1 measurement and errors
TRANSCRIPT
Dr. Khairul Anuar Mohamad
MEASUREMENT AND ERRORS1
CONTENTS
1.1 Principles of Measurement
1.2 SI Systems
1.3 Performance Characteristic
1.4 Errors in Measurements
1.5 Statistical Analysis of Measurement Data
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1.1 Principles of Measurement
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Measurement
• Measurement is the process of comparing an unknown quantity with an accepted standard quantity.
• It involves connecting a measuring instrument into the system under consideration and observing the resulting response on the instrument.
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Process of Comparison(Measurement)
Standard(Known Quantity)
Measurand(Quantity to be Measured)
Result(Output)
Fundamental Measuring Process
Measurand
• The physical quantity or the characteristic condition which is the object of measurement in an instrumentation system.
• Also called:
Measurement variable
Instrumentation variable
Process variable
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• The measurand may be: Fundamental quantity: length, mass, and time Derived quantity : speed, velocity, acceleration
Measurement Process
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Before measurement• Methods/procedures of
measurement.• Characteristics of the parameter.• Quality: time and cost, instrument
capabilities, knowledge of measurement, acceptable result.
• Instrument to use.
During measurement• Quality- best instrument chosen,
suitable position when taking the data, etc..
• Safety- electric shock, overloaded, instrument limits, read instruction manual.
• Sampling – observe parameter changing, taking enough sample.
After measurement• Analyse the data
mathematically/statistically.• Full result must be reported
completely and accurately.
What is an instrument?
• Device that communicates, denotes, detects, indicates, measures, observes, records, or signals a quantity or phenomenon, or controls or manipulates another device.
• A tool or device used for a particular purpose; especially : a tool or device designed to do careful and exact work.
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Instrumentation
• Instrumentation - The technology of using instruments to measure and control the physical and chemical properties of materials
• Process Instrumentation - When the instruments are used for the measurement and control of industrial manufacturing, conversion or treatment process
• Control system - When the measurement and control instruments are combined so that measurements provide impulse for remote automatic action.
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The basic requirements for getting meaningful result
1. The standard employed for comparison purpose may be accurately defined and should be commonly acceptable.
2. The standard must be of the same character as the measurandand usually but not always, is prescribed and defined by a legal or recognised organisation, e.g. the International Organisation of Standards (ISO).
3. The apparatus used and method adopted for the comparison purposes must be provable.
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Why do we need measurements?
• Measurement plays a very significant role in every branch of scientific research and engineering processes which include the following:
Control systems;
Process instrumentation
Data reduction.
• The whole area of automation or automatic control is based on measurements.
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Cont…
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Cont…
• The measurements confirm the validity of a hypothesis and also add to its understanding. This eventually leads to new discoveries that require new and sophisticated measuring techniques.
• Through measurements a product can be designed or a process be operated with maximum efficiency, minimum cost, and with desired degree of reliability and maintainability.
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1.2 SI Systems
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Review: Why do We Need Measurement
• Measurement is KEY to the knowledge and interaction.
• A Science & Technology of a measured understanding.
• Science is about doing and making, not just thinking.
• It is crucially an experimental activity, directed to measurement.
• In Engineering & Technology;• Responsible people seek the most measured way to understand
their situation.• Any inquiry will get ignited as Engineering only when its practitioners
become serious about the practice of measurement.• Measurement functions not simply to furnish a test of some theory,
but rather as a direct argument to a specific theoretical conclusion .
• The more the measured understanding is in practice, the more harmonizing its engagement of the evidence will be.
Review: What is An Outcome of A Measurement?
• Measurement leads to the expression of characteristics of systems in terms of numbers.
• Present culture is crazy about numbers.
• We seek standardization, we revere precision, and we aspire for control.
• If you can number it, you make it real.
• Once made real, it's yours to manage and control.
• We increasingly depend on numbers to know how we are doing for virtually everything.
• We ascertain our health with numbers.
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Standards
• Standard
• All measurement are based on comparison to some known quantity or reference (standard). Standards is a physical devices that have stable characteristics and accurately defined.
• Categorize to 4 type
1. international standard
2. primary standard
3. secondary standard
4. working standard
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ISO 216 Paper Sizes
Standards
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PS
IS
SS
WS
Diagram Traceability
SI System
International system of units (S.I) are divided into three classes:
• Unit: a set of size of physical quantities.
• Different systems of units are based on different choices of a set of fundamental units.
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S.I Unit
Base units Derived unitsSupplementary
units
S.I Base Units – 7 base units
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Base Quantity Base Unit
Name Symbol
Length Meter m
Mass Kilogram Kg
Time Second s
Electric Current Ampere A
Thermodynamic Temperature Kelvin K
Amount of substance Mole mol
Luminous Intensity Candela cd
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* SI covers all areas, although certain units outside SI are so useful that they are accepted for general use together with the SI.
Derived Unit
• Derived Quantities are formed by combining two or more of the fundamental quantities.
• Examples:
• Area = length x width
• Volume = length x width x height
• Speed = distance/time
• Density = mass/volume
• Most of the units in the International System are derived units, that is units defined in terms of base units and supplementary units.
• Derived units can be divided into two groups - those that have a special name and symbol, and those that do not.
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Mathematical operation
Cont…
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With Names and Symbols
Unit Measure of Symbol Derivation
coulomb electric charge C A·s
farad electric capacitance F A·s/V
henry inductance H V·s/A
hertz frequency Hz cycles/s
joule quantity of energy J N·m
ohm electric resistance Ω V/A
tesla magnetic flux density T Wb/m2
volt voltage V W/A
watt power W J/s
weber magnetic flux Wb V·s
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Cont…
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Without Names and Symbols
Measure of Derivation
acceleration m/s2
angular acceleration rad/s2
angular velocity rad/s
density kg/m3
electric field strength V/m
magnetic field strength A/m
velocity m/s
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Supplementary Units
• Third class of S.I units
• Supplementary units may be regarded either as base units or as derived units
• Example of S.I derived units formed by using supplementary units
• - Angular velocity (rad/s)
• - Angular acceleration (rad/s^2)
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Quantity S.I Units
Name Symbol
Plane angle radian rad
Solid angle steradian Sr
Volume litre L
Pressure bar bar
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Extra: SI Prefix
• A prefix that can be applied to an SI unit to form a decimal multiple or submultiples.
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10n Prefix Symbol Long scale
1024 yotta Y Quadrillion
1021 zetta Z Trilliard
1018 exa E Trillion
1015 peta P Billiard
1012 Tera T Billion
109 Giga G Milliard
106 Mega M Million
103 Kilo k Thousand
102 hecto h Hundred
101 deca Da Ten
10n Prefix Symbol Long scale
10-1 Deci d Tenth
10-2 Centi c Hundredth
10-3 Mili m Thousandth
10-6 Micro µ Millionth
10-9 Nano n Milliardth
10-12 pico p Billionth
10-15 Fento f Billiardth
10-18 Atto a Trillionth
10-21 Zecto z Trilliardth
10-24 vocto y QuadrillionthElectrical Measurements & Instrumentation (BEV20103)
Dimensional Analysis
• Conceptual tool applied in physics, chemistry and engineering to understand physical situations that involve physical quantities and derive equation for relationship
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Length MassTime Current
Length/time=Velocity (m s-1)
Velocity/time=Acceleration (m s-2)
Acceleration x mass = Force (kg m s-2)
Current x time = Electric charge (A s)
Force/charge = Field strength (kg m s-3 A-1)
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Dimensional Analysis
• Example:
Velocity = length/time; [v] = [L]/[T] = [LT-1]
Acceleration = velocity/time; [a] = [v]/[T] = [LT-2]
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Length MassTime Current
Length/time=Velocity (m s-1)
Velocity/time=Acceleration (m s-2)
Acceleration x mass = Force (kg m s-2)
Current x time = Electric charge (A s)
Force/charge = Field strength (kg m s-3 A-1)
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END PART 1
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