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Lecture _02 Error in Surveying .pptx
- 1. 1 CHAPTER -02 Lecture 02– Error in Surveying
- 2. 2 Definition Error is thedifference between a measured or calculated value of a quantity and the true value of that quantity
- 3. 3 Cont.… ♠ It canbe stated completely that 1. no measurement is exact, 2. every measurement contains errors, 3. the true value of a measurement is never known, and thus 4. the exact sizes of the errors present are always unknown. ****The true value of a quantity is,a value which is,absolutely free from all types of errors*****
- 4. 4 Conti… ♠ The truevalue cannot be determined because some errors always creep in the measured quantities ♠ As better equipment is developed, environmental conditions improve, and observer ability increases, the observations will approach their true values more closely, but they can never be exact.
- 5. 5 Mistake ( blunders) ♠ A blunder, also called a mistake, is an unpredictable, human mistake. Although a small blunder may remain undetected and have the same effect as an error, it is not an error. ♠ Mistakes occur in measurements due to carelessness, inattention, miss- communication, inexperience or poor judgment of the surveyor. For example, recording 79.36 or 73.69 instead of 73.96
- 6. 6 EXAMPLES OF MISTAKES Transposing two numbers Neglecting to level an instrument Not placing the sighting point over the correct point Misplacing the decimal point Misunderstanding a call out Not sighting the point that corresponds to the point name or number put in the data collector
- 7. 7 Conti… Mistakes aredetected and eliminated by using proper procedures, such as: Checking each recorded and the calculated value Making independent and redundant measurement Calculating repeatedly etc.
- 8. 8 Source of Error Errorsource are classified in to three types such as Personal, Instrumental, Natural, however, some errors do not clearly fit in to one of these categories and may be due to a combination of factors
- 9. 9 Personal Error a. Personalerror : occur due to human limitations, such as sense of sight and touch. Personal errors can be characterized as either systematic or random. Personal systematic errors are caused by an observer tendency to react the same way under the same conditions (inconsistency). When there is no such tendency, the personal errors are considered to be random. An example of a personal error is an error in the measured value of a horizontal angle, caused by the inability to hold a range pole perfectly in the direction of the plumb line.
- 10. 10 Instrumental Errors b. Instrumentalerrors: Those error which occurs due to the imperfection of the instrument The different parts of instruments cannot be adjusted exactly with respect to each other. Moreover, with time the wear and tear of the instruments causes errors. Examples of instrument error are: Imperfect linear or angular scales Instrument axes are not perfectly parallel or perpendicular to each other Misalignment of various part of the instrument Optical distortions causing “what you see is not exactly what you are supposed to see”
- 11. 11 Conti.. For example,the divisions on a theodolite or total station instrument may not be spaced uniformly. Another example, if the tape used in measuring the distance is actually 29.95m long where as the nominal length is 30m, the instrumental error occurs because of the imperfect tape.
- 12. 12 Conti.. Most instrumentalerrors are eliminated by using proper procedures, such as Observing angles in direct and reverse modes, Balancing foresights and back sights and repeating measurements. Since not all instrument errors can be eliminated by procedures, Instruments must be periodically checked, tested and adjusted (or calibrated.) Instruments must be on a maintenance schedule to prevent inaccurate measurements.
- 13. 13 Natural Errors a. Naturalerrors : are caused by changes in natural phenomena, such as temperature, wind, humidity, refraction, and magnetic field. Examples of natural errors are: A steel tape whose length varies with changes in temperature. Sun spots activity and its impact on the ionosphere, hence on GPS surveying. For example if a tape has been calibrated at 20ºc, but the field temperature is 30ºc there will be a natural error due to temperature variation.
- 14. 14 Conti.. ♠ Natural errorsare mostly systematic and should be corrected or modeled in the adjustment. ♠ Some natural errors such as the effect of curvature and refraction in leveling can be eliminated by balancing back sight and foresight
- 15. 15 Types of Error Insurveying, errors can be broadly classified into the following two types. 1. Systematic or cumulative errors 2. Accidental or random errors A systematic error is an error that will always have the same magnitude and the same algebraic sign under the same conditions. systematic errors follow some well-defined mathematical or physical law or system ♠ In most cases, systematic errors are caused by physical and natural conditions that vary in accordance with fixed mathematical or physical laws.
- 16. 16 Conti.. ♠ The magnitudeand the sign of the systematic errors can be determined and a suitable correction can be applied to the measured quantity. ♠ So, systematic errors can be corrected or eliminated Random/accidental / errors These are the errors that remain after all mistakes and systematic errors have been removed from the measured values. Random errors are random in nature and occur beyond the control of the surveyor. They usually do not follow any physical and mathematical law and therefore must be dealt with according to the mathematical laws of probability. It is impossible to avoid random errors in measurements entirely
- 17. 17 Conti.. ♠ Theoretically, random/ accidental error has an equal chance of being negative or positive.Thus, errors of this type tend to be compensating. Nature of Random error Positive and negative errors equal chance to occur Small errors have most probability to occur Large errors has small chance occurs Random / Accidental errors occur due to: Imperfection in the instruments Human limitation or Change in atmospheric conditions
- 18. 18 Accuracy and Precision Accuracy:-refers to the degree of perfection obtained in measurements. It denotes how a given measurement close to the true value of the quantity. Precision:- it is the closeness of one measurement to another. ♠ If a quantity is measured several times and the values obtained are very close to each other, the precision is said to be high.
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- 21. 21 BASIC DEFINITIONS RELATEDTO ERROR i. Most probable value (mean) is the arithmetic mean or average value of a series of repeated measurements It has more chance to be a true value of a quantity Residual is the difference between measured value of a quantity and its most probable value
- 22. 22 Conti… i. The standarddeviation (σ) It is a statistical measure of precision It is the amount of deviation from mean of any single measurement It shows how much variation or 'dispersion' there is from the 'average' (mean, or expected/budgeted value). the smaller the value of the standard deviation,the greater the precision and vise versa In surveying, it is used to analyze random errors
- 23. 23 Conti… Standard deviation(σ ) can be calculated using
- 24. 24 Conti… i. Standard errorof the mean ( m) The standard error of the mean of a number of observations of the same quantity is given by 2 1 v n n
- 25. 25 Conti… i. Maximum error In surveying generally 99.9% error (E99.9) is taken as the maximum error It corresponds to a range of +3.29σ and -3.29σ The maximum error is often used to separate mistakes (gross errors) from the random errors If any measurement deviates from the mean by more than ±3.29σ it is considered as a mistake, and that measurement is rejected
- 26. 26 Conti… i. Most probableerror of the mean (Em) 2 0.6745 1 v Em n n
- 27. 27 Conti… i. Different percentageErrors Sometimes, the following percentages of error are also required (a) 90% Error (E90) ≈ + 1.645σ (b) 95% Error (E95) ≈ + 1.960σ (c) 95.5% Error (E95.5) ≈ + 2.0σ (d) 99.7% Error (E99.7) ≈ + 2.968σ ≈+3σ
- 28. 28 Weighted Measurement The weightof the measurement indicates the reliability of a quantity. It is inversely proportional to the variance (σ2) of the observation, and can be expressed as
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- 30. 30 Relative Precision ♠ Therelative precision or the degree of precision is used to express the precision of the various measurements ♠ It is usually expressed as a ratio of the standard error of the mean ( m) to the mean value (M) of the quantity Relative Precision = 1 m M δ
- 31. 31 Conti… ♠ Relative precision= m/m ♠ It is usually expressed with numerator as unit Example - if the standard deviation is ± 0.03m for the mean value of the length of the line of 615.41m , The relative precision = δ 0.03 1 20,500 615.41
- 32. 32 Degree of Accuracy ♠The degree of accuracy indicates the accuracy attained in the measurements ♠ It is usually expressed as the ratio of the error to the measured quantity For example, a degree of accuracy of 1 in 10,000 indicates that there is an error of 1 unit in 10,000 units.
- 33. 33 Degree of AccuracyIn Different Measurement i. Linear measurements ----The degree of accuracy of the linear measurement is usually expressed as the ratio of the standard deviation to the measured distance Degree of Accuracy For example if there is a standard deviation of + 0.05m in a measured distance of 584.65m, the degree of accuracy is 1 in 11700
- 34. 34 Conti.. i. Angular measurements-For angular measurements, the degree of accuracy is usually expressed as k W/r N = Number of angles measured K = Angular error of closure Number of angles measured N
- 35. 35 Conti.. i. Traverse -the degree of accuracy of a traverse is usually expressed as the ratio of the error of closure to the perimeter of the traverse thus: . . Error of closure D of Accu Total Perimeter of traverse
- 36. 36 Conti.. i. Leveling -the degree of accuracy is usually expressed as degree of accuracy = K Where L= Horizontal length of the route in meter K = For example: - if there is an error of 0.2m in a route of 5000m, what will be the degree of accuracy? L Error of in elevation HOrizontal length of route
- 37. 37 EXAMPLE Question Suppose that aline has been measured 10 times using the same equipment and procedures. It is assumed that no mistakes exist, and any systematic errors have been eliminated. The measured value (538.57, 538.39, 538.37, 538.39, 538.48, 538.49, 538.33, 538.46, 538.47, 538.55) all measurement are in ft. Compute a) The most probable value, b) standard deviation and c) Errors having 50%, 90% & 95% probability
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