Measurements & Instrumentations
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Transcript of Measurements & Instrumentations
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