Instrument Calibration & Error ISAT 253 Spring 2005.

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