1
Introduction to measurement and statistical analysis
V. Rouillard 2003
METHODS OF MEASUREMENT
Direct comparison:
• Compare unknown quantity (measurand) against a known quantity (standard). Eg:
tape measure.
• Direct comparison not always possible or practical. Eg: measuring sound levels.
Indirect comparison (calibrated system):
• Makes use of a sensor or transducing device (transducer) to transform the
measurand into an analogous form.
• The sensor is connected to a series of instruments which convert the output of the
sensor into a useful analogous form which presents the measurand in a useful and
practical format.
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Introduction to measurement and statistical analysis
V. Rouillard 2003
METHODS OF MEASUREMENT
• Processing of the analogous signal is often necessary to extract the desired information
from the signal.
• For reasons related to signal processing, automatic recording and process control, the
majority of measuring systems convert the measurand into an analogous electrical form.
Introduction to measurement and statistical analysis
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V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Most measuring systems consist of three stages:
1.
2.
3.
Detection-transduction stage (sensor-transducer)
Intermediate stage (signal conditioning)
Terminating stage (readout, display, recorder)
Indicator
measurand
(raw) signal
Sensortransducer
Conditioned
signal
Signal
conditioner
Recorder
Processor
Controller
Human
(eyes, pen, paper)
Introduction to measurement and statistical analysis
4
V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Detection-transduction stage (sensor-transducer)
•
•
Function: to detect or sense the measurand without affecting it.
•
Unwanted sensitivity is a measuring error.
Ideally, must also be insensitive to other variables. Eg: Pressure sensor must be
insensitive to acceleration, strain gauge must be insensitive to temperature.
•
•
Noise: high frequency (fast)
Drift: low frequency (slow)
Introduction to measurement and statistical analysis
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V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Signal conditioning stage
•
Function: to modify (improve) the transduced information for compatibility with the
terminating (readout / recording/ processing) stage
•
These include amplification (most common) , filtering (noise removal), offset
adjustment, differentiation, integration, telemetry….
•
Sometimes also used to provide electrical power or excitation signal required by
sensor.
Introduction to measurement and statistical analysis
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V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Terminating stage (readout, display, recorder)
•
Function: to provide information on measurand in a format suitable for the
application.
•
For (immediate) human recognition, the display usually comprises:
•
1.
A relative displacement indicator. Eg: needle, / pointer, trace in a screen
(oscilloscope), stylus on a chart, a level change (thermometer)…
2.
In digital (numeric) form. Eg: counter (odometer), numeric LCD etc..
For recording or processing purposes, the terminating stage may comprise of
magnetic recorders, chart (paper) recorders, digital recorders (PC-based data
acquisition systems, digital storage oscilloscopes), process controllers (PLCs,
computer-based control systems).
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Introduction to measurement and statistical analysis
V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Example: Pressure gauge
Indicator:
Visual scale
Signal
conditioning:
none
Sensor-transducer:
Piston/cylinder
(pressure to force)
and spring
(force to displacement)
measurand:
Pressure
Introduction to measurement and statistical analysis
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V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Example: Rocket velocity
Sensortransducer
Accelerometer
Recording & display
Signal conditioning
Low-pass
filter
Integrator
Amplifier
PC Data
acquisition
Printer
Introduction to measurement and statistical analysis
9
V. Rouillard 2003
THE GENERALISED MEASURING SYSTEM
Example: Rocket velocity
Sensortransducer
Accelerometer
Recording & display
Signal conditioning
Low-pass
filter
Integrator
Amplifier
PC Data
acquisition
Printer
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Introduction to measurement and statistical analysis
V. Rouillard 2003
Dial Gauge
11
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: micrometer
Micrometer
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Linear Variable Differential Transformer (LVDT)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Linear Variable Differential Transformer (LVDT)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Linear Variable Differential Transformer (LVDT)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Laser (triangulation)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Laser (triangulation)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Time-of-flight distance sensors:
Ultrasonic (Sonar), Radio waves (Radar), Optical (Ladar),
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Time-of-flight distance sensors:
Ultrasonic (Sonar), Radio waves (Radar), Optical (Ladar),
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Time-of-flight distance sensors:
Ultrasonic (Sonar), Radio waves (Radar), Optical (Ladar),
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Displacement / distance: Time-of-flight distance sensors:
Ultrasonic (Sonar), Radio waves (Radar), Optical (Ladar),
• Laser diode is pulsed every microsecond
• The reflection is detected by a photo diode
Animation courtesy Banner Engineering
Introduction to measurement and statistical analysis
21
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain: (resistance strain gauge)
•
When the conductor (wire) is strained (extended), its cross-sectional area reduces and
the total electrical resistance increases.
•
The change in resistance is used to measure the strain of the material or component
onto which the strain gauge is bonded.
Bi-axial gauge
Tri-axial gauge
(rosette) for
Principal strains
Bi-axial gauge for
normal or shear
strains
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain: (resistance strain gauge)
R =  L/A
or
R =  L/CD2
•C=1 O: C=/4 (1)
When the conductor is strained, its geometry will change. Differentiating (1)
dR = CD2(L d +  dL) – 2C LD dD / (CD2)2
= [(L d +  dL) - 2 L dD/D] / CD2
(2)
Dividing (2) by (1)
dR/R = dL/L - 2dD/D + d/
(3)
Dividing by dL/L throughout:
(dR/R) / (dL/L) = 1 – 2(dD/D)/(dL/L) + (d/)/(dL/L)
(4)
Since dL/L = a = axial strain, dD/D = L = lateral strain and  = Poisson’s Ratio =
(dD/D)/(dL/L), Eqn. (4) can be written to define the Gauge Factor, G:
G = (dR/R)/(dL/L) = (dR/R)/ a
or a = (dR/R)/G
(5)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Force
•
Force and torque are often measured by
bonding a number of strain gauges on a
carefully designed component called a load
cell. The load cell is usually manufactured
using steel which has very linear (elastic)
properties as well as having a high elastic
modulus (low deformation under load).
•
Load cells can be designed to measure a
wide variety of forces such as
compression, bending, tension, shear and
torque.
Strain gauge type load cells
24
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain: (resistance strain gauge)
The Wheatstone bridge
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
27
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
28
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
29
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
30
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
31
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
32
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
33
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Strain gauge type load cells
34
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Time response
35
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Time response
36
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Time response
37
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Time response
38
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Temperature
•
Thermocouples are based on the principle that when two dissimilar metals are joined
a predictable voltage will be generated that relates to the difference in temperature
between the measuring junction and the reference junction (connection to the
measuring device).
•
RTDs are wire wound and thin film devices that work on the physical principle of the
temperature coefficient of electrical resistance of metals. They are nearly linear over a
wide range of temperatures and can be made small enough to have response times
of a fraction of a second. They require an electrical current to produce a voltage drop
across the sensor that can be then measured by a calibrated read-out device.
39
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Velocity: Interferometry (Michelson interferometer)
40
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Velocity: Interferometry
41
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
42
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
43
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
44
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
45
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
46
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
47
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Accelerometer performance:






Sensitivity (Pc/g or V/g)
Range
Resolution
Transverse sensitivity
Amplitude linearity
Frequency response or frequency
range
48
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Accelerometer performance:
Introduction to measurement and statistical analysis
49
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Environmental effects:

Temperature – may affect sensitivity, natural frequency and damping.
Effects sometimes characterised by manufacturer.

Humidity – mainly affects high impedance transducers.

Acoustic noise.

Strain sensitivity – may generate spurious signals when the case is
strained or distorted (ie. badly mounted)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Accelerometer mounting:
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Accelerometer mass loading:
The vibrational characteristics of a structure can be altered by adding
mass to that structure. An accelerometer that is too heavy, with respect
to the test structure, will affect the vibrational behaviour of the structure
and give erroneous measurements. Care must be used when selecting
an accelerometer and mounting hardware to avoid the effects of mass
loading.
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Charge amplifiers
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
Piezoelectric sensors
Frequency Response:
Introduction to measurement and statistical analysis
54
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
(Ref: Mechanical Measurements 5th ed. Beckwith, Marangoni & Leinhard)
Instrument type
Measurand
Method
Typical hardware
Potentiometer
Displacement
Electrical Resistance DC power supply - voltage
divider (metre - ohms - volt)
LVDT
Displacement
Inductance
AC excitation signal
(Modulator) & Demodulator
(metre - henry - volt)
Ultrasonic
Displacement
Time of flight
Ultrasonic generator,
ultrasonic microphone &
Clock (metre - second - volt)
Laser Triangulation
Displacement
Geometrical
variations
Optical encoder
Displacement
Optical masking
Laser light source &
photodiode array (metre count - volt)
Optical source, counter
(metre - count s- pulses)
Laser Interferometer
Displacement /
velocity
Optical interference
Laser light source, optical
splitters, photodiode,
frequency counter /
converter. (metre - count/rate
- volt)
55
Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
(Ref: Mechanical Measurements 5th ed. Beckwith, Marangoni & Leinhard)
Instrument type
Measurand
Accelerometer
Acceleration
Pressure sensor
Fluid pressure
Force sensor
Dynamic force
Pressure sensor
Fluid pressure
Water surface
Surface elevation
elevatuion (waves) (displacement )
Load cell
Force
Method
Piezoelectric effect
Typical hardware
Charge amplifier (g -coulomb
- volt)
Piezoelectric effect
Charge amplifier (Pascal coulomb - volt)
Piezoelectric effect
Charge amplifier (Newton coulomb - volt)
Capacitive (distance) Capacitance bridge modulator/demodulator
(metre - Farad - volt)
Change in permitivity Capacitance bridge -capacitance
modulator/demodulator
(metre - Farad - volt)
Component strain
Resistance bridge (newton (dimentional change) metre - ohm - volt)
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Introduction to measurement and statistical analysis
V. Rouillard 2003
MEASURING SYSTEMS : SELECTED EXAMPLES
(Ref: Mechanical Measurements 5th ed. Beckwith, Marangoni & Leinhard)
Instrument type
Measurand
Thermocouple
Temperature
RTD (Resistance Temperature
Temperature
Detector)
Semiconductor- Temperature
Junction
Temperature
sensors
Fluid flow rate
Flow rate
Fluid flow rate
Flow rate
Fluid flow rate
Flow rate
Fluid flow rate
Flow rate
Method
Seedbeck effect
(emf across different
metals)
Thermo-resistive
effect
Typical hardware
Amplifier / lineariser (C microvolt - volt)
Semiconductor
junction
Integrated circuit (C - volt)
Obstruction effect :
pressure drop
across venturi, flow
nozzle, orifice plate
Turbine speed
(m^3/s - pascal -volt)
Magnetic induction
(Faraday's law)
Vortex shedding
frequency
Weathstone bridge &
amplifier (C -ohm - volt)
Pulse / frequency counter
(m^3/s - hertz -volt)
(m^3/s - gauss -volt)
Pulse / frequency counter
(m^3/s - hertz -volt)