Experimental Researches in Defining Deformations by Free Station Method and Results Processing by Search Method

Full text

Experimental Researches in Defining Deformations by
Free Station Method and Results Processing by Search
Method
Shevchenko G. G.1[0000-0003-1849-4718], Bryn M. J.2[0000-0002-4722-9289], Afonin D.A. 2[0000-0002-
5685-3606], Gura D. A.1[0000-0002-2748-9622]
1 Kuban State Technological University, Krasnodar, Russia
grettel@yandex.ru
2 Emperor Alexander I St. Petersburg state transport university, Saint-Petersburg, Russia
3046921@mail.ru
Abstract. This article proposes a method of monitoring the buildings stability
with free station positioning which includes a geodetic monitoring technique
with a free station. Processing and adjustment of data is proposed to be con-
ducted with the search method by a specially designed software program. The
sequence of monitoring is as follows. The location of the stations is chosen in
such a way that each of them shows as many deformation and support points as
possible and at least three points should be determined from any other station. It
is preferable to choose stations approximately in the alignment of one pair of
support points so that the planes of the marks being defined are perpendicular to
the line of sight. Measurements of all horizontal angles, zenith and slant dis-
tances to all visible reference points and deformation marks are made at each
station with an electronic total station. As a result, redundant measurements ap-
pear in the measurement scheme, which in turn increase the accuracy of the fi-
nal result. The coordinates determination of the defining marks is performed by
deducing the minimal sum of the measured angles deviations squares and of
distances squares calculated from the preliminary coordinates of the marks tak-
ing into account the weights of the measurements.It is proposed to search for
the objective function minimum with a search method using a specially devel-
oped program in the form of a macro in the Microsoft Excel software product
which provides special features to accelerate the problem solving process. The
buildings deformation monitoring technique mentioned above was successfully
tested at several sites.
Keywords: Geodetic monitoring, Three-dimensional coordinates, Setting and
displacement, The search method of adjustment.
1 Introduction
When solving problems of determining the three-dimensional coordinates of de-
formation marks located along the perimeter of a building under construction as a rule

2
the measurements are performed from geodetic points fixed on the ground from cycle
to cycle especially if such measurements are made by electronic total station. [1-4].
However, there is often a problem to ensure the stability of such observation points
due to the continuous work on the construction site. In addition, in a city the high
built-up density often complicates work arrangement [5]. This is especially evident
when it is necessary to determine the planned-high-altitude position of deformation
marks on the object.
The article describes issues related to the method of determining the displacement
and setting of buildings. A new developed technique is confirmed by experimental
data.
The novelty of the proposed technique based on the fact that geodetic observations
of the buildings deformation are suggested to be carried out by performing angular
and linear measurements of the reference points and deformation marks by an elec-
tronic total station installed in any locations accessible for measurement without fix-
ing observation stations. So, it is not needed to center the device above the point. In
this case, the linking of stations with each other will be done at common points cap-
tured at all stations. So, this method of an object observation can be compared with
shooting in scanning method. Thus, the linking of stations is carried out as well as
during scanning by common points visible from several positions.
The vertical and horizontal displacements themselves are determined relatively to
the stated reference points located in stable locations. The points used in the setting
out of the axes of the structure are also offered as reference points. The reference
points and initial geodetic points will be used to determine the location of the total
station points. The presence of reference points is prerequisite in an amount of at least
3 pieces.
Thus, to monitor all three axes of the structure it is proposed to measure the follow-
ing types of points fixed in the work area:
- reference points;
- deformation marks (located along the perimeter of the object under study).
By observing each of these points data are taken to determine the value data of hor-
izontal angles, zenith and slope distances.
Numerical methods and methods of comparative analysis were used in the pro-
cessing of measurement results. Mathematical calculations were carried out in Mi-
crosoft Excel using a specially created macro written in the programming language
Visual Basic. Processing and analysis of the measurement results are proposed to be
made on the basis of the least squares search method.
2 The sequence of monitoring
Determination of three-dimensional coordinates of points, and displacements and
settings based on them are supposed to be carried out in the following sequence.
Stage I. Reconnaissance of the territory. Preparation of the territory and the ob-
ject under study for geodesic observations:
1) installation of deformation marks:

3
a) marks are located at a certain height;
b) marks are located along the perimeter of the building;
c) in this case, reflective films fixed in the required place substitute the marks
(Fig. 1). For the convenience of targeting deformation marks and to eliminate errors
for the inclination of the collimating ray to the mark plane, a special rotating reflec-
tive film was proposed at the Cadastre and Geoengineering department of the Kuban
State Technological University (Fig. 1, c). It is mounted in the wall and allows to be
targeted at almost any position due to the rotation of the mark without shifting the
center. The usage of this kind of marks has increased greatly [6].
2) installation of reference points.
As reference points, the points on buildings nearby can be used, for example,
buildings that have been built for a long time, fence posts, pylons of electric lines, etc.
Points received at setting out the axes of the structure can be used as reference
points. The minimum number of reference points is 3 pcs. Theoretically, the reference
point can be used to determine the location of standing points of the total station (sta-
tions) by linear-angular ticks.
а) b) c)
Fig. 1. Reflective film fixed on the object
3) Determination of the stations location.
Since this method of measurement is suggested to be carry out without fixing sta-
tions on the ground, the method to conduct observations of the location of the instru-
ment is selected based on the following requirements:
- stations are selected in such a way that as many deformation marks, auxiliary
marks and reference points as possible can be observed from each of them;
- it is preferable to choose stations aligned to one pair of reference points so that
the planes of the observed marks are perpendicular to the collimating line. The colli-
mating ray and the plane of the reflective film should make an angle of at least 450
[7];
- every station is chosen to target at least three points detected by the previous sta-
tion or some other one. This is necessary to ensure "rigid" connection between sta-
tions.
If the deformation marks and reference points are not enough to link the stations
with each other, auxiliary points could be set.
Stage II. Conducting field work. Measurements are taken at all reference points
and deformation marks visible from each station. To make these measurements an
electronic total station is used. At first, only reference points are measured thus creat-
ing a reference points network. Then integrated measurements are performed on all

4
deformation marks and reference points visible from the stated station. For each de-
formation mark, measurements should be taken by two or more stations, however, the
coordinates of the mark can be calculated by using only one station measurements. As
a result, redundant measurements appear in the measurement scheme which in its turn
increases the accuracy of the final result.
In order to determine the value of displacement or setting, it is necessary to carry
out measurements in several stages (cycles), each of them contains three-dimensional
coordinates computation of the observed marks. Positioning is carried out based on
the measured values of the horizontal angles, zenith and slope distances for each de-
fined mark. That is, measurements for each determined point during field work are
performed with a reciprocal observation. Sometimes the distance cannot be measured
correctly due to the acute angle between the mark plane and the collimating ray. In
this case, only two measured values will be processed – the horizontal angle and the
zenith distance. Subsequently, the differences in the X and Y coordinates reveal the
possible displacements of elements and the differences in the H marks show the set-
ting of the structure.
Stage III. Processing and adjustment of measurement results. Processing and
adjustment of data is proposed to be fulfilled by Microsoft Excel using specially de-
signed software. At first, all the measured values of angles and distances (βtaken; Ztaken;
Dtaken) from the instrument are exported to this software. Then the coordinates of the
reference points are entered and the coordinates of the determined deformation marks
are arbitrarily indicated.
The coordinates positioning of the detected marks is performed by finding the min-
imum of the squares sum of the measured angles and distances deviations v from the
calculated values using the previously entered coordinates of the detected points tak-
ing into account weights p .The calculated values of βcalc, Zcalc, Dcalc are deduced by a
computer using the inverse geodesic problem formulas. The weight of the measure-
ment p is taken into account by multiplying the difference between the measured and
calculated values by √p [8]. As a result, the target cell contains the calculated sum
[pυ2].
To search for a minimum, a computer program is compiled as a macro in the Mi-
crosoft Excel software product [9]. To operate the target cell is given a name. Then
the cells with previously entered coordinates of the detected marks are selected. To
search for a minimum it is needed to indicate the appropriate value of ∆ to change
arbitrarily entered values of X, Y, H. The technique of finding the minimum is that
the computer for each unknown calculates three values of y0, y1 and y2 in the target
cell which correspond to the three values of the selected unknown x0, x1 and x2. A
parabola is constructed at three points, the parameters of which provide an allowance
to go to the parabola vertex.
The computer makes consequent calculations for all unknowns then proceeds to
the second cycle of iterations over all unknowns and so on until the value in the target
cell stops decreasing. Sometimes it is useful to reduce the value of ∆ at the end of the
iterations.

5
3 Study value
This software program is a useful addition to the well-known universal minimum
search programs in Microsoft Excel and Math Cad software products. However, the
studies show that the built-in functions of such search programs do not always give
correct results, as calculations are made with gradient method. It is hard enough to
deduce derivatives in the form of analytic functional relations as the problems have
fairly great number of variable data [10-12]. As a result the mentioned above mini-
mum search program has been written.
When solving monitoring tasks, one of the two mentioned above programs is used
first, and then the final adjustment to the minimum is made by the algorithm devel-
oped by the authors. Some special features are introduced into the program. So, in
addition to automatically stopping the calculations when the minimum is reached, the
calculations could be continued by setting the desired number of iteration cycles. The
order of transition from one unknown to another in a cycle can be changed that some-
times speeds up the process of solving a problem.
4 Testing of the technique
This technique was tested at several construction sites. So, 4 cycles of measure-
ments of displacements and settings of three buildings under construction were per-
formed. These buildings include a swimming pool, a hotel, and a house of athletes.
The measurements were made with the Nikon NPL-332 total station № 043256.
The accuracy of the instrument is: 5// when measuring angles of standard deviation,
measuring angles and 3mm + 2mm ∙ D 10-6 when measuring distances.
For processing all measurements, a left system of spatial rectangular coordinates
was used, where were given the coordinates of the marks for the setting out of the 3
buildings axis were given.
4.1 The location coordinate of marks along the perimeter of the objects
To monitor of buildings, measurements were made on reflective films placed along
the perimeter of the objects.
So, 18 marks (B1-B18) are fixed at a height of 3-4 meters from the ground along
the perimeter of the basin. Along the perimeter of the hotel complex there are15
marks (G1-G15) at the floor level of the 4th floor at a height of about 17 m. Also, 4
marks (D1-D4) are fixed at a height of 3 m along the perimeter of the sports center.
9 marks previously fixed and intended for superimposing down the axes of struc-
tures and 9 aligning marks located along the perimeter of the sanatorium mainly on
metal fences were used as reference and initial geodetic points. The view of both
mark types is similar to the deformation marks (Fig. 1). Aligning marks are used to
determine the standing points coordinates of the total station (stations) with a linear-
angular tick. The stations are selected approximately at the alignment of one pair of

6
aligning marks in so that the plane of the marks to be perpendicular to the collimating
line which gives the minimum error in the measured distance.
Measurements are made from 14 stations. Measurements were made on all the
above-mentioned marks visible from this position from each station.
When targeting the marks, horizontal angles, zenith and slope distances were
measured and recorded in the memory of the total station. Measurements from 1–2
and up to 5 stations were made for each deformation mark.
The coordinates were calculated using the least squares method by means of a spe-
cially designed software program. The program changes one-by-one the coordinates
of all points previously entered into the computer so that the sum of squared devia-
tions of the measured values differ from the values calculated from the coordinates in
minimum. The processing took into account the weights of measurements and errors
of the initial data.
Table 1 shows the adjusted coordinates of all marks and deviations in the 4th cycle from the
coordinates in the 1st and 3rd cycles. Coordinates of stations, reference and aligning marks are
not given.
Table 1. Marks coordinates on the building.
Points/
marks
Coordinates in the 4th
cycle
Differences: 4th cycle
minus 3rd cycle
Differences: 4th cycle
minus 1st cycle
Х, m
У, m
Н, m
dХ, mm
dУ, mm
dН, mm
dХ, mm
dУ, mm
dН, mm
B1
224,865
116,992
6,911
-3
-1
0
0
-2
-1
B2
210,082
116,790
6,951
-3
-2
-1
2
-2
-3
B3
198,164
124,290
6,577
0
-2
-1
3
-5
-3
B4
168,916
124,296
6,599
5
-5
-3
17
-7
-3
B5
159,542
119,403
7,519
6
-6
-2
14
-7
-1
B6
143,071
117,695
7,060
4
-6
-1
13
-2
-2
B7
139,716
103,918
6,023
3
0
-2
10
0
-3
B8
139,711
73,336
6,165
1
-2
-1
11
3
-2
B9
139,714
43,934
6,205
3
3
-1
11
11
-2
B10
142,795
30,466
6,580
2
5
-1
10
9
-2
B11
157,819
30,299
6,791
3
6
-1
12
13
-3
B12
175,104
23,698
6,060
-6
2
-1
0
10
-4
B13
192,252
23,710
6,092
-8
1
0
-6
9
-2
B14
209,556
30,686
7,241
-2
0
-1
6
5
-4
B15
223,666
30,208
7,044
-3
1
-1
4
3
-2
B16
227,291
45,867
6,024
-2
-1
-1
0
6
-2
G1
81,703
197,145
20,070
7
2
-13
7
-1
-33
G2
74,428
197,310
20,142
7
2
-12
5
-4
-29
G3
66,177
192,298
20,097
7
-1
-12
0
-4
-36
G4
60,475
186,639
20,101
7
-1
-12
-2
-1
-36
G5
37,493
160,869
20,178
3
5
-9
1
15
-26

7
G6
52,421
146,148
20,103
9
6
-7
17
18
-19
G7
70,490
159,188
20,001
8
5
-14
14
12
-32
G8
84,866
159,192
19,994
1
0
-13
10
9
-31
G9
97,757
151,414
20,355
-4
-2
-8
-
-
-
G10
103,742
146,062
20,129
-1
1
-6
4
10
-15
G12
118,088
160,390
20,122
-3
3
-7
-2
6
-17
G13
109,734
171,735
20,100
2
0
-8
0
3
-24
G14
98,429
183,185
19,950
2
2
-13
5
3
-34
G15
48,934
173,775
20,062
4
1
-11
0
3
-34
D1
105,107
72,151
6,382
0
-5
-2
6
-2
-1
D2
70,956
72,174
6,381
6
1
-1
14
5
-1
D3
70,942
55,143
6,388
5
0
0
13
7
2
D4
105,113
55,215
6,309
-1
-1
-2
4
6
-2
Comparing the deformation measurements between cycles shows the following.
1. The height difference for the five points of the sports center does not exceed 2
mm, which indicates the stability of the building in height over the observation peri-
od. 2. For a universal pool, there is a slight setting in average for all marks by 2-3 mm
comparing to the 1st cycle.
3. The height difference for a hotel complex between 4 and 3 cycles (48 days) is
from -6 to -14 mm, and between 4 and 1 cycles (126 days) it constitutes from -15 to -
36 mm, which is apparently due to the increasing weight of the building during con-
struction. For clarity, settings are shown in Fig. 2 and 3.
Analysis of the uneven setting of the hotel complex shows that the northwestern
part of the building has a less setting. The unequal setting of the opposite parts of the
Fig. 2. Settings (mm) of the hotel complex
in 48 days
Fig. 3. Settings (mm) of the hotel complex
in 126 days
-13
-12
-12
-12
-9
-7
-14
-13
-8
-6
-7
-8
-13
-11
-34
-34
-24
-17
-15
-31
-32
-19
-26
-36
-36
-29
-33

8
building leads to a tilt of the hotel complex. The difference in settings over the obser-
vation period between the northwest and southeastern parts of the building is in aver-
age 18 mm, which at a distance of 60 meters gives a tilt in relative units of about
1:3300.
4.2 Determining the coordinates of the pools corners
16 marks are fixed on the 1st storey of the universal pool. Eight marks (B1b-B8b)
are placed in the upper corners of both bowls of pools and 8 marks (B1a-B8a) - on the
floor of the 1st storey at a distance of about 1 meter from the first one so that both
marks overlap the gap between the bowls of the pools and the ceiling of the ground
floor . Marks are placed on a horizontal surface. In this case, the marks are not reflec-
tive films but have the shape of a cross with a dot in the middle for which all 3 coor-
dinates are defined. The cross is patterned using red auto enamel on a white circle
with a diameter of 16 cm. The diameter of the center point is 6 mm.
The measurements were made with an electronic total station from one station, the
coordinates and heights of which are determined by linear-angular tick of the refer-
ence points visible from the station. The coordinates of all points are calculated by the
measured distances, horizontal and vertical angles (Table 2).
Discrepancies in the X and Y coordinates (columns 5, 6, 8, and 9 of Table 2) in-
dicate deformations. Meanwhile, there is a slight setting of both the floor of the 1st
storey and the pool bowls of about 4-6 mm in the last 48 days.
Table 2. Points coordinates on the 1st storey of the pool.
Points/
marks
The 4th cycle coordinates
Differences: the 4th cycle
minus the 3rd
Differences: the 4th cycle
minus the 3rd
Х, m
У, m
Н, m
dХ, mm
dУ, mm
dН, mm
dХ, mm
dУ, mm
dН, mm
Floor points at the corner of the pool bowls
B1a
169,97
119,02
6,135
-6
-12
-3
1
0
-5
B2а
170,05
66,89
6,197
-2
-6
-3
5
7
-4
B3а
169,93
60,32
6,170
-4
-5
-3
3
9
-4
B4а
169,96
28,98
6,178
-13
-6
-6
-1
5
-11
B5а
197,03
28,96
6,138
-6
-3
-5
2
13
-9
B6а
197,01
61,02
6,162
-8
-3
-3
10
6
-4
B7а
197,09
67,76
6,164
-10
-4
-2
6
9
-4
B8а
197,08
119,08
6,148
-2
-3
-4
2
0
-6
Top corners of pool bowls
B1b
170,83
118,18
6,288
-3
5
-6
1
2
-4
B2b
170,78
67,80
6,283
-10
-5
-3
5
10
-3
B3b
170,82
60,17
6,275
-5
-7
-3
11
0
-3
B4b
170,83
29,84
6,278
-8
-13
-4
8
6
-5
B5b
196,19
29,83
6,282
-12
-10
-5
5
10
-5
B6b
196,16
60,19
6,274
-4
0
-4
3
6
-4

9
B7b
196,22
67,79
6,281
1
-5
-4
5
12
-4
B8b
196,20
118,20
6,268
-10
-5
-6
-5
0
-5
5 Summary of the results of the deformations determination
The results of measurements performed in the 4th cycle compared with the results
of measurements in the 1st cycle showed the following:
1. Displacements and settings were not found in the building of the sports center.
2. There is setting of marks along the perimeter of the building on average 3-4 mm
in a universal pool. Settings close to them of 4-6 mm were detected on 16 marks on
the 1st storey of the pool.
3. Marks around the perimeter of the hotel complex had uneven setting from 15 to
36 mm. The northwestern part of the building had less setting. As a result, there was a
slight tilt of a building of about 1: 3300.
4. Experimental studies have confirmed that the time spent on processing meas-
urements is proportional to the cube of the number of unknowns. So, if the number of
unknowns is about 10, the program calculates minimum in a split second, but if there
are 200 unknowns like in this example, it takes several hours. In this case, the pro-
gram performs calculations without operator intervention. Therefore, a large amount
of computation time is not a significant drawback of the method.
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