Measurements Lab
4600 483
Basic Concepts of Measurements
Dr. Siam ak Farhad
Departm ent of Mechanical Engineering
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Measurements
• A measurement is an act of assigning a specific
value to a physical variable.
– Example: By measurements we assign the value of
70°F to the room temperature as a physical variable.
• To conduct a successful measurement, the selection of appropriate
measurement equipment and measurement technique are
required.
• Upon completion of this course, you should be able to
–
–
–
–
–
Identify the major components of a measurement system
Develop an experimental test plan
Identify various errors in a measurement system
Conduct a measurement and analyze data
Report the measured value and its uncertainty
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Components of Measurement Systems
• To do a measurement, we need a measurement system.
• This system is composed of several components that work
together.
Input
signal
Output
signal
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Components of Measurement Systems (Cont’d)
• Sensor-Transduce Stage: the physical quantity senses by changing one of
the sensor’s properties (e.g., the sensor volume or resistance). This
property may be transformed to another property using a Transducer.
• Signal Conditioning Stage: takes the transducer signal and modifies it to a
desired magnitude.
• Output Stage: Indicates or records the value measured. This might be a
simple readout display, a marked scale, or even a recording device such as a
computer disk drive.
• Control Stage: Uses the output signal to control the physical variable. This
stage may not be available for a measurement system.
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Example: Liquid-in-Glass Bulb Thermometer
• The physical variable is temperature.
• The heat exchange between the liquid in the
bulb and its surroundings is the input signal.
• The liquid in the bulb acts as the sensor (the
volume of liquid changes with temperature).
• The capillary tube acts as a transducer
(transforms volume to displacement).
• The diameter of the capillary tube amplifies /
conditions the liquid displacement.
• The output stage is the readout marked scale
(calibration) of the bulb thermometer.
• There is no control stage in this measurement
system.
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Experimental Test Plan
• An experimental test plan is necessary for conducting a
successful measurement with minimum effort and cost.
• To achieve a successful experimental test plan,
1. Determine the measurement objectives.
2. Identify all variables that are important for measurement and
means for their control.
3. Determine the acceptable error of measurement
4. Select a measurement technique, equipment and test
procedure.
5. Design the measurement system and choose its components
and find the design stage error.
6. Plan how to analyze and present the measured data.
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Definitions
• A variable that can be changed independently of other variables
is known as an Independent Variable.
• A variable that is affected by changes in one or more other
variables is known as a Dependent Variable.
• A variable which is held constant and unchanged
throughout the experiment is called a Control Variable.
• A variables that is not controlled during measurement but can
affect the value of the measured variable is called Extraneous
Variable or Uncontrolled Variables.
• The extraneous variables can be defined as Noise and
Interference.
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Definitions (Cont’d)
• Noise is a random variation of the value of the measured signal. Noise
increases data scatter.
• Interference imposes undesirable deterministic trends on the measured
value.
If measurements
are done in a
random order,
interference trends
w ill be broken up.
This is called
Random ization.
a wave is
superimposed
onto the
measured
signal
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Definitions (Cont’d)
• Repetition: Repeated measurements made during any single test run
or on a single batch.
• Replication: An independent duplication of a set of measurements
using similar operating conditions.
• Concomitant Method: Obtaining two or more estimates for the
physical variable, each based on a different method, which can be
compared as a check for agreement. E.g., Measurement of volume
through dimensions and through mass & density.
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Calibration
• The relationship between the
input and output of measurement
system is established by a
calibration.
• The most common type of
calibration is the static calibration.
• In the static calibration, a known
value is input to the system and
the system output is recorded.
• The known input value is called
the standard.
Input operating range ≡ Input span:
Output operating range ≡ Output span:
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Error & Accuracy
• The value of a variable as indicated by a measurement system is called
the measured value.
• The exact value of a variable is called the true value.
• Errors are effects that cause a measured value to differ from its true
value.
• Equations to calculate Absolute and relative errors:
Absolute error:
𝐸𝐴 = 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 − 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒
Relative error:
𝐸𝑅 =
𝐸𝐴
𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒
• The accuracy of a measurement refers to the closeness of agreement
between the measured value and the true value.
• Often an estimate for the value of error is based on a reference value
used during the measurement system’s calibration as a surrogate for
the true value.
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Random and Systematic Errors
• Precision Error ≡ Random Error: causes a random variation in measured
values found during repeated measurements of a variable.
• Bias Error ≡ Systematic Error: causes an offset between the mean value
of the data set and its true value.
• Low precision and bias errors means high accuracy.
• Low precision error
• High Bias error
• High precision error
• Low Bias error
• Low precision error
• Low Bias error
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Random and Systematic Errors (Cont’d)
Precision error
Bias error
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Uncertainty
• In any measurement, the error is not known exactly since the
true value is rarely known exactly.
• However, based on available information we might feel
confident that the error is within certain bounds, a plus or
minus range of the indicated reading. This is the assigned
uncertainty.
• The value assigned to each error is the uncertainty.
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Hysteresis Error
• Hysteresis Error: refers to differences between an upscale sequential
test and a downscale sequential test.
• A sequential test applies a sequential variation in the input value over
the desired input range. This may be accomplished by increasing the
input value (upscale direction) or by decreasing the input value
(downscale direction) over the full input range.
y
Hysteresis Uncertainty:
Absolute uncertainty:
𝑢 ℎ = 𝑦𝑢𝑝𝑠𝑐𝑎𝑙𝑒 − 𝑦𝑑𝑜𝑤𝑛𝑠𝑐𝑎𝑙𝑒
𝑚𝑎𝑥
Relative uncertainty:
𝑒ℎ (%) =
𝑢ℎ
× 100
𝑟0
x
𝑟0 = 𝐹𝑢𝑙𝑙 𝑆𝑐𝑎𝑙𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 𝑟𝑎𝑛𝑔𝑒 (𝐹𝑆𝑂)
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Linearity Error
• Linearity Error: measures the difference between the linear static
calibration curve and the measured value.
y
Linearity Uncertainty:
Absolute uncertainty:
𝑢 𝐿 = 𝑦(𝑥) − 𝑦𝐿 (𝑥)
𝑚𝑎𝑥
Relative uncertainty:
𝑒𝐿 (%) =
𝑢𝐿
× 100
𝑟0
𝑟0 = 𝐹𝑢𝑙𝑙 𝑆𝑐𝑎𝑙𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 𝑟𝑎𝑛𝑔𝑒 (𝐹𝑆𝑂)
x
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Sensitivity Error
• Sensitivity Error: A statistical measure of the precision error in the
estimate of the slope of the calibration curve is the sensitivity error. This
error is established during calibration.
y
• Calculation of UK
and eK will be
shown later.
x
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Zero Error
• Zero Error: measures the shift in the zero intercept of the calibration
curve. Zero error is common, particularly with electronic and digital
equipment subjected to temperature variations.
• Calculation of Uz
and ez will be
shown later.
y
x
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Repeatability Error
• Repeatability Error: measures the ability of the measurement system to
indicate the same value upon repeated but independently applied
identical input.
y
• Calculation of UR
and eR will be
shown later.
x
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Overall Instrument Error
• Overall Instrument Error: The overall instrument error is obtained
by combining all errors using the RSS (Root Sum Square) method.
Overall instrument uncertainty:
Absolute ov erall uncertainty:
𝑢𝐶 =
𝑢12 + 𝑢 22 + ⋯ + 𝑢 2𝑁
Relativ e ov erall uncertainty:
𝑒𝐶 =
𝑒12 + 𝑒22 + ⋯ + 𝑒𝑁2
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