s VD V WD W (13) V = W (14) Finally, we can solve the unknown orthogonal transformation matrix. Obviously, a direct computation of the sum of squared distances between corresponding points of two configurations seems the simplest way of measuring the degree of resemblance. However, such a direct computation is not very meaningful due to the likely arbitrary location, orientation, and scale of one configuration relative to the other. As noted in the above section, it is more appropriate to compare the difference between

3 configurations after linear transformations have been performed on one configuration relative to the other [Gower & Dijksterhuis, 2004]. Geometrically, a linear transformation can be seen as a rigid movement of a network, where the network equals the internal relationships of reference points in a configuration. Initially, two types of movement that preserves distances among the points are performed, translation and rotation. When comparing shapes of configurations, the origins to which they refer are irrelevant [Gower & Dijksterhuis, 2004]. Hence, a shape-preserving translation is performed that centers the coordinates of one object to the other. Finally, the coordinate of survey points could be attained as timehistory data set which has minimized standard deviation. 3. est model and configuration of equipments 3.1 est site est site is new construction site named Lotte Castle Firenze in Pusan as shown in Figure 2. Figure 4. Measuring Control Point 2 able 1 and 2 shows the comparison of CP1 and CP2 measurement result. As observed in these tables, the each baseline of CP1 and CP2 have 6.757mm difference with both method. able 1. Conventional measurement result of CP1 and CP2 Conventional Survey Measurement E N B.M(Level) Point EL= CP EL= CP (m) CP1-CP2 Baseline able 2. RK measurement result of CP1 and CP2 GPS Measurement (RK-fixed) Latitude (dms) Longitude (dms) CP CP (m) CP1-CP2 Baseline 3.2 Installation, Equipment and measurement software Figure 2. Gang form plan and form survey point Figure 3 shows the aerial photograph of the reference sites for network adjustment. As shown in figure, the survey point should be in the triangle of three reference site. he GPS antenna was installed in the survey point, gang form of under construction building. Figure 5 shows the GPS antenna of the gang form and the equipment list is able 3. LOERIA BUILDING Construction site Office 4F 1F Figure 5. GPS antenna of the survey point Figure 3. Aerial photograph of the reference point s network able 3. Equipment list of main measurement system Equipment Name Model Manufacture Items GPS AeroAntenna Septentrio PolaNt Antenna ech., Inc. GPS Receiver RF Modem Septentrio NV FreeWave PolarRx2@ PolarRx2 PolarRx2e HP-900RE IM-800X009 Septentrio FreeWave ech., Inc 1EA 1EA 2EA

4 E component (m) Geodetic and ENU coordinates transformation, NMEA ASCII data conversion and decoder, Real-time Procrustes Network Adjustment module and Optimization programming modules were in the integrated software as shown in Figure RK-fixed raw data :σ =7.2846(mm), m= (m) 3P Network Adjustment : σ =5.9235(mm), m= (m) 4P Network Adjustment : σ =3.6905(mm), m= (m) (a) East Component N component (m) RK GANG FORM : σ = (mm), m= (m) 3P Network Adjustment : σ = (mm), m= (m) 4P Network Adjustment : σ =9.6031(mm), m= (m) (b) North Component Figure 8. Network adjustment result of survey point able 4 is the result of standard deviation of one hour measurement data. As observed in the table, 4P PANA(Procrustes Analysis Network Adjustment) could be the more minimized. (a) Front panel (b) Block diagram Figure 6. Integrated measurement software 4. est Result 4.1 Network Adjustment Result RK fixed raw data: σ=6.3442(mm), m= (m) P Network Adjustment : σ=2.9456(mm), m= (m) 4P Network Adjustment : σ=3.4005(mm), m= (m) RK fixed raw data: σ= (mm), m= (m) 3P Network Adjustment : σ=7.8272(mm), m= (m) ests of network adjustment which is 3-point (only reference points) and 4-point (including a survey point as reference) optimization were implemented. As observed in Figure 7, the each time history for 1hour result of reference points have the same differential components and the standard deviation of each data were reduced P Network Adjustment : σ=7.9889(mm), m= (m) able 4. Standard deviation of one hour measurement data Standard deviation (σ) Site Method East (mm) North (mm) RK-fixed F RK-fixed F RK-fixed Lotteria RK-fixed Gang Form Form Adjustment Result Figure 9 shows the result of form adjustment result corresponding to each 9, 13, 16 and 19 story. As shown in Figure, those optimized points were in the control line each direction with 10mm. Between 16 story and 19 story, gang form was adjusted (a) 1F East (b) 1F North 15 RK fixed raw data: σ=9.0285(mm), m= (m) P Network Adjustment : σ=1.8578(mm), m= (m) 4P Network Adjustment : σ=2.0758(mm), m= (m) F Story 13 Story 16 Story 19 Story RK fixed raw data: σ= (mm), m= (m) 3P Network Adjustment : σ=3.5686(mm), m= (m) 4P Network Adjustment : σ=3.5534(mm), m= (m) (c) 4F East RK fixed raw data: σ=6.1846(mm), m= (m) 3P Network Adjustment : σ=2.8771(mm), m= (m) RK fixed raw data: σ=21.181(mm), m= (m) 3P Network Adjustment : σ=4.3686(mm), m= (m) P Network Adjustment : σ=3.4724(mm), m= (m) (d) 4F North Y (mm) 4P Network Adjustment : σ=8.5527(mm), m= (m) 9 Story 19 Story 0 13 Story Story (e) LOERIA East -10 (f) LOERIA North Figure 7. Network adjustment result of each reference points As observed in Figure 8, the each time history result of survey point has the same differential components and the standard deviation of data was reduced in the control value range, 10mm X (mm) 5 10 Figure 9. Form adjustment result 15 20

5 5. Concluding remarks he vertical alignment maintenance technique of building form was implemented by using GNSS in skyscraper. An example test building, RK-DGPS, Real-time network adjustment and the four point reference sites were chosen. he network adjustment result showed that the standard deviation of survey point could be reasonably minimized. For the further study, with this system, sets up the accuracy standard that compare the data set from the accelerometer by creating an algorithm that has a common system mode. the data set from the accelerometer and the GNSS was combined, and then a system transfer function model which defines the condition of status and its standard was created. With this result, next test could be planned with more upgrade one than previous experiments. Acknowledgement he work presented in this paper was supported by the Lotte Engineering & Construction. Reference 1. Gower, J.C., (1975) Generalized Procrustes analysis. Psychometrika, 40(1), pp Luo, B., Hancock, W.R. (1999) Feature matching with Procrustes alignment and graph editing. 7th International Conference on Image Processing and its Applications. 3. Schoenemann, P.H., Carroll, R., (1970). Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 35(2), pp Gower, John C. and Dijksterhuis, Garmt B. (2004) Procrustes Problems, Oxford University Press.