EI - Lecture 1 - Measurement Systems & Their Properties
elements of a measurement system
- measuring instrument - measurement system
inaccuracy definition
- the extent to which a reading might be wrong - usually given as a percentage of the full scale output (%f.s.o)
computer
- the last step includes recording, or presentation/display
precision
- the measure of precision is the standard deviation - good precision implies a small standard deviation
active instrument ex.
- The change in fluid level moves a potentiometer arm and the output signal consists of a proportion of the external voltage source applied across the two ends of the potentiometer. - The energy in the output signal comes from the external power source. - In this active instrument, primary transducer float system is merely modulating the value of the voltage from this external power source.
passive instrument ex.
- We want to measure the pressure of a fluid in a pipe. - The pressure of the fluid is translated into a movement of a pointer against a scale. - The energy expended in moving the pointer is derived entirely from the change in pressure measured. - In this passive instrument, there are no other energy inputs to the system.
piezoresistive effect
- a change in the electrical resistivity of a metal when mechanical strain (pressure/force/acceleration) is applied
accuracy ex.
- a force gauge of range 0-10N has a quoted inaccuracy of 1.0% f.s. then the maximum error to be expected in any reading is 0.1N - means that when the instrument is reading 1.0 N, the possible error is 10% of this value
precision definition
- a measurement system is highly precise if it gives the same value each time it is used to read a measurand - describes an instrument's degree of freedom from random errors
a linear system means...
- a proportional variation btwn the input and output - as a consequence, it avoids large variations in the output as a result of small variations in the input
range or span ex.
- a thermometer has a scale that reads from -40 degree C to 100 degee C - its range is -40 to 100 - its span is 140 deg C
classes of instruments: criteria that subdivide instruments into separate classes
- active and passive instruments - analog and digital instruments - indicating and instruments w/ signal output
active vs. passive instruments
- active: adjustments of the magnitude of the external energy input allows much greater control over measurement resolution compared to passive instruments - in terms of cost, passive instruments are cheaper to manufacture - choice btwn active and passive instruments for particular application involves carefully balancing the measurement resolution requirements against cost
what is a data logger?
- an electronic instrument that records measurements at set intervals over a period of time
electrical signal transmission
- analog voltage - simplest method via a shield wire/cable to reduce noise
analog meters
- are electromechanical devices that drive a point against a scale - ex. bathroom scale
low accuracy measurements from a high precision instrument
- are normally caused by a bias in the measurements, which is removable by recalibration
optical sensors
- based on the modulation of light travelling btwn a light source and a light detector - the transmitted light can travel along either an air path or a fibreoptic cable - light emitting diodes (LEDs) emit light in a narrow frequency band in the infrared region - air-path optical sensors are commonly used to measure proximity, translational motion and rotational motion
ex. analog instrument
- bathroom scale - as the input value (weight) changes, the point changes w/ a smooth continuous motion
precision repeatability and reproducibility
- both terms describe the spread of output readings for the same input
signal conditoning
- can include amplification, filtering, isolating - signal modification element
drift
- change in output of the transducer over time that is not a function of the measurand - usually determined in the absense of the signal at the input - doesn't depend on the input signal, but can depend on the external conditions - measurement systems are sensitive to temperature
instruments w/ signal type output
- commonly used in measurement system where the output measurement signal is recorded in some way for later use - usually, the measurement signal involved is an electrical voltage but it can take other forms in some systems such as an optical signal
thermometer: signal modification
- connecting the bulb to the stem to "amplify" the expansion of mercury
tolerance
- define the maximum error that is to be expected in measurement - not strictly speaking, a static characteristic - the accuracy of some instruments is sometimes quoted as a tolerance value - when used correctly, tolerance describes the maximum deviation of a manufactured component from some specified value
range or span
- define the minimum and maximum values of a quantity that the instrument is designed to measure
accuracy definition
- defined as the difference between the measurand value and true (correct) value
span
- defined as the range of an instrument from the minimum to maximum scale value - reported as one value - accuracy is defined as a percentage of time
measuring instrument
- describes a measurement system, whether it contains only one or many elements
high precision
- does not imply anything about measurement accuracy - a high precision instrument may have a low accuracy
drift ex.
- elasticity of a spring is temperature dependent
tolerance ex.
- electric circuit components such as resistors have tolerances of 5% - one resistor chosen at random from a batch having a nominal value 1000W and tolerance of 5% might have an actual value anywhere between 950W and 1050W
how can measured signals be transmitted?
- electrically - optically - radiotelemetry
evaluating linearity
- evaluation is based on the equation of a line that defines the relationship between the instrument output and the reference values
signal conditioning
- exists to improve the of a measurement system in some way
strain gauges
- experience a change in resistance when they are stretched or strained - able to detect very small displacements - bonded to the object whose displacement is to be measured
to determine the accuracy in terms of % full scale output
- find the worst point from comparing the difference btwn the measured and true values - assume the other points are at least that good
the degree of repeatability/reproducibility in measurements
- from an instrument - an alternative way of expressing its precision
transducer definition
- gives an output that is a function of the measurand (the input applied to it) - transforms energy from one form to another
analog instrument
- gives an output that varies continuously as the quantity being measured changes - the output can have an infinite number of values w/in the range that the instrument is designed to measure
digital instruments
- has an output that varies in discrete steps and so can only have a finite number of values - a computer performs its computations in digital form
potentiometer
- have a resistive element inside a long strip w/ a terminal at each end - wiper travels along the resistive strip when the knob is turned - the closer the wiper is to the end terminal it is wired in conjunction w/, the less the resistance b/c the path of the current will be shorter - the further away it moves from the terminal, the greater the resistance will be
what is one major drawback with indicating devices?
- human intervention is required to read and record a measurement - this process is particularly prone to error in the case of analogue output displays
ADC
- if a signal needs to be digitized, analog-to-digital conversion is needed
reproducibility
- if the measurement conditions vary
ex. solution
- if these values are plotted on a graph, the straight line relationship btwn voltage changes and temperature change is obvious - for a change in temperature of 30 degC, the change in volts of 7 - hence the measurement sensitivity = 7/30 = 0.233 volts/degC
ex. 2
- if we found the worst error btwn true and the indicated pressure is 0.5 psi we can calculate the %f.s. value by dividing the error value by the full scale output value (10 psi) - %F.S. = 0.5/10 = 5% - this means that at any point on the measurement scale there will or could be 5% error
importance of signal conditioning
- important where the primary transducer has a low output - ex. a thermocouple has an output of only a few millivolts and requires electronic amplification thus improving the sensitivity and resolution of measurement - other types of those that filter out electronic noise and remove bias etc.
how these subclasses are useful:
- in establishing several attributes of particular instruments such as > accuracy > cost > general applicability to different applications
transducer ex.
- in response to changes in its deformation under a given load, a strain gauge has a change in resistance which is changed to a voltage by a bridge circuit - in response to changes in temperature, a thermocouple outputs an electric voltage
analog meters are prone to errors from:
- inaccurate scale marking during manufacture, bearing friction, bent pointers and ambient temperature variations
indicating instruments
- include most passive ones - indicators can also be further divided into those that have an analogue output and those that have a digital display
where can you use a data logger?
- indoors, outdoors and underwater - can record data for up to months at a time, unattended
passive instrument
- instrument type in which the output entirely depends on the quantity to be measured
indicating vs. instruments w/ signal output
- instruments can also be classified as those that: > give an audio or visual indication of the magnitude of the physical quantity measured > give an output in the form of a measurement signal whose magnitude is proportional to the measured quantity
analog meters: human errors
- introduced through parallax error and mistakes in interpolating between scale markings - parallax error - quoted inaccuracy figures are between +/-0.1 and +3%
R^2
- lets us know what amount of variation in the values the regression line explains - if R^2 is 0.6 (60%) or more, the regression line is an adequate representation of the line of best fit
static characteristics of instruments
- linearity - sensitivity - accuracy - precision - range & span - resolution
piezoelectric transducer application
- many biomechanical applications include force & acceleration measurement
data logger size
- may fit into the palm of the hand - or it may be a multi-channel data collection instrument equipped w/ one or more external sensors
transducer
- measurand - the quantity to be measured (acceleration/force/light) - sensing element
linearity
- measurement systems w/ linear behaviour are desirable due to the linear relationship between input and output - only need 2 points to perform a calibration whereas non-linear systems require many
thermometer: sensing element
- mercury expands w/ increase in temperature
accuracy
- more usual to quote the inaccuracy figure - the manufacturer cannot guarentee the same error if the measurement system is used out of its range - important to choose a measurement system that has the best accuracy w/in the range of your expected value of the measurand
common measurement transducers
- piezoelectric transducers - piezoresistive transducers - strain gauges - potentiometer - optical sensors
potentiometer examples
- position sensor - used in kinematic measurement (electrogoniometer)
measurement system
- provides information about the physical value of some variables being measured
radiotelemetry signal transmission
- radio wireless transmission - data are transmitted in frequency modulated (FM) format
ADC + computer
- recorder / indicator / display element
static characteristics of an instrument
- related w/ a steady state response - these characteristics are quoted in specification or data sheets that are provided w/ equipment
analog meters continued...
- relatively simple and inexpensive - suffer less from noise - do not need a power supply
accuracy ex: how should instruments should be chosen?
- so that their range is appropriate to the spread of values being measured in order that the best possible accuracy is maintained in instrument readings
analog to digital conversion (ADC)
- takes a continuous signal (ex. voltage) and converts it into a discrete signal (1s and 0s) - needed for better recording, display and storage of data
computer (display, storage, recording): signal display or record
- takes the form either of a signal presentation unit or of a signal-recording unit
digitial meters continued...
- technically superior to analogue meters - have a greater cost due to the higher manufacturing costs - better measurement reliability and accuracy since the problem of analogue meter parallax error is eliminated - quoted inaccuracy figures are between +/-0.005% and +2%
piezoelectric effect
- the ability of certain materials to generate an electric charge in response to applied mechanical stress
digital meters
- the major part of a digital meter is the circuitry that converts the analog voltage being measured into a digital quantity - enables measurements to be recorded with much greater accuracy than that of an analog meter scale
range
- the measure of the instrument between the lowest and highest readings it can measure - reported as two values
sensitivity ex.
- the output volts of a thermocouple was measured at a range of temperatures - determine the measurement sensitivity of the thermometer in volts/degree Celsius
parallax error
- the perceived shift of an object's position as it is viewed from different angles
sensitivity
- the ratio between the change in the transducer signal and the corresponding change in the measured value - defined as the slope of the calibration curve - if the input/out relation is linear, the sensitivity is constant and all values of input
thermometer: indicator
- the reading scale
steady state response
- the relationship between the input and output when the input does not change - or the input is changing at a slow rate
full scale output
- the resulting output signal or displayed reading produced when the maximum measurement for a given device is applied
as strain is applied to the gauge...
- the shape of the cross-section of the resistance wire distorts, changing the cross-sectional area - as the resistance of the wire per unit length is inversely proportional to the cross sectional area, there is a consequential change in resistance
resolution
- the smallest interval between 2 distinguishable neighboring discrete values of the output signal - one of the major factors influencing resolution of an instrument is how finely its output scale is divided into subdivisions - the characteristic of the instrument is that it only can be changed via re-design
piezoresistive transducers
- transducers that are piezoresistive utilize the piezoresistive effect
optical signal transmission
- transmission of a signal as light - fibre-optic cable
active instrument
- type in which the quantity to be measured modules or adapts to magnitude of external power source
how does a data logger work?
- typically compact, battery-powered devices equipped w/ an internal microprocessor, data storage, and one or more sensors
piezoelectric transducers
- use the *piezoelectric effect to produce an output voltage
resolution ex.
- using a car speedometer, this has subdivisions of typically 5 km/h - means that when the needle is btwn the scale markings, we cannot estimate speed more accurately than to the nearest 5 km/h - thus 5km/h represents the resolution of the instrument
how to determine the goodness of fit
- using results of the regression eqn - calculating coefficient of determination - R^2
piezoelectric transducers continued...
- w/in the instrument electrodes are placed on the surface of the material under strain, surface charges can be measured as an output voltage - several materials have piezoelectric properties including quartz - the electric output of quartz is low and requires amplification to make the signal readable
accuracy ex.: if we were measuring forces w/ expected values btwn 0 and 1 N
- we would not use an instrument w/ a range of 0-10N
repeatability
- what a spread is called if the measurement conditions (ex. observer, location) are constant
when do the values quoted for instrument characteristics in such a data sheet apply?
- when the instrument is used under specified standard calibration conditions
2 groups of errors arising from measurement process
1) systematic errors 2) random errors
sensitivity is the ratio
scale deflection / value of measurand producing deflection
steps in the elements of a measurement system
transducer > signal conditioning > ADC > computer
