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CVEN9840-Lacture2-2020copy.pdf
Structural Health Monitoring
(CVEN9840)
Lecture 2
Dr Mehri Makki Alamdari
School of Civil and Environmental Engineering
1
Measurement and Sensing
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Fundamentals of Instrumentation and Measurement By Dominique Placko
Recommended Textbook
It presents the general principles of instrumentation processes. It explains the theoretical analysis of physical phenomena used by standard sensors and transducers to transform a physical value into an electrical signal.
Measurement and instrumentation: theory and application By Alan S. Morris and Reza Langari
It introduces engineering students to measurement principles and the range of sensors and instruments used for measuring physical variables. This updated edition provides new coverage of the latest developments in measurement technologies, including smart sensors, intelligent instruments, microsensors, digital recorders, displays, and interfaces, also featuring chapters on data acquisition and signal processing.
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The Structural Health Monitoring Process
Operational evaluation
Measurement and data acquisition
Feature selection & extraction
Probabilistic decision making
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Measurement Science Is Everywhere!
The action of measuring something where measuring ascertains the size, amount or degree (of something) by using an instrument or device marked in standard units.
Measurement Determining the value of a quantity Quantity Property of a phenomenon or object that can be qualitatively distinguished, and quantitatively determined
Example: length, time, mass, temperature, electrical resistance
We do measurement to: • Validate a design • Test a theory • Monitor a critical parameter
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Importance of Precision Measurement
Examples: • Satellite navigation systems depend on ultra-stable clocks. • Nuts ordered from one supplier will fit together and work with bolts ordered from
another supplier. • Food producers know the optimal temperature for preparing and storing a food
product.
Things can go wrong!!
The Gimli Glide . An Air Canada Boeing 767-233 jet was refuelled in Montreal using 22 300 pounds of fuel instead of 22 300 kilograms. The pilot calculated how much fuel he needed thinking he was getting his fuel in pounds per litre. When the plane ran out of fuel mid-flight, the pilot had to make an emergency 'gliding' landing at Gimli Canadian Air Force Base.
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International System of Units (SI)
The SI is at the centre of all modern science and technology and is used worldwide to ensure measurements can be standardised everywhere.
There are seven base units of the SI, in terms of which all physical quantities can be expressed.
All measurements can be expressed using combinations of the seven base units
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International System of Units (SI)
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Prefixes Used for Multiples of Units
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Measurement Concepts: Precision and Accuracy
Precision is about how close measurements are to one another. A measurement with high precision has good repeatability.
• Accuracy is about how close measurements are to the target, e.g. true answer .
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Measurement Concepts: Uncertainty
In reality, it is not possible to know the true answer and so we introduce the concept of uncertainty to help quantify how wrong our answer might be.
Uncertainty Quantification of the doubt about the measurement result and tells us something about its quality. It indicates how far our estimate is likely to lie from the true answer .
Every measurement y of a quantity x is subject to measurement uncertainty
Example: we might say that a particular stick is 200 cm long with an uncertainty of ±1 cm.
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a confidence interval: “the mass is (100.02147 ± 0.00079) kg, at a confidence level of 95%
Measurement uncertainty can be quantified by:
a anda d de ia ion: “the mass is 100.02147 g with a standard deviation of 0.35 mg
A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.
Measurement Concepts: Uncertainty
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Measurement Uncertainty vs. Measurement Error
Measurement uncertainty measurement error
Error: difference be een mea red al e and he r e al e
Uncertainty: quantification of the doubt about the measurement
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What Affects Measurements?
Many factors can reduce accuracy or precision and increase the uncertainty of measurement result.
Environmental conditions – changes in temperature or humidity can expand and contract materials as well as affect the performance of measurement equipment.
Inferior measuring equipment – equipment which is poorly maintained, damaged or not calibrated will give less reliable results.
Poor measuring techniques – finite resolution / incorrect reading
Inadequate training
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Measurement Concepts: Repeatability and Reproducibility
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Measurement Concepts: Tolerance
The tolerance is the agreed allowable variation in the shape of the nuts and bolts that allow them to still fit together.
Tolerance the maximum acceptable difference between the actual value of a quantity and the value specified for it.
Example: If an electrical resistor has a specification of 10 ohms and there is a tolerance of ±10 % on that specification, the minimum acceptable resistance would be 9 ohms and the maximum would be 11 ohms.
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Calibration
Calibration makes a connection between • measurement values produced by a measurement instrument • corresponding values realized by standards
Calibration procedure: • comparison of an instrument with a (more accurate)
Calibration Adjusting transfer function so the output matches the input
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Calibration of a resistance thermometer
Calibration Example
Calibration procedure: • comparison to a more accurate reference thermometer at various calibration
temperatures • list of measured temperatures and resistance values with measurement uncertainty • determination of the coefficients of a formula that relates measured resistance to
temperature • R(t) = R0 ( 1 + A × t + B × t 2)
• determination of the corresponding measurement uncertainty
Next, when using the thermometer, this formula will be used to translate a measured resistance into temperature.
Sensors
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Structure of a Measurement System
• Amplification • Fil e ing ,
Transformation of information from non- electrical domain into electrical domain
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Sensors
SENSORS convert energy information:
One energy form must be converted into the same or another energy form with exactly the same information content as the originating energy form.
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Sensors
Electrical Sensor: Transfer of non-electrical signals to electrical signals
Advantages: • Electrical amplification and attenuation can be easily done • Mass-inertia effects are minimized • Effect of friction are minimized • The output can be indicated and recorded remotely at a distance from the sensing medium • The output can be modified to meet the requirements of indicating or controlling units • The signal can be conditioned or mixed to obtain any combination with outputs of similar
transducers or control signal
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Analog vs. Digital Sensors
Analog sensors produce a continuous output signal or voltage which is generally proportional to the quantity being measured.
Physical quantities (such as Temperature, Speed, Pressure, Displacement, etc.) are all analog or continuous in nature.
Digital sensors produce a discrete digital output signal or voltage which is a digital representation of the quantity being measured.
Example: The fluid temperature could be measured by a thermometer which responds continuously to the temperature change.
Example: A key encoder is used to identify whether the system is on or off.
Sensors may output signals in different formats:
0
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Analog to Digital Conversion (A/D convertor)
ADC will sample at some fixed frequency (x axis)
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Analog to digital conversion The process of converting the analog signal from a sensor to a digital signal that accurately represents the measured time- varying physical parameter.
For example if we measure every 0.1 second, ADC will produce 10 samples per second the sampling frequency is 10 Hz.
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Analog to Digital Conversion
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Aliasing o Aliasing is an effect in signal processing that causes
deferent signals to become indistinguishable (or aliases of one another) when sampled.
o This happens when signals are sampled at too low of a rate, below the Nyquist frequency (fs/2), where fs is the sampling frequency.
o As a result, high frequencies, e.g. f>(fs/2) in the original signal, "fold back" into the lower frequencies.
Nyquist criterion: The sampling frequency must be minimum at 2 * max frequency of the signal being measured.
Example: A signal with a frequency of fa , where fa>fs/2 will appear as an aliased signal with a frequency of fs-fa.
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Aliasing
Example: o Suppose a sinusoid signal with a frequency of fa = 0.6fs.
o Nyquist condition: fs> 2×fa
o In this setting, we do not meet Nyquist condition
o As a result of this under-sampling a with frequency of samples of a pure 0.6fs sinusoid would produce a 0.4fs sinusoid instead.
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Resolution of Analog/Digital-Converters
ADC will sample at some fixed resolution (y axis)
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For a 24-bit ADC the resolution will be 144dB.
216 65536
In practice most Analogue to Digital Converters (ADC) have a voltage range of ± 10V. Determine the resolution of a measurement system for a 16-bit and 24-bit device.
ADC with two-bit resolution ADC with three-bit resolution
Resolution of Analog/Digital-Converters
Example:
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Characteristics of a Sensor
Linearity Relationship between physical parameter and resulting electrical signal must be linear
Sensitivity Defined as the electrical output per unit change in physical parameter Resolution Smallest change in the input that causes a noticeable change in the
output
Dynamic Range Operating range should be wide to permit it use under wide range of measurement condition
Repeatability Input or output relationship for a transducer should be predictable over a long period of time
Physical Size Minimum weight and volume
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Using the transfer function H, output signal y1 can be translated back to a measurement value x1.
Ideal linear transfer: sensitivity S = ∆y / ∆x
Non-linear transfer: differential sensitivity around x0:
Characteristics of a Sensor: Linearity
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Example: Nonlinear Transfer Function
A sensor with non-linear transfer function:
Mass-spring-damper (accelerometer)
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Characteristics of a Sensor: Sensitivity
For a more sensitive sensor an observed change of the sensor signal ∆y corresponds to a smaller change ∆x of the measured quantity. Sensor 1 is more sensitive than Sensor 2.
Sensitivity The Change in electrical output per unit change in physical parameter.
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Sensitivity to Extraneous Measurands
The elements of many sensors are often sensitive to unintended inputs (due to their construction, operation, or connection to other elements), making the sensor produce a signal even when an actual intended signal is not present.
Temperature temperature variation changes the resistivity A resistive strain gauge will be sensitive to temperature change!
Sensor attachment the acceleration reading may change depending on how an accelerometer is attached to a surface.
Examples
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Cross-sensitivity
Cross Sensitivity Unwanted sensitivity to an influence quantity c
Sensor signal changes depending on variable which different to the measurement quantity
Compensation: Remove cross (secondary) sensitivities.
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Change in Sensitivity: Deviations in the Transfer
x1 actual value of quantity to be measured y1 output signal of measurement system x 1 measured value determined based on nominal transfer x 1 – x1 measurement error
Re-calibration can help to reduce this error.
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Cross-Axis Sensitivity
Design imperfections often cause the intended sensing axis to be misaligned with the actual sensitivity vector, leading to cross-axis sensitivity.
The sensitivity vector for a single intended axis may be characterized by its orientation in and :
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Trade-off: Sensitivity vs Bandwidth
The mechanical design of motion sensors often involve design trade-offs between performance properties higher sensitivity often means a lower transmission band
Frequency
Tr an
sf er
F un
ct io
n
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Characteristics of Sensors
Resolution: smallest change in x that causes a noticeable change in y
Expressed in two ways: • absolute: Dx
• relative to the full scale: Dx / xmax often in bits: -log2 (Dx / xmax)
Dx = 0.01 V Dx / xmax = 0.01 V / 199.99 V = 5 10-5 in bits: -log2 (5 10-5) = 14.3 dB
Range - min and max values of input or output variables Example: input range 100-250°C or output range 4 to 20 mA
Span - maximum variation of input or output Example: 150 °C or 16 mA
The ability of a sensor to see small differences in readings. e.g. a temperature sensor may have a resolution of 0.000,01º C, but only be accurate to 0.001º C.
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Repeatability
Sensor system delivers not the same value, even if the measurement conditions remain the same.
Possible Causes: • Environmental Noise • Material change
Repeatability is the ability of a sensor to repeat a measurement when put back in the same environment. A sensor can be inaccurate yet be repeatable in making observations.
Repeatability Error Repeatability Error
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Drift
Properties of the sensor system change with time.
Drift: is a special type of aging describing slow changes with time.
Causes: Materials properties of the sensor system change with time.
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Active and Passive Sensors
Sensors according to whether sensor output is produced entirely by the quantity being measured or whether the quantity being measured simply modulates the magnitude of some external power source are divided into:
Self-Generating (Active)
Modulating (Passive)
The active sensor is also known as the self- generating sensor because they self-develop their electrical output signal. The energy requires for generating the output signals are obtained from the physical quantity which is to be measured.
Passive sensors require an external power source to operate. The signal is modulated by the sensor to produce an output signal. For example, a strain gauge does not generate any electrical signal, but by passing an electric current through it, its resistance can be measured by detecting variations in the current or voltage.
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Self-Generating Sensors
Self-generating sensors generate output voltages or currents relative to the quantity being measured, such as thermocouples or piezoelectric element. Self-generating transducer requires no auxiliary energy source.
Information and energy drawn from the measured object Pros: minimal sources of error Cons: load is imposed on the source
An example of a self-generating instrument is the pressure- measuring device shown. The pressure of the fluid is translated into movement of a pointer against a scale. The energy expended in moving the pointer is derived entirely from the change in pressure measured: there are no other energy inputs to the system.
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Modulating Sensors
Modulating sensors change their physical properties, such as inductance or resistance relative to the quantity being measured such as inductive sensors and require an auxiliary energy source.
An example of this type of sensors is a strain gauge or LVDT as they require voltage excitation.
The output is proportional to both the input signal and an auxiliary signal.
Information of measured object modulates energy transfer from external auxiliary source. Pros: minimal load on source Cons: extra sources of error
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Electrical Sensors
Resistive sensors
Capacitive sensors
Inductive sensors
Piezoelectric sensors
Different Types of Electrical Sensors:
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Resistive Sensors
Resistance of a wire-shaped conductor:
= resistivity [Wm] Material-dependant constant
Resistive gauges are simply resistive circuits that can be attached to a structure to determine its local deformations.
Resistive sensors can be used to measure temperature, pressure, displacement, force, vibrations, etc. Their ability to function in many conditions and their low prices explain their widespread usage.
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Resistive Sensors
There are two modes of resistance change when we deform/strain a device:
Mode 1: Physical change in dimensions. • the conductor length is directly proportional to resistance of the conductor and it is
inversely related with area of the conductor.
Mode 2: Re i i i i a f nc ion of ain .
Note that this function is non-linear. For semiconductor piezo-resistors, mode >> mode .
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Resistive Sensors
k is the gauge factor
For metals, =0.3
C is of the order of 1
For semiconductors, C can reach 200 and the gauge factor is high, of the order of C.
C is Bridgman s constant is Poisson ratio
k is approximately 2
This means that measuring very weak deformation must be done with semiconductive gauges, but in this case it is important to remember that R is very dependent on the temperature, which, in practice, limits the use of these gauges to temperatures below 200°C.
k is approximately 200
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Resistive Sensors
Example: weighing scale with strain gauges
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Example: Weighing Scale
Determine the sensitivity S = ∆Uo / ∆M [V/kg] of the measurement system?
The gauge factor k=2 The source voltage is: Ug = 10 V The relative sensitivity of the length change is The sensor circuit is as shown below:
We have a weighing scale as shown. When we put a mass on top of the scale, the resistivity of the gauge changes. With the following given information:
Answer: S ∆
∆ ∆ ∆
Ug = ∆ ∆
Ug = 10 ∆ ∆
= 6.2 𝑉/𝐾𝑔
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Cross-sensitivity Example: Weighing Scale
Temperature sensitivity of resistors typically is expressed as:
Temperature coefficient:
Cross sensitivity:
Let: = 20 × 10-5 K-1, Ug = 10 V
= S temp = 0.10mV/K
Stemp/Smass=16.12
Error: 16.12 kg / K!
S temp = 0.10mV/K S mass = 6.2 V / kg
The weight scale is more sensitive to temperature than weight!
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Gauge factor for semiconductor materials ~ 50-70 x that of metals due to stronger piezoresistive effect
Semiconductors have much higher TCR
TCR = temperature coefficient of resistivity (ºC-1)
Cross-sensitivity Example: Weighing Scale
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Capacitive Sensors
Parallel-plate capacitor:
C capacitance = permittivity of the dielectric medium between the plates [F/m] Material-dependant constant
o = the permittivity of free space 8.854 x 10-12 Farad/meter
=k o
Capacitive sensors consist of two parallel metal plates in which the dielectric between the plates is either air or some other medium.
Capacitive sensors can be used as a displacement sensor by applying the motion to be measured to the moveable capacitor plate. Capacitive displacement sensors commonly form part of instruments measuring pressure, sound, or acceleration.
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Capacitive Sensors
Parallel-plate capacitor:
Vertical displacement
• Non-linear transfer • Linear approximation will quickly result in large errors!
Single
Lateral displacement
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Capacitive Sensors: Applications
One application of capacitive sensor is where the dielectric medium is air and the device is used as a humidity sensor by measuring the moisture content of the air.
absorption of moisture by the sensor results in an increase in sensor capacitance.
Another common application is as a liquid level sensor, where the dielectric is part air and part liquid according to the level of the liquid that the device is inserted in.
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Capacitive Sensor Example
Two square metal plates, side 6cm separated by a gap of 1 mm. For the given parameters below:
Calculate the capacitance of the sensor when the input displacement of x is:
(a) 0 cm
(a) 3 cm
Question
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Capacitive Sensor Example
Answer
(a) 0 cm
𝐶 𝑘𝜀0 5 8.854 10 . . .
159.38 𝑝𝐹
(a) 3 cm
𝐶 5 8.854 10 . . .
1 8.854 10 . . .
63.75 𝑝𝐹
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Capacitive Sensor Example
Using a capacitive sensor for vertical displacement measurement, how can one improve the sensor linearity?
Single configuration
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Capacitive Sensor Example
• Error term scales with (∆d / d)2 instead of ∆ d / d • Much smaller for small ∆ d / d
Differential configuration
Differential configuration provides better linearity than single configuration.
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Inductive sensors
approximation valid for a long, thin coil (diameter << length)
= permeability [H/m] Material-dependant constant
L Inductance in Henrys [H]
Inductive sensors translate movement into a change in the mutual inductance between magnetically coupled parts.
Ampere’s Law: flow of electric current will create a magnetic field. Faraday’s Law: a magnetic field passing through an electric circuit will create a voltage.
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Inductive sensors
One example of this is the inductive displacement transducer shown below.
The single winding on the central limb of an “E -shaped ferromagnetic body is excited with an alternating voltage. The displacement to be measured is applied to a ferromagnetic plate in close proximity to the “E piece.
Movements of the plate alter the flux paths and hence cause a change in the current flowing in the winding.
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Inductive sensors
Inductive displacement sensor: coil with movable core
Better linearityLimited linearity
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Inductive sensors: LVDT
LVDT = Linea l - a iable diffe en ial an fo me
LVDT: An inductive transducer Measures displacement in terms of voltage difference between its two secondary voltages. Secondary voltages are nothing but the result of induction due to the flux change in the secondary coil with the displacement of the iron bar.
Modulating or self-generating?
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Piezoelectric Sensors
Piezoelectric sensors produce an output voltage when a force is applied to them.
Piezoelectricity derives its name from the Greek word “piezo , meaning “to press .
Piezoelectric sensors are made from piezoelectric materials. The piezoelectric effect is the conversion of pressure into electricity.
Piezoelectric effect:
Piezoelectric effect only exists in crystals, ceramics and polymers with an asymmetrical lattice of molecules that distorts when a mechanical force is applied to it.
Due to the action of microscopic deformations, charges will appear on the surface of a solid.
By implanting electrodes into the surface of the material, these surface charges can be measured as an output voltage.
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Piezoelectric Sensors
• Voltage: Q on sensor capacitance Cs open voltage Us = Q / Cs
• Charge: Connect sensor to charge amplifier
Two readout approaches
Polarization charge Q = Sq × F
Sq : Charge sensitivity F: Force
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Piezoelectric Devices
The use of piezoelectric materials in structural dynamics problems (as sensors and actuators) is an active research area. This field is called “smart structures or “intelligent material systems .
In a piezoelectric actuator, voltage is applied to the piezoelectric material, causing expansion and contraction.
Example: Vibration control Unwanted vibration is eliminated by adding the exact opposite vibration.
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Piezoelectric Devices
The piezoelectric effect is widely adopted to convert mechanical energy to electrical energy, due to its high energy conversion efficiency, ease of implementation, and miniaturization. This field is called “Energy Harvesting .
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Piezoelectric Accelerometer
Test mass M exerts a force F = M × a on a piezoelectric crystal
Resulting polarization charge Q = Sq × F is integrated on Cf
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Piezoelectric materials exhibit electromechanical coupling characteristics.
They have the ability to communicate between two different domains.
For example, if a PZT patch is attached to a mechanical structure, the mechanical impedance can be directly related to the electrical impedance. Therefore, any change or flaw in the analyzed mechanical structure can be interpreted by the PZT transducers.
Piezoelectric Sensors for Damage Identification in SHM
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Piezoelectric Sensors for Damage Identification
Piezoelectric zirconate-titanate (PZT) patches are used to couple the electrical impedance and mechanical impedance of structures.
Electromechanical Impedance Method
Due to the presence of the electromechanical coupling in the piezoelectric transducer, its electrical impedance is directly related to the mechanical properties of the host structure and is named the electromechanical impedance.
Variations of dynamical parameters of the structure, i.e. as a result of damage, influence the measured impedance plots, which in turn can be used for damage assessment.
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Piezoelectric Sensors for Damage Identification in SHM
Advantages
• Low power consumption • Localized SHM sensing capability • Sensor diagnostic capability • Can detect incipient damage • Sensors are low-cost and non-intrusive • Unaffected by changes in boundary and environmental conditions or operational vibrations
Disadvantages
• Localized sensing requires too many sensors and actuators • Installation of piezoelectric active sensors are not always straightforward • Long term reliability of PZT sensors and associated installation condition has not been
substantially investigated
Common Sensors for SHM
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Strain Measurement
The amount of deformation a material experiences due to an applied force is called strain.
It is the ratio of the change in length of a material to the original, unaffected length.
Strain can be positive (tensile), due to elongation, or negative (compressive), due to contraction.
In practice, the magnitude of measured strain is very small, so it is often expressed as micro-strain (µ ), which is x 10-6.
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The most common strain measurements are:
• Axial strain: It measures how a material stretches or compresses as a result of a linear force in the horizontal direction.
• Bending strain: It measures a stretch on one side of a material and the contraction on the opposite side due to a bending action.
Strain Measurement
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Strain is measured by a strain gauge. The most widely used strain gauge is the bonded metallic strain gauge. The metallic strain gauge consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction.
The electrical resistance of metallic grid changes in proportion to the amount of strain experienced by the test specimen.
Strain Measurement
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Strain Measurement
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Strain Measurement
A fundamental parameter of the strain gauge is the gauge factor (GF). GF is the ratio of the fractional change in electrical resistance to the fractional change in length, or strain:
Gauge factor k = k
The GF for metallic strain gauges is usually around 2. In practice, strain measurements rarely involve quantities larger than a few milli-strain (e x 10-3).
To measure the strain, we have to accurately measure very small changes in resistance.
To measure such small changes in resistance, and to compensate temperature effects strain gauge configurations are based on the concept of a Wheatstone bridge.
Example
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A resistant strain gauge with a gauge factor of 2 is fastened to a steel member, which is subjected to strain of 1x10-6. If the original resistance value of the gauge is 130 , calculate the change in resistance.
= k ∆𝑅 𝑘𝑅 =2 × 130 × 1x10-6 = 260
We should be able to measure a change in electrical resistance of 260 which is very small.
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The general Wheatstone bridge, is a network of four resistive arms with an excitation voltage, Ub, that is applied across the bridge.
Strain gauges are configured in Wheatstone bridge circuits to detect small changes in resistance.
This is a very useful circuit to measure low value of resistance. It is used to determine relative changes in resistance.
The Wheatstone Bridge
Strain Measurement
It enables relative changes of resistance in the strain gauge, which are usually around the order of 10-4 to 10-2 / to be measured with great accuracy.
A
B
C D
Passive or active?
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A
B
C D
The Wheatstone Bridge
The four arms or branches of the bridge circuit are formed by the resistances R1 to R4.
The corner points A and B of the bridge designate the connections for the bridge excitation voltage Ub;
The bridge output voltage U0 , that is the measurement signal, is available on the corner points C and D.
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A
B
C D
The Wheatstone bridge is the electrical equivalent of two parallel voltage divider circuits.
R1 and R4 compose one voltage divider circuit, and R2 and R3 compose the second voltage divider circuit.
The output of a Wheatstone bridge, Uo, is measured between the middle nodes of the two voltage dividers, e.g. C and D.• Left divider:
• Right divider:
• Output voltage:
The Wheatstone Bridge
81CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
From this equation, you can see that when
The voltage output UO is zero. Under these conditions, the bridge is said to be balanced.
Any change in resistance in any arm of the bridge results in a nonzero output voltage. Therefore, if we replace R4 with an active strain gauge, any changes in the strain gauge resistance unbalance the bridge and produce a nonzero output voltage that is a function of strain.
A
B
C D
The Wheatstone Bridge
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Strain Measurement
Depending on the number of active elements in the Wheatstone bridge, the orientation of the strain gauges, and the type of strain being measured, there are three different types of strain gauge configurations:
Configuration Number of active elements Quarter-bridge 1 Half-bridge 2 Full-bridge 4
A precision voltmeter is used in the centre of the bridge to provide an accurate measurement of imbalance.
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Quarter-Bridge
Quarter-bridge: A single element of the bridge changing resistance in response to the measured variable (mechanical force).
Typically, R2 in the diagram is set at a value equal to the strain gauge resistance with no force applied. The two ratio arms of the bridge R1 and R4 are set equal to each other.
Thus, with no force applied to the strain gauge, the bridge will be symmetrically balanced and the voltmeter will indicate zero volts, representing zero force on the strain gauge.
As the strain gauge is either compressed or tensed, its resistance will decrease or increase, respectively, thus unbalancing the bridge and producing an indication at the voltmeter.
84CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Sensitivity of Quarter-Bridge
𝑈𝑜 𝑈𝑏
𝑅 𝑅 ∆𝑅 𝑅. 𝑅 2𝑅 ∆𝑅 2𝑅
𝑅. ∆𝑅 4𝑅2 2𝑅. ∆𝑅
~ ∆𝑅 4𝑅
85CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Resistance Change with Temperature!!
An unfortunate characteristic of strain gauges is that the resistance changes with changes in temperature.
Thus, a quarter-bridge circuit works as a thermometer just as well as it does a strain indicator!!
To resolve the issue, a “dummy strain gauge can be placed in place of R2, so that both elements will change resistance in the same proportion when temperature changes, thus cancelling the effects of temperature change.
Dummy gauge is place at location where we are certain there is no mechanical strain. For example: On top of a bolt!!
dummy strain gauge
Quarter-Bridge with Temperature Compensation
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Quarter-Bridge with Temperature Compensation
Resistors R1 and R4 are of the equal resistance value, and the strain gauges are identical to one another.
With no applied force, the bridge should be in a perfectly balanced condition and the voltmeter should register 0 volts.
Both gauges are bonded to the same test specimen, but only one is placed in a position and orientation so as to be exposed to physical strain (the active gauge).
dummy strain gauge
87CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Quarter-Bridge with Temperature Compensation
The other gauge is isolated from all mechanical stress and acts merely as a temperature compensation device (the “dummy gauge).
Even though there are now two strain gauges in the bridge circuit, only one is responsive to mechanical strain, and thus we would still refer to this arrangement as a quarter-bridge.
If the temperature changes, both gauge resistances will change by the same percentage, and the bridge s state of balance will remain unaffected. Only a differential resistance (difference of resistance between the two strain gauges) produced by physical force on the test specimen can alter the balance of the bridge.
dummy strain gauge
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Half Bridge: Bending Strain Only
If we place the upper strain gauge so that it is exposed to the opposite force as the lower gauge (i.e. when the upper gauge is compressed, the lower gauge will be stretched, and vice versa), we will have both gauges responding to strain, and the bridge will be more responsive to applied force.
This utilization is known as a half-bridge.
Since both strain gauges will either increase or decrease resistance by the same proportion in response to changes in temperature, the effects of temperature change remain cancelled and the circuit will suffer minimal temperature-induced measurement error.
89CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Half Bridge: Bending Strain Only
half-bridge strain gauges are two times more sensitive than quarter-bridge strain gauges.
𝑈𝑜 𝑈𝑏
𝑅 𝑅 ∆𝑅 𝑅 ∆𝑅 . 𝑅 2𝑅 2𝑅
2𝑅. ∆𝑅 4𝑅2
~ ∆𝑅 2𝑅
90CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Half Bridge: Bending and Axial Strain
te n si le st ra in
Strain Gauge Tensile Strain
Strain Gauge Poi on effec
𝑈𝑜 𝑈𝑏
𝑅 𝑅 ∆𝑅 𝑅 ∆𝑅 . 𝑅 2𝑅 1 ∆𝑅 2𝑅
~ 1 ∆𝑅 4𝑅
91CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Full Bridge: Bending Strain Only
It may be advantageous to make all four elements of the bridge “active for even greater sensitivity. This is called a full-bridge circuit: When possible, the full-bridge configuration is the best to use. It is more sensitive than the others.
𝑈𝑜 𝑈𝑏
𝑅 ∆𝑅 2 𝑅 ∆𝑅 2
2𝑅 2𝑅 ~ 4𝑅. ∆𝑅 4𝑅2
∆𝑅 𝑅
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Example
A resistant strain gauge with a gauge factor of 2.13 and RA= 120 is used in the bridge. In this circuit R1= R4 = 120 . The dummy gauge has RD = 120 . If a strain of 1000 m/m is applied, find the bridge output voltage if Vs=10V.
Dummy Gauge RD 120
Active Gauge RA 120
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Solution
A resistant strain gauge with a gauge factor of 2.13 and RA= 120 is used in the bridge. In this circuit R1= R4 = 120 . The dummy gauge has RD = 120 . If a strain of 1000 m/m is applied, find the bridge output voltage if Vs=10V.
Dummy Gauge RD 120
Active Gauge RA 120
. . .
= 5.41e-04
𝑈𝑜=5.41mV
∆𝑅=k𝜀𝑅 2.13 1000 120 0.26 𝛺 → 𝑅𝐴 120 0.26 120.26𝛺
94CVEN9840 – Structural Health Monitoring 2020Dr Mehri Makki Alamdari
Strain Gauge Installation
The task of bonding strain gauges to test specimens may appear to be very simple, but i i no . Ga ging i a c af in i o n igh , ab ol el e en ial fo ob aining accurate, stable strain measurements.
https://www.youtube.com/watch?v=s4Bq8MvwbyU
Installing strain gauges can take a significant amount of time and resources, and the amount varies greatly depending on the bridge configuration.
The number of bonded gauges, number of wires, and mounting location all can affect the level of effort required for installation.
Certain bridge configurations even require gauge installation on opposite sides of a structure, which can be difficult or even impossible.
Quarter-bridge type I is the simplest because it requires only one gauge installation.
For Strain Gauge Installation Tutorial Watch:
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Vibrating Wire Strain Gauges
Other types of strain gauges
Fibre Optic Strain Gauges
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Fibre Optic Strain Gauges (Fibre Bragg Grating (FBG))
FBG is composed of a fiber like a cylindrical length of transparent material. The fiber has a number of material interferences, i.e. thin slices in it (Fiber Bragg Grating (FBG) which are placed at certain intervals. When the light from the laser hits this pattern, certain wavelengths are reflected and also transmitted. When an external compression or stretching force is induced in the fibre, it is subjected to positive or negative strain. As a result, the interval at which the fibre-grating interference are placed will change. When the FBG is under strain, the reflected light takes a little longer or shorter to travel back also the wavelength that is reflected also changes.
The technology is based on light that propagates through a fiber.
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Fibre Optic Strain Gauges (Fibre Bragg Grating sensors)
Compared to traditional electrical strain gauges, optical strain gauges do not need electricity. Therefore, the sensors are completely passive and immune, for example, to electromagnetic interference.
Fibre Bragg Grating (FBG) technology allows to: • Minimize noise • Eliminate the need for electrical power supply for operation • Enable long-range measurements
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Vibrating Wire Strain Gauges
The vibrating wire strain gauge operates on the principle that a tensioned wire as a result of strain, vibrates at a frequency that is proportional to the strain in the wire. A length of steel wire is tensioned between two mounting blocks that are welded to the surface being studied. Deformations of the surface will cause the two mounting blocks to move in relation to each other, altering the tension in the steel wire. This change in tension is measured as a change in the resonant frequency of vibration of the wire.
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M is the mass per unit length of the wire L is the length of the wire T is the tension due to the applied force
Measurement of the output frequency of the oscillator allows the strain applied to the wire to be calculated.
Vibrating Wire Strain Gauges
Displacement Measurement
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Displacement Measurement
• A Displacement Sensor is a device that measures the distance between the sensor and an object by detecting the amount of displacement.
• Generally limited to low frequency applications (< 50 Hz).
• Linear Variable Differential Transformer (LVDT)
• Optical Displacement Sensor
• Ultrasonic Displacement Sensor
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Electromechanical sensor to measure linear displacement along one single axis. A reliable and accurate sensing device that converts linear position or motion to a proportional electrical output. It consist of a hollow metal cylinder and a shaft which can move freely back and forth inside the cylinder.
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Linear Variable Differential Transformer (LVDT)
The LVDT's primary winding, P, is energized by a constant amplitude AC source.
The magnetic flux thus developed is coupled by the core to the adjacent secondary windings, S1 and S2.
If the core is located midway between S1 and S2, equal flux is coupled to each secondary so the voltages, E1 and E2, induced in windings S1 and S2 respectively, are equal. At this reference midway core position, known as the null point, the differential voltage output, (E1 - E2), is essentially zero.
If the core is moved closer to S1 than to S2, more flux is coupled to S1 and less to S2, so the induced voltage E1 is increased while E2 is decreased, resulting in the differential voltage (E1 - E2). Conversely, if the core is moved closer to S2, more flux is coupled to S2 and less to S1, so E2 is increased as E1 is decreased, resulting in the differential voltage (E2 - E1).
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Linear Variable Differential Transformer (LVDT)
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Relationship between displacement and voltage
Core position
Core voltage
Linear Variable Differential Transformer (LVDT)
Passive or active?
Friction-Free Operation
In normal use, there is no mechanical contact between the LVDT's core and coil assembly so there is no rubbing, dragging, or other source of friction.
Excellent Resolution
Since an LVDT operates on electromagnetic coupling principles in a friction-free structure, it can measure infinitesimally small changes in core position. These same factors also give an LVDT its outstanding repeatability.
Unlimited Mechanical Life
Because there is no contact between the LVDT's core and coil structure, no parts can rub together or wear out. This means that an LVDT features unlimited mechanical life.
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Linear Variable Differential Transformer (LVDT)
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Single Axis Sensitivity
An LVDT responds to motion of the core along the coil's axis but is insensitive to cross-axis motion of the core or to its radial position.
Environmentally Robust The materials and construction techniques used in assembling an LVDT result in a rugged, durable sensor that is robust to a variety of environmental conditions.
Drawback: It requires a fixed reference point.
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Linear Variable Differential Transformer (LVDT)
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LVDT Example
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An LVDT has the following details: VIn=Input voltage 6.3V Vout=Output voltage ±5.2V Range ±0.50 in.
Determine: a) Calculate the displacement when VOut is +2.6V. b)The plot of the output voltage versus core position for a core movement going from +0.45 in to -0.03 in.
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a)
Δ 0.5 2.6 5.2
0.25𝑖𝑛
b) 𝑉 0.45 .
. +4.68 V
𝑉 0.03 . .
-0.312 V
Solution
LVDT Example
Optical Displacement Sensor
There can be different ways of implementing this idea:
Example: Light from the light source is condensed by the lens and directed onto the object. Light reflected from the object is condensed onto a one- dimensional position sensing device (PSD) by the receiving lens. If the position of the object (the distance to the measuring device) changes, the balance of the two PSD outputs A and B will change.
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• Non-contact sensing • High accuracy detection • Requires reflective surface
Optical displacement sensors are based on the transmission of light between a light source and a light detector.
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TRIANGULATION
One method for accurately measuring the distance to targets is through the use of laser triangulation. They are so named because the sensor enclosure, the emitted laser and the reflected laser light form a triangle.
Optical Displacement Sensor Principles
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Light: 300,000,000 m/sec in vacuum
TIME OF FLIGHT
Optical Displacement Sensor Principles
TOF is acronym of "Time Of Flight".
TOF is the way of measurement that converts the time to the distance.
It measures the time from the pulse emission of laser to its return in the sensor.
For example, when it takes 10 ns (Nano second) from emitting laser pulse up to receiving reflected laser pulse, it takes 5 ns for one way from sensor to the target object, because the velocity of light is 300,000 km/sec, the distance is calculated as 5 ns x 300,000 km/s = 1.5 m.
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TIME OF FLIGHT vs TRIANGULATION
TRIANGULATION When the distance X is short, the difference of distance on the image sensor is bigger, but when the distance X is long, the difference of distance on the image sensor is small and measurement accuracy gets worse.
TOF Measurement accuracy does not change even if the distance X changes because the sensor convert time difference to distance.
Measurement error increases if the object gets further from the sensor.
Measurement error does not change if the object gets further from the sensor.
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Ultrasound displacement sensing is based on the time-of- flight principle.
Sound travels at a constant speed, which varies slightly based on ambient temperature. At room temperature, sound travels at 331 m/s.
Ultrasonic Displacement Sensor
o The emitter produces a "chirp" of sound (at very high frequency)
o Sound travels away from emitter, bounces off barrier, returns to detector
o The time elapsed is measured o The distance is measured by detecting and calculating
the time from the emission to receipt of the ultrasonic wave.
Acceleration Measurement
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Acceleration Measurement
An accelerometer is an electromechanical or mechanical device that will measure acceleration. Acceleration forces may be static, like the constant force of gravity pulling at your feet, or they could be dynamic caused by movement or vibration.
In the computing world, IBM and Apple have recently started using accelerometers in their laptops to protect hard drives from damage. If you accidentally drop the laptop, the accelerometer detects the sudden freefall, and switches the hard drive off so the heads don't crash.
In a similar fashion, high g accelerometers are the industry standard way of detecting car crashes and deploying airbags at just the right time.
Examples
There are approximately 2000 accelerometer sensors under the bus lane in the Sydney Harbour Bridge.
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Acceleration Measurement
• No external reference required. • Accelerometer can detect acceleration, displacement, tilt (angle of orientation).
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There are two classes of accelerometers in general:
• AC-RESPONSE ACCELEROMETER It cannot be used to measure static acceleration such as gravity and constant centrifugal acceleration. They generally also can't measure slow vibrations (below a few hertz). AC-response accelerometers are the preferred option for all vibration testing due to their wide frequency response and high signal-to-noise ratio.
• DC-RESPONSE ACCELEROMETER Can respond down to zero Hertz which is required to measure the gravity vector and other sustained accelerations. It therefore can be used to measure static, as well as dynamic acceleration.
It's also required for shock applications where you want to integrate the acceleration data for velocity or displacement. Accelerometers that do not have a DC response will have an intrinsic decay function that will result in significant error during numeric integration, especially over long duration events.
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Measurement Range: +/- g
• The level of acceleration supported by the sensor s output signal specifications, typically specified in ±g.
• This is the greatest amount of acceleration the sensor can measure and accurately represent as an output.
If you only care about measuring tilt using earth's gravity, a ±1.5g accelerometer will be more than enough. If you are going to use the accelerometer to measure the motion of a car, plane or robot, ±2g should give you enough headroom to work with. For a project that experiences very sudden starts or stops, you will need one that can handle ±5g or more.
Sensitivity mV/g
• This means that for a given change in acceleration, there will be a larger change in signal. The more sensitivity the better. Since larger signal changes are easier to measure, you will get more accurate readings.
• Sensitivity change due to temperature is generally specified as a % change per °C.
Resolution (mg) • Smallest measurable acceleration level.
Accelerometer Specifications
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Nonlinearity • Ideally, the relationship between voltage and acceleration is linear and described by the sensitivity of the device.
• Nonlinearity is a measurement of deviation from a perfectly constant sensitivity, specified as a percentage with respect to either full-scale range (%FSR).
Accelerometer Specifications
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Accelerometer Specifications
Cross-Axis Sensitivity (%)
• A measure of how much output is seen on one axis when acceleration is imposed on a different axis, typically specified as a percentage. The coupling between two axes can result from a combination of alignment errors.
Zero-g Bias Level
• Specifies the output level when there is no acceleration (zero input).
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Number of axes
• If you are measuring vibration of a pylon in a bridge, maybe you need to consider a tri-axial accelerometer.
Frequency Response or Bandwidth
• Bandwidth is the frequency range that the sensor operates in. It is the highest frequency signal that can be sampled without aliasing.
For slow moving tilt sensing applications, a bandwidth of 50Hz will probably suffice. If you intend to do vibration measurement, or control a fast moving machine, you will want a bandwidth of several hundred Hz.
Accelerometer Specifications
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Noise density g/ (H )
• Some accelerometers will define residual noise as a broadband RMS value, usually with the units of µV or µg. This is calculated by taking the root mean square of the signal without any mechanical excitation. Accelerations below the broadband noise level will not be resolvable.
• Some accelerometer datasheets provide a spectral noise parameter which will be specified as µV/√Hz or µg/√Hz. When this value is multiplied by the square root of the measurement, this result is the nominal RMS acceleration noise of the sensor.
Accelerometer Specifications
The model 86 and 87 are ultra-low-noise accelerometers.
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Acceleration Measurement
123
Sensitivity vs. Bandwidth
Operating frequency is much lower than ωn
• A higher resonant frequency implies less displacement low sensitivity
Measure displacement due to acceleration
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Piezoelectric Accelerometer
Piezoelectric Accelerometers are the most commonly used AC-response accelerometers.
Piezoelectric sensors use materials, such as quartz crystals or specially formulated ceramics, which generate a charge across the faces when an accelerative force is applied.
Under acceleration, the seismic mass of the accelerometer causes the piezoelectric element to “displace a charge, producing an electrical output voltage proportional to acceleration.
Advantages: Accuracy Durability Large dynamic range Ease of installation Long life span
Although these devices cost more than other types, in many situations their benefits outweigh the higher price.
Micro-Electro-Mechanical Systems (MEMS)
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Micro-Electro-Mechanical Systems (MEMS) is a fabrication technology that can be used to manufacture accelerometers. Silicon is the base material for many MEMS technologies. Silicon is a material with unique electrical and mechanical properties, such as semi conductivity, piezoresistive, high mechanical strength and mechanically elastic behaviour.
MEMS accelerometers: Capacitive accelerometers Piezoresistive accelerometers
MEMS fabrication technology has brought lower manufacturing costs and smaller sizes (as the name implies!) to accelerometers.
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MEMS Accelerometers: Reliable Smaller Less expensive than Piezoelectric accelerometers
Piezoelectric Effect: It is merely the result of stressing a piezo element—crystal, ceramic, or biological matter—to generate a charge or voltage.
Self-Generating (Active)
Piezoresistive Effect: It is a change in electrical resistance of a semiconductor material due to mechanical stress. When pressure is applied to a piezo resistor, depending on the material, its resistance increases.
Modulating (Passive)
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Difference Piezoelectric and Piezoresistive Effects
• Piezoresistive The resistance of the piezoresistive gauges changes in response to strain. This consists of a relatively large moving mass, connected to a flexible beam that will deform (strain) as a result of acceleration of the mass.
• Capacitive Another way to do it is by sensing changes in capacitance. If you have two microstructures next to each other, they have a certain capacitance between them. If an accelerative force moves one of the structures, then the capacitance will change.
MEMS Accelerometers
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The resistance of the piezoresistive gauges changes in response to strain. This consists of a relatively large moving mass, connected to a flexible beam that will deform (strain) as a result of acceleration of the mass.
Acceleration Bending moment Strain Δresistance Δvoltage
2 or 4 gauges arranged in a Wheatstone bridge circuit.
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Piezoresistive Accelerometer
128
Displacement is proportional to acceleration, and can be picked up.
Capacitive Accelerometer
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Capacitive Accelerometer
Differential Capacitive Sensing • Improves linearity
Single Capacitive Sensing
• Capacitance is function of gap or area • Transfer function is not perfectly linear.
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Capacitive Piezoresistive Piezoelectric They are DC coupled and therefore best suited for measuring low- frequency vibration, motion, and steady-state acceleration.
They have a very wide bandwidth which allows these to be used for measuring short duration (high frequency) shock events such as crash testing.
They are the first choice for most vibration measurements due to their wide frequency response, good sensitivity, and easy installation. The only exclusion is for applications where velocity and displacement data are needed because they are AC coupled.
They suffer from a poor signal to noise ratio, a limited bandwidth, and mostly restricted to smaller acceleration levels.
They measure down to zero hertz so they can also be used to accurately calculate velocity or displacement information.
They can also not measure static accelerations and generally can't measure vibrations below a few hertz.
They are very low cost and easy to integrate into your electrical system.
They typically have a very low sensitivity which makes them less useful for accurate vibration testing.
Suitable for use in a range of very harsh environments; they can also tolerate very high temperatures.
They are much more expensive than the capacitive MEMS accelerometers.
The sensor elements are self- powered so they re intrinsically low- power devices.
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Comparison
Other Sensors in SHM
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Wind Measurement Sensors
Anemometer
Usually is placed on top of the pylon in cable-stayed bridges.
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Weigh-in-motion Stations (WIM)
Weigh-in-motion Stations (WIM)
Measure the axle weight of the passing vehicles, the sum of the weight (gross weight), velocity of the vehicles and distance between the axles.
Bridge Weigh in MotionWeigh in Motion
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Laser Doppler Vibrometer(LDV)
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LDV is used to make non-contact vibration measurements of a surface by sending a laser beam.
Unmanned Aerial Vehicle (UAV, Drones)
Implemented with cameras to generate various data including images, video, infrared images, site maps and 3D models.
IR image of the deck clearly showing the girder locations.
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Others
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References
1. Regtien, P.P.L., 2005. Electronic instrumentation (Vol. 2). VSSD. 2. https://www.npl.co.uk/resources/gpgs 3. https://ocw.tudelft.nl/course-lectures/analog-digital-convertors/?course_id=5197
