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Measurement Characteristics

Measurement Characteristics. Meelis Sildoja. Introduction.

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Measurement Characteristics

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  1. Measurement Characteristics Meelis Sildoja

  2. Introduction • Measurement is the experimental process of acquiring any quantitative information. When doing a measurement, we compare the measurable quantity – measurand - with another same type of quantity. This other quantity is called measurement unit • Measurand – a physical quantity, property, or condition which is measured Measurement Characteristics - Meelis Sildoja, MRI

  3. Measurements • Can be divided into direct or indirect measurements • Direct measurement – measured quantity is registered directly from the instruments display. • Measuring voltage vith voltmeter • Measuring length with ruler • Indirect measurement – result is calculated (using formula) from the values obtained from direct measurements • Finding work done by current: • U – voltmeter • I – ammeter • t – clock • A=U*I*t Measurement Characteristics - Meelis Sildoja, MRI

  4. Classification of physical quantites • Can be divided for quantities which value • is determined uniquely and does not depend on the zero level • mass • can only be determined as a reference to some fixed zero level • potential energy (zero level can be ground floor or 3d floor and result depends on that) • Time • but time interval and change in potential energy belong to the upper class Measurement Characteristics - Meelis Sildoja, MRI

  5. Measurements main equation • The value of the measured quantity can be expressed as • where [Y] is the measurement unit and y is the number, which shows how many times the measurable quantity differs from the unit Measurement Characteristics - Meelis Sildoja, MRI

  6. What is instrument • Instrument is a device that transforms a physical variable of interest (the measurand ) into a form that is suitable for recording (the measurement) • An example is ruler • the measurand is the length of some object • the measurement is the number of units (meters, inches, etc.) that represent the length • In order for the measurement to have consistent meaning, it is necessary to employ a standard system of units Measurement Characteristics - Meelis Sildoja, MRI

  7. Physical Measurement Variable Signal Variable Measurement SENSOR Measurand X S M Physical Process Display Simple Instrument Model • The key functional element of the instrument model is the sensor, which has the function of converting the physical variable input into a signal variable output • Due to the property that signal variables can be manipulated in a transmission system, such as an electrical or mechanical circuit, they can be transmitted to a remote output or recording device • In electrical circuits, voltage is a common signal variable Measurement Characteristics - Meelis Sildoja, MRI

  8. Simple Instrument Model Measurement Characteristics - Meelis Sildoja, MRI

  9. Physical Measurement Variable Analog Signal Variable Analog Signal Variable Digital Signal Variable A/D Converter SENSOR AMPLIFIER Computer Measurand X S Memory Output Physical Process Simple Instrument Model • If the signal from Sensor output is small, it is needed to be amplified. In many cases it is also necessary for the instrument to provide a digital signal output for connection with a computer-based data acquisition systems. Measurement Characteristics - Meelis Sildoja, MRI

  10. Sensors • Sensor -the part of a measurement system that responds directly to the physical variable beingmeasured • Sensors can be categorized into two broad classes • Passive sensors • Active sensors Measurement Characteristics - Meelis Sildoja, MRI

  11. Passive Sensors • Passive sensors do not add energy as part of the measurement process, but may remove energy in their operation, ie energy is converted to measurable quantity • One example of a passive sensor is a thermocouple, which converts a physical temperature into a voltage signal Measurement Characteristics - Meelis Sildoja, MRI

  12. Active Sensors • Active sensors add energy to the measurement environment as part of the measurement process • An example of an active sensor is a radar or sonar, where actively out-sended radio (radar) or acoustic (sonar) waves reflect off of some object and thus measures its range from the sensor Arecibo Observatory in Puerto Rico Besides being most powerful radio telescopes and the largest single unit telescope in the world, it is also a radar probably the world biggest active sensor though Measurement Characteristics - Meelis Sildoja, MRI

  13. Instruments SENSOR FUSION SENSOR 1 X1 SENSOR 2 X2 X3 S1 S2 S3 SENSOR 3 Physical Process Sensor Fusion (uniting of sensors) • Sensor fusion - in this case, two or more sensors are used to observe the environment and their output signals are combined in some manner (typically in a processor) to provide a single enhanced measurement Examples: Sensor output relation to the ambient temp is taken account during the measurements Image synthesis where radar, optical, and infrared images can be combined into a single enhanced image Measurement Characteristics - Meelis Sildoja, MRI

  14. Operational Modes of Instrumentation I(Null instrument) • Null Instrument - A measuring device that balances the measurand against a known value, thus achieving a null condition. Two inputs are essential to the null 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 comparator 3. and a null deflection at parity Measurement Characteristics - Meelis Sildoja, MRI

  15. Null instrument • Advantages: • Minimizes measurement loading errors (i.e. alter the value of the measured signal). Effective when the measurand is a very small value. • minimizes interaction between the measuring system and the measurand, by balancing the unknown input against a known standard input • Achieving perfect parity (zero condition) is limited only by the state of the art of the circuit or scheme being employed • Disatvantages: • Slow - an iterative balancing operation requires more time to execute than simply measuring sensor input. Not suitable for fast measurements i.e. only for static measurements Measurement Characteristics - Meelis Sildoja, MRI

  16. Null instrument - example • An equal arm balance scale with manual balance feedback • Potetntiometer AB is the potentiometer wire with resistance R1. The EMF of a standard DC source is e volts. The rheostat resistance is R . If the null point is obtained at point C, then the EMF of e and e1 are equal Measurement Characteristics - Meelis Sildoja, MRI

  17. Operational Modes of Instrumentation II(Deflection instrument) • Deflection instrument - a measuring device whose output deflects (deviates) proportional to the magnitude of the measurand • Deflection instruments are the most common measuring instruments • Advantages: • high dynamic response i.e. can be used for fast measurements • can be designed for either static or dynamic measurements or both • Disadvantages: • by deriving itsenergy from the measurand, the act of measurement will influence the measurand and change the valueof the variable being measured. This change is called a loading error. Measurement Characteristics - Meelis Sildoja, MRI

  18. Deflection isnstrument - example Spring scale as a deflection instrument. Scale has to be calibrated. Measurement Characteristics - Meelis Sildoja, MRI

  19. Flow chart of a deflection instrument (e.g.multiplication of deflection signal due to amplification ) The logic flow chart for a deflection instrument is straightforward • Examples of signal conditioning are to multiply the deflection signal by some scaler magnitude, such as in amplification or filtering, or to transform the signal by some arithmetic function Measurement Characteristics - Meelis Sildoja, MRI

  20. Analog and Digital Sensors • Analog sensors - provide a signal that is continuous in both its magnitude and its temporal (time) or spatial (space) content • Digital sensors - provide a signal that is a direct digital representation of the measurand. Digital sensors are basically binary (“on” or “off ”) devices. Essentially, a digital signal exists at only discrete values of time (or space) Measurement Characteristics - Meelis Sildoja, MRI

  21. Analog sensor • The defining word for analog is “continuous” i.e. if a sensor provides a continuous output signal that is directly proportional to the input signal, then it is analog Thermocouple as an analog sensor Measurement Characteristics - Meelis Sildoja, MRI

  22. Digital sensor • A common representation of digital signal is the discrete sampled signal, which represents a sensor output in a form that is discrete both in time or space and in magnitude. Data can be sent either in serial or parallel format A rotating shaft with a revolution counter. Each revolution generates a spike. In this example, the continuous rotation of the shaft is analog but the revolution count is digital. The amplitude of the voltage spike is set to activate the counter and is not related to the shaft rotational speed. Measurement Characteristics - Meelis Sildoja, MRI

  23. Analog Readout Instruments • An analog readout instrument provides an output indication that is continuous and directly analogous to the behavior of the measurand • For example • deflection of a pointer or an ink trace on a graduated scale • the intensity of a light beam or a sound wave Measurement Characteristics - Meelis Sildoja, MRI

  24. Digital Readout Instruments • A digital readout instrument provides an output indication that is discrete • Many digital devices combine features of an analog sensor with a digital readout or, in general, convert an analog signal to a discrete signal. In such situations, an analog to digital converter (ADC) is required.  HP3458A digital multimeter, most widely used device in MRI Measurement Characteristics - Meelis Sildoja, MRI

  25. Input Impedance • In the ideal case, the act of measurement should not alter the value of the measured signal. Any such alteration is a loading error • Loading errors can be minimized by impedance matching of the source with the measuring instrument – reduce the power needed for measurement • The power loss through the measuring instrument • where Z(W) is the input impedance of the measuring instrument, and E(V) is the source voltage potential beingmeasured • To minimize the power loss, the input impedance should be large Measurement Characteristics - Meelis Sildoja, MRI

  26. Input impedance - connecting instruments An equivalent circuit is formed by applying a measuring instrument (device 2) to the output terminals of an instrument (device 1). • The potential actually sensed by device 2 will be • The difference between the actual potential E1 and the measured potential E2 is a loading error. High input impedance Z2relative to Z1minimizes this error. • A general rule is for the input impedanceto be at least 100 times the source impedance to reduce the loading error to 1%. Measurement Characteristics - Meelis Sildoja, MRI

  27. dynamic range Saturation region Calibration • Calibration is the relationship between the physical measurement variable (input) and the signal variable (output) for a specific sensor • Calibration curve – graph that characterizes sensor or instrument response to a physical input • Sensitivity of the device isdetermined by the slope of the calibration curve. • Dynamic range - the difference between the smallest and largest physical inputs that can reliably be measuredby an instrument • Saturation - increasing the physical input value to the level where there is no change in output signal Calibration curve example. Measurement Characteristics - Meelis Sildoja, MRI

  28. Random error (precision) Systematic error (bias) Error types and sources Systematic errors (bias) – measured values have similar deviation from correct value Random errors (noise)– measured values deviate randomly around mean value. Noise describes the precison of measurements Measurement Characteristics - Meelis Sildoja, MRI

  29. Correct terms • Measurement is described by its discrimination , its precision , and its accuracy • These are too often used interchangeably, but they cover different concepts: • Discrimination - the smallest increment that can be discerned. Term resolution is used as a synonym, but according to the “book", it is now officially decleared as incorrect! • Precision - the spread of values obtained during the measurements. Two terms that should be used here are: • repeatability - variation for a set of measurements made in a very short period • reproducibility – same concept, but for measurements made over a long period • Accuracy - is the closeness of a measurement to the value defined to be the true value Measurement Characteristics - Meelis Sildoja, MRI

  30. thickness of the hole decides the discrimination Better precision i.e. better repeatability Better accuracy i.e. Mean value closer to bullseye Discrimination, precision and accuracy Two sets of arrow shots fired into a target to understand the measurement concepts of discrimination, precision, and accuracy Measurement Characteristics - Meelis Sildoja, MRI

  31. If measurements are made at temperature other than the sensor was calibrated it introduces systematic error. If systematic error source is known, it can be corrected for by the use of compensation methods Aging of the components will change the sensor response and hence the calibration Damage or abuse of the sensor can also change the calibration Invasiveness - the measurement process itself changes the intended measurand. This is key concern in many measurement problems. Reading measurements by human observer – common error source is parallax i.e. reading dial from non-normal angle NB! Interaction between measurand and measurement device is always present Systematic error sources Measurement Characteristics - Meelis Sildoja, MRI

  32. Invasivness - example • Reducing invasivness • to use high impedance electronic devices to measure voltage • Extreme invasiveness • large warm thermometer to measure the temperature of a small volume of cold fluid Measurement Characteristics - Meelis Sildoja, MRI

  33. Periodical calibration • In order to prevent systematic errors, sensors should be periodically recalibrated Measurement Characteristics - Meelis Sildoja, MRI

  34. Sensor Noise Transmission Noise Environmental Noise N2 N3 N1 AMPLIFIER SENSOR X Physical Process Random error sources • The noise will be amplified along with the signal as it passes through the amplifier • Noise is presented as signal to noise ratio (SNR). • SNR(dB)=10*log(Psignal/Pnoise) • An example for N1 would be background noise received by a microphone • An example of N2 would be thermal noise within a sensitive transducer, such as an infrared sensor • A common example of N3 is 50 Hz interference from the electric power grid Measurement Characteristics - Meelis Sildoja, MRI

  35. Random noise • What if Psignal < Pnoise ? • If some identifying characteristics of that signal are known and sufficient signal processing power is available, then the signal can be interpreted. • Example of such signal processing is the human ability to hear a voice in a loud noise environment Measurement Characteristics - Meelis Sildoja, MRI

  36. Estimating the measurement accuracy • Error is defined as the difference between the measured value and the true value of the measurand • E =(measured) - (true) • where • E = the measurement error • (measured) = the value obtained by a measurement • (true) = the true value of the measurand • Error can almost not be ever known, becuse we don’t know the (true) value, error can only be estimated. Measurement Characteristics - Meelis Sildoja, MRI

  37. What is uncertainty? • Uncertainty of measurement is a parameter that describes the distribution of the (thinkable) measured values • The word ‘uncertainty’ expresses the boubt to the exactness of the result of the measurement • Measurementresult is the measurement value with its uncertainty Measurement Characteristics - Meelis Sildoja, MRI

  38. Classification of uncertainties • Standard uncertainty – uncertainty of a measurement expressed as a standard deviation • Standard uncertainty consists of many components which are divided into two categories • type A uncertainty which is estimated using statistical methods • uA(x), where x denotes the measured value for which the uncertainty is given • type B uncertainty which is estimated using means other than statistical analysis • uB(x) • Combined standard uncertainty - • Expanded uncertainty – Where k is the coverage factor, typically in range 2-3 Measurement Characteristics - Meelis Sildoja, MRI

  39. How to estimate uncertainties? • Type A – when taking multiple values the distribution of these values corresponds to normal or Gaussian distribution • Where the sx describes the broadness of the curve and its square is called variance • s = standard deviation • s2 = variance Measurement Characteristics - Meelis Sildoja, MRI

  40. How to estimate uncertainties II? • Standard deviation • Where xt is the true value • Since we don’t know the true value, we use • Where is the mean value and sx experimental standard deviation • and Measurement Characteristics - Meelis Sildoja, MRI

  41. How to estimate uncertainties III? • If you take e.g. 100 measurements and divide them to 10 series each consisting 10 values and then calculate the mean to each series, you can show that the Stdev of the mean of the series is related to the Stdev of one series as follows • Number n under the square-root, is the number of measurements in one series Measurement Characteristics - Meelis Sildoja, MRI

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