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Study on Vertical Alignment Maintenance Technique using GNSS in

Skyscraper

Conference Paper · November 2009

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 Study on Vertical Alignment Maintenance Technique using GNSS in Skyscraper
Eunchurn Park1, Yu-Seung Kim1, Joong-Yub Lee1, Jun-Sung Choi1*
and Yeon-Back Jung2, Won-Kyun Seok2 , Kwang-Soo Jung2, Soon-Jeon Park2, Joo-Ho Lee2

1
Korea Maintenance Co., LTD., Seoul, South Korea
(Tel:82-2-830-7071, E-mail: 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
(Tel:82-2-718-4688, E-mail: 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, RTK-DGPS was chosen and for insuring the data set accuracy of RTK-
DGPS measurements, the network adjustment method was used. This method is data processing which
has compensating and differential process by using multi-reference point data sets except survey point.
The standard deviation of survey point can be reduced by optimizing the reference network. The
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.
This technique effectively assumes that the coordinate have an isotropic covariance structure. The four
point reference sites were chosen for Procrustes analysis. The 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 close to more accurate and precise operating system. In addition,

these types of measurement research are evaluated with the
In recent years there has been considerable interest in the accelerometer in safety of structure and usability during wind
construction of super high-rise buildings. To keep pace with the load. But if we implicate a GNSS system in the on-going
recent high-rise construction techniques, GNSS technology has construction field, it would be difficult to measure the
been developed tremendously with effort in architectural and displacement at the present due to vibrations, a short measuring
civil engineering measurement and survey field each year. From time and the other noise problems. To secure our accuracy of the
the prior art, various procedures and devices for surveys during system, three RTK reading stations were used with real-time
and after the phase of erection of a high-rise building are known. network adjustment reference coordinate, which lead to adjust
High-rise buildings are subject to strong external tilt effects the structure’ coordinate.
caused, for instance, by wind pressures, unilateral thermal effects
by exposure to sunlight, and unilateral loads. Such effects are a 2. Elements of the theory
particular challenge in the phase of construction of a high-rise
building, inasmuch as the high-rise building under construction
In this chapter, the theoretical frameworks describing the
is also subject to tilt effects, and will at least temporarily lose its
processes were summarized. First, the post processing DGPS
as a rule exactly vertical alignment. Yet construction should
method which has taken a long time to calculate and convince
progress in such a way that the building is aligned as planned,
coordinates. It is not proper to apply to construction processes of
and particularly so in the vertical, when returning into an un-
building, because reducing times of the each term of works is
tilted basic state.
very important element in the construction processes of a high-
This paper has been implicated in a GNSS system into our
rise building. In order to overcome the accuracy and precision of
skyscraper project that maintains a construction by a mechanized
RTK-DGPS, the real-time network adjustment using multipoint
system in each development. With this research, a system that
controlling and displacement compensation using accelerometers
mechanically control and maintain the skyscraper’s vertical-
were applied to proposed method.
alignment was developed and arranged. The 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 2.1 Real-time Procrustes analysis network adjustment
station creates the system of structure and attitude and applies to
the field condition to confirm the system’s possibilities. There 2.1.1 Basic concept of network adjustment
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
 Reference 2
∂F
= 2AT AT − 2AT B + T ( L + LT ) = 0 (5)
∂T

where ( AT A ) and ( L + LT ) are symmetric matrices.

Multiplying Eq. (5) on the left side by TT ,

Survey point 2
L + LT
TT AT AT − TT AT B + =0 (6)
2
( L + LT )
Survey point 1 = TT ( AT B ) − TT ( AT B ) − TT ( AT A ) T
2
(7)
⎡ ( L + LT ) ⎤T
= ⎢⎢ ⎥
⎥
2
Reference 1
Reference 3 ⎣⎢ ⎦⎥
Figure 1. Basic conceptual diagram of network adjustment
Since TT ( AT B ) T is symmetric, TT ( AT B ) must also be
For insuring the data set accuracy of RTK-DGPS measurements,
the network adjustment method was used. This method is data symmetric. Remind that ( L + LT ) is also symmetric.
processing which has compensating and differential process by Therefore, the following condition must be satisfied.
using multi-reference point data sets except survey point. As the
coordinates of reference points were measured by the post-
TT ( AT B ) = ( AT B ) T
T
processing DGPS method, it could be assumed as convincible (8)
reference coordinates. The standard deviation of survey point can
be reduced by optimizing the reference network. The Multiplying Eq.(8) on the left side by T ,
optimization method was chosen as the Procrustes analysis
method.
( AT B ) = T ( AT B )
T
In order to transform the WGS84 coordination to TM T (9)
coordination, the translation matrix which was Geodetic to ECEF and on the right side by T , T
and ECEF to ENU transformation was needed.
TT ( AT B ) TT = ( AT B )
T
(10)
2.1.2 Applied Procrustes analysis

We suppose that A is the set of floating points surveyed from Finally, we have the following equation using Eq.(9) and (10),
RTK-fixed mode data. B is the set of reference points surveyed
( AT B )( AT B ) = T ( AT B ) ( AT B ) TT
T T
from the post-processed DGPS data. (11)

A = {( xi , yi ) , i = 1,", k } , B = {( xi , yi ) , i = 1,", k } (1) ⎡ AT B AT B T ⎤ and ⎡ AT B T AT B ⎤

Matrices ⎢⎣ ( )( ) ⎥⎦ ⎢⎣ ( ) ( ) ⎥⎦ are
Orthogonal Procrustes problem [Schoenemann, 1970] is the least symmetric. Both of them have same eigenvalues.
squares solution of the problem that is the transformation of a
given matrix A into a given matrix B by an orthogonal
transformation matrix T in such a way to minimize the sum of
svd {( A B )( A B ) } = Tsvd {( A B )
T T T T T
( AT B )} TT (12)
squares of the residual matrix E=AT-B. Matrices A and B are
(p k) dimensional, in which contain p corresponding points in where svd { } stands for Singular Value Decomposition,
the k-dimensional space. A least squares solution must satisfy the
namely Eckart-Young Decomposition. The result is,
following condition,
minimize to : tr { ET E } = tr {( AT − B )T ( AT − B )}
VDs VT = TWDs WT TT (13)
The problem also has another condition, which is the orthogonal
transformation matrix, This means that,
TT T = TTT = I
Both of the conditions can be combined in a Lagrangian function, V = TW (14)

F = tr { ET E } + tr { L ( TT T − I ) } (2) Finally, we can solve the unknown orthogonal transformation

matrix T.
F = tr {( AT − B )T ( AT − B )} + tr { L ( TT T − I )} (3)
Obviously, a direct computation of the sum of squared distances
F = tr { TT AT AT − TT AT B − BT AT + BT B }
(4) between corresponding points of two configurations seems the
+tr { L ( TT T − I )} 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
where L is a matrix of Lagrangian multipliers, and tr{ } stands
configuration relative to the other. As noted in the above section,
for trace of the matrix. The derivation of this function with
it is more appropriate to compare the difference between
respect to unknown T matrix must be set to zero.
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 time-
history data set which has minimized standard deviation.

3. Test model and configuration of equipments Figure 4. Measuring Control Point 2

3.1 Test site Table 1 and 2 shows the comparison of CP1 and CP2
measurement result. As observed in these tables, the each
Test site is new construction site named ‘Lotte Castle Firenze’ in baseline of CP1 and CP2 have 6.757mm difference with both
Pusan as shown in Figure 2. method.

Table 1. Conventional measurement result of CP1 and CP2

Conventional Survey Measurement
E N B.M(Level) Point
206122.630 187997.490 EL=16.825 CP1
206196.050 188001.330 EL=19.760 CP2
73.52035092 (m) CP1-CP2 Baseline

Table 2. RTK measurement result of CP1 and CP2

GPS Measurement (RTK-fixed)
Latitude (dms) Longitude (dms)
35˚11´28.2444984˝ 129˚04´4.2990396˝ CP1
35˚11´28.36783412046˝ 129˚04´7.200966627˝ CP2
73.51359392 (m) CP1-CP2 Baseline

3.2 Installation, Equipment and measurement software

Figure 2. Gang form plan and form survey point The GPS antenna was installed in the survey point, gang form of
under construction building. Figure 5 shows the GPS antenna of
Figure 3 shows the aerial photograph of the reference sites for the gang form and the equipment list is Table 3.
network adjustment. As shown in figure, the survey point should
be in the triangle of three reference site.

LOTTERIA
BUILDING Construction site

Office

4F Building

1F Building
Figure 5. GPS antenna of the survey point

Table 3. Equipment list of main measurement system

Equipment Name Model Manufacture Items
Figure 3. Aerial photograph of the reference point’s network GPS
Septentrio PolaNt
AeroAntenna
4EA
Antenna Tech., Inc.
PolarRx2@ 1EA
GPS Septentrio
PolarRx2 Septentrio 1EA
Receiver NV
PolarRx2e 2EA
HTP-900RE FreeWave 4EA
RF Modem FreeWave
IM-800X009 Tech., Inc 4EA
 19.63

19.62
Geodetic and ENU coordinates transformation, NMEA ASCII 19.61

E component (m)
data conversion and decoder, Real-time Procrustes Network 19.6

Adjustment module and Optimization programming modules 19.59

19.58
were in the integrated software as shown in Figure 6. 19.57 RTK-fixed raw data :σ =7.2846(mm), m=19.5864592(m)
19.56 3P Network Adjustment : σ =5.9235(mm), m=19.5898911(m)
4P Network Adjustment : σ =3.6905(mm), m=19.5901835(m)
19.55
500 1000 1500 2000 2500 3000 3500
samples

(a) East Component

64.35

64.3

N component (m)
64.25

64.2

64.15
RTK GANG FORM : σ =20.6448(mm), m=64.1953661(m)
64.1 3P Network Adjustment : σ =15.4139(mm), m=64.1959707(m)
4P Network Adjustment : σ =9.6031(mm), m=64.1911750(m)
64.05
500 1000 1500 2000 2500 3000 3500
samples

(b) North Component

Figure 8. Network adjustment result of survey point

Table 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
Table 4. Standard deviation of one hour measurement data
Standard deviation (σ)
Site Method
East (mm) North (mm)
RTK-fixed 6.3442 17.2193
1F
3P PANA 2.9456 7.8272
Building
4P PANA 3.4005 7.9889
RTK-fixed 9.0285 18.3166
4F
3P PANA 1.8578 3.5686
Building
4P PANA 2.0758 3.5534
(b) Block diagram
RTK-fixed 6.1846 21.1810
Figure 6. Integrated measurement software Lotteria
3P PANA 2.8771 4.3686
Building
4P PANA 3.4724 8.5527
4. Test Result RTK-fixed 7.2846 20.6448
4.1 Network Adjustment Result Gang
3P PANA 5.9235 15.4139
Form
4P PANA 3.6905 9.6031
Tests of network adjustment which is 3-point (only reference
points) and 4-point (including a survey point as reference)
optimization were implemented. 4.2 Form Adjustment Result
As observed in Figure 7, the each time history for 1hour result of
reference points have the same differential components and the Figure 9 shows the result of form adjustment result
standard deviation of each data were reduced. corresponding to each 9, 13, 16 and 19 story. As shown in
Figure , those optimized points were in the control line each
64.85
RTK fixed raw data: σ=6.3442(mm), m=64.7939(m)
-55.05
RTK fixed raw data: σ=17.2193(mm), m=-55.1939(m)
direction with 10mm. Between 16 story and 19 story, gang form
64.84 3P Network Adjustment : σ=2.9456(mm), m=64.7977(m) -55.1 3P Network Adjustment : σ=7.8272(mm), m=-55.1956(m)

was adjusted.
E Component (m)

4P Network Adjustment : σ=7.9889(mm), m=-55.1983(m)

N Compenent (m)

64.83 4P Network Adjustment : σ=3.4005(mm), m=64.7988(m)

64.82 -55.15

64.81
-55.2
64.8
64.79 -55.25
64.78 20
-55.3
500 1000 1500 2000 2500 3000 3500 9 Story
500 1000 1500 2000 2500 3000 3500
samples
samples 13 Story
(a) 1F Building East (b) 1F Building North
4F Building 15 16 Story
-83.95 19 Story
258.92 RTK fixed raw data: σ=9.0285(mm), m=258.8741(m) RTK fixed raw data: σ=18.3166(mm), m=-84.0455(m)
258.91 3P Network Adjustment : σ=1.8578(mm), m=258.8813(m) 3P Network Adjustment : σ=3.5686(mm), m=-84.0485(m)
4P Network Adjustment : σ=2.0758(mm), m=258.8801(m) 4P Network Adjustment : σ=3.5534(mm), m=-84.0485(m)
N Compenent (m)
E Component (m)

-84
258.9

258.89 -84.05
10
258.88

258.87 -84.1

258.86
-84.15
258.85 5
500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500
samples samples
(c) 4F Building East (d) 4F Building North 9 Story 19 Story
Y (mm)

RTK fixed raw data: σ=6.1846(mm), m=-11.4954(m) RTK fixed raw data: σ=21.181(mm), m=75.0402(m) 0 13 Story
-11.46 75.1
3P Network Adjustment : σ=2.8771(mm), m=-11.4925(m) 3P Network Adjustment : σ=4.3686(mm), m=75.0411(m)
4P Network Adjustment : σ=3.4724(mm), m=-11.4919(m) 4P Network Adjustment : σ=8.5527(mm), m=75.0358(m)
N Compenent (m)
E Component (m)

-11.48 75.05

-11.5
75
-5 16 Story
74.95
-11.52
74.9
500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500
samples samples -10
(e) LOTTERIA Building East (f) LOTTERIA Building North

Figure 7. Network adjustment result of each reference points -15

As observed in Figure 8, the each time history result of survey -20

-20 -15 -10 -5 0 5 10 15 20
point has the same differential components and the standard X (mm)

deviation of data was reduced in the control value range, 10mm. Figure 9. Form adjustment result
5. Concluding remarks
The vertical alignment maintenance technique of building
form was implemented by using GNSS in skyscraper. An
example test building, RTK-DGPS, Real-time network
adjustment and the four point reference sites were chosen. The
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
The 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. 33-51.
2. 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. 245-255.
4. Gower, John C. and Dijksterhuis, Garmt B. (2004) Procrustes
Problems, Oxford University Press.

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