MEASUREMENT ANALYSIS AND ADJUSTMENT Capital Project Skill Development Class (CPSD) G100398 By Jeremy Evans, P.L.S. Psomas Supplemented by Caltrans Staff
Introduction “The dark side of surveying is the belief that surveying is about measurements, precisions and adjustments. It is not and never will be.” Dennis Mouland P.O.B. Magazine July, 2002
Introduction Much has been written lately about least squares adjustment and the advantages it brings to the land surveyor. To take full advantage of a least squares adjustment package, the surveyor must have a basic understanding of the nature of measurements, the equipment he uses, the methods he employs, and the environment he works in.
Introduction • Measurements and Adjustments: “War Stories”
Class Outline • Survey Measurement Basics - A Review • Measurement Analysis • Error Propagation • Introduction to Weighted and Least Squares Adjustments • Least Squares Adjustment Software • Sample Network Adjustments
Measure First, Adjustment Last • Adjustment programs assume that: • Instruments are calibrated • Measurements are carefully made • Networks are stronger if: • They include Redundancy • They have Strength of Figure • Adjust only after you have followed proper procedures!
Survey Measurement Basics A Review of Plumb Bob 101
Surveying (Geospatial Services?) • Surveying – “That discipline which encompasses all methods for measuring, processing, and disseminating information about the physical earth and our environment.” – Brinker & Wolf • Surveyor - An expert in measuring, processing, and disseminating information about the physical earth and our environment.
Measurement vs. Enumeration • A lot of statistical theory deals with enumeration, or counting. It’s a way to take a test sample instead of a census of the total population. • The surveyor is concerned with Measurement. The true dimensions can never be known.
Instrument Testing • Pointing error of typical total station
Instrument Specifications • Distance Measurement • sm = ±(0.01’ + 3ppm x D) • What is the error in a 3500 foot measurement? • sm= ±(0.01’+(3/1,000,000 x 3500)) = ± 0.021’
Calibration or “Don’t shoot yourself in the foot.” • Leica instruments should be serviced every 18 months. • EDM’s should be calibrated every six months • Tribrachs should be adjusted every six months, or more often as needed. • Levels pegged every 90 days
Is It a Mistake or an Error? • Mistake - Blunder in reading, recording or calculating a value. • Error - The difference between a measured or calculated value and the true value.
Blunder • a gross error or mistake resulting usually from stupidity, ignorance, or carelessness.
Blunder • Setup over wrong point • Bad H.I. • Incorrect settings in equipment
Types of Errors • Systematic • Random • An error is the difference between a measured value and the true value. Later we will compare this to the definition of residual
Systematic • an error that is not determined by chance but is introduced by an inaccuracy (as of observation or measurement) inherent in the system
Systematic • Glass with wrong offset • Poorly repaired chain • Imbalance between level • sightings Each measurement made with the tape is 0.1' shorter than recorded.
Random an error that has a random distribution and can be attributed to chance. without definite aim, direction, or method
Random • Poorly adjusted tribrach • Inexperienced Instrument • operator • Inaccuracy in equipment
Nature of Random Errors • A plus or minus error will occur with the same frequency • Minor errors will occur more often than large ones • Very large errors will rarely occur (see mistake)
Normal Distribution Curve #1 • A plus or minus error will occur with the same frequency, so • Area within curve is equal on either side of the mean
Normal Distribution Curve #2 • Minor errors will occur more often than large ones, so • The area within one standard deviation (s) of the mean is 68.3% of the total
Normal Distribution Curve #3 • Very large errors will rarely occur, so • The total area within 2s of the mean is 95% of the sample population
2s 2s 1s 1s Histograms, Sigma, & Outliers MEAN Histogram: Plot of the Residuals \ Bell shaped curve / Outlier \ -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1 s : 68% of residuals must fall inside area 2 s 95 % of residuals must fall inside area Residuals
Measurement Components • All measurements consist of two components: the measurement and the uncertainty statement. 1,320.55’ ± 0.05’ • The uncertainty statement is not a guess, but is based on testing of equipment and methods.
Accuracy Vs. Precision • Precision - agreement among readings of the same value (measurement). A measure of methods. • Accuracy - agreement of observed values with the “true value”. A measure of results.
Measurement Analysis Determining Measurement Uncertainties
Determining Uncertainty • Uncertainty - the positive and negative range of values expected for a recorded or calculated value, i.e. the ± value (the second component of measurements).
Your Assignment • Measure a line that is very close to 1000 feet long and determine the accuracy of your measurement. • Equipment: 100’ tape and two plumb bobs. • Terrain: Basically level with 2’ high brush. • Environment: Sunny and warm. • Personnel: You and me.
Planning the Project • Test for errors in one tape length. • Measure 1000 foot distance using same methods as used in testing. • Determine accuracy of 1000 foot distance.
Test Data Set Measured distances: 99.96 100.02 100.04 100.00 100.00 99.98 100.02 100.00 99.98 100.00
Averages • “Measures of Central Tendency” • The value within a data set that tends to exist at the center. • Arithmetic Mean • Median • Mode
Averages • Most commonly used is Arithmetic Mean • Considered the “most probable value” n = number of observations • Mean = 1000 / 10 • Mean = 100.00’
Residuals • The difference between an individual reading in a set of repeated measurements and the mean • Residual (n) = reading - mean • Sum of the residuals squared (Sn2) is used in future calculations
Residuals • Calculating Residuals (mean = 100.00’): Readings residual residual2 99.96’ -0.04 0.0016 100.02’ +0.02 0.0004 100.04’ +0.04 0.0016 100.00’ 0 0 100.00’ 0 0 99.98’ -0.02 0.0004 100.02’ +0.02 0.0004 100.00’ 0 0 99.98’ -0.02 0.0004 100.00’ 0 0 Sn2 = 0.0048
Standard Deviation • The Standard Deviation is the ± range within which 68.3% of the residuals will fall or … • Each residual has a 68.3% probability of falling within the Standard Deviation range or … • If another measurement is made, the resulting residual has a 68.3% chance of falling within the Standard Deviation range.
Standard Deviation • Standard Deviation is a comparison of the individual readings (measurements) to the mean of the readings, therefore… • Standard Deviation is a measure of….
Standard Deviation • Standard Deviation is a comparison of the individual readings (measurements) to the mean of the readings, therefore… • Standard Deviation is a measure of…. PRECISION!
Standard Deviation of the Mean • This is an uncertainty statement regarding the mean and not a randomly selected individual reading as is the case with standard deviation. • Since the individual measurements that make up the mean have error, the mean also has an associated error. • The Standard Deviation of the Mean is the ± range within which the mean falls when compared to the “true value”, therefore the Standard Deviation of the Mean is a measure of ….
Standard Deviation of the Mean This is an uncertainty statement regarding the mean and not a randomly selected individual reading as is the case with standard deviation. Since the individual measurements that make up the mean have error, the mean also has an associated error. The Standard Error of the Mean is the ± range within which the mean falls when compared to the “true value”, therefore the Standard Deviation of the Mean is a measure of …. ACCURACY!
Standard Deviation of the Mean Distance = 100.00’±0.007’ (1s Confidence level)
Probable Error Besides the value of s =68.3%, other error values are used by statisticians An error value of 50% is called Probable Error and is shown as “E” or “E50” E50= (0.6745)s
90% & 95% Probable Error A 50% level of certainty for a measure of precision or accuracy is usually unacceptable. 90% or 95% level of certainty is normal for surveying applications
95% Probable Error • Distance = 100.00’±0.015’ (2s Confidence Level)
Meaning of E95 “If a measurement falls outside of two standard deviations, it isn’t a random error, it’s a mistake!” Francis H. Moffitt