Study program:
Mine Surveying (VII semester -BsC) |
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Name of subject: Computation of adjustment |
Instructors:
Prof. Aleksandar Ganić, Zoran Gojković |
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Status: Compulsory |
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ECTS: 5 |
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Prerequisites: - |
Course Objectives:
Learn basic concepts of measurement results, errors that are present in them, and statistical processing of measurement results and functions of measured values in order to quality assessment of their accuracy. Mastering the knowledge of processing the measurement results - by adjustment directly measured values, indirect and condition measurements using the least squares method in order to calculate the most probable values of measured and unknown quantities, as well as their assessment of accuracy. |
Learning Outcomes:
Adequate observation of measurement, independent statistical processing of the measurement results and the ability to solve parametric and condition adjustment. |
Content:
Theory teaching
The concept of measurement, measurement conditions, errors and types of errors present in the measurement results. Statistical processing of measurement results and indicators of uncertainty. Gaussian normal distribution and least squares method. Assessment of accuracy of functions of measured values. The law of error propagation. Determining the required accuracy of the measured values if a function error is known according to the principle of equal and unequal effects. Adjustment of directly measured values using the least squares method - arithmetic mean and weighted mean. The notion of weight. Assessment of accuracy of measured values, arithmetic and weighted means. Parametric adjustment, observation equations and residuals, normal equations, assessment of accuracy. Methods of solving normal equations - Gaussian method of elimination, Banakiev-Cholesky’s method, iterative and matrix solving of normal equations. Condition adjustment, condition equations, correction equations, normal equations, assessment of accuracy. Practical teaching
Computational examples of statistical distribution of measurement results and histogram development. Computational examples of error calculation of linear and nonlinear functions. Calculation of argument errors when a function error is known for the principle of equal and unequal effects. Calculating arithmetic mean and assessment of accuracy of measured values and arithmetic mean. Weights and weight functions. Calculating the weighted mean and assessment of accuracy of the weight unit, the measured values and the weighted mean. Measurement pairs. Assessment of accuracy of the measurement of horizontal directions from the disagreement of round of horizontal angles. Assessment of accuracy of angular measurement from non-triangle measurement. Computational examples of parametric adjustment. Calculation examples of condition adjustment. |
Suggested Reading List:
- Ganić A., 2008.: Račun izravnanja, RGF, Beograd
- Ganić A., 1996.: Zbirka zadataka iz računa izravnanja, RGF, Beograd
- Tomković D., 2003.: Merna nesigurnost, VGGŠ, Beograd
- Vulić M., 2007.: Metoda najmanjših kvadratov, Univerza v Ljubljani
- Džeparoski V., 1995.: Račun izravnanja, RGF, Beograd
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Conduct of the Course:
Lectures, individual practical lessons. |
Fund hours:
| Lectures |
Exercises |
Other forms of teaching |
Study research |
| 2 |
2 |
0 |
0 |
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Assessment:
| Final Exam |
ECTS |
| Oral Exam | 30 |
| Classwork Assessment |
ECTS |
| Class Participationа | 10 | | Practical Classes | 15 | | Written tests | 45 |
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Additional Assessment Criteria: - |
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