static characteristics in measurement system

01. PENDAHULUAN

03. CHARACTERISTICS OF MEASUREMENT SYSTEMS(static)Deddy KurniadiAugie WidyotriatmoRizki ArmantoEngineering Physics Program Institut Teknologi Bandung

TF 3102 METODA PENGUKURANTF 3102 METODA PENGUKURANCHARACTERISTICS OF MEASUREMENT SYSTEMSStatic CharacteristicsDynamic CharacteristicsTF - 3102 : Static Characteristics1STATIC CHARACTERISTICSCharacteristics of measurement system associated with a given constant input, and observed after a steady-state condition is achieved

Systematic Characteristics Statistical CharacteristicsIdentification of Static CharacteristicsTF - 3102 : Static Characteristics2SYSTEMATIC CHARACTERISTICS TF - 3102 : Static Characteristics3SYSTEMATIC CHARACTERISTICS Systematic characteristics are those that can be exactly quantified by mathematical or graphical means. RANGESPANLINEARITYNON-LINEARITYSENSITIVITYENVIRONMENTAL EFFECTSHYSTERESISRESOLUTIONWEAR & AGINGERROR BANDS

TF - 3102 : Static Characteristics4

SYSTEMATIC CHARACTERISTICS RANGEInput RangeThe input range of an element is specified by the minimum and maximum values of Input, i.e. IMIN to IMAXEx.: : Input Range of a pressure transducer 0 s/d 104 PaOutput RangeThe output range is specified by the minimum and maximum values of Output , i.e. OMIN to OMAXEx.: Output Range of a pressure transmitter 4 s/d 20 mA

TF - 3102 : Static Characteristics5Range Input : 0 s/d 104 PaRange Output : 4 s/d 20 mA

SYSTEMATIC CHARACTERISTICS SPANThe maximum variation in input or output of a measurement system Input Span = Inputmax InputminOutput Span = Outputmax OutputminExampleA Pressure Transmitter has span as follows Input Span = 104 PaOutput Span = 16 mA

TF - 3102 : Static Characteristics6Input span : 104 PaOutput span : 16 mA

SYSTEMATIC CHARACTERISTICS LINEARITYAn element is said to be linear if corresponding values of Input and Output lie on a straight line.Output of a linear system as follows


SYSTEMATIC CHARACTERISTICS TF - 3102 : Static Characteristics8NON-LINEARITYAn element is said to be non-linear if corresponding values of Input and Output does not lie on a straight line Ex. : linear and non-linear curves :

SYSTEMATIC CHARACTERISTICS In many cases Output O(I) can be expressed as a polynomial in Input In :

TF - 3102 : Static Characteristics9Ex.: The output of a thermocouple of copper-constantan (type T), is expressed in the following polynomial ,

For range of 0 to 400 oC, the output voltage E(T=0) = 0 V & E(T=400oC) = 20869 V. The linear equation in this range,

The non linear correction function is :

EXAMPLESTF - 3102 : Static Characteristics10A differential pressure transmitter has an input range of 0 to 2 104 Pa and an output range of 4 to 20 mA. Find the equation to the ideal straight line ?A non-linear temperature sensor has an input range of 0 to 400 C and an output range of 0 to 20 mV. The output signal at 100 C is 4.5 mV. Find the non-linearity at 100 C in millivolts and as a percentage of span ?

SYSTEMATIC CHARACTERISTICS SENSITIVITYThe ratio of output change and the input changeTF - 3102 : Static Characteristics11

Sensitivity of Thermocouple (Copper-Constantant) :

SYSTEMATIC CHARACTERISTICS ENVIRONMENTAL EFFECTSIn general, the output of measurement system depends not only on the signal input but on environmental inputs such as ambient temperature, atmospheric pressure, relative humidity, supply voltage, etc.

Two main types of environmental input Modifying InputThis input causes the linear sensitivity of an element to changeInterfering InputThis input causes the straight line intercept or zero bias to change

TF - 3102 : Static Characteristics12SYSTEMATIC CHARACTERISTICS Environmental EffectsTF - 3102 : Static Characteristics13

SYSTEMATIC CHARACTERISTICS HYSTERESISFor a given value of Input, the Output may be different depending on whether Input is increasing or decreasing. Hysteresis is the difference between these two values of Output


SYSTEMATIC CHARACTERISTICS RESOLUTIONthe largest change in Input that can occur without any corresponding change in Output.TF - 3102 : Static Characteristics15

SYSTEMATIC CHARACTERISTICS WEAR & AGINGThese effects can cause the characteristics of an element, e.g. K and a, to change slowly but systematically throughout its life.

ERROR BANDSNon-linearity, hysteresis and resolution effects in many modern sensors and transducers are so small that it is difficult and not worthwhile to exactly quantify each individual effect.The performance of a system is described in error bands and in the probability density functionTF - 3102 : Static Characteristics16SYSTEMATIC CHARACTERISTICS TF - 3102 : Static Characteristics17

ERROR BANDS (pita error)

GENERAL MODEL OF MEASUREMENTTF - 3102 : Static Characteristics18

GENERAL MODEL OF MEASUREMENTStrain GaugeR = 100 Ohm ; Gauge Factor = 2,0Dynamic effect and non-linearity are neglectedThe resistance of the gauge is affected by ambient temperature as well as strainThe temperature acts as both a modifying and an interfering input, i.e. it affects both gauge sensitivity and resistance at zero strain.TF - 3102 : Static Characteristics19

GENERAL MODEL OF MEASUREMENTModel of thermocouple Copper Constantant TF - 3102 : Static Characteristics20

STATISTICAL CHARACTERISTICS TF - 3102 : Static Characteristics21STATISTICAL CHARACTERISTICSOBSERVATIONMeasurement of an individual variable SAMPLEOverall results of observation AVERAGE The total value of all samples are divided by the number of samplesTF - 3102 : Static Characteristics22

ABSOLUTE AVERAGE DEVIATION :

STATISTICAL CHARACTERISTICSSTANDARD DEVIATIONVariability of a sampleTF - 3102 : Static Characteristics23

Note :To obtain a reliable estimation of s, at least 20 data are needed for a small number of data, unbiased or sample standard deviation is defined by the following equation :

STATISTICAL CHARACTERISTICSExample : The following readings are taken of a certain physical length. Compute the mean reading, standard deviation, variance and average of the absolute value of the deviation using the biased basis

TF - 3102 : Static Characteristics24ReadingX, cm15.3025.7336.7745.2654.3365.4576.0985.6495.81105.75

The mean value is given by :STATISTICAL CHARACTERISTICSProbability or Variability of a measurement output (x) is the distribution of measurement data to the central value (mean) or average


Error 3s is called as a limit errorError 0,68s is called the probable error, with 50% confidence level

STATISTICAL CHARACTERISTICSRepeated measurement :RepeatabilityThe ability of measurement system to give the similar output for a repetitive input

TF - 3102 : Static Characteristics26Lack of Repeatabilityrandom effect on measurement system and environmentThe common cause of lack of repeatability on the output, is the fluctuative and random environment input IM & IISTATISTICAL CHARACTERISTICSDeviation of output from its average caused by environmental inputs :TF - 3102 : Static Characteristics27

Standard Deviation :

Mean value of output for a single element :

Probability density function :STATISTICAL CHARACTERISTICSAccuracy & Precision


STATISTICAL CHARACTERISTICSAccuracy & Precision


STATISTICAL CHARACTERISTICSACCURACYThe Accuracy indicates the deviation of the reading from a known input, and usually expressed as a percentage of full scale reading.Ex. : A 100 kPa pressure gage having an accuracy of 1% would be accurate within 1 kPa over the entire range of the gage

PRECISIONThe precision indicates its ability to reproduce a certain reading with a given accuracyTF - 3102 : Static Characteristics30IDENTIFICATION OF STATIC CHARACTERISTICS TF - 3102 : Static Characteristics31CALIBRATIONPrinciple of CalibrationThe static characteristics of an instrument can be found experimentally by measuring corresponding values of the input I, the output O and the environmental inputs IM and II, when I is either at a constant value or changing slowly.TF - 3102 : Static Characteristics32calibration

CALIBRATIONWhy calibrationConcept of Traceability LadderTF - 3102 : Static Characteristics33Note : Review for a measurement system

CALIBRATIONEx.: Calibration for unit of length TF - 3102 : Static Characteristics34BIPMInternational Bureau of Weights and MeasuresNPLNational Physical LaboratoryBCSBritish Calibration Service

CALIBRATIONDefinition of MEASUREMENT STANDARDStandard of Measurement is all tools, artifacts, procedures, instruments, systems, protocols or processes used to define or realization of units of measurement which has higher level of accuracy

Standard of Measurement is the physical manifestation of a unit of measurement with a value set to be used in the calibration process. Generally only applies to a particular environmental condition

Standars of Measurement is an instrument with a known quantity or dimension of which can be compared with other measuring instrument.

TF - 3102 : Static Characteristics35CALIBRATORCalibrator is a device used to calibrate an instrument.Ex.: Block CalibratorsBlock Calibrators is a device used to calibrate the temperature probe. It consists of a block of metal that can be heated with precision temperature. Temperature probe placed in the block and the results compared with the temperature probe measurements of temperature controlled blockSimulators and Signal ReferencesTo produce a reference electrical signal Voltage Current Frequency


KALIBRATORPressure CalibratorThis device is a pressure measuring instrument calibrator based on the principle of elements of liquid columnTF - 3102 : Static Characteristics37

Dead weight Tester

CALIBRATORMass CalibratorPrimary Kilogram P1New Zealand primary standard of mass (called P1) is a stainless steel weight, nominally (but not exactly) of mass 1 kilogram. Every 5 years a kilogram weight is sent to BIPM for calibration, and when this returns it is weighed against P1, thus ensuring traceability of the mass of P1 to the International Prototype Kilogram (IPK). The mass of P1 has proven to be stable to within 5 parts in 100 million since its commissioning in 1956. The stability of the mass of this weight is monitored between calibrations by regular weighing against two other "primary" kilograms and by weighing against mass standards of other countries.


CALIBRATION WITH CONSTANT INPUT Ex. 1 : Calibration of Pressure Gage Find the instrument parameter with constant inputTF - 3102 : Static Characteristics39NoOutput (kPa)NoOutput (kPa)110,021110,05210,201210,17310,261310,42410,201410,21510,221510,23610,131610,1179,97179,98810,121810,10910,091910,04109,90209,81True value : = 10,000 0,001 kPa

Ambient temperature = 20 1 oCCALIBRATION WITH CONSTANT INPUT TF - 3102 : Static Characteristics40

Average value Standard Deviation :

Normalized DataSebelum NormalisasiNormalization is performed to find the probability of measurement dataCALIBRATION WITH CONSTANT INPUT Distribution FunctionTF - 3102 : Static Characteristics41

ProbabilityCumulative Probability

CALIBRATION WITH CONSTANT INPUT Normalizationz = 0 and scale of z is dimensionless Normal distribution curve is valid for all data set the normal distribution table f(z) and F(z) F(z) describes the probability and the data is in the range of z to +z


CALIBRATION WITH CONSTANT INPUT Result of Ex. 1 :Calibration result of Pressure Gage Average (mean) = 10,11 kPa Variance : 0,14 kPa, Confidence level of data,9,97 to 10,25 kPa : confidence level is 67%9,83 to 10,39 kPa : confidence level is 95%9,69 to 10,53 kPa : confidence level is 99,7%

Pressure-gageMean = 10,11 Standard Deviation, s = 0,14True Value, xo = 10,00Precision = 3 s = 3 x 0,14 = 0,42 Relative Precision = 0,42/10,11 x100%= 4,1%Bias = 10,11 10 = 0,11Accuracy = bias + 3s = 0,53Relative Accuracy = 0,53/10 x 100% = 5,3%Error = 5,3%TF - 3102 : Static Characteristics43

CALIBRATION WITH CONSTANT INPUT Normalized DistributionAccuracy, precision and error are previously mentioned, under the assumption that the probability function is a normal distribution function

To test, the data is normally distributed or not, a normal test can be performed with,Linear Test around the mean value or z = 0Chi-Square (c2) test

TF - 3102 : Static Characteristics44CALIBRATION WITH CONSTANT INPUT Linear test on Z = 0 (mean value)TF - 3102 : Static Characteristics45

The data are arranged from the smallest to the biggest value F(z) or F(x) are plotted (around z = 0)If a straight line were obtained, and the intersection of F(x) is around x = 0.5, then the distribution of data is normalF (z) : Cumulative ProbabilityCALIBRATION WITH CONSTANT INPUT TF - 3102 : Static Characteristics46xzF(z)9.81-2.140.059.9-1.500.19.97-1.000.159.98-0.930.210.02-0.640.2510.04-0.500.310.05-0.430.3510.09-0.140.410.1-0.070.4510.110.000.510.120.070.5510.130.140.610.170.430.6510.20.640.710.20.640.7510.210.710.810.220.790.8510.230.860.910.261.070.9510.422.211

Pada z= 0CALIBRATION WITH INPUT CHANGE Instrument Parameters with input change Sensitivity Threshold Resolution HysteresisOffsetRange

TF - 3102 : Static Characteristics47CALIBRATION WITH INPUT CHANGE To determine the instrument parameter with input changeTF - 3102 : Static Characteristics48Linear input - output

CALIBRATION WITH INPUT CHANGE TF - 3102 : Static Characteristics49Linear equation : eo = 1.0823 ei -0,847output (eo)eo eiinput (ei)ei2naikturunnaikturun00-1.12-0.6900110.210.420.210.42241.181.652.363.3392.092.486.277.444163.333.6213.3214.485254.54.7122.523.556365.265.8731.5635.227496.596.8946.1348.238647.737.9261.8463.369818.689.178.1281.9101009.810.2981025538548.2552.17360.3379.9CALIBRATION WITH INPUT CHANGE TF - 3102 : Static Characteristics50

CALIBRATION WITH INPUT CHANGE Linear equation (increasing): eo = 1,08236 ei 1,025Linear equation (decreasing) : eo = 1,08227 ei 0,669Dead space: 0,37 kPaHysterisis:Increasing : eo = 0 ei = 0,9474Decreasing: eo = 0 ei = 0,6178Hysteresis = 0,9474 0,6178 = 0,33 kPa

Dead space:Increasing : ei = 0 eo = -1,025Decreasing : ei = 0 eo = -0,669Dead space = -0,669 (-1,025) = 0,37 kPa


static characteristics in measurement system

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