instrument calibration & error isat 253 spring 2005
Post on 23-Dec-2015
232 Views
Preview:
TRANSCRIPT
Instrument Calibration & Error
ISAT 253
Spring 2005
Dr. Ken Lewis 2
Objectives Define instrument calibration and explain its
purpose. Describe, for different kinds of instruments, how
calibration standards are used and where they come from.
Understand static and dynamic calibration.
Dr. Ken Lewis 3
Key notions in instrument calibration Sensitivity Precision Accuracy Errors
Precision Bias
SI Units
Measurement Standards Calibration standards Calibration Repositories of
measurement standards.
Dr. Ken Lewis 4
What is the POINT?Measurement Standards There are many basic standards. Before the French Revolution every different duchy
had their own version of standards of weight, length, etc. Need to standardize to allow transfers of knowledge Need to have standards to allow calibration of
instruments to make results reliable and interchangeable.
Dr. Ken Lewis 5
What’s the Point? Here it is a $200,000,000 blunder…
Mars Polar Lander
December 3, 1999 EDWARD EULER, Lockheed
Martin: The mistake was that we had to give the Jet Propulsion Lab some data that is used to compute very, very small little thrust pulses onboard the spacecraft. And we did give them the data in the wrong units... and in English units, and it should have been in metric. And they used the data as if it were metric, and underestimated the magnitude of these small, little pulses that come out of the jets of the Orbiter by about a factor of five. And that in turn made it very difficult to get the proper navigation, or determine the position and velocity of the spacecraft, which eventually led to the failure.
http://www.pbs.org/newshour/bb/science/july-dec99/mars_lander_12-2.html
Dr. Ken Lewis 6
Measurement Standards Many standards;
1 foot is 12 inches 2.54 centimeters is exactly 1 inch There are 28 grams in 1 ounce A CD is 12 centimeters in diameter All video players (VHS) can interpret correctly any
VHS tape The electric voltage and current in California is the
same as it is in New Hampshire
Dr. Ken Lewis 7
Selected Primary Standards Mass
The International Prototype Kilogram is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France
Time 9,192,631,770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of cesium-133
Length The length of the path traveled by light at sea level during
1/299,792,458 of a second
Dr. Ken Lewis 8
Fixed Points (International Temperature Scale of 1990) = Temperature Standards
Fixed Points Temperature (K)
Triple Point of Hydrogen 13.8033
Triple Point of Oxygen 54.3584
Triple Point of Water 273.16
Freezing Point of gallium 302.9146
Freezing Point of zinc 692.677
Freezing Point of silver 1234.93
Freezing Point of copper 1357.77
Dr. Ken Lewis 9
Seven SI Base Units
Quantity Dimension SI Unit Symbol
Time [t] second s
Length [L] meter m
Mass [m] kilogram kg
Current [i] ampere A
Temperature [T] Kelvin K
Luminosity --- candela cd
Amount --- mole mol
Dr. Ken Lewis 10
Standards All primary standards except mass “can” be
reproduced in a good well equipped laboratory. Standards for all other physical variables are;
Derived from the base standards Physical laws
Dr. Ken Lewis 11
Derived Standard Example -- Force Recall Newton’s second law
Force = mass X acceleration Acceleration = meter/second/second
=length/second2
2 Force =
ml
t
Dr. Ken Lewis 12
Some SI Derived UnitsQuantity Dimension SI Unit Symbol
Area [L2] meter2 m2
Volume [L3] meter3 m3
Velocity [L/t] meter/second m/s
Acceleration [L/t2] meter/second2 m/s2
Force [mL/t2] Newton N or (kg-m/s2)
Energy [mL2/t2] joule J or (N-m)
Power [mL2/t3] watt W or (J/s)
Voltage [mL2/(t3i)] volt V or (W/A)
Pressure [m/(Lt2)] Pascal Pa or (N/m2)
Viscosity [m/(Lt)] Pascal-second Pa-s
Dr. Ken Lewis 13
Some Standard SI Prefixes
Multiple Prefix Symbol
10-12 pico p
10-9 nano n
10-6 micro
10-3 milli m
10-2 centi c
10-1 deci d
10+3 kilo k
10+6 mega M
10+9 giga G
10+12 tera T
Dr. Ken Lewis 14
Traceable Weight Standards
Courtesy Henry Troemner Company
Dr. Ken Lewis 15
Static Calibration In the calibration process, a known input value is
applied to the measurement system and the output is measured.
Calibrations Static (independent of time) Dynamic (magnitude and frequency change with
time) Calibrations
Sequential Random
Dr. Ken Lewis 16
Static Calibration The output is correlated with the input known values
through a calibration curve Usually one sequences up the input range and back
down again (helps uncover Hysteresis)
Dr. Ken Lewis 17
Example: Static Scale Calibration Spring Scale Used in the 0 – 5 lb range Calibrate using standards 0 – 5 lbs in
½ lb increments Regress a straight line curve Determine the accuracy, hysteresis,
and any linearity errors Estimate the maximum systematic and
random errors.
Dr. Ken Lewis 18
The Raw Data
True weight (lb) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Avg0.50 0.20 0.08 0.17 0.19 0.11 0.151.00 0.70 0.78 0.64 0.61 0.70 0.691.50 1.18 1.26 1.25 1.24 1.23 1.232.00 1.81 1.93 1.81 1.93 1.88 1.872.50 2.62 2.49 2.46 2.46 2.58 2.53 2.523.00 3.15 3.18 3.24 3.28 3.13 3.203.50 3.90 3.84 3.86 3.97 3.96 3.914.00 4.59 4.71 4.61 4.60 4.60 4.624.50 5.41 5.35 5.49 5.46 5.39 5.425.00 6.24 6.27 6.10 6.24 6.16 6.204.50 5.71 5.74 5.78 5.87 5.82 5.784.00 4.96 5.11 5.08 5.03 5.03 5.043.50 4.22 4.34 4.21 4.22 4.24 4.253.00 3.57 3.64 3.66 3.55 3.67 3.622.50 2.98 2.86 2.98 2.98 2.94 2.952.00 2.22 2.23 2.26 2.29 2.26 2.251.50 1.57 1.70 1.69 1.63 1.57 1.631.00 1.07 1.07 1.11 1.16 1.11 1.100.50 0.52 0.61 0.61 0.61 0.45 0.560.00 0.02 0.08 0.08 -0.03 0.06 0.04
Weights cycled up and down 5 times. Started in middle of cycle 1 and ended in middle
of cycle 6
Dr. Ken Lewis 19
The Calibration PlotScale Calibration Data
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
True Weight (lb)
Sca
le R
ead
ing
(lb
)
Wheeler & Ganji, Introduction to Engineer ing Exper imentation
Best Fit Line
Regression Line: R = 1.29 T – 0.37
Good for obtaining the correlating function
To estimate the errors, it is best to use the deviations of the data from the best fit or regression line.
Deviations from best fit Data
True Weight
(lb)Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6
Average of down cycles
Average of up - down
Repeat
Average of up
cycles
0.0 0.41 0.410.5 -0.07 -0.19 -0.10 -0.08 -0.16 -0.12 0.09 0.12 0.291.0 -0.22 -0.14 -0.28 -0.31 -0.22 -0.23 -0.03 0.17 0.181.5 -0.38 -0.30 -0.31 -0.32 -0.33 -0.33 -0.13 0.08 0.072.0 -0.40 -0.28 -0.40 -0.28 -0.33 -0.34 -0.15 0.12 0.042.5 -0.23 -0.36 -0.39 -0.39 -0.27 -0.32 -0.35 -0.13 0.16 0.103.0 -0.35 -0.32 -0.26 -0.22 -0.37 -0.30 -0.09 0.15 0.123.5 -0.24 -0.30 -0.28 -0.17 -0.18 -0.23 -0.06 0.13 0.114.0 -0.20 -0.08 -0.18 -0.19 -0.19 -0.17 0.04 0.12 0.254.5 -0.02 -0.08 0.06 0.03 -0.04 -0.01 0.17 0.14 0.355.0 0.16 0.19 0.02 0.16 0.08 0.12 0.12 0.17 0.124.5 0.28 0.31 0.35 0.44 0.39 0.35 0.164.0 0.17 0.32 0.29 0.24 0.24 0.25 0.153.5 0.08 0.20 0.07 0.08 0.10 0.11 0.133.0 0.07 0.14 0.16 0.05 0.17 0.12 0.122.5 0.13 0.01 0.13 0.13 0.09 0.10 0.122.0 0.01 0.02 0.05 0.08 0.05 0.04 0.071.5 0.01 0.14 0.13 0.07 0.01 0.07 0.131.0 0.15 0.15 0.19 0.24 0.19 0.18 0.090.5 0.25 0.34 0.34 0.34 0.18 0.29 0.160.00 0.39 0.45 0.45 0.34 0.43 0.41 0.11
Dr. Ken Lewis 21
Repeatability error Repeatability
Maximum variability of successive measurements of the same value of input approached from the same direction.
Dr. Ken Lewis 22
Repeatability ErrorTrue
Weight (lb)
Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Repeat
0.00.5 -0.07 -0.19 -0.10 -0.08 -0.16 0.121.0 -0.22 -0.14 -0.28 -0.31 -0.22 0.171.5 -0.38 -0.30 -0.31 -0.32 -0.33 0.082.0 -0.40 -0.28 -0.40 -0.28 -0.33 0.122.5 -0.23 -0.36 -0.39 -0.39 -0.27 -0.32 0.163.0 -0.35 -0.32 -0.26 -0.22 -0.37 0.15
Repeat error for 0.5 lb = |-0.19| - |-0.07| = 0.12Repeat error for 1 lb = |-0.31| - |-0.14| = 0.17
Maximum Repeat Error for this calibration turns out to be 0.17 lb at a true weight of 1 lb.
Dr. Ken Lewis 23
Hysteresis Error Hysteresis Error
Maximum difference between the “up” and corresponding “down” reading for any calibration cycles
Deviations from best fit Data
True Weight
(lb)Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6
0.00.5 -0.07 -0.19 -0.10 -0.08 -0.161.0 -0.22 -0.14 -0.28 -0.31 -0.221.5 -0.38 -0.30 -0.31 -0.32 -0.332.0 -0.40 -0.28 -0.40 -0.28 -0.332.5 -0.23 -0.36 -0.39 -0.39 -0.27 -0.323.0 -0.35 -0.32 -0.26 -0.22 -0.373.5 -0.24 -0.30 -0.28 -0.17 -0.184.0 -0.20 -0.08 -0.18 -0.19 -0.194.5 -0.02 -0.08 0.06 0.03 -0.045.0 0.16 0.19 0.02 0.16 0.084.5 0.28 0.31 0.35 0.44 0.394.0 0.17 0.32 0.29 0.24 0.243.5 0.08 0.20 0.07 0.08 0.103.0 0.07 0.14 0.16 0.05 0.172.5 0.13 0.01 0.13 0.13 0.092.0 0.01 0.02 0.05 0.08 0.051.5 0.01 0.14 0.13 0.07 0.011.0 0.15 0.15 0.19 0.24 0.190.5 0.25 0.34 0.34 0.34 0.180.00 0.39 0.45 0.45 0.34 0.43
HysteresisMax at 2.5 lbs
0.52 lb± 0.26 lb
Dr. Ken Lewis 25
Deviation PlotCalibration Deviation Plot
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
True Weight (lb)
Dev
iati
on
(lb
)
Accuracy LimitsAccuracy
+0.44lb/ -0.40 lb
Average Deviation Data
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
True Weight (lb)
Ave
rag
e D
evia
toin
(lb
)
Average of dow n cycles
Average of up - dow n
Average of up cycles
Linearity0.44 lb
Dr. Ken Lewis 27
Dynamic Calibration Static
Measurand is independent of time and the measurement system instantly (quickly) shows a response.
If not – dynamic Dynamic
Oral thermometer Takes time to reach equilibrium
Dr. Ken Lewis 28
Dynamic Response of Measurement Systems Three categories of dynamic response:
Zero Order Ideally they respond instantaneously to measurands There is no real zero order systems There are many that approximate this state with
slowly changing measurands
Dr. Ken Lewis 29
Dynamic Response of Measurement Systems Three categories of dynamic response:
First Order Capacitance type energy storage response Springs Hot water bottles
Dr. Ken Lewis 30
Dynamic Response of Measurement Systems Three categories of dynamic response:
Second Order Inertial effects plus capacitance These systems have damping
Bathroom scales Shock absorbers
Dr. Ken Lewis 31
Some Standards Organizations
National Institute of Standards and Technology (NIST) http://www.nist.gov
American National Standards Institute (ANSI) http://www.ansi.org
International Organization for Standards (ISO) http://www.iso.org
top related