Measurements & Instrumentations

Module 1

Grading policy

• Participation 10 marks– Preparation, Promptness, Level of Engagement,

Behavior• HWs 10 marks• Quizzes 10 marks• Practical 30 marks– Lab activities and Practical exam

• IAT competency exams (practical and knowledge ) 40 marks

Preparation marks

• Print the modules and cover it and bring it to every class with you• Calculator • Stationary • Lab coat

Participation Marks

• Promptness: On time or Late• Level of Engagement• Behavior

Objectives

• What is measurements• Measurements elements • Measurement methods / types

Introduction to measurements

• All physical parameters are measurable, and the first step in any engineering process is measurement.

• Measurement of abstract quantities like intelligence.

• If we cannot measure something, we can not control it. This ‘something’ is referred to as a ‘physical quantity’.

Measurements forms

• Physical dimensions of an object• Count of an object• Temperature of an object• Fluid pressure / flow rate / volume • Electrical voltage / current / resistors• Machine position / speed

What we are trying to measure ?

What is measurements ?• Measurement is the process of determining the magnitude of a physical

quantity such as length or mass, relative to a standard unit of measurement, such as the meter.

• It could be also defined as a comparison between a standard and a physical quantity to produce a numeric value

Measurements Elements

Measuring Devices

• The measuring devices could be sensors, transducers or instruments.

• A ruler (length)

• A thermometer (temperature)

• A light dependent resistor (LDR) measures (light intensity)

Skill 1: Identify the measurement elements

Physical quantity:

Measuring device:

Numeric value::

Standard unit:

Physical quantity:

Measuring device:

Numeric value::

Standard unit:

Methods of measurement

• The two basic methods of measurement are– Direct measurement

– Indirect measurement.

Direct Measurement

• In direct measurement, the physical quantity is compared directly with a standard.

Indirect Measurement• In an indirect type of measurement, the physical quantity measured is

converted to an analog form that can be processed and presented. • For example, the mercury in the mercury thermometer expands and

contracts based on the input temperature, which can be read on a calibrated glass tube.

A bimetallic thermometer

Question

Physical quantity: diameter of the ball

Measuring device: Vanier caliper

Numeric value: -----------

Standard unit: cm

Recap

• Define measurements• Measurements elements • Measurement types / methods

Warm up

• Give an example of an error that occur when you are taking a measurement.

Objectives

• Definition of the error• Types of the errors• Error analysis – mean & standard deviation• Calibration

Definition of the error

• Error = Instrument reading – true value

• Error types – Systematic errors– Random errors

Systematic Errors• The zero error of the instrument• The shortcomings of the sensor• Improper reading of the instrument due to the improper

position of the person’s head/eye (Parallax error)• The environmental effect

Parallax error demonstration

Systematic Errors

• Systematic errors can be corrected by calibration.

• Systematic errors can be traced and reduced

Random errors

• Measuring the same quantity using the same instrument and every time you get different reading

• Example of random error is – measuring the mass of gold on an electronic scale several

times, and obtaining readings that vary in a random fashion.

Random errors

• The reasons for random errors are not known and therefore can not be avoided

• They can be estimated and reduced by statistical operations

Picture Measurement type

Direct Measurements

Direct Measurements

Indirect Measurements

Skill 2: Identify the type of measurement

Error analysis

• Error analysis are done for the random error

• Average / Mean

• Standard Deviation

Error analysis• Measuring the same input variable a number of times,

keeping all other factors affecting the measurement the same, the measured value would differ in a random way.

• The readings normally follow a particular distribution and the random error may be reduced by taking the average or mean.

• The average/mean gives an estimate of the ‘true’ value

Error analysis

Example 1

• A mass of gold is measured 5 times find the mean

• Mean / Average =

Reading 1 Reading 2 Reading 3 Reading 4 Reading 5

10g 10.2g 10.3g 10.1g 10.4g

g2.105

4.101.103.102.1010

Standard Deviation

• The standard deviation, denoted by the letter ‘σ’ tells us about how much the individual readings deviate or differ from the average/mean of the set of readings.

Example 2Reading (Reading – average) (Readings – average)2

16 -1 119 2 418 1 116 -1 117 0 019 2 420 3 915 -2 417 0 013 -4 16

Sum 40

1.2110

401

nsumSTD

Example 3

• A diameter of a wire is measured by a group of students with a micrometer, and the reading are shown below:

• Assuming that only random errors are present, calculate the following:

a) mean / Average

b) Standard deviation

mm566.2569.249.245.265.255.2

Reading (Reading – average) (Readings – average)2 2.55 -0.016 0.0002562.65 0.084 0.0070562.45 -0.116 0.0134562.49 -0.076 0.0057762.69 0.124 0.015376

Sum 0.04192

0.10237215

04192.01

nsumSTD

Excersice

Recap

• Error• Systematic Error • Random Error• Mean • Standard deviation

Warm Up

• Define measurements• Measurements type • Error• Systematic Error • Random Error• Mean • Standard deviation

Instrument Performance Evaluation

• Any measuring instrument/device has a set of specifications that inform the user of its function.

• These characteristics are described in the catalogue or datasheet provided by the manufacturer

Accuracy• Accuracy of an instrument is how close a measured value is to

the true value.

Precision

• The ability of an instrument to give the similar reading when the same physical quantity is measured more than once

– The closer together a group of measurements are, the more precise the instrument.

– A smaller standard deviation result indicates a more precise measurement.

Small STD

Large STD

Precision

Precision of the

instrument

Measuring the same thing using the same instrument and every

time a different reading is obtained

Precision of the measurement

Measuring the same thing using different instruments and every

time a different reading is obtained

Precision Calculation

STD = σ

It will tell you which instrument is more precise

Value

max (Avg – Min), (Max – Avg)

What is the difference between precision and accuracy ?

Accuracy

Maximum deviation form the conventional true value

=max (CTV– Min), (Max – CTV)

Precision

Maximum deviation form the average value

=max (Avg – Min), (Max – Avg)

Student 1 5 mm

Student 2 5.2mm

Student 3 4.5 mm

Student 4 4.7 mm

Student 1 5 mm

Student 2 5.1mm

Student 3 4.9 mm

Student 4 5 mm

STD = σ = 0.310913 STD = σ = 0.08165

Precision of the instrument

Which one is more precise ?

Trial 1 5 kΩ

Trail 2 5.5 kΩ

Trail 3 4.5 kΩ

Trail 4 4.3 kΩ

Trial 1 5 kΩ

Trail 2 5.1 kΩ

Trail 3 4.9 kΩ

Trail 4 4.8 kΩ

Trial 1 5 kΩ

Trail 2 4 kΩ

Trail 3 6 kΩ

Trail 4 5 kΩ

STD = 0.537742

STD = 0.129099

STD = 0.816497

Which instrument is more precise ?

Precision of the instrument

Bias

• The difference between the true value (TV) and average value (AV).

• Ideally, the bias should be zero.

• 𝑩𝒊𝒂𝒔 = − 𝑻𝑽 𝑨𝑽

Example

• A mass of silver is measured four times and the values are shown below. If it the true value is 6 kg, find the bias

Trail 1 6.3 kgTrail 2 6.5 kgTrail 3 6 kg Trail 4 6 kg

kgAVTVBais

kgAverageMean

2.02.66

2.64

665.63.6/

Range

• The range of an instrument defines the minimum and maximum values that the instrument can measure.

Min value = -40oFMax value = 120 oFRange = 120oF – (-40oF) = 160oF

Min Value 0 Unit cm

Max value 15 Unit cm

Range =15-0=15 Unit cm

Min Value -40 Unit oC

Max value 50 Unit oC

Range 50-(-40)=90 Unit oC

Sensitivity

• The sensitivity of a measuring instrument is its ability to detect small changes in the measured quantity.

• Sensitivity = Change in output (y-axis)/Change in input (x-axis)

Linearity

• Some measuring instruments/devices output a signal that is proportional to the input physical quantity.

• These instruments are called linear devices. • Other instruments that don’t have a

proportional relationship between the output signal and the input are non-linear devices.

Lab Activity 1

Resistor Color Code

R = 25 * 10 1 Ω ± 5% = 25 * 10 Ω ± 12.5 ΩRmin = 237.5 ΩRmax = 262.5 Ω

Resistor color code

Colors: Red – Violet – green – GoldR = (27 x 105) ± 5% Ω

Colors: Brown – Black – yellow – Silver R = (10 x 104 )± 10% Ω

Unit Conversion

M 106

k 103

m 10-3

µ 10-6

Unit Conversion Examples

27.0 x 105 2.7 x 106 = 2.7 M10.0 x 104 100 x 103 = 100 k 10.0 x 10-4 10-3 = 1m 500.0 x 10-5 5000 x 10-6 =50µ

How to use DMM ?

How to use DMM ?

Always must be connected

Part 1 color code Resistance

valueTrue Value

DMM range

Measured values

% Error Within tolerance?

Yellow – violet – brown - gold

470 Ω 2kΩ 466Yes

Brown – Black – Red Gold

1 k Ω 2kΩ 1.13 kΩNO

Orange- orange – red -

gold

3.3 k Ω 20kΩ 3.31kΩYes

Orange – white – orange

- gold

39 k Ω 200kΩ 38.5 kΩYes

Brown – green – green - gold

1.5 M Ω 2MΩ 1.51 MΩYes

%85.0100*470

466470

%13100*1

13.11

%3.0100*3.3

31.33.3

%2.1100*39

5.3839

%66.0100*5.1

51.15.1

Part 2 Resistor Reading

DMM1 1.1 kΩ

DMM2 1.2 kΩ

DMM3 1.09 kΩ

DMM4 0.99 kΩ

DMM5 0.97 kΩ

Resistor True value: Brown – Black – Red - Gold

kMAX

kAveragemaen

134.0134.0,096.0)066.12.1(),97.0066.1MAX(

R_avg)-(R_m_max, R_m_min)-MAX(R_avgPrecision

066.15

95.099.009.12.11.1/

20% within accurate is device the20%,%Accuracy2.0200/1000 accuracy Relative

200 200 ,30 ofmax accuracy Absolute2000.2k1-1.2CTV– d_MAX)(R_Measure

300.03k 0.97– 1 d_MIN)(R_Measure - CTV

Part 3Reading Reading

(diameter in mm)Reading – Mean (Reading – Mean )2

Student 1

Student 2

Student 3

Student 4

Student 5

Mean

Standard deviation

Recap • Define measurements • Measurements form • Measurements types • Error • Systematic Error / Random Error• Mean • Standard deviation• Accuracy• Precision• Bias• Range