measurement characteristics meelis sildoja. 26.04.2006 2measurement characteristics - meelis...

Measurement Measurement CharacteristicsCharacteristics

Meelis SildojaMeelis Sildoja

26.04.2006 2Measurement Characteristics - Meelis Sildoja, MRI

IntroductionIntroduction

MeasurementMeasurement is the experimental process of is the experimental process of acquiring any quantitative information. When acquiring any quantitative information. When doing a measurement, we compare the doing a measurement, we compare the measurable quantity – measurable quantity – measurandmeasurand - with - with another same type of quantity. This other another same type of quantity. This other quantity is called quantity is called measurement unitmeasurement unit

MeasurandMeasurand – – a a physical quantity, property, physical quantity, property, or condition which is measuredor condition which is measured


MeasurementsMeasurements Can be divided into Can be divided into directdirect or or indirectindirect measurements measurements

Direct measurement – measured quantity is registered Direct measurement – measured quantity is registered directly from the instruments display.directly from the instruments display. Measuring voltage vith voltmeter Measuring voltage vith voltmeter Measuring length with rulerMeasuring length with ruler

Indirect measurement – result is calculated (using formula) Indirect measurement – result is calculated (using formula) from the values obtained from direct measurementsfrom the values obtained from direct measurements Finding work done by current: Finding work done by current:

U – voltmeterU – voltmeter I – ammeterI – ammeter t – clockt – clock A=UA=U**II**tt


Classification of physical Classification of physical quantitesquantites

Can be divided for quantities which valueCan be divided for quantities which value is determined uniquely and does not depend is determined uniquely and does not depend

on the zero level on the zero level massmass

can only be determined as a reference to can only be determined as a reference to some fixed zero levelsome fixed zero level

potential energy (zero level can be ground floor potential energy (zero level can be ground floor or 3d floor and result depends on that)or 3d floor and result depends on that)

TimeTime

but time interval and change in potential energy but time interval and change in potential energy belong to the upper classbelong to the upper class


Measurements main Measurements main equationequation

The value of the measured quantity can be The value of the measured quantity can be expressed asexpressed as

where [Y] is the measurement unit and where [Y] is the measurement unit and yy is is the number, which shows how many times the the number, which shows how many times the measurable quantity differs from the unitmeasurable quantity differs from the unit

Y y Y [ ]


What is instrumentWhat is instrument IInstrument nstrument is a device that transforms a is a device that transforms a physical physical

variable variable of interest (the of interest (the measurand measurand ) into a form that ) into a form that is suitable for recording (the is suitable for recording (the measurementmeasurement))

An example is An example is rulerruler the the measurandmeasurand is the is the

length of some objectlength of some object the the measurementmeasurement is the is the

number of units (meters, number of units (meters, inches, etc.) that inches, etc.) that represent the lengthrepresent the length

In order for the measurement to have consistent meaning, it In order for the measurement to have consistent meaning, it is necessary to employ a is necessary to employ a standard system of unitsstandard system of units


Simple Instrument Simple Instrument ModelModel

The key functional element of the instrument model is theThe key functional element of the instrument model is the sensor, sensor, which has the function of converting the which has the function of converting the physical physical variable input variable input into a into a signal variable outputsignal variable output

Due to the property that Due to the property that signal variablessignal variables can be can be manipulated in a transmission system, such as an manipulated in a transmission system, such as an electrical or mechanical circuit, they can be transmitted to electrical or mechanical circuit, they can be transmitted to a remote output or recording devicea remote output or recording device

In electrical circuits, voltage is a common signal variableIn electrical circuits, voltage is a common signal variable

Measurement

Physical Process

Display

Physical Measurement

Variable

Signal Variable

SENSOR

X S M

Measurand



Common physical variables Typical signal variables

• Force • Voltage

• Length • Current

• Temperature • Displacement – spring of newtonmeter

• Acceleration • Light – change in intensity

• Velocity

• Pressure

• Frequency

• Capacity

• Resistance

• Time

• …



If the signal from Sensor output is small, it is If the signal from Sensor output is small, it is needed to be amplified. In many cases it is also needed to be amplified. In many cases it is also necessary for the instrument to provide a digital necessary for the instrument to provide a digital signal output for connection with a computer-signal output for connection with a computer-based data acquisition systems.based data acquisition systems.

Physical Process

Output

Physical Measurement

Variable

Analog Signal

Variable

SENSOR

X S

Measurand AMPLIFIER A/D Converter

Digital Signal

Variable

Computer

Memory

Analog Signal

Variable


SensorsSensors

Sensor Sensor -- the part of a the part of a measurement system measurement system that responds directly that responds directly to the physical variable to the physical variable beingbeing measuredmeasured

Sensors can be Sensors can be categorized into two categorized into two broad classes broad classes Passive sensorsPassive sensors Active sensorsActive sensors


Passive SensorsPassive Sensors Passive sensors Passive sensors do not add do not add

energy as part of the energy as part of the measurement process, but measurement process, but may remove energy in their may remove energy in their operation, ie energy is operation, ie energy is converted to measurable converted to measurable quantity quantity

One example of a One example of a passive passive sensorsensor is a thermocouple, is a thermocouple, which converts a physical which converts a physical temperature into a voltage temperature into a voltage signalsignal


Active SensorsActive Sensors Active sensorsActive sensors add energy to add energy to

the measurement the measurement environment as part of the environment as part of the measurement processmeasurement process

An example of an active An example of an active sensor is a radar or sonar, sensor is a radar or sonar, where actively out-sended where actively out-sended radio (radar) or acoustic radio (radar) or acoustic (sonar) waves reflect off of (sonar) waves reflect off of some object and thus some object and thus measures its range from the measures its range from the sensorsensor

Arecibo Observatory in Puerto Arecibo Observatory in Puerto RicoRico

Besides being most powerful radio Besides being most powerful radio telescopes and the largest single unit telescopes and the largest single unit telescope in the world, it is also a telescope in the world, it is also a radarradar probably the world biggest probably the world biggest active sensor thoughactive sensor though


Sensor Fusion (uniting of Sensor Fusion (uniting of sensors)sensors)

Sensor fusionSensor fusion - in this case, two or more sensors are used to - in this case, two or more sensors are used to observe the environment and their output signals are combined observe the environment and their output signals are combined in some manner (typically in a processor) to provide a single in some manner (typically in a processor) to provide a single enhanced measurementenhanced measurement

Physical Process

SENSOR1X1

SENSOR FUSION

Instruments

SENSOR2

SENSOR3X3

X2

S1

S2

S3

Examples:Examples:

1.1. Sensor output relation to the ambient temp is taken account Sensor output relation to the ambient temp is taken account during the measurementsduring the measurements

2.2. Image synthesis where radar, optical, and infrared images can be Image synthesis where radar, optical, and infrared images can be combined into a single enhanced image combined into a single enhanced image


Operational Modes of Operational Modes of Instrumentation IInstrumentation I(Null instrument)(Null instrument)

Null InstrumentNull Instrument - A - A measuring device that measuring device that balances the measurand balances the measurand against a known value, against a known value, thus achieving a null thus achieving a null condition. Two inputs are condition. Two inputs are essential to the null essential to the null instrument.instrument.

Null measurement devices usually consist of 1. automatic or manual feedback system that allows the comparison of

known standard value,2. an iterative balancing operation using some type of comparator3. and a null deflection at parity


Null instrumentNull instrument Advantages:Advantages:

Minimizes measurement loading errors Minimizes measurement loading errors (i.e. (i.e. alter the value of the measured signalalter the value of the measured signal). ). Effective when the measurand is a very Effective when the measurand is a very small value.small value.

minimizes interaction between the minimizes interaction between the measuring system and the measurand, by measuring system and the measurand, by balancing the unknown input against a balancing the unknown input against a known standard inputknown standard input

Achieving perfect parity (zero condition) is Achieving perfect parity (zero condition) is limited only by the state of the art of the limited only by the state of the art of the circuit or scheme being employedcircuit or scheme being employed

Disatvantages:Disatvantages: Slow - an iterative balancing operation Slow - an iterative balancing operation

requires more time to execute than simply requires more time to execute than simply measuring sensor input. Not suitable for measuring sensor input. Not suitable for fast measurements i.e. only for static fast measurements i.e. only for static measurementsmeasurements


Null instrument - Null instrument - exampleexample

An equal arm balance An equal arm balance scale with manual scale with manual balance feedbackbalance feedback

PotetntiometerPotetntiometer

AB is the potentiometer wire with resistance RAB is the potentiometer wire with resistance R11. .

The EMF of a standard DC source is The EMF of a standard DC source is volts. volts.

The rheostat resistance is R . If the null pointThe rheostat resistance is R . If the null point

is obtained at point C, then the EMF of is obtained at point C, then the EMF of and and 11

are equalare equal


Operational Modes of Operational Modes of Instrumentation IIInstrumentation II

(Deflection instrument)(Deflection instrument) Deflection instrument - Deflection instrument - a measuring device whose output a measuring device whose output

deflects (deviates) proportional to the magnitude of the measuranddeflects (deviates) proportional to the magnitude of the measurand

Deflection instruments are the most common measuring Deflection instruments are the most common measuring instrumentsinstruments

Advantages:Advantages: high dynamic response i.e. can be used for fast measurementshigh dynamic response i.e. can be used for fast measurements can be designed for either static or dynamic measurements or can be designed for either static or dynamic measurements or

bothboth

Disadvantages:Disadvantages: by deriving itsby deriving its energy from the measurand, the act of energy from the measurand, the act of

measurement will influence the measurand and change the measurement will influence the measurand and change the valuevalue of the variable being measured. This change is called a of the variable being measured. This change is called a loading errorloading error..


Deflection isnstrument - Deflection isnstrument - exampleexample

Spring scale as a deflection instrument. Scale has to be calibrated.Spring scale as a deflection instrument. Scale has to be calibrated.


Flow chart of a deflection Flow chart of a deflection instrument instrument

Examples of signal conditioning are to multiply Examples of signal conditioning are to multiply the deflection signal by some scaler magnitude, the deflection signal by some scaler magnitude, such as in amplification or filtering, or to such as in amplification or filtering, or to transform the signal by some arithmetic functiontransform the signal by some arithmetic function

The logic flow chart for a deflection instrument is straightforwardThe logic flow chart for a deflection instrument is straightforward

(e.g.multiplication of deflection signal due to amplification )


Analog and Digital Analog and Digital SensorsSensors

Analog sensorsAnalog sensors - provide a signal that is - provide a signal that is continuous in both its magnitude and its continuous in both its magnitude and its temporal (time) or spatial (space) contenttemporal (time) or spatial (space) content

Digital sensors - Digital sensors - provide a signal that is provide a signal that is a direct digital representation of the a direct digital representation of the measurand. Digital sensors are basically measurand. Digital sensors are basically binary (“on” or “off ”) devices. Essentially, binary (“on” or “off ”) devices. Essentially, a digital signal exists at only discrete a digital signal exists at only discrete values of time (or space)values of time (or space)


Analog sensorAnalog sensor

The defining word for analog is “continuous” i.e. The defining word for analog is “continuous” i.e. if a sensor provides a continuous output signal if a sensor provides a continuous output signal that is directly proportional to the input signal, that is directly proportional to the input signal, then it is analogthen it is analog

Thermocouple as an analog sensorThermocouple as an analog sensor


Digital sensorDigital sensor A common representation of digital signal is the A common representation of digital signal is the

discrete sampled signal, which represents a discrete sampled signal, which represents a sensor output in a form that is discrete both in sensor output in a form that is discrete both in timetime or or spacespace and in and in magnitudemagnitude..

A rotating shaft with a revolution counter. Each revolution generates A rotating shaft with a revolution counter. Each revolution generates a spike.a spike.

In this example, the continuous rotation of the shaft is analog but In this example, the continuous rotation of the shaft is analog but the revolution count the revolution count

is digital. The amplitude of the voltage spike is set to activate the is digital. The amplitude of the voltage spike is set to activate the counter and iscounter and is

not related to the shaft rotational speed.not related to the shaft rotational speed.

Data can be sent Data can be sent either in serial or either in serial or parallel formatparallel format


Analog Readout Analog Readout InstrumentsInstruments

An An analog readout analog readout instrument instrument provides an provides an output indication that is output indication that is continuous and directly continuous and directly analogous to the behavior analogous to the behavior of the measurandof the measurand

For example For example deflection of a pointer deflection of a pointer

or an ink trace on a or an ink trace on a graduated scalegraduated scale

the intensity of a light the intensity of a light beam or a sound wavebeam or a sound wave


Digital Readout Digital Readout InstrumentsInstruments

A A digital readout instrument digital readout instrument provides an output provides an output indication that is discreteindication that is discrete

Many digital devices combine features of an analog sensor Many digital devices combine features of an analog sensor with a digital readout or, in general, convert an analog with a digital readout or, in general, convert an analog signal to a discrete signal. In such situations, an analog to signal to a discrete signal. In such situations, an analog to digital converter (ADC) is required.digital converter (ADC) is required.

HP3458A digital multimeter, most widely used device in MRIHP3458A digital multimeter, most widely used device in MRI


Input ImpedanceInput Impedance In the ideal case, the act of measurement In the ideal case, the act of measurement

should not alter the value of the measured should not alter the value of the measured signal. Any such alteration is a signal. Any such alteration is a loading loading errorerror

Loading errors can be minimized by Loading errors can be minimized by impedance matchingimpedance matching of the source with of the source with the measuring instrument – reduce the the measuring instrument – reduce the power needed for measurementpower needed for measurement

The power loss through the measuring The power loss through the measuring instrument instrument where where Z(Z() ) is the input impedance of is the input impedance of

the measuring instrument, and the measuring instrument, and E(V) E(V) is is the source voltage potential beingthe source voltage potential being measured measured

To minimize the power loss, the To minimize the power loss, the input input impedance should be largeimpedance should be large

Z

EP

2

Z

EP

2


Input impedance - Input impedance - connecting instruments connecting instruments

The potential actually sensed by The potential actually sensed by device 2device 2 will be will be

The difference between the actual potential EThe difference between the actual potential E11 and the and the measured potential measured potential EE22 is a is a loading errorloading error. High input . High input impedance impedance ZZ22 relative torelative to Z Z11 minimizes this error. minimizes this error.

A general rule is for the input impedanceA general rule is for the input impedance to be at least 100 to be at least 100 times the source impedance to reduce the loading error to 1%.times the source impedance to reduce the loading error to 1%.

An An equivalent circuitequivalent circuit is formed by applying a is formed by applying a measuring instrument (measuring instrument (device 2device 2) to the output ) to the output terminals of an instrument (terminals of an instrument (device 1device 1).).

2112 /1

1

ZZEE


CalibrationCalibration Calibration Calibration is the relationship is the relationship

between the physical between the physical measurement variable (input) and measurement variable (input) and the signal variable (output) for a the signal variable (output) for a specific sensorspecific sensor

Calibration curve – Calibration curve – graph that graph that characterizes sensor or characterizes sensor or instrument response to a physical instrument response to a physical inputinput

Sensitivity Sensitivity of the device isof the device is determined by the slope of the determined by the slope of the calibration curve.calibration curve.

Dynamic rangeDynamic range - the difference - the difference between the smallest and largest between the smallest and largest physical inputs that can reliably physical inputs that can reliably be measuredbe measured by an instrument by an instrument

Saturation - increasing the Saturation - increasing the physical input value to the level physical input value to the level where there is no change in where there is no change in output signaloutput signal

dynamic rangedynamic rangeSaturation regionSaturation region

Calibration curve example.Calibration curve example.


Error types and sourcesError types and sources

Systematic errors (bias) Systematic errors (bias) – measured values – measured values have similar deviation have similar deviation from correct valuefrom correct value

Random errors (noise)– Random errors (noise)– measured values measured values deviate randomly deviate randomly around mean value. around mean value. Noise describes the Noise describes the precison of precison of measurements measurements

Randomerror

(precision)Systematic error(bias)


Correct termsCorrect terms Measurement is described by its Measurement is described by its discriminationdiscrimination , ,

its its precisionprecision , and its , and its accuracyaccuracy

These are too often used interchangeably, but they These are too often used interchangeably, but they cover different concepts:cover different concepts: DiscriminationDiscrimination - the smallest increment that can be - the smallest increment that can be

discerned. Term discerned. Term resolutionresolution is used as a synonym, is used as a synonym, but according to the “book", it is now officially but according to the “book", it is now officially decleared as incorrect!decleared as incorrect!

PrecisionPrecision - the spread of values obtained during the - the spread of values obtained during the measurements. Two terms that should be used here measurements. Two terms that should be used here are:are:

repeatabilityrepeatability - variation for a set of measurements - variation for a set of measurements made in a very short periodmade in a very short period

reproducibilityreproducibility – same concept, but for measurements – same concept, but for measurements made over a long periodmade over a long period

Accuracy Accuracy - is the closeness of a measurement to the - is the closeness of a measurement to the value defined to be the true valuevalue defined to be the true value


Discrimination, precision and Discrimination, precision and accuracyaccuracythickness of the hole

decides the discrimination

Better accuracy i.e. Mean value closer to bullseye

Better precision i.e. better repeatability

Two sets of arrow Two sets of arrow shots fired into a shots fired into a target to target to understand the understand the measurement measurement concepts of concepts of

discrimination, discrimination,

precision, and precision, and

accuracyaccuracy


Systematic error sources Systematic error sources If measurements are made at If measurements are made at

temperature other than the temperature other than the sensor was calibrated it sensor was calibrated it introduces introduces systematic error. systematic error. If systematic error source is If systematic error source is known, it can be corrected known, it can be corrected for by the use of for by the use of compensation methodscompensation methods

Aging Aging of the components will of the components will change the sensor response change the sensor response and hence the calibrationand hence the calibration

DamageDamage or or abuse abuse of the of the sensor can also change the sensor can also change the calibrationcalibration

Invasiveness - Invasiveness - the the measurement process itself measurement process itself changes the intended changes the intended measurand. This is key measurand. This is key concern in many measurement concern in many measurement problems. problems.

Reading measurements by Reading measurements by human observer – common human observer – common error source is parallax i.e. error source is parallax i.e. reading dial from non-reading dial from non-normal anglenormal angle

NB! Interaction between NB! Interaction between measurand and measurand and measurement device is measurement device is always presentalways present


Invasivness - exampleInvasivness - example

Reducing Reducing invasivnessinvasivness to use high to use high

impedance electronic impedance electronic devices to measure devices to measure voltagevoltage

Extreme Extreme invasivenessinvasiveness large warm large warm

thermometer to thermometer to measure the measure the temperature of a temperature of a small volume of cold small volume of cold fluidfluid


Periodical calibrationPeriodical calibration

In order to prevent In order to prevent systematic errors, sensors systematic errors, sensors should be should be

periodically recalibratedperiodically recalibrated


Physical Process

Environmental Noise

SENSORX

AMPLIFIER

N1

SensorNoise

N2

Random error sourcesRandom error sources

An example for NAn example for N11 would be would be background noise received by a background noise received by a microphonemicrophone

An example of NAn example of N22 would be thermal would be thermal noise within a sensitive transducer, noise within a sensitive transducer, such as an infrared sensorsuch as an infrared sensor

A common example of NA common example of N33 is 50 Hz is 50 Hz interference from the electric power interference from the electric power gridgrid

TransmissionNoise

N3

The noise will be amplified The noise will be amplified along with the signal as it along with the signal as it passes through the amplifierpasses through the amplifier

Noise is presented as Noise is presented as signal to signal to noise ratio noise ratio ((SNRSNR). ).

SNR(dB)=10*log(Psignal/SNR(dB)=10*log(Psignal/PnoisePnoise))


Random noiseRandom noise

What if PWhat if Psignalsignal < P < Pnoise noise ??

If some identifying characteristics of that If some identifying characteristics of that signal are known and sufficient signal signal are known and sufficient signal processing power is available, then the processing power is available, then the signal can be interpreted.signal can be interpreted.

Example of such signal processing is the Example of such signal processing is the human ability to hear a voice in a loud human ability to hear a voice in a loud noise environmentnoise environment


Estimating the Estimating the measurement accuracymeasurement accuracy

Error Error is defined as the difference between the is defined as the difference between the measured value and the true value of the measurand measured value and the true value of the measurand

E E =(=(measuredmeasured) - () - (truetrue))

wherewhere E E = the measurement error= the measurement error (measured) = the value obtained by a measurement(measured) = the value obtained by a measurement (true) = the true value of the measurand(true) = the true value of the measurand

Error can almost not be ever known, becuse we don’t Error can almost not be ever known, becuse we don’t know the (true) value, error can only be estimated.know the (true) value, error can only be estimated.


What is uncertainty?What is uncertainty?

UncertaintyUncertainty of measurement is a of measurement is a parameter that describes the distribution parameter that describes the distribution of the (thinkable) measured valuesof the (thinkable) measured values

The word ‘The word ‘uncertaintyuncertainty’ expresses the ’ expresses the boubt to the exactness of the result of the boubt to the exactness of the result of the measurementmeasurement

MeasurementMeasurement resultresult is the is the measurement measurement valuevalue with its with its uncertaintyuncertainty


Classification of Classification of uncertaintiesuncertainties

Standard uncertaintyStandard uncertainty – uncertainty of a measurement – uncertainty of a measurement expressed as a standard deviation expressed as a standard deviation

Standard uncertaintyStandard uncertainty consists of many components which consists of many components which are divided into two categoriesare divided into two categories type A uncertainty which is estimated using statistical type A uncertainty which is estimated using statistical

methodsmethods uuAA(x), where x denotes the measured value for which the (x), where x denotes the measured value for which the

uncertainty is givenuncertainty is given type B uncertainty which is estimated using means other type B uncertainty which is estimated using means other

than statistical analysisthan statistical analysis uuBB(x)(x)

Combined standard uncertainty - Combined standard uncertainty -

Expanded uncertainty –Expanded uncertainty –Where Where kk is the coverage factor, typically in range 2-3 is the coverage factor, typically in range 2-3


How to estimate How to estimate uncertainties?uncertainties?

Type A – when taking Type A – when taking multiple values the multiple values the distribution of these values distribution of these values corresponds to normal or corresponds to normal or Gaussian distributionGaussian distribution

Where the Where the xx describes the describes the broadness of the curve and broadness of the curve and its square is called varianceits square is called variance

standard deviationstandard deviation

variancevariance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

75.2 75.5 75.7 75.9 76.2 76.4 76.7 76.9 77.1 77.4 77.6 77.9

x [mm]

f(x)

[m

m-1

]

_

x + x

_

x + 2x

_x

_

x - x

_

x - 2x

_

x + 3x

_

x - 3x


How to estimate How to estimate uncertainties II?uncertainties II?

Standard deviationStandard deviation

Where xWhere xt t is the true valueis the true value

Since we don’t know the true value, we useSince we don’t know the true value, we use

Where is the mean value and sWhere is the mean value and sxx experimental experimental

standard deviationstandard deviation

and and


How to estimate How to estimate uncertainties III?uncertainties III?

If you take e.g. 100 measurements and divide If you take e.g. 100 measurements and divide them to 10 series each consisting 10 values and them to 10 series each consisting 10 values and then calculate the mean to each series, you can then calculate the mean to each series, you can show that the Stdev of the mean of the series is show that the Stdev of the mean of the series is related to the Stdev of one series as followsrelated to the Stdev of one series as follows

Number n under the square-root, is the number Number n under the square-root, is the number of measurements in one series of measurements in one series

measurement characteristics meelis sildoja. 26.04.2006 2measurement characteristics - meelis...

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