ME56 Ch1-Measurement System

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Last updated Nov. 10, 2006

Lecture 1Measurement Systems & Uncertainty

ME56

Instrumentation

& Control Engineering

Asst. Prof. Yong Gyun Kim

College of EngineeringSilliman University


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Topics

Part 1 Measurement systems The functional elements of Measurement sys.

Loading

Requirements of Measurement system

Part 2 The Expression of Measurement

results to comply internationalstandard

Introduction to uncertainty of measured andanalyzed values


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Part 1

Measurement systems


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Measurement system elements

Sensor

Sensing physical quantity Signal processor

Converting physical value to electrical value Amplifying weak electrical value

Truevalue ofvariable

Signalprocessor

Input OutputMeasuredValue of

variable

Display

Record

Transmit

Sensor


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Methods of Measurement

Deflection Method

Analog multi-tester

Zero Method or Null Method

Thermocouple

Compensation Method

Substitution Method

Coincidence Method Differential Method

Assignments

Show Examples


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Loading in Measurement

An Act of attempting to make themeasurement has modifiedmeasurand

A problem encountered during measurement

Hotwater

otwater

Coldthermometer

Physical quantityto be measured

R

R

Ammeter RAVoltmeter

R

RI

I

P = IR

P = (I- IV)R

IV


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Requirement of Measurement

Fitness of purpose

Needs to deliver required accuracy

Calibration must be done

Calibration

A process of comparing the output of ameasurement system against standards ofknown accuracy

Relationship between the output of ameasurement system and the quantity it senses


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Calibration

Tip: Never trust a manufacturers calibration unlessyou have to - they have a vested interest


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Policy to control quality

Refer. Note Pages 6-7

Establish and maintain a system for calibration

Adequate training

Reviewing the calibration system periodically Consider errors and uncertainties in measurement

process

Keep Documented procedure of calibration

Calibration records must be kept

Use the measurement equipment traceable back toNational standard


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Traceability chain

National Standard

Calibrationcenter standard

In-company Standard

Process Instrument


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Primary Standards

1. Mass 2. Length 3. Time

4. Current 5. Temperature 6. Luminous intensity 7. Amount of substance

They are used to define the other quantities.

Supplementary standards Plane angle : Radian Solid angle : Steradian


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Reliability

Being the probability that it will operate toan agreed level of performance, for aspecific period, subject to specifiedenvironmental condition.

Reliability = f(t, environment conditionshot, dusty, humid, corrosion..))

Improved by choosing proper materials.

Failure rate No. of failures / no. of system observed x time observed


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Repeatability

Difference between multiplemeasurements of the same quantity

Affected by fluctuation in environment

Ability of a measurement system to givesame value for repeated measurements ofthe same value of a variable.


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Testing a measurement system

1. Pre-installation testing

Checking calibration and operation of of Eachelement or instrument.

2. Cabling and piping testing Checking shield, continuity, insulation, leak..

3. Pre-commissioning

Checking the completion of installation

Checking full operation order when interconnected.


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Assignment

Solve the Problems


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Part2

Uncertainty Analysis

TechniqueExpression of Measurement results to comply

international standard


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Evaluation of Uncertainty

An essential process of measurement

Gives a measure of reliance of measuredvalues


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Accuracy v.s Precision

Not Precise, Not Accurate Precise, Not Accurate

accurate, Not Precise Precise, Accurate


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Accuracy vs. Precision

Accuracy the agreement between a measured quantity and the

true value of that quantity.

Difference between the value indicated by measurementsystem and true value.

How close the measurement comes to the true value ?

Every component that appears in the analog signal pathaffects system accuracy.

Precision

how exactly the result is determined withoutreference to what the result means.

The relative precision indicates the uncertainty in ameasurement as a fraction of the result.


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Accuracy

Standard Deviation

Repeatability Difference between multiple measurements of the same

quantity

S.D of values measured repeatedly within limited time underthe same environment, method, measurer

Presented as % of F.S

Reproducibility A measure of consistency of measured values with changing

methods or place, condition under the repeatability condition Presented as % of F.S


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Uncertainty(How to estimate an error)

Background For an unified rule in measurements

A book - "Guide to the Expression of Uncertainty in Measurement, ISO in1993

Suggested by CIPM with BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML

The result of measurement = the best estimate instead of truevalue

Uncertainty is the error you dont know about

Definition

Parameter, associated with the result of measurement, thatcharacterizes the dispersion of the values that could reasonably beattributed to the measurand

Quantified value Could be S.D, times of S.D, .

It is the existing range of the object being measured


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Errors vs. Uncertainty

Error = Systematic Error + Accidental Error= Measured value true value

Systematic Error = average of values measured infinitelyunder repeatable condition - true value Accidental Error = Measured value the average of values

measured infinitely under repeatable condition


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Systematic Error Due to Instrumental error, Due to Environmental errors - temperature, wiring, stress Enable to decrease it through calibration Ex) Bias error If you always got same values when you

measured the measurand repeatedly No Error?

Accidental Error Random error or Non-repeatable error due to Uncertain

causes Possible Causes : wear, environment, thermal deformation Calculating it using the average value through many trials

Error Distribution : Normal or Gaussian Distribution For infinite trials Average : Zero


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Then Corrected or compensated value through calibration isalways certain? Uncertain (error) Because cant trust the calibration

Uncertainty by systematic effect

If the measured values were random whenever you

measured them repeatedly after calibration of systematicerror? Accidental Error Because the measurer couldnt know or control parameters to affect

the measurement. Average of accidental errors about the values infinitely measured = 0 But cant do infinite trials of measurement Uncertain exists

Uncertainty by Accidental Effect

Uncertainty : doubts (about results and processes ofmeasurement


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4 Steps calculating the Uncertainty

Set relating formula

Calculate Standard Uncertainty

Calculate Combined Standard Uncertainty Calculate Expanded Uncertainty


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Set the relating formula

Let y as Estimated value of measuring value

Let x as Estimated values of related parameters y = f(x1, x2, . . ., xn)

Ex) To Measure an Area, a ruler is used

Assume that the Uncertainty of the measurer and calibration ofthe ruler

A = XY

Then the formula following ISO guide must be A =(x + 1)( y+ 2 )

Where 1 and2 are the uncertainty due to the calibration of theeach length


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ExamplePower dissipated in a resistor

The power dissipated by a resistor in an electrical circuit is beingestimated using the voltage across it measured using a digitalvoltmeter. The resistance R has a nominal value of 100. Thevoltmeter reads 28.0 volts, with a resolution of 0.1V. Estimate theuncertainty in the power measurement

1) Uncertainty in primary measurements ?

2) Uncertainty in power ?

1) Uncertainty in primary measurements Resistance:

A glance through any manufacturers specifications will show youthat most often nominal resistances are only accurate to within

5%. We shall therefore take our primary uncertainty hereas (R)=5.

ii) Voltage:The uncertainty in the reading of a digital voltmeter is usually halfthe resolution (the true voltage could lie anywhere between 27.95and 28.05). We therefore have(V)=0.05V.


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Example

2) Uncertainty in powerThe relationship between power, voltage and resistance is simply

Preparing to apply the equation we have,

And so,

Or


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Example

about 5%. You will notice that apart from giving us anuncertainty estimate this analysis also shows that the likelyerror in our power measurement is almost entirely due tothe uncertainty in resistance. To improve the accuracy weshould therefore concentrate on reducing the uncertainty ofthe resistance measurement, not on improving the

voltmeter. This kind of information can save a lot of timeand money (voltmeters are expensive, resistors are not).


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Calculate Standard Uncertainty u(xi)

Uncertainties according to the parameters u(xi)

Two methods to calculate it

uncertainty evaluation following Type A By S.D of the average through many trials of measurement

uncertainty evaluation following Type B

If there were only one measured value for the parameter, from

the data or materials measured before, the characteristic of themeasurement system, By the specification presented bymanufacturer, calibration data, calculate the equivalent S.D


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Uncertainty evaluation followingType A

Where,Xi,k; each independentmeasured value for parameter i

xi,=/Xi ; estimated value of therelated parameterxi,=/Xi

/Xi ; Average ofXi,kofn trials


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Uncertainty evaluation followingType B

u2(xi) ; Estimated S.D related to estimated value(xi) of input value Xi,not many trials

Or

Standard Uncertainty u(xi) evaluated from thedata or materials measured before, thecharacteristic of the measurement system, the

specification presented by manufacturer andcalibration data Need to estimate S.D Technique


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Uncertainty evaluation followingType B

Evaluation of B type Uncertainty according to the characteristic ofdata distribution through estimating S.Estimate the S.D using the distributions shown below.

It shows the estimated value of input value Xi and uncertaintyevaluation from probability distribution of Xi based on theinformation obtained


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Combined Standard Uncertainty uc(y)

Could be calculated using the equation , by propagation law of uncertainty Assumption : No corelations among the parameters or

individual standard uncertainty


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Expanded uncertainty, U

If degrees of freedom is bigger

It approaches to normal distribution

k=2 in 95 % confidence interval

k=3 in 99 % confidence interval

U = k uc


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What must be described inMeasurement Report

Measured data

Method used to calculate uncertainty

Parameters to contribute uncertainty

Its evaluation method Data analysis method

Correction value and constants used inanalysis and their sources


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Noise in Measurement

White Noise Essential Noise due to Thermal movement of electron

Electrons start moving @ above 0 oK

Electrostatic Induction Noise

Prevent it by electrostatic shield (Ground, Earth) Electromagnetic Induction Noise

Affected by change of magnetic flux

Twisting pair wiring

Avoid vibration of wire

Ripple in Power 60Hz noise

Preventing it by line filter or capacitors


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Primary measurement

A measurement not derived from anyother

Ex.

A distance from a dial gauge

Height from a manometer

(not Velocity from a pitot tube)


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Determining Uncertainty in aPrimary measurement

.. .)()()()(222

c

c

Rb

b

Ra

a

RR

Experimental result R is determined from one or moreprimary measurements a,b,c

R=f(a,b,c)

Uncertainty in R is due to the primary measurements maybe determined by multiplying the uncertainty in thatmeasurement by the sensitivity of R to that measurement.

Total Uncertainty R


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Example1-Calculating Uncertainty

Uncertainty in velocity for a pitot tube p0-p=0.22kPa (by manometer reading)

Patm=941.1mBar=94110Pa

Tatm

=17.0C=290.0K

atm

atm

RT

p

ppU

)(20

smU /72.19

290287

94110

2202


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Step1 : primary uncertainty

Manometer

(p-p0)=0.02kPa = 20pa (eyeball)

Barometer(patm)=0.5mBar=50Pa

Thermometer

(Tatm)=0.5C

0.2123


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Example-Calculating Uncertainty

Step2 : Partial Derivatives

atm

atm

RT

p

ppU

)(20

0448.0)(2

12)(221

)( 0

2/1

0

0

ppU

pRT

pRTpp

ppU

atm

atm

atm

atm

0340.02

1

atmatm T

U

T

U

000105.02

1

atmatm p

U

p

U


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Step3 : Combine Uncertainty

222

0

0

)()()()(

)(

atm

atm

atm

atm

pp

UT

T

Upp

pp

UU
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Example2-Calculating Uncertaintyusing computer

Reynolds number
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ME56 Ch1-Measurement System