Tiêu chuẩn iso 17123 5 2012

© ISO 2012 Optics and optical instruments — Field procedures for testing geodetic and surveying instruments — Part 5 Total stations Optique et instruments d’optique — Méthodes d’essai sur site des ins[.]

Requirement

Before commencing the measurements, it is important that the operator ensures that the precision in use of the measuring equipment is appropriate for the intended measuring task.

The total station and its associated equipment must be properly calibrated and maintained in accordance with the manufacturer's reference manual Additionally, it is essential to utilize tripods and reflectors as recommended by the manufacturer to ensure accurate measurements.

The coordinates are considered as observables because on modern total stations they are selectable as output quantities.

All coordinates shall be measured on the same day The instrument should always be levelled carefully The correct zero-point correction of the reflector prism shall be used.

Meteorological conditions, particularly temperature gradients, significantly impact test results, with overcast skies and low wind speeds providing optimal conditions To ensure accuracy, actual meteorological data must be collected to apply atmospheric corrections to raw distances Factors such as air temperature, wind speed, cloud cover, and visibility should be considered, as they can vary based on the task location It's essential to account for the prevailing weather conditions during measurement and the type of surface involved The testing conditions should align with those anticipated during the actual measuring task, in accordance with ISO 7077 and ISO 7078 standards.

Laboratory tests deliver results that are largely unaffected by atmospheric conditions, offering significantly higher precision than field tests However, the high costs associated with these laboratory tests make them impractical for most users.

This part of ISO 17123 describes two different field procedures as given in Clauses 5 and 6 The operator shall choose the procedure which is most relevant to the project’s particular requirements.

To evaluate angle measurement and distance measurement separately, see ISO 17123-3 and ISO 17123-4.

Procedure 1: Simplified test procedure

The simplified test procedure provides an estimate as to whether the precision of a given total station is within the specified permitted deviation in accordance with ISO 4463-1.

The simplified test procedure utilizes a minimal set of measurements, focusing on x-, y-, and z-coordinates within a test field that lacks nominal values Precision is assessed by calculating the maximum deviation from the mean value.

To achieve a more accurate evaluation of the total station in field conditions, it is advisable to follow the comprehensive testing procedure outlined in Clause 6, as a significant standard deviation cannot be achieved otherwise.

Procedure 2: Full test procedure

The full test procedure shall be adopted to determine the best achievable measure of precision of a total station and its ancillary equipment under field conditions.

Copyright International Organization for Standardization

Provided by IHS under license with ISO Licensee=University of Alberta/5966844001, User=sharabiani, shahramfs

This procedure involves measuring coordinates in a test field that lacks nominal values The experimental standard deviation for the coordinate measurement of an individual point is calculated using least squares adjustments.

The test procedure outlined in Clause 6 of ISO 17123 aims to assess the precision of a specific total station This precision is quantified by the experimental standard deviations of coordinates measured in both face positions of the telescope, denoted as \$s_{ISO-TS XY}\$ and \$s_{ISO-TS-Z}\$.

This procedure can assess the precision of total stations utilized by a single survey team with one instrument and its equipment at a specific time It also evaluates the precision of a single instrument over time and compares the precision of multiple total stations under similar field conditions.

Statistical tests are essential for assessing if the experimental standard deviations align with the theoretical standard deviations of the instrumentation Additionally, these tests help determine whether two tested samples originate from the same population.

Configuration of the test field

Two target points, T1 and T2, must be established as shown in Figure 1, ensuring they are securely anchored to the ground The distance between these targets should exceed the average distance, such as 60 meters, based on the specific measuring task Additionally, the heights of the targets should vary as much as the terrain permits.

Two instrument stations, S1 and S2, will be positioned in alignment with two target points Station S1 will be located 5 to 10 meters from target T1, directed away from target T2 Meanwhile, station S2 will be set between the two target points, maintaining a distance of 5 to 10 meters from target T2.

Figure 1 — Configuration of the test field

Measurement

One set consists of two measurements to each target point in one telescope face at one of the instrument stations.

The coordinates of two target points are measured using four sets of observations (telescope face: I – II – I – II) at the instrument station S1 After shifting the instrument to station S2, the same measurement sequence is repeated The coordinates of the stations and their reference orientations are determined at the discretion of each set.

On-board or stand-alone software shall be used for the observations It is preferable to use the same software which will be used for the practical work.

The sequence of the measurements is shown in Table 1.

Table 1 — Sequence of the measurements for one series Seq No

Calculation

The evaluation of the test results is given by the deviation of the horizontal distance of each set from the mean value of all measured horizontal distances.

Each horizontal distance between two target pointsl i k , is calculated as l i k , = ( x i k , , 2 − x i k , , 1 ) 2 + ( y i k , , 2 − y i k , , 1 ) 2 i = 1 2 , k = 1 2 3 4 , , , (1) Their mean value L is calculated as

The half values of the deviation of each distance from its mean value, r j k , are calculated ri k , li k L , i k

The maximum value d xy of the r i k , is defined as d xy = max r i k , i = 1 2 , k = 1 2 3 4 , , , (4)

The height differences d z i k , between target points are calculated using measured z-coordinate values in each set. d z i k , = z i k , , 2 − z i k , , 1 i = 1 2 , k = 1 2 3 4 , , , (5)

The mean value a z of height difference in all sets is a z d z i k k i

The differences r z i k , between height differences of two target points and the mean value a z are rz i k dz i k az , = , , − i = 1 2 , k = 1 2 3 4 , , , (7)

Half of the maximum difference value d z is calculated as d z = 1 r z i k

The differences $d_{xy}$ and $d_z$ must remain within the allowed deviations $p_{xy}$ and $p_z$ as specified by ISO 4463-1 for the intended measurement task In cases where $p_{xy}$ and $p_z$ are not provided, the conditions $d_{xy} \leq 2.5 \times 2 \times s_{ISO-TS-XY}$ and $d_z \leq 2.5 \times 2 \times s_{ISO-TS-Z}$ apply, where $s_{ISO-TS-XY}$ and $s_{ISO-TS-Z}$ represent the experimental standard deviations of the x, y, and z measurements, respectively, determined through the complete testing procedure using the same instrument.

Configuration of the test field

Three target points (T1, T2, T3) will be established at the corners of a triangle, as illustrated in Figure 2 These targets must be securely anchored to the ground, with varying distances between them; at least one distance should exceed the average distance of 60 meters based on the measurement requirements Additionally, the heights of the targets should vary according to the natural contours of the terrain.

Three instrument stations (S1, S2, S3) shall be set out close to each triangular side approximately 5 m to

Figure 2 — Example of field configuration for full test

Measurement

One set consists of three measurements to each target point with a single telescope face at each instrument station.

From the instrument stations S1, S2, S3, the coordinates of the three target points shall be measured by four sets of observation sequences (telescope face: I – II – I – II).

The coordinates and orientation of each station are flexible and should remain unchanged during the measurement of four sets of observations from the same location.

On-board or stand-alone software shall be used for the observations It is preferable to use the same software which will be used for the practical work.

The sequence of the measurements is shown in Table 2.

Table 2 — Sequence of the measurements for one series Seq No

Calculation

Construction of the mathematical model of the triangle is carried out as follows.

Calculate the horizontal distances l i k , , 3 between T 1 and T 2 ; l i k , , 1 between T 2 and T 3 ; l i k , , 2 between T 3 and T 1 respectively by measured coordinates ( x i j k , , ,y i j k , , ) l i j k , , = ( x i j , − 1 , k − x i j , + 1 , k ) 2 + ( y i j , − 1 , k − y i j , + 1 , k ) 2 (9) i = 1, 2, 3; j = 1, 2, 3 (if j −1 is 0 or j+1 is 4, then replace it by 3 or 1 respectively); k = 1, 2, 3, 4.

The mean length of each sideL j :

The coordinates of the mathematical model of the triangle M i (i = 1,2,3) is defined based on M 1 = (0,0) and the line from M 1 to M 2 as the x-axis. © ISO 2012 – All rights reserved ``,,,``,,`,```,,,,`,```,```,,,-`-`,,`,,`,`,,` - 7

Figure 3 — Mathematical model of the triangle

The coordinates of the centre of gravity of the mathematical model, ( X Y g g , ) :

The coordinates of the centre of gravity of the triangle obtained at each instrument station, ( x g i , , y g i , ) : x y x y g i g i i j k k j i j k k j

Shift the coordinates to coincide the centre of gravity of the mathematical model on the centre of gravity of the measured triangle.

The coordinates of the centre of gravity of the mathematical model ( X t i j k t i j k , , , , Y , , , ) after the shift are calculated as

Rotate the mathematical model around the centre of gravity to minimize residuals of the apex coordinates between the mathematical model and respective measured triangles.

Apex coordinates of mathematical model ( X m i j k m i j k , , , , Y , , , ) after the rotation:

Residuals ( r x i j k y i j k , , , , r , , , ) of the coordinates of the measured triangles from those of the rotated mathematical model are r x i j k , , , = x i j k , , − X m i j k , , , i = 1 2 3 , , j = 1 2 3 , , k = 1 2 3 4 , , , (21) ry i j k yi j k Ym i j k , , , = , , − , , , i = 1 2 3 , , j = 1 2 3 , , k = 1 2 3 4 , , , (22) The sum of squares of residuals is r r x i j k r y i j k k j i xy

The mathematical model consists of three sides, leading to a total of 21 unknown parameters, calculated as 3 (sides) + 6 (center of gravity points from 2 components at 3 instrument stations) + 12 (rotation parameters from 4 sets at 3 instrument stations) Consequently, the degrees of freedom are determined to be 51, derived from the equation ν XY = 72 − 21.

The experimental standard deviation is s r xy

Finally, the standard uncertainty of x-, y-coordinates is: u ISO-TS-XY=s XY (26)

The height difference between T1 and T2 (and T3) is calculated using measured z-values for each set. d z z i j k z i j k , , , i j k , , i k , ,

The mean values of d z , , , i k 2 and d z , , , i k 3 are a z j d z i j k j k i

The residuals r z i j k , , of the height differences d z i k , , 2 ,d z i k , , 3 from obtained mean values for each set of measurements are calculated as r z i j k , , , = d z i j k , , , − a z j , i = 1 2 3 , , , j = 2 3 , , k = 1 2 3 4 , , , (29) The sum of the squares of the residuals is obtained by r r z i j k k j i z

The number of degrees of freedom is ν Z = 24 − = 2 22 (31)

Finally, the standard deviation of z-coordinate is s r

Its standard uncertainty is u ISO-TS- Z = s Z

Statistical tests

Statistical tests are applicable for the full test procedure only.

To interpret the results, statistical tests will be conducted using the experimental standard deviation of a coordinate measured on the test triangle The analysis aims to address two key questions: first, whether the calculated experimental standard deviation, \$s\$, is less than or equal to the manufacturer's specified value, \$\sigma\$, or another predetermined value; second, whether two experimental standard deviations, \$s\$ and \$\tilde{s}\$, derived from different measurement samples, belong to the same population, given that both samples share the same degrees of freedom, \$v\$.

The experimental standard deviations, denoted as \$s\$ and \$\tilde{s}\$, can be derived from two sets of measurements taken with the same instrument but by different observers, or from measurements taken at different times using the same instrument.

``,,,``,,`,```,,,,`,```,```,,,-`-`,,`,,`,`,,` - two samples of measurements by different instruments.

For the upcoming tests, a confidence level of 95% (1 - α = 0.95) is established, with the degrees of freedom set at ν XY = 51 for the x- and y-coordinates, and ν Z " for the z-coordinate based on the measurement design.

Table 3 — Statistical tests Question Null hypothesis Alternate hypothesis a) b) s ≤ σ σ σ =  s > σ σ σ ≠ 

The null hypothesis asserts that the experimental standard deviation, $ s $, is less than or equal to a predetermined theoretical value, $ \sigma $ This hypothesis remains accepted if the condition involving $ x $, $ y $, and $ z $ is satisfied, specifically for $ s_{XY} $ and $ s $.

Otherwise, the null hypothesis is rejected.

When comparing two distinct samples, a test determines if the experimental standard deviations, $ s $ and $ \tilde{s} $, originate from the same population The null hypothesis, $ \sigma = \tilde{\sigma} $, is upheld if specific conditions involving $ x $, $ y $, and $ z $ are satisfied.

Otherwise, the null hypothesis is rejected.

The number of degrees of freedom and, thus, the corresponding test values χ1 α 2

2 − / and F 1 − α / 2 ( ) ν ν ,(taken from reference books on statistics) change if a different number of measurements is analysed.

Combined standard uncertainty evaluation (Type A and Type B)

The sources of uncertainty (influence quantities) are described in Table 4 as an uncertainty budget.

Table 4 — Typical influence quantities of the total station

Sources of uncertainty Symbol Evaluation Distribution

Standard deviation of x-, y- and z-coordinates u ISO TS − Type A normal

II Relevant sources of the total station

Distance uncertainty, denoted as $ u_{r, ts} $, is classified as Type B normal or defined by the manufacturer Similarly, horizontal angle uncertainty, represented as $ u_{\phi, ts} $, follows the same classification Additionally, vertical angle uncertainty, indicated as $ u_{\theta, ts} $, is also categorized as Type B normal or specified by the manufacturer.

Minimum display digit u disp Type B rectangular

III Error patterns from the mechanical setup

Torsion of a tripod (ISO 12858-2) u trd Type B rectangular

Stability of a tripod height (ISO 12858-2) u hs Type B rectangular

IV Error sources of the atmospheres

Relative humidity u rh Type B normal

Uncertainty on the polar coordinates system is described as u r = u r ts 2 − + u temp 2 + u prs 2 + u rh 2 (42) u φ = u φ − ts + u trd

``,,,``,,`,```,,,,`,```,```,,,-`-`,,`,,`,`,,` - uz 2 = ( sin θ ⋅ u r ) 2 + ⋅ ( r cos θ ⋅ u θ ) 2 (46) Combined uncertainty is u xy = u ISO-TS-XY 2 + ( ux 2 + uy 2 ) + u disp 2 (47) u z = u ISO TS Z − − + uz + u

Expanded uncertainty is, with coverage factor k = 2

Example of the simplified test procedure

In Table A.1 all measurements are compiled according to the observation scheme given in Table 1.

Instrument type and number: NT xxx 309090

LV,3942 and according to Formula (3): r r r r r

3 170 and according to Formula (6): a z = − 3 1705 , and according to Formula (7): r r r r r

Example of the full test procedure

Table B.1 contains an example of observed data taken in accordance with the full test procedure.

According to Formula (32): s ISO-TS-Z = 0 00139 ,

B.3.1 Statistical test according to Question a)

At a 95% confidence level, the null hypothesis that the experimental standard deviation $ s_{ISO-TS-XY} = 1.10 \, \text{mm} $ and $ \sigma = 5.0 \, \text{mm} $ is less than or equal to the manufacturer's value is not rejected.

The null hypothesis, which asserts that the experimental standard deviation $ s_{ISO-TS-Z} = 1.39 \, \text{mm} $ is less than or equal to the manufacturer's value $ \sigma = 5.0 \, \text{mm} $, is not rejected at a 95% confidence level.

B.3.2 Statistical test according to Question b)

The null hypothesis, which posits that the experimental standard deviations of s = 1.10 mm and s̄ = 1.15 mm originate from the same population, is upheld at a 95% confidence level.

The null hypothesis, which posits that the experimental standard deviations of $ s = 1.39 \, \text{mm} $ and $ s \sim = 1.55 \, \text{mm} $ originate from the same population, is upheld at a 95% confidence level.

Example for the calculation of a combined uncertainty budget

The analysis of measurements: u ISO-TS s ISO-TS are obtained from Annex B s ISO-TS-XY = 0 00110 , m s ISO-TS-Z = 0 00139 , m

According to the specification by the manufacturer, the uncertainty of distance u r-ts is obtained by applying the manufacturer’s specification ± (3 + 2ppm × D) and maximum measured distance = 57 m. u r-ts = + × 3 2 57000 × 10 − 6 = 3 1 , mm

The uncertainty of horizontal angle measurement u φ -ts is obtained by applying the manufacturer’s specification 5” (according to ISO 17123-3) as u φ -ts = 5"

The uncertainty of vertical angle measurement u θ -ts is obtained by applying the manufacturer’s specification 5” (according to ISO 17123-3) as u θ − ts = =

2 89 , ″ The uncertainty of minimum display digit u disp u dispx = u dispy = u dispz = 0 5 = mm

, 0 29 , when minimum digit is 1 mm.

The influenced quantity of the tripod u trd u trd = 3 = ′′

1 73 , with the estimated torsion according to ISO 12858-2 and rectangular distribution.

The stability of the tripod height u hs is estimated within 0,5 mm according to ISO 12858-2, which can be omitted from the budget.

The uncertainty of temperature u temp : u temp = × 1 57000 × 10 − 6 = 0 057 , mm, with ±1 °C from experience

The uncertainty of pressure u prs : u prs = 0 3 , × × 5 57000 × 10 − 6 = 0 086 , mm, with 5 hPa on experience

The uncertainty of humidity u rh can be omitted from the budget, as its influence is so small for the maximum distance of 100 m in the test.

The uncertainty on polar coordinate is calculated according Formula (42), (43), (44): u r = u r ts 2 − + u temp 2 + u prs 2 = 3 114 , 2 + 0 057 , 2 + 0 086 , 2 = 3 116 ,  mm u φ = u φ − ts + u trd = + = ′′

The uncertainty on rectangular coordinate is calculated according to Formula (45), (46): ux 2 + uy 2 = 11 85 , mm uz 2 = 3 12 , mm

Combined uncertainty is calculated according to Formula (47), (48): u xy = 1 10 , 2 + 11 85 , + 0 29 , 2 = 3 63 , u z = 1 39 , 2 + 3 12 , + 0 29 , 2 = 2 27 ,

Table C.1 — Uncertainty budget on rectangular coordinate

Input quantity Input estimates

Standard uncertainty u x ( ) i / mm Distribution Sensitivity coefficient u c c u x i xy i i

( ) ≡ × ( ) / mm Evaluation Remark u ISO−TS―XY - 1,06 normal 1 1,06 Type A eq (25) u ISO−TS―Z - 1,39 normal 1 1,39 Type A eq.(32)

(ux 2 +uy 2 ) 0,5 DmaxWm,Va=1° 3,44 normal 1 3,44 Type B u z DmaxWm,Va=1° 1,77 normal 1 1,77 Type B u disp 0 0,29 rectangle 1 0,29 Type B

Va=Elevation Angle Final results u xy 3,63 u z 2,27

Sources which are not included in uncertainty evaluation

The sources of uncertainty shown in Table D.1 are not to be evaluated individually, since those are already considered in the corresponding influence quantities listed in Table 4 or not relevant.

Table D.1 — Sources of uncertainty not to be evaluated individually

Source of uncertainty Distance Vertical angle Horizontal angle

Sighting axis and vertical axis •

Vertical-axis tilt of total station • • •

[1] ISO 1101:2012, Geometrical product specifications (GPS) — Geometrical tolerancing — Tolerances of form, orientation, location and run-out

[2] ISO 2854:1976, Statistical interpretation of data — Techniques of estimation and tests relating to means and variances

[3] ISO 3494:1976, Statistical interpretation of data — Power of tests relating to means and variance

and additional resources available at the **OIML website**.

[5] JCGM 100:2008 Evaluation of measurement data — Guide to the expression of uncertainty in measurement http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

The JCGM 104:2009 document serves as a foundational guide for understanding the evaluation of measurement data, specifically focusing on the expression of uncertainty in measurement It outlines essential principles and methodologies that are crucial for accurate data interpretation and reporting This guide is vital for professionals in metrology and related fields, ensuring compliance with international standards and enhancing the reliability of measurement results.

[7] NIST Technical Note 1297:1994, Guidelines for Evaluating and Expressing the Uncertainty of NIST

Measurement Results http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf

[8] NIST SOP No29:2003 Standard Operating Procedure for the Assignment of Uncertainty http:// ts.nist.gov/WeightsAndMeasures/upload/SOP_29_Mar_2003.pdf

Tiêu đề	Field Procedures for Testing Geodetic and Surveying Instruments
Trường học	University of Alberta
Chuyên ngành	Optics and Optical Instruments
Thể loại	tiêu chuẩn
Năm xuất bản	2012
Thành phố	Switzerland

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