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ABE425 Engineering Measurement ABE425 Engineering Measurement SystemsSystems

General Characteristics of Measurement Systems

Dr. Tony E. Grift

Dept. of Agricultural & Biological EngineeringUniversity of Illinois

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Agenda

1. What is a measurement system2. Validity of measurement3. Calibration

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General measurement system components

• Generally, a measurement system consists of • Sensing element (in “contact” with the measurand), • Signal conditioning (amplifiers, limiters, inverters, filters)• An indicator or recorder (computer)

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You can only measure objectively what is defined and standardized

• Mass• Distance• Time• Voltage• Current• Power• Work• Luminous intensity

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How would you go about measuring something like this? What is the unit?

• Charisma• Patriotism• Pain• Hate• Fear• Odor

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How would you measure happiness?

• Mona Lisa Was 83 Percent Happy

• AMSTERDAM, Netherlands (AP) —The mysterious half-smile that has intrigued viewers of the Mona Lisa for centuries isn't really that difficult to interpret, Dutch researchers said Thursday. She was smiling because she was happy —83 percent happy, to be exact, according to scientists from the University of Amsterdam.

• In what they viewed as a fun demonstration of technology rather than a serious experiment, the researchers scanned a reproduction of Leonardo da Vinci's masterpiece and subjected it to cutting-edge "emotion recognition'' software, developed in collaboration with the University of Illinois. The result showed the painting's famous subject was 83 percent happy, 9 percent disgusted, 6 percent fearful and 2 percent angry. She was less than 1 percent neutral, and not at all surprised.

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How would you measure love?

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Question

• What is the basic principle of this Mercury in glass thermometer?

• What is the measurand?• What is the signal conditioning subsystem?• What is the indicator?• How would you calibrate such a device?• Is calibration in measurement systems always necessary?

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Answer

• The basic principle is thermal expansion of Mercury, relative to its glass container? This is the model that we use for the measurement system.

• The measurand is the temperature of either fluid, or gas• The stem is a very small volume compared to the bulb• A scale (in deg C or deg F or both)• You calibrate it against a measurement system of higher

accuracy or against a standard • The far majority of measurement systems needs calibration

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Errors in measurement

• Error is the difference between the measured value and the true value of the measurand

• Types of errors• Bias errors (Fixed systematic errors,offsets)• Random errors

• Sources of bias error• Calibration error

• Instrument out of specification

• Loading error• Measurement device itself affects the measurement

• External influence error• Measure a temperature in a gas near a cold or hot wall

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Terms in dictionary.com

• ac·cu·ra·cy       ˈæk yər ə si/ [ak-yer-uh-see] –noun, plural -cies. • 1. the condition or quality of being true, correct, or exact;

freedom from error or defect; precision or exactness; correctness.

• pre·ci·sion       prɪˈsɪʒ ən/ [pri-sizh-uh n] –noun• 1. the state or quality of being precise. • 2.accuracy; exactness: to arrive at an estimate with precision.

• cal·i·brate       ˈkæl əˌbreɪt/ [kal-uh-breyt] –verb (used with object), -brat·ed, -brat·ing. • 1.to determine, check, or rectify the graduation of (any

instrument giving quantitative measurements). • 2.to divide or mark with gradations, graduations, or other

indexes of degree, quantity, etc., as on a thermometer, measuring cup, or the like.

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Terminology of measurement systems (Wheeler/Ganji)

• Accuracy is how close you are to the true value of the measurand. Accuracy is often given as a percentage of Full Scale (FS)

• Precision is the difference between an actual measurement and the mean among all readings of the same measurand. This error is caused by a lack of repeatability

• Bias (a systematic error that remains constant)

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Example 2.1

• True value of measurand is 6.11 Volt • 10 measurements, 5.98, 6.05,

6.1,6.06,5.99,6.02,6.09,6.03,5.99 Volt

• Estimate the bias error• Estimate the maximum precision error

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Example 2.1 Answer

• True value of measurand is 6.11 Volt. 10 measurements, 5.98, 6.05, 6.1, 6.06, 5.99, 6.02, 6.09, 6.03, 5.99 Volt

• Estimate the bias error• Average is 6.03. Bias is average value – true value =

6.03-6.11 = -0.08 Volt

• Estimate the maximum precision error• Maximum error is 5.96 – 6.03 = -0.07 Volt

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An ideal measurement device has a zero offset and a constant uncertainty interval across the span

• Uncertainty interval often given as percentage of Full Scale (FS)

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Hysteresis is a constant predictable error and therefore counted as a bias

• Causes are mechanical friction (play), flex in mechanical parts and capacitance

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Linearity between the measurand and the measured output is desired, but not required.

• Terminal-point-based straight line, connects measured values at the extremes of the measurement span. The maximum deviation of the transducer output with respect to this terminal-point straight line represents the linearity.

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A high sensitivity is desirable for accurate measurements

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Measurement of Mass (or is it weight?)

• Mass (kg) is independent of gravity• Weight (N) is Mass * Gravity• Compare playing pool on the moon and Earth

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Measurement of Mass and Weight

Which one is dependent upon gravity?

Balance (null method)Analytical Balance (deflection methods)

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Calibration of a spring scale can be done with objects of known mass

• When calibrating the spring scale one can• Go up and down in known increments • Choose random ‘weights’

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Curve fitting is a method of calibration

• Classical curve fitting uses Ordinary Least Squares (OLS) estimation to ‘freeze’ the behavior of the instrument

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The deviation (residual) plot gives the differences among measured values and the fit curve

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Averaging the values to assess accuracy, precision and non-linearity

• The averages of up and downward readings give the hysteresis error

• The terminal point based straight line is used to express non-linearity Terminal point straight line

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Dynamic calibration

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A loading error is caused by the measurement device itself affecting the measurand

• The thermometer itself cools the water temporarily, and therefore the initial measured value is lower than the original

• After a while the temperature of the thermometer is equal to the water temperature (equilibrium) and the true value is read

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Dynamic response of the measurement device can be zero, 1st or 2nd order

• The graph shows the response of a dynamic system to a step input when the measurement device is brought in contact with the measurand

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The frequency response is the window in which the measured value is unaffected

• The measurement system has a limited frequency response and acts like a band pass filter

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Classification of measurement systems

• Intrusive / non-intrusive• Null method / deflection method• Digital / analog

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Summary and terms

• Measurand• Measured value• Accuracy• Precision• Errors (systematic vs random)

• Bias (offset)• Hysteresis• Calibration error • Loading error • External influence error• Drift

• Calibration (static/dynamic)• Linearity• Terminal point straight line Step response

• Zero/1st, 2nd order• Frequency response• Ordinary Least Squares fitting

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ABE425 Engineering Measurement ABE425 Engineering Measurement SystemsSystems

General Characteristics of Measurement Systems

The End

Dept. of Agricultural & Biological EngineeringUniversity of Illinois