数字水准仪和无反射棱镜全站仪在大地工程测量时的精度分析..doc

【精品文档】如有侵权，请联系网站删除，仅供学习与交流数字水准仪和无反射棱镜全站仪在大地工程测量时的精度分析.精品文档.Investigating the accuracy of digital levels and reflectorless total stations for purposes of geodetic engineeringKEY WORDS : Total station;Digital level,Accuracy;Capacity of battery, Reflecting surfaceAbstract In order to achieve the results that meet the specifications of a given project, like engineering surveys and deformation measurements, the knowledge of the reliability and accuracy of the surveying equipment is inevitable. Precise digital levels and reflectorless total stations are used nowadays for several applications in geodetic engineering due to their highly accurate and fast measurements in an automated measuring process. A shortcoming is that they give less accurate measurements in some cases of observations. There are several sources of errors which have an effect on the accuracy of staff reading during digital leveling such as the effect of sun, and therefore have to be investigated. The quality and accuracy of measurements of electronic surveying instrumentsmay be affected by the capacity of instrument battery which may be worked for long time in the field. This paper investigates the effect of sun on the accuracy of digital level measurements and investigates also the effect of battery capacity on the accuracy of total station and digital levels observations. The paper is performed also to find out the effect of inclined angle of reflecting surface,its colors and types on the accuracy of reflectorless total station measurements which have a great influence on monitoring the deformation of cylindrical and domical structures. The results of practical measurements, calculations and analysis of the interesting tests using least squares theory and computer programs are also presented.a 2012 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.All rights reserved.1. IntroductionThe appearance of new surveying instruments, such as precise digital level and reflectorless total station, requires investigating its basic technical parameters to improve the geodetic measurement techniques. Digital leveling is a system of determining height differences between two points using near fully automatic instruments and methods. This isaccomplished by the use of a pattern recognition imaging system built into the level instrument and level rods graduated with a special bar code. The user points the instrument at one of the special rods, focuses as clearly as possible, and presses a button to take the measurement. An image of the barcode rod is received at the instrument and is correlated to an internal digital image of the rod 1. This allows the internal software to determine, where the level line of sight is intercepting the rod. The height above the footplate or zero point is then computed along with the horizontal distance to the rod. These measurements are displayed andused to compute the difference of elevation between the backsight and foresight rods. Apart from this automation, leveling with a digital level is much the same as with an optical level. In fact most digital levels can be used optically, but digital level eliminates reading errors, observer fatigue errors and the need of a manual recorder person 1,2. There are several sources of errors arising in digital leveling which are known to have a systematic effect on the accuracy of staff readings and therefore it is necessary to investigate these modern level instruments to check that they meet the degree of accuracy required by leveling specifications of the specified project.The emergence of reflectorless total station allows working without special reflectors (prisms). It is now possible to measure without long and tedious search of prisms to lift the reflector under the roof of buildings, stands for the installation of the prism above the floor in a room with high ceilings, just to see the necessary point. The principle of work of reflectorless total station is the same as that of a simple total station: measuring the inclined (slope) distance to the object, as well as two angles (horizontal and vertical),which ultimately makes it possible to calculate the point coordinates.As known from the laws of reflection that the incident ray, the reflected ray emitted from reflectorless total station and the normal to the reflection surface at the point of the incidence lie in the same plane and the angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal 5. Therefore,the inclined angle, type and color of the reflecting surface will substantially affect the energy of the reflected ray from this surface to total station and consequently the accuracy of instrument observations. So, it is necessary to investigate the effect of inclined reflecting surfaces which are made from different materials and painted in different colors.2. Comparing the accuracy of precise optical level and digital level observationsTo study practically the accuracy of digital level observations and compare its value with the accuracy of precise optical level,the first experimental test is done in laboratory. The used digital level is Trimble DiNi No. 706531, which has least count staff reading 0.01 mm, and its associated bar-code staff and the used automatic precise level is NI007. The test depends on determining the mean square error (standard deviation) of 25 measurements of height readings from different distances between level and staff. The position of automatic precise level is the same position of digital level position. Measurements were made at six stations of level, each of which was carried out 25 times on the staff at distances: 4.2 m, 10.1 m, 15.2 m,21.4 m, 25.1 m and 28.7 m. The test was carried out during the daytime under natural light and temperature of 27 C.For the analysis of the results, the mean square error of staff readings measurements was calculated for all positions depending on the following formulae:（1）where vi the difference between staff reading i and the mean of all observations.A comparison of mean square errors of staff readings resulted from digital level Trimble DiNi and precise automatic level NI007 is done. The results are illustrated in Fig. 1. As seen in Fig. 1, the difference between measurement errors resulted from used digital levels and optical levels differs on average by 1015%.3. Studying the effect of sun position on the accuracy of digitallevelingAs known that there are several sources of error which have an effect on the accuracy of digital level observations; for example the daytime of field observations because of the sun position.In this paper, the effect of sun position on the accuracy of staff readings and horizontal distances measured by digital level is investigated practically.The test was carried out outdoors (open area) using digital level Trimble DiNi and its bar-code staff. Measurements were made from different level positions at different distances to staff; namely 5.1 m, 10.2 m, 15.1 m, 20.3 m, 25.3 m and 30.1 m. The readings were taken in the direction of the sun and in the direction opposite to sun 25 times at each level position.The test was carried out in the daytime at a temperature of 34 _C. The results of staff readings and horizontal distances in the directions of sun and opposite to sun are illustrated in Table 1. Based on the obtained results, a comparison of staff readings and horizontal distances resulted from digital level in the direction of sun and opposite to sun is done. From the results, it is seen that: Increasing the distance between the digital levels and barcode staff will increase the errors of staff readings and horizontal distances. The difference between errors of staff readings and distances, obtained in the direction of sun and opposite to sun becomes greater.Based on the results of the experimental study, formula for determining the errors of the staff readings resulted from digital levels can be established. The derived equations of staff reading errors are formed and satisfied by the method of least squares technique, depending on the length of sight ray of digital level (the distance from level to bar-code staff) for different conditions of observations, as shown in Table 2. Thus, experimental studies have shown that the value and accuracy of point elevations substantially affected by illumination of the incident sunlight.The effect of sun on the accuracy of digital leveling appears clearly at sun rising and sunset in the case of carrying out observations in eastwest direction. In this case of observations,one of the bar-code staves will be in the direction of sun and the other will be opposite this direction, so the resulted accuracy of leveling will not be the same. To overcome this obstacle, we recommend carrying out leveling in a staggeredpath as shown in Fig. 2.4. Investigating the effect of battery capacity on the digital levelsand total stations observations The quality and accuracy of measurements of modern electronic surveying instruments may be affected by the capacityof instrument battery which may be worked for long time in the field. The author of 3 offers a method of investigating the stability of the measuring unit of terrestrial laser scanner (TLS) to deduce the required heating time of scanner in order to ensure stable operation of the measuring units. In this paper,a study of the influence of battery capacity on the accuracy and reliability of slope distances, horizontal and vertical angles measured by reflectorless total station, as well as observations of digital levels is presented. The first test was carried out to investigate the influence of battery capacity of reflectorless total station on the accuracy of its measurements. An electronic total station Leica TCR 405 Power was used, which has the accuracy of measuring distance is 3 mm± 3 mm/km in reflectorless mode; and the accuracy ofmeasurements of vertical and horizontal angles equal to 5. The test was carried out afternoon from 1:35 pm to 4:55 pm (the period of battery work equals 3 hours and 20 min) in laboratory by recording five continuous reflectorless measurements of distances and directions at intervals of about every 7.5 min during the period of total station working powerwithout further adjustment of orientation of the telescope (horizontal, vertical angles and distances have not changed during the test). Short distance between the instrument and the target 7 m is chosen to reduce the atmospheric effect as minimum as possible. Based on the measured values (inclined distance, horizontal and vertical directions), three charts were constructed; on which the X-axis expresses the time of work of total station battery, and the vertical axis expresses the values of measured parameters (distances or angles), one of these charts is shownin Fig. 3. On each chart a straight forward plot is developed and it is constructed on the basis of the trend line equation, in which the unknowns are the coefficient a, characterizing the degree of stability (S, c and a), and the free term b, characterizing the magnitude of systematic errors of measured distances,horizontal or vertical angles. The initial data for constructing the trend is the deviation of the measured value from the mean value and the time of the total station from the beginning of its run (ti). Determination of unknowns a and b are executed by the method of least squares. From analysis the results, it is seen that the average distance decreases by about 0.5 mm, and vertical and horizontal directions increased by about 3/ and 4/, respectively, for the period of batterywork (3 h and 20 min). The results of determining the coefficientsare shown in Table 3.By the same way the second test was carried out for digital level Trimble DiNi No. 706531 in order to study the influence of battery capacity on the accuracy of digital level observations (staff readings and horizontal distances). The test is done from 1:40 pm to 4:10 pm (period of battery working 2 h and 30 min). During this period the digital level recorded the staff readings and the horizontal distances every 5 min. The telescopeof the instrument did not change during the period of testing. Based on the obtained results, a graphical representation is established to explain the relation between the working time of digital level battery and the staff readings and also the horizontal distance. A straight line is constructed on the basis of the trend line equation. From analysis the results of practical study, it is deduced that the staff readings decreased by 0.35 mm and the measured horizontal distance also decreasedby 4 mm during the time of battery (2 h and 30 min). Therefore, we recommend when performing more accurate measurements,like deformation monitoring, it is necessary to begin with a full charged battery.5. Accuracy of point coordinates from reflectorless total stationThe principle of work of reflectorless total station is determining the position of any point B in three dimension coordinates (XB, YB and ZB) from its basic measurements (horizontal and vertical angles together with slope distances) without using reflectors (prisms).The coordinates of any point (B) can be determined by using total station as following :（2）where XB, YB, XB the coordinates of observed point B; XA,YA, ZA the coordinates of the occupied station A; and c, a,S the vertical, horizontal angles and inclined distance respectively.Eq. (2) have three unknown parameters (XB, YB, XB) and three observations. So there is no redundancy of observations,then this situation has a unique solution so the multivariate propagation technique (Jacobean method) will be used to determine the accuracy of coordinates of point B:（3）where CX variancecovariance matrix of unknowns, J coefficientmatrix (Jacobean coefficient), CL variancecovariance matrix of unknowns.By differentiating Eq. (2) and substituting in Eq. (3), the following formulae can be deduced:（4）where mS, m , m standard deviation (accuracy) of measured inclined distance, vertical and horizontal angles of the used instrument respectively.The values m s, m , m can be taken from the specifications of the instrument or from experimental tests. By substitution with Eq. (2) in Eqs. (4) assuming that the occupied station (point A) has coordinates (0, 0, 0), we deduce the following formulae:（5）It is important to note that Eq. (5) can be used for determining the accuracy of any point from the cloud of points which are measured from terrestrial laser scanner because in all cases of field observation of laser scanner, the coordinates of occupied instrument station equal (0, 0, 0). The best position of the total station for achieving good accuracy, especially in deformation monitoring,