introduction instruments and errors in measurements

1
UNIT I
Concepts of Measurement
 Measurements( Ref 4, Chapter 1,pg no 1-11)
 Instrumentation( Ref 4, Chapter 1,pg no 1-11)
 Errors in measurements (Ref 4, Chapter 3,pg
no 60)
 Calibration
 Standard (Ref 4, Chapter 5,pg no 181)

2
Measurements
 Measurement: Comparison between a
standard and what we want to measure (the
measurand).
 Two quantities are compared the result is
expressed in numerical values.

3
Basic requirements for a
meaningful measurement
 The standard used for comparison purposes
must be accurately defined and should be
commonly accepted.
 The apparatus used and the method adopted
must be provable (verifiable).

4
Two major functions of all branch
of engineering
 Design of equipment and processes
 Proper Operation and maintenance of
equipment and processes.

5
Methods of Measurement
 Direct Methods
 Indirect Methods

6
 DIRECT METHODS: In these methods, the
unknown quantity (called the measurand ) is
directly compared against a standard.
 INDIRECT METHOD: Measurements by direct
methods are not always possible, feasible
and practicable. In engineering applications
measurement systems are used which require
need of indirect method for measurement
purposes.

7
Instruments and Measurement
Systems.
 Measurement involve the use of
instruments as a physical means of
determining quantities or variables.
 Because of modular nature of the
elements within it, it is common to refer
the measuring instrument as a
MEASUREMENT SYSTEM.

8
Evolution of Instruments.
a) Mechanical
b)Electrical
c) Electronic Instruments.
 MECHANICAL: These instruments are
very reliable for static and stable conditions.
But their disadvantage is that they are unable
to respond rapidly to measurements of
dynamic and transient conditions.

9
Contd
 ELECTRICAL: It is faster than mechanical,
indicating the output are rapid than mechanical
methods. But it depends on the mechanical
movement of the meters. The response is 0.5 to
24 seconds.
 ELECTRONIC: It is more reliable than other
system. It uses semiconductor devices and weak
signal can also be detected.

10
Classification Of Instruments
 Absolute Instruments.
 Secondary Instruments.
ABSOLUTE: These instruments give the
magnitude if the quantity under
measurement terms of physical constants
of the instrument.
SECONDARY: These instruments are
calibrated by the comparison with absolute
instruments which have already been
calibrated.

11
Further its classified as
 Deflection Type Instruments
 Null Type Instruments.

12
 Functions of instrument and measuring
system can be classified into three. They are:
i) Indicating function.
ii) Recording function.
iii) Controlling function.
 Application of measurement systems are:
i) Monitoring of process and operation.
ii) Control of processes and operation.
iii) Experimental engineering analysis.

13
Types Of Instrumentation
System
 Intelligent Instrumentation (data has been
refined for the purpose of presentation )
 Dumb Instrumentation (data must be
processed by the observer)

14
Elements of Generalized
Measurement System
 Primary sensing element.
 Variable conversion element.
 Data presentation element.
 PRIMARY SENSING ELEMENT: The
quantity under measurement makes its first
contact with the primary sensing element of a
measurement system.
 VARIABLE CONVERSION ELEMENT: It
converts the output of the primary sensing
element into suitable form to preserve the
information content of the original signal.

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Contd..
 DATA PRESENTATION ELEMENT:
The information about the quantity under
measurement has to be conveyed to the
personnel handling the instrument or the
system for monitoring, control or analysis
purpose.

16
Functional Elements of an
Instrumentation System
PRIMARY
SENSING
ELEMENT
VARIABLE
CONVER
-SION
ELEMENT
VARIABLE
MANIPULATI-
ON ELEMENT
DATA
TRANSMISSIO
-N ELEMENT
DATA CONDITIONING ELEMENT
INTERMEDIATE STAGE
DETECTOR
TRANSDUCER
STAGE
TERMINATING
STAGE
QUANTITY
TO BE
MEASURED
DATA
PRESENTA
TION
ELEMENT

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Static Characteristics Of
Instruments And Measurement
Systems ( Ref 4, Chapter 2)
 Application involved measurement of
quantity that are either constant or varies
slowly with time is known as static.
Accuracy
Drift
Dead Zone
Static Error
Sensitivity
Reproducibility

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Static Characteristics
Static correction
Scale range
Scale span
Noise
Dead Time
Hysteresis.
Linearity

19
 ACCURACY: It is the closeness with an
instrument reading approaches the true
value of the quantity being measured.
 TRUE VALUE: True value of quantity
may be defined as the average of an infinite
no. of measured value.
 SENSITIVITY is defined as the ratio of
the magnitude of the output response to
that of input response.

20
 STATIC ERROR: It is defined as the
difference between the measured value
and true value of the quantity.
A=Am-At
Where Am =measured value of quantity
At =true value of quantity.
It is also called as the absolute static error.

21
 SCALE RANGE: The scale range of an
instrument is defined as the difference
between the largest and the smallest reading
of the instrument.
Suppose highest point of calibration is Xmax
units while the lowest is Xmin units, then the
instrument range is between Xmin and Xmax.
 SCALE SPAN: Scale span or instrument
span is given as Scale span= Xmax - Xmin
It is the difference between highest and
lowest point of calibration.

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 Reproducibility is specified in terms of
scale readings over a given period of time.
 Drift is an undesirable quality in industrial
instruments because it is rarely apparent
and cannot be maintained.
It is classified as
a) Zero drift
b) Span drift or sensitivity drift
c) Zonal drift.

23
Dynamic Characteristics of
Measurement System
( Ref 4, Chapter 4)
• Speed of response
• Measuring lag
• Fidelity
• Dynamic error

24
.
 SPEED OF RESPONSE :It is defined as
the rapidity with which a measurement
system responds to changes in measured
quantity. It is one of the dynamic
characteristics of a measurement system.
 FIDELITY: It is defined as the degree to
which a measurement system indicates
changes in the measured quantity without
any dynamic error.

25
Dynamic Error
 It is the difference between the true value
of the quantity changing with time and the
value indicated by the measurement
system if no static error is assumed. It is
also called measurement error. It is one the
dynamic characteristics.

26
Measuring Lag
 It is the retardation delay in the response of
a measurement system to changes in the
measured quantity. It is of 2 types:
 Retardation type: The response begins
immediately after a change in measured
quantity has occurred.
 Time delay: The response of the
measurement system begins after a dead
zone after the application of the input.

27
Errors in Measurement
 Limiting Errors (Guarantee Errors)
 Known Error
Classification
Gross
Error
Systematic Or
Cumulative
Error
Random Or
Residual Or
Accidental
Error
Instrumental Environmental Observational

28
Gross Error
 Human Mistakes in reading , recording and
calculating measurement results.
 The experimenter may grossly misread the
scale.
 E.g.: Due to oversight instead of 21.5o
C,
they may read as 31.5o
C
They may transpose the reading while
recording (like reading 25.8o
C and
record as 28.5o
C)

29
Systematic Errors
 INSTRUMENTAL ERROR: These errors arise
due to 3 reasons-
• Due to inherent short comings in the
instrument
• Due to misuse of the instrument
• Due to loading effects of the instrument
 ENVIRONMENTAL ERROR: These errors
are due to conditions external to the measuring
device. These may be effects of temperature,
pressure, humidity, dust or of external electrostatic
or magnetic field.
 OBSERVATIONAL ERROR: The error on
account of parallax is the observational error.

30
Residual error
This is also known as residual error. These
errors are due to a multitude of small
factors which change or fluctuate from one
measurement to another. The happenings or
disturbances about which we are unaware
are lumped together and called “Random”
or “Residual”. Hence the errors caused by
these are called random or residual errors.

31
Arithmetic Mean
 The most probable value of measured variable is
the arithmetic mean of the number of readings
taken.
 It is given by
Where = arithmetic mean
 x1,x2,.. x3= readings of samples
 n= number of readings
n
x
n
x
x
x
x n 




.....
2
1
x

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Deviation
 Deviation is departure of the observed reading
from the arithmetic mean of the group of readings.
0
)
...
(
)
(
..
)
(
)
(
)
(
0
.....
3
2
1
3
2
1
3
2
1
3
3
2
2
1
1































X
n
X
n
X
n
x
x
x
x
X
x
X
x
X
x
X
x
ie
d
d
d
d
X
x
d
X
x
d
X
x
d
X
x
d
n
n
n
n
n

33
Standard Deviation
 The standard deviation of an infinite number of
data is defined as the square root of the sum of the
individual deviations squared divided by the
number of readings.
 
 
n
observatio
n
d
n
d
d
d
d
s
D
S
n
observatio
n
d
n
d
d
d
d
D
S
20
1
1
...
.
20
...
.
2
2
4
2
3
2
2
2
1
2
2
4
2
3
2
2
2
1






















34
Variance
 
 
 
 
n
observatio
n
d
s
D
S
Variance
n
observatio
n
d
D
S
Variance
20
1
.
20
.
2
2
2
2
2
2













35
Probable Error
 Probable error of one reading(r1)=0.6745s
 Probable error of mean (rm)
1
1


n
r
rm

36
Problem
Question: The following 10 observation were
recorded when measuring a voltage:
41.7,42.0,41.8,42.0,42.1,
41.9,42.0,41.9,42.5,41.8 volts.
1. Mean
2. Standard Deviation
3. Probable Error
4. Range.

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Answer
 Mean=41.97 volt
 S.D=0.22 volt
 Probable error=0.15 volt
 Range=0.8 volt.

38
Calibration
 Calibration of all instruments is important since it
affords the opportunity to check the instruments
against a known standard and subsequently to find
errors and accuracy.
 Calibration Procedure involve a comparison of the
particular instrument with either
 a Primary standard
 a secondary standard with a higher accuracy than
the instrument to be calibrated.
 an instrument of known accuracy.

39
Standards
A standard is a physical representation of
a unit of measurement. The term ‘standard’
is applied to a piece of equipment having a
known measure of physical quantity.

40
Types of Standards
–International Standards (defined based
on international agreement )
–Primary Standards (maintained by
national standards laboratories)
–Secondary Standards ( used by industrial
measurement laboratories)
–Working Standards ( used in general
laboratory)

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