Measurement & Metrology

Instrumentation and Control

Measurement

Contents What is measurement? Units of measure Fundamental units of measure Derived units of measure Conversion of units of measure Dimensional analysis Purpose of measurement systems Essential requirements of measurement system Types of measurements Essential elements of measurement system Calibration Accuracy and Precision Concept Accuracy and Errors in system Source of measurement errors in system Error reduction techniques

What is a Measurement?

Encyclopedia Definition

In classical physics and engineering , measurementgenerally refers to the process of estimating ordetermining the ratio of a magnitude of a quantitativeproperty or relation to a unit of the same type

of quantitative property or relation.

Process of measurement involves the comparison ofphysical quantities of objects or phenomena.

What is a Measurement?

Wikipedia

Measurement is the estimation or determination ofextent, dimensions or capacity, usually in relation tosome standard or unit of measurement.

Comparison to a Standard (Metrology) Metrology is the study of measurement.

- In general, a metric is a sale of measurement defined interms of a standard: i.e. in terms of well defined unit.

- If one says I am 5, that person is indicating a measurementwithout supplying an applicable standard.

- They could mean I am 5 years old or I am 5 feet high.

- Measurements are at best ambiguous, or at worst,meaningless, without units!

Units of Measure What is a Unit of Measure?

- Act of m measuring involves comparing themagnitude of a quantity possessed by an object witha standard unit by using an instrument undercontrolled conditions.

- Examples of measuring

instruments include:

Thermometers (Deg.)

Current Meter (Amps)

Pressure Sensor (psi)

What are These gagesReadings?

Without prior knowledge of units we have no idea!

Units of Measure (contd)

Same quantity,

.. Different units.

Units of Measure (contd) System of Units

Imperial (English)

Before SI units were widely adopted around theworld, the British systems of English units and laterImperial Units were used in Britain, theCommonwealth and the United States.

Sometimes called foot-pond-second system afterImperial units for distance , weight (mass), and time.

Units of Measure (contd) System of Units

Metric (MKS)

The metric system is a decimalised system of measurementsbased on the Meter (M), Kilogram (Kg), and seconds (S).

The main advantage of the metric system is that it has a singlebase unit for each physical quantity. All other units are powers often or multiples of ten of this base unit.

Unit conversions are always simple because they will be in theratio of ten, one hundred, one thousand, etc.

Also referred to as System International (SI) Units.

Fundamental Units of Measure

A system of measurement is a set of units which can beused to specify anything which can be measured. Somequantities are designated as fundamental units meaningall other needed units can be derived from them.

Historically a wide range of units were used for the samequantity; for example, in several cultural settings , lengthwas measured in inches, feet, yards, fathoms, rods,chains, furlongs, miles, nautical miles, leagues, withconversion factors which are no simple powers of ten oreven always simple fractions.

Fundamental Units of Measure(contd)

The disagreement of units had serious military,cultural, and Fiscal impacts and eventually the BritishRoyal Society headed by Michael Faraday adopted 3fundamental Units, distance (ft), weight (lb), andtime (sec).

Later (1824) it was determined to be morefundamental to substitute Mass (slugs) for weight(lb) as a fundamental unit of measure

2sec

ftsluglbf 11maF

Fundamental Units of Measure(contd)

In the 19th century, science developments showed thateither electric charge or electric current must be addedto complete the minimum set of fundamental quantities.

Mesures usuelles (French for customary measurements)were a system of measurements introduced to act ascompromise between metric and traditionalmeasurements.

This system of measures will eventually lead to theevolution of the modern SI system of measurements.

Fundamental Units of Measure(SI System)

Quantity Name of Unit Symbol

Length Meter m

Mass Kilogram Kg

Time Second s

Electric current Ampere A

Thermodynamic Temperature

Kelvin K

Luminous intensity candela cd

Plane angle Radian rad

Amount of substance mole mol

Derived Units of Measure, SI system

Derived units arealgebraiccombinations of theeight base units withsome of thecombinations beingassigned specialnames and symbols

QuantityName of

UnitSymbol

Expression in terms of SI base units

Expression in terms of

other units

Absorbed radiation

gray Gy m2s2 J/kg

Electrical capacitance

farad F m-2kg-1s4A2 C/V

Electricalcharge

coulomb C As

Electricalconductance

siemens S m-2kg-1s3A2 A/V

Electrical inductance

Henry H m2kg s-2A-2

Electrical potential

volt V m2kg s-3A-1 W/A

Electrical resistance

Ohm m2kg s-3A-2 V/A

Force Newton N Kgms-2

Derived Units of Measure, SI system(contd)Quantity Name of Unit Symbol

Expression in terms of SI base units

Expression in terms of other units

Frequency Hertz Hz s-1

Luminance lux lx m-2cdsr lm/m2

Luminous flux Lumen lm cd sr

Magnetic flux Weber Wb m2kg s-2A-1 V s

Magnetic fluxdensity

Tesla T kg s-2A-1 Wb/m2

Power or radiant flux

Watt W kg m2s-3 J/s

Pressure Pascal PaKg/(ms2) =

(N/m2)

Radioactivity Becquerel Bq s-1

Work, energy,heat

Joule J m2kg s-2 Nm

Conversion of Units of Measure

Although the Imperial System of units is graduallybeing replaced by SI system, these units are still incommon use.

This use of the Imperial system is especially prevalentfor mechanical units like distance, force, moments ofinertia, pressure, and volume.

Accurate conversion from one system to another isessential.

Conversion of units of measure (contd)

The mars climate orbiter (1998) wasdestroyed when a navigation error caused thespacecraft to miss its intended 150 kmaltitude above mars during orbit insertion

Instead the spacecraft entered the Martianatmosphere at about 57 km altitude

The spacecraft was destroyed by atmosphericstresses and friction at this low altitude.

Conversion of units of measure (contd)

Not important?!

A review board found that thruster impulse datawas calculated on the groud in imperial units(pound-seconds) and reported that way tonavigation team, who were expecting the data inmetric units (newton-seconds)

Anticipating a different set of units, systemsaboard the spacecraft were not able to reconcilethe two systems of measurement, resulting in thenavigation error and loss of spacecraft.

Dimensional analysis

Most physical quantities can be expressed interms of combination of five basic dimensions.These are mass (m), distance (D,L), time (t),electrical current (I), temperature (T).

Dimensions are not the same as units i.e thephysical quantity, speed may be measured inunits of meters per second, knots . . . ; butregardless of the units used, speed is always adistance divided by time, so we say that thedimension of speed are distance divided by time,or instantaneously dD/dt.

Dimensional analysis (contd)


1. Volume L3

2. Acceleration (velocity/time) L/t3

3. Density ( mass/volume M/L3

4. Force (mass acceleration) M.L/t2

5. Charge (currenttime) I.t


more complex dimensional analysis examples

1. Pressure (force/area) M.L-1 .t-2

2. (Volume)2 L6

3. Electric field (force/charge) M.L.I-1.t-3

4. Work (force x distance) M.L2/T2

5. Energy (gravitational, potential mgh) M.L2/t2

6. Square root of area L


In algebric expression, additive terms must have samedirections. each term on the left hand side of an equation must

have the same dimensions as each term on the righthand side

a = b.c + x . Y

a must have same dimensions as the product bc and(1/2) xy must also have same dimensions as a and bc

Equation is dimensionally correct when terms have consistentdimensionality.

Dimensional analysis is a valuable tool for validating thecorrectness of an algebraic derivation i.e. finding algebraerrors.

Purpose of measurement systems

Process machine or system being

measured

Measurement system

Observer

INPUT OUTPUT

Measured value of variables

True value of

variables

Essential requirement of measurement system

Descriptive

Provide relationship between output and state

Selective

Provide desirable information only

Objective

Be independent of arbitrary observers

Validated

Represent the true value

Types of measurement

Manufacturing measurements

Discreetly monitoring products quality

Performance measurements

Providing performance evaluation as needed

Operational measurements

Continuously monitoring operation processes

Control measurements

Continuously providing feedback signals

Essential elements

Input Output

The value Measured value

of variables of variables

Measurement System

Sensing elementConditioning

elementProcessing

elementDisplaying element

Sensing elements

In contact with the information carrier or medium

Given a signal output related to the quantity being measured

Examples Strain gauge, Resistance depends on mechanical strain

Thermo couple, Voltage depends on the temperature

Signal conditioning elements

Prepares sensor outputs suitable for furtherprocessing

Mostly use various conditioning circuits Examples

A deflection bridge, converts an impedance change into avoltage change

Amplifier, amplifies millivolts to volts

Signal processing elements

Converting conditioning output into formsmore suitable for presentation

Calculation secondary variable frommeasureable variables.

Examples Analog-to-digital converter

Analog or digital filter

Signal compensation

Data display elements

Display and/or store measured signals inrecognizable form

Use analog and/or digital form Examples

Visual display units, like oscilloscope

Analog chart recorders

Digital data array

CALIBRATION

The relationship between the physicalmeasurement variable (x) and the signalvariable (s)

A sensor or instrument is calibrated byapplying a number of KNOWN physical inputsand recording the response of the system

Accuracy and Precision

AccuracyDeviation of the output from thetrue value

indicates the closeness of measuredand true values

Precision

Degree of reproducibility of a

measurement

indicates the repeatability ofmeasured values

Definition of Accuracy

Accuracy is a property of complete measurementrather than a single element.

Accuracy is quantified using measurement error:

E = measured value true value

= system output system input

Definition of Precision

The capacity of measuring instrument to give thesame reading when repetitively measuring thesame quantity under the same prescribedconditions.

Precision implies agreement between successive readings,NOT closeness to the true value.

Precision is a necessary but not sufficient condition foraccuracy.

Definition of Precision

Two terms are closely related to precision:

Repeatability:

The precision of a set of measurements taken over a shorttime interval.

Reproducibility:

The precision of a set of measurements BUT taken over along time interval or performed by different operators orwith different instruments or in different laboratories.

Accuracy and Precision

Accuracy and Errors

Systematic errors:Result from a variety of factors:

Interfering or modifying variables (e.g. temperature)

Drift (i.e., changes in chemical structure or mechanical stresses)

The measurement process changes the measurand (i.e., loading error)

The transmission process changes the signal (i.e., attenuation)

Human observers

Systematic errors can be corrected with COMPENSATION methods (i.e.,feedback, filtering etc.)

Accuracy and Errors

Random errors:Also called Noise: a signal that carries no information.

True random errors (white noise) follow a Gaussian distribution

Sources of randomness:

Repeatability of measurand itself (i.e., height of a rough surface)

Environmental noise (i.e., background noise picked by a microphone)

Transmission noise (i.e., 60Hz hum)

Signal to noise ratio (SNR) should be >> 1

With knowledge of the signal characteristics it may be possible tointerpret a signal with a low SNR (i.e., understanding speech in a loudenvironment)

Sources of Measurement Errors

Improper sensing position

Improper element calibration

Improper data acquisition method

Improper sampling rate

Elements non-linearity

Environmental effects

Error Reduction Techniques (1)

The most effective methodof reducing measurementerror is to:

Set the sensing element atthe right position.


An effective and usefulmethod of reducingmeasurement error is to:

Calibrate each element toeliminate or reduce bias.

Bias (offset) is the residual error

between the output and the truevalue after all possiblecompensation.


Another effective methodof reducing measurementerror is to:

Setup a proper samplingrate for a data acquisition.


An effective and usefulmethod of reducingmeasurement error is to:

Compensate sensingelement non-linearity.


Another effective methodof reducing measurementerror is to:

Compensate theenvironmental effects.

Environmental effects isolation:

Itotal = Itrue

Environmental input cancellation:

Iactual = Itotal - IEnvironmental

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Measurement & Metrology