114

1.9 Response Time and Drift Testing

H. M. HASHEMIAN

(2003)

Off-line calibration of the zero and span of measurement wasthe topic of the previous section. In this section, the on-linemethods of response time determination and calibration ver-ification will be described for sensors that have already beeninstalled in operating processes. As in Section 1.8, the discus-sion here will also focus on temperature and pressure sensors.

FUNDAMENTALS OF RESPONSE TIME TESTING

The response time of an instrument is measured by applyinga dynamic input to it and recording the resulting output. Therecording is then analyzed to measure the response time ofthe instrument. The type of analysis is a function of both thetype of instrument under test and on the type of dynamicinput applied, which can be a step, a ramp, a sine wave, oreven just random noise.

The terminology used in connection with time responseto a step change was defined in Figure 1.3z. The time constant(

T

) of a first-order system was defined as the time requiredfor the output to complete 63.2% of the total rise (or decay)resulting from a step change in the input. Figures 1.9a and1.9b show the responses of instruments to both step changesand ramps in their inputs and identify the time constant (

T

)and response times (

τ

) of these instruments.As shown in Figure 1.9a, the time constant of an instru-

ment that responds as a first-order system equals its responsetime and it is determined by measuring, after a step change inthe input, the time it takes for the output to reach 63.2% of itsfinal value. The response of a first-order system is mathemat-ically described by a first-order differential equation,

c

(

t

)

=

K

(1 –

e

–

t

/

τ

)

1.9(1)

where

c

=

output

t

=

time

K

=

gain

τ

=

time constant of the instrument

The 63.2% mentioned earlier is obtained from this equa-tion by calculating the output when the time equaling thetime constant (

t

=

τ

) has passed.

c

(

τ

)

=

K

(1

−

e

−

1

)

=

0.632

K

1.9(2)

Although most instruments are not first-order systems, theirresponse time is often determined as if they were, and as iftheir response time were synonymous with their time con-stant. However, if the system is of higher than first order,there is a time constant for each first-order component in thesystem. In spite of this, in the field, the definition of the first-order time constant is often also used in connection withhigher-order systems.

The ramp response time is the time interval by which theoutput lags the input when both are changing at a constantrate. For a ramp input, the response time (

τ

) is defined as thedelay shown in Figure 1.9b. This is also referred to as

ramptime delay

and can be measured after the initial transient,when the output response has become parallel with the inputramp signal. For a first-order system, the ramp time delay,response time, and time constant are synonymous. The ramptime delay can be mathematically described as

c

(

t

)

=

C

(

t

−

τ

)

1.9(3)

FIG. 1.9a

Illustration of step response and calculation of time constant.

Input OutputSensor

Res

pons

e

τ Time

63.2% of A

A

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing

115

where

C

is the ramp rate of the input signal. The derivationsof Equations 1.9(1) through 1.9(3) and the topic of Laplacetransformation is covered in the second volume of the

Instru-ment Engineers’ Handbook

and also in Reference 1.

LABORATORY TESTING

The response time of temperature sensors is measured by usinga step input, whereas the response time of pressure sensors isusually detected by using ramp input signals. This is becauseobtaining a step change in temperature is easier and morerepeatable than obtaining a step change in pressure. Rampinputs are also preferred for the testing of pressure sensors,because a step input can cause oscillation of the pressure trans-mitter output, which may complicate the measurement.

Testing of Temperature Sensors

Figure 1.9c illustrates the equipment used in determining theresponse time of a temperature sensor. This experiment iscalled the

plunge test.

At the beginning of the test, the sensoris held by a hydraulic plunger, and its output is connected toa recorder. The heated sensor is then plunged into a tank ofwater at near-ambient temperature. This step change in tem-perature determines the type of transient in its output, as wasillustrated in Figure 1.9a. To identify the response time ofthe temperature sensor, the time corresponding to 63.2% ofthe full response is measured.

Because the response time of a temperature sensor is afunction of the type, flow rate, and temperature of the mediain which the test is performed, the American Society forTesting and Material (ASTM) has developed Standard E644(Reference 2), which specifies a standard plunge test. Thisdocument specifies that a plunge test should be performed inwater that is at near room temperature and is flowing at avelocity of 3 ft/sec (1 m/sec). A plunge test can therefore beperformed by heating the sensor and then plunging it into arotating tank that contains water at room temperature. Bycontrolling the speed and the radial position of the sensor,the desired water velocity can be obtained for the plunge test.

There can be other ways for performing the plunge test.For example, the sensor can be at room temperature andplunged into warm water. Although the actual temperatureshave an effect on response time, this effect is usually small;therefore, the response time is not significantly different if thewater is at a few degrees above or below room temperature.

Testing of Pressure Sensors

The response time of pressure sensors is usually determinedby using hydraulic ramp generators, which produce the ramptest input signals. A photograph of a hydraulic ramp generatoris provided in Figure 1.9d. This equipment consists of twopressure bottles, one bottle filled with gas or air and the other

FIG. 1.9b

Illustration of ramp response and calculation of ramp time delay.

Input OutputSensor

Res

pons

e

Time

ResponseTime

Input

Output

τ

FIG. 1.9c

Plunge test setup.

Channel 2

Channel 1

Response Time

Timing Signal

Test Transient

Trigger

IN OUT

SignalConditioning

Sensor

Hot AirBlower

RotatingTank

Timing Probe

Multimeter

Ch. 1 Ch. 2

Data Recorder

ω

0.632 × AΑ

Waterr

© 2003 by Béla Lipták

116

General Considerations

with water, as shown in Figure 1.9e. In the outlet from thegas bottle, an on–off and a throttling valve is provided. Thesetting of the adjustable valve determines the flow rate of thegas into the water bottle. Therefore, the desired ramp pressurerate can be generated by adjusting the throttling valve.

The water pressure is detected simultaneously by twosensors, a high-speed reference sensor and the sensor undertest, as shown in Figure 1.9f. The outputs of the two sensorsare recorded on a two-pen recorder, and the time difference(delay) between the two outputs is measured as the responsetime of the sensor being tested. This delay time measurementis taken after the pressure in the water bottle has reached apredetermined setpoint or after the input and output curveshave become parallel.

The pressure setpoint is based on the requirements of theprocess where the sensor is going to be used. For example, ifa full process shutdown is initiated, and if the pressure exceedsa certain upper limit, then this pressure is likely to be used asthe setpoint pressure at which the response time of the pres-

sure sensor is measured. When testing differential-pressuresensors (serving the measurement of level or flow), the set-point pressure can be selected to correspond to the low levelor flow alarm setpoint of the process. In such cases, a decreas-ing ramp input signal is used during the response time testand the setpoint that initiates the test reading corresponds tothe low d/p pressure setting at which the alarm or shutdownis triggered in the process.

These response time measurements can be important tooverall process safety if the instrument delay time is signif-icant relative to the total time available to take correctiveaction after the process pressure has exceeded safe limits.

IN SITU

RESPONSE TIME TESTING

The laboratory testing methods described earlier are usefulfor testing of sensors if they can be removed from the processand brought to a laboratory for testing, but this is often notthe case. For testing installed sensors, a number of new tech-niques have been developed as described below. They arereferred to as

in situ

, on-line, or in-place testing techniques.To measure the in-service response time of a temperature

sensor,

in situ

testing is mandatory. This is because theresponse time of a temperature sensor always is a functionof the particular process temperature, process pressure, andprocess flow rate. The most critical effect is process flow rate,followed by the effect of process temperature and then pres-sure. The reason why the response time is affected by theprocess pressure and flow rate is because they affect the heattransfer of the film of the temperature-sensing surface of thedetector. In contrast, the process temperature affects not onlythe heat transfer of the film but also the properties of thesensor internals and sensor geometry.

Consequently, it is not normally possible to accuratelypredict or model the effect of process temperature on theresponse time of temperature sensors; predicting the effects

FIG. 1.9d

Photograph of pressure ramp generator for response time testing ofpressure sensors.

FIG. 1.9e

Simplified diagram of pressure ramp generator.

GasSupply

Gas

SignalRateAdjust

SignalInitiateSolenoid

ReferenceSensor

SensorUnder Test

DataRecorder

Water

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing

117

of process pressure and flow rate are easier. This is becausewe know that, as the process pressure or flow rate increases,the heat transfer coefficient on the sensor surface alsoincreases and causes a decrease in the response time, andvice versa. In contrast, an increase in process temperaturecan cause either an increase, or a decrease in the responsetime of a sensor. This is because, on the one hand, an increasein process temperature can result in an increase in the heattransfer coefficient, which reduces sensor response time. Onthe other hand, an increase in process temperature can alsoexpand or contract the various air gaps in the internals of thetemperature sensor, causing dimensional changes or alteringmaterial properties, which can increase or decrease theresponse times of the various sensors.

In the case of pressure sensors, the response time is nor-mally not changed by variations in process conditions. Thus,for pressure sensors, the choice of

in situ

response time testingis based on considering the convenience of

in situ

testing andless on the basis of the accuracy of the test results. Therefore,one can measure the response time of an installed pressuresensor without removing it from the process by taking the ramptest generator (Figure 1.9d) to the installed sensor (if this canbe done efficiently and safely). In fact, this operation is oftentedious, time consuming, and expensive, especially in hazard-ous locations or in processes such as exist in nuclear powerplants. Still, if one can afford it, using an

in situ

technique tomeasure the response time of a pressure sensor is preferred.

Testing of Temperature Sensors

The

in situ

response time testing of temperature sensors isreferred to as the

loop current step response (LCSR)

test. LCSRis performed by electrically heating the temperature sensor bysending electric current through the sensor extension leads.This causes the temperature of the sensor to rise above theambient temperature. Depending on the sensor involved, theamount of current and the amount of temperature rise used inthe LCSR test can be adjusted. When testing resistance tem-perature detectors (RTDs), the use of 30 to 50 mA of DCcurrent is normally sufficient. This amount of current raisesthe internal temperature of the RTD sensor by about 5 to 10

°

C(8 to 18

°

F) above the ambient temperature, depending on theRTD and the process fluid surrounding it.

For thermocouples, a higher current (e.g., 500 mA) istypically required. This is because the electrical resistance ofa thermocouple is distributed along the length of the thermo-couple leads, but the resistance of an RTD is concentrated atthe tip of the sensing element. In the case of thermocouples,the LCSR current heats the entire length of the thermocouplewire, not only the measuring junction. Because, in testingthermocouples, we are interested only in heat transfer at themeasuring junction, it is preferred to heat up the thermocou-ple first and measure its output only after the heating currenthas been turned off. Also, for LCSR testing of thermocouples,AC current is used instead of DC to avoid Peltier heating orcooling, which can occur at the thermocouple junction if DCcurrent is used. The direction of the DC current determineswhether the measuring junction is cooled or heated.

Testing RTDs

As shown in Figure 1.9g, a Wheatstone bridgeis used in the LCSR testing of RTDs. The RTD is connectedto one arm of the bridge, and the bridge is balanced while theelectrical current in the circuit is low (switch is open). Underthese conditions, the bridge output is recorded, and the currentis then switched to high (switch closed) to produce the bridgeoutput for the LCSR test shown in Figure 1.9h. In preparingfor the LCSR test, the power supply is adjusted to provide alow current within the range of 1 to 2 mA and a high currentin the range of 30 to 50 mA. The actual values depend on theRTD and on the environment in which the RTD is operating.In addition, the amplifier gain is adjusted to give an output inthe range of 5 to 10 V for the bridge.

Figure 1.9i shows a typical LCSR transient for a 200-

Ω

RTD that was tested with about 40 mA of current in anoperating power plant. In some plants, because of process

FIG. 1.9f

Ramp test setup.

PressureTest Signal

Pres

sure

Time

Test Sensor

Reference Sensor

Output

Time

τ

FIG. 1.9g

Wheatstone bridge for LCSR test of RTDs.

R1Rd

RRTD

R1

RS

LCSRTransient

VariableResistorFixed

Resistors

SwitchDC Power

Supply

Amplifier

© 2003 by Béla Lipták

118

General Considerations

temperature fluctuations, the LCSR transient is not as smoothas shown in Figure 1.9i. In such cases, the LCSR test isrepeated several times on the same RTD, and the results areaveraged to obtain a smooth LCSR transient as in Figure 1.9i.The LCSR test duration is typically 30 sec for RTDs mountedin fast-response thermowells and tested in flowing water. TheLCSR test duration, when the sensor is detecting the temper-ature of liquids, typically ranges from 20 to 60 sec but ismuch longer for air or gas applications.

Testing Thermocouples

The LCSR test equipment for ther-mocouples includes an AC power supply and circuitry shownin the schematic in Figure 1.9j. The test is performed by firstapplying the AC current for a few seconds while the thermo-couple is heated above the ambient temperature. After that,the current flow is terminated, and the thermocouple is con-nected to a millivolt meter to record its temperature as it coolsdown to the ambient temperature (Figure 1.9k). The millivoltoutput records a transient representing the cooling of thethermocouple junction alone. The rate of cooling is a functionof the dynamic response of the thermocouple.

Figure 1.9l shows an LCSR transient of a thermocouplethat was tested in flowing air. As in the case of RTDs, LCSRtransients for thermocouples can also be noisy as a result offluctuations in process temperature and other factors. To over-come noise, the LCSR test can be repeated a few times, andthe resulting transients can be averaged to produce smooth

FIG. 1.9h

Principle of LCSR test.

FIG. 1.9i

In-plant LCSR transients for RTDs.

Ele

ctri

c C

urre

ntB

ridg

e O

utpu

t

Time

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30

Res

pons

e

Single Transient

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Time (sec)

Res

pons

e

Averaged Transient

FIG. 1.9j

Simplified schematic of LCSR test equipment for thermocouples.

V

SensorOutput

PowerSupply

Test Medium

Thermocouple

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing

119

LCSR results. In the case of thermocouples, extraneous high-frequency noise superimposed on the LCSR transient can beremoved by electronic or digital filtering.

Analysis of LCSR Test Results

The raw data from the LCSRtest cannot be interpreted easily into a response time reading.This is because the test data is the result of step change intemperature inside the sensor, whereas the response time ofinterest should be based on a step change in temperature out-side the sensor. Fortunately, the heat from inside the sensor tothe ambient fluid is transferred through the same materials asthe heat that is transferred from the process fluid to the sensor(Figure 1.9m). Therefore, the sensor response due to internaltemperature step (LCSR test) and external temperature step

(plunge test) are related if the heat transfer is unidirectional(radial) and the heat capacity of the sensing element is insig-nificant. These two conditions are usually satisfied for indus-trial temperature sensors. Nevertheless, to prove that the LCSRtest is valid for an RTD or a thermocouple, laboratory testsusing both plunge and LCSR methods should be performedon each sensor design to ensure that the two tests produce thesame results.

Because, for most sensors, the heat transfer path duringLCSR and plunge tests is usually the same, one can use LCSRtest data to estimate the sensor response of a plunge testwhere the step change in temperature occurs outside the sensor.The equivalence between the two tests has been shown math-ematically (theoretically) as well as in numerous laboratorytests (see References 3 through 5). Therefore, it can be con-cluded that the test results gained from internal heating of asensor (LCSR) can be analyzed to yield the response time ofa sensor to a step change in temperature that occurred in themedium outside the sensor.

One can mathematically prove the similarities between thetransient outputs, which are generated by the same temperaturesensor, when evaluated by the plunge and the LCSR tests. Forthe plunge test, the sensor output response

T

(

t

) to a step changein the temperature of the surrounding fluid is given by

1.9(4)

Each of the three (or more) elements in Equation 1.9(4) isreferred to as a mode, while the terms

τ

1

and

τ

2

are calledthe

modal time constants

, and the terms (

A

0

,

A

1

,

A

2

,…) arecalled the

modal coefficients.

For the LCSR test, the sensoroutput response

T

′

(

t

) to a step change in the temperatureinside the sensor is given by

1.9(5)

Note that the exponential terms in the above two equations areidentical; only their modal coefficients are different. Theresponse time (

τ

) of a temperature sensor is defined by Equation

FIG. 1.9k

Illustration of LCSR test principle for a thermocouple.

FIG. 1.9l

LCSR transient from a laboratory test of a sheathed thermocouple.

Tes

t Sig

nal

Out

put

Time

Time

Ambient Temperature

0

1

0 5 10 15 20 25 30

Time (sec)

LC

SR R

espo

nse

(Nor

mal

ized

)

1/16" Dia. K-Type

FIG. 1.9m

Heat transfer process in plunge and LCSR tests.

Heat Transfer:Surrounding Fluidto Sensor

Heat Transfer: Sensorto Surrounding Fluid

LCSR

Plunge

T t A A e A et t( ) / /= + + +− −0 1 2

1τ τ L

′ = + + +− −T t B B e B et t( ) / /0 1 2

1 2τ τ L

© 2003 by Béla Lipták

120

General Considerations

1.9(5), and it is therefore independent of the modal coefficients,although it does depend on the modal time constants.

1.9(6)

The other terms in the equation are the natural logarithm,

ln

,and the response time (

τ

) of the sensor. Therefore, one mightlist the steps required in the LCSR test to obtain the responsetime of a temperature sensor as follows:

1. Perform the LCSR test and generate the raw data.2. Fit the LCSR data to Equation 1.9(5) and identify the

modal time constants (

τ

1

,

τ

2

,…).3. Use the results of Step 2 in Equation 1.9(6) to obtain

the sensor response time.

The above procedure has been successfully used fordetermining the response times of both RTDs and thermo-couples, both in laboratory and

in situ

applications. As aresult, it has been demonstrated that the LCSR test can deter-mine the response time of a temperature sensor within about10% of the conclusions of a plunge test if both were per-formed under the same conditions.

Applications of LCSR Testing

Nuclear industry applica-tions of the LCSR test include the response time determina-tion of reactor coolant temperature sensors. The LCSR tech-nique has been approved by the U.S. Nuclear RegulatoryCommission (NRC) for in situ measurement of the responsetime of RTDs in nuclear power plants.6 The LCSR test hasalso been used in aerospace applications to correct transienttemperature data and in solid rocket motors to determine thequality of the bonding of thermocouples with the solid mate-rials such as the nozzle liners.7

In addition to response time measurements, the LCSRtest has been used for sensor diagnostics such as

1. The in situ determination of discontinuities or nonho-mogeneities in thermocouples.8 In this case, the pur-pose of running the LCSR test on the thermocouple isto check if the resulting LCSR signal is normal. Thistest is especially useful if a reference set of baselineLCSR data is available, representing the test resultson normal thermocouples so that gross nonhomoge-neities can be easily noted.

2. Determining if “strap-on” RTDs are properly bondedto pipes or tubes. In case of the Space Shuttle mainengine,7 in an experiment, the LCSR test was used toverify the quality of “strap-on” RTD bonding withinthe fuel lines. In this application, the RTD-based tem-perature measurement is used to detect fuel leakages.

3. Verifying the bonding of strain gauges to solid sur-faces. Figure 1.9n illustrates how the transients resultingfrom LCSR tests change as a function of the strengthof RTD bonding to the pipe. Therefore, the LCSR test

can determine the degree of bonding between the solidsurface and RTDs or strain gauges (Figure 1.9o).

Figures 1.9p and 1.9q illustrate the commercial equipmentused in LCSR testing of RTDs and thermocouples. InFigure 1.9p, an LCSR test system includes six channels forRTD response time measurements so that six RTDs can besimultaneously tested. This system automatically performsthe LCSR test, obtains and analyzes the LCSR data, and

τ τ ττ

ττ

= − −

− −

12

1

3

1

1 1 1ln ln K

FIG. 1.9nLCSR test to verify the attachment of a temperature sensor to a solidsurface.

FIG. 1.9oLCSR test to verify the attachment of a strain gauge to a solid surface.

FIG. 1.9pRTD response time test equipment.

0

1

0 10 20 30 40 50 60

Time (sec)

LC

SR R

espo

nse

(Nor

mal

ized

)

Good Bond

75% Bonded

25% Bonded

Unbonded

0

1

0 5 10 15 20 25 30

Time (sec)

LC

SR S

igna

l

Good Bond

Medium Bond

Partial Bond

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing 121

determines the response times for each RTD. The system cansend the data to a printer and print a table of RTD responsetimes. A response time test transient display of a thermocoupleis illustrated in Figure 1.9q.

In Situ Testing of Pressure Sensors

The response time of installed pressure sensors can be mea-sured remotely while the plant is in operation. This techniqueis called noise analysis and is based on the monitoring of thenormally present fluctuations of the pressure transmitter outputsignals. In Figure 1.9r, such an output signal is shown at asteady state that corresponds to the normal process pressure.This steady-state value is referred to as the DC reading. Whenmagnified, it displays some small fluctuations. This magnifiedsignal is called the noise or the AC component of the signal.

Analyzing of Noise Data The noise is produced by twosources. The first source is the fluctuation of the process pres-sure caused by turbulence, random heat transfer, vibration, andother effects. Second, there is electrical noise superimposedon the pressure transmitter output signal. Fortunately, thesetwo phenomena occur at widely different frequencies and thus

can be separated by filtering. This is necessary, because onlythe process pressure fluctuations are of interest.

Figure 1.9s illustrates how the noise can be extracted froma raw signal that includes both the DC and the AC components.The first step to remove the DC component is by adding anegative bias or by highpass electronic filtering. Next, thesignal is amplified and passed through a lowpass filter, whichremoves the extraneous noise and provides for anti-aliasing.Next, the signal is sent through an analog-to-digital (A/D)converter and subsequently to a data acquisition computer. Thecomputer samples the data and stores it for analysis.

The raw noise data from a pressure transmitter (Figure 1.9t)represents the natural process pressure fluctuations and includesthe information required to determine the response time of thepressure sensor that generated the steady-state (DC) signal.The raw noise data is a small portion of a noise record, whichis normally about 30 to 60 min.

For noise data analysis, the two techniques available arethe frequency-domain analysis and the time-domain analysis.The first uses the power spectral density (PSD) techniqueinvolving fast Fourier transform (FFT). The PSD is obtainedby bandpass filtering the raw signal in a narrow frequencyband and calculating the variance of the result. This varianceis divided by the width of the frequency band, and the resultsare plotted as a function of the center frequency of the bandpass. This procedure is repeated from the lowest to the highestexpected frequencies of the raw signal to obtain the PSD. InFigure 1.9u, the frequency spectrum of the noise signal froma pressure transmitter in an operating power plant is shownagainst PSD. If the pressure transmitter is a first-order system,its response time can be determined on the basis of measuringthe break frequency of the PSD as shown in Figure 1.9v.

FIG. 1.9qThermocouple response time test analyzer.

FIG. 1.9rPrinciple of noise analysis technique.

Sens

or O

utpu

t

Noise

DC Signal

Time

FIG. 1.9sBlock diagram of the noise data acquisition equipment.

FIG. 1.9tRaw noise data from a flow sensor in a power plant.

V V V V

t t t t

Data Samplingand Storage

Device

Low-PassFilter

High-PassFilter

or Bias

IsolatedPlantSignal

Amplifier

−4.0

−2.0

0.0

2.0

4.0

0 2 4 6 8 10

Time (sec)

Flow

(%

)

© 2003 by Béla Lipták

122 General Considerations

However, pressure sensors are not necessarily first order,and PSD plots for actual process signals are not smoothenough to allow the accurate measurement of the break fre-quency. In addition, PSDs often also contain resonance andother disturbances that further complicate the response-timeanalysis. Therefore, both experience and a validated dynamicmodel of the sensor are needed to obtain the sensor responsetime by analyzing a PSD plot. The model, which usually isa frequency-domain equation, is fit to the PSD to yield themodel parameters, which are then used to calculate theresponse time of the pressure sensor. A PSD for a flow sensorin an operating power plant and its model fit are shown inFigure 1.9w.

Autoregressive (AR) modeling is used for noise dataanalysis in the time domain. An AR model is a time series

equation to which the noise data is fit and the model param-eters are calculated. These parameters are then used to cal-culate the response time of the sensor.9 Time-domain analysisis generally simpler to code in a computer and thereforeis preferred for automated analysis. However, in time-domain analysis, it is often difficult to remove noise datacomponents that are unrelated to the sensor response time.For example, if the noise data contains very low-frequencyprocess fluctuations, the AR model will take them intoaccount. In such a case, it gives an erroneously large responsetime value. In contrast, in frequency-domain analysis, it iseasier to ignore low-frequency process fluctuations and tofit the PSD to that portion of the data that most accuratelyrepresents the sensor.

Commercial, off-the-shelf equipment is available forboth the frequency-domain and the time-domain analysisof noise data. A number of companies provide spectrum ana-lyzers (also called FFT analyzers), which take the raw noisedata from the output of a sensor and provide the necessaryconditioning and filtering to analyze it and calculate the sen-sor response time. However, because of resonance and otherinfluences, simple FFT analysis does not always yield thecorrect response time reading. This is not a shortcoming ofthe FFT equipment but a consequence of the inherent natureof the input signal with which they must work.

ON-LINE VERIFICATION OF CALIBRATION

The calibration of installed instruments such as industrialpressure sensors involves (1) the decision whether calibrationis needed at all and (2) the actual calibration, when necessary.The first step can be automated by implementing an on-linedrift monitoring system. This system samples the steady-stateoutput of operating process instruments and, if it is found tohave drifted, it calls for it to be calibrated. Conversely, ifthere is no (or very little) drift, the instrument is not calibratedat all (or calibrated less frequently). The accuracy require-ments of the sensor involved determines the amount of allow-able drift.

Drift Evaluation Using Multiple Sensors

In drift evaluations, it is necessary to distinguish the drift thatoccurs in the process from instrument drift before a referencelimit of “allowable drift” can be defined. For example, ifredundant sensors are used to measure the same processparameter, their average reading can be assumed to closelyrepresent the process and used as the reference. This is doneby first sampling and storing the normal operating outputs ofthe redundant instruments and then averaging these readingsfor each instant of time. These average values are then sub-tracted from the corresponding individual readings of theredundant instruments to identify the deviation of each fromthe average.

FIG. 1.9uPressure sensor PSD.

FIG. 1.9vFirst-order system PSD.

FIG. 1.9wFlow sensor PSD and its model fit.

1.0E−06

1.0E−05

1.0E−04

1.0E−03

1.0E−02

1.0E−01

1.0E+00

0.01 0.1 1 10

Frequency (Hz)

PSD

(%

/Hz)

1

Frequency (Hz)

PSD τ = 1

Fb

Fb= Break Frequency

Fb

1.0E−06

1.0E−04

1.0E−02

1.0E+00

1.0E+02

0.01 0.1 1 10

Frequency (Hz)

PSD

(%

/Hz)

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing 123

In Figure 1.9x, the results of on-line monitoring of foursteam-generator level transmitters in a nuclear power plantare shown. The difference between the average of the fourtransmitters and the individual readings are shown on they axis as a function of time in months. The data are shownfor a period of about 30 months of operation, and the foursignals show no significant drift during this period. Conse-quently, one can conclude that the calibration of these trans-mitters did not change and, therefore, they do not need to berecalibrated. If it is suspected that all four transmitters aredrifting in an identical manner (drifting together in one direc-tion), the data for deviation from the average would not revealthe drift. Therefore, to rule out any systematic or commondrift, one of the four transmitters can be recalibrated.

Empirical Models, Neural Networks Another approach fordetecting systematic drift is to obtain an independent estimateof the monitored process and track that estimate along withthe indication of the redundant sensors. Both empirical andphysical modeling techniques are used to estimate systematicdrift. They each monitor various related process variablesand, based on their values, evaluate the drift in the monitoredparameter. For example, in a process involving the boilingof water (without superheating of the steam), temperatureand pressure are related. Thus, if temperature is measured,the corresponding saturated steam pressure can be easilydetermined, tracked, and compared with the measured pres-sure as a reference to identify systematic drift. The use of thismethod of drift detection does not require the use of multiplesensors, and individual sensors can also be tracked and theircalibration drift evaluated on line.

The relationship between most process variables is muchmore complex than the temperature–pressure relationship ofsaturated steam. Therefore, most process parameters cannotbe evaluated from measurement of another variable. In addi-tion, an in-depth knowledge of the process is needed to pro-vide even an estimate of a parameter on the basis of physical

models. Therefore, for the verification of on-line calibration,empirical models are often preferred. Such empirical modelsuse empirical equations, neural networks, pattern recognition,and sometimes a combination of these, including fuzzy logicfor data clustering, are used to generate the model’s output(s)based on its multiple inputs.10–14

Before using the empirical model, it is first trained undera variety of operating conditions. As shown in Figure 1.9y,if the output parameter (y) is to be estimated on the basis ofmeasuring the input parameters x1, x2, and x3, then, duringthe training period, weighting factors are applied to the inputvariables. These factors are gradually adjusted until the dif-ference between measured output and the output of the neuralnetwork is minimized. Such training can continue while theneural network learns the relationship between the threeinputs and the single output, or while additional input andoutput signals are provided to minimize the error in theempirical model. Training of the model is completed whenthe measured output is nearly identical to the estimate gen-erated by the neural network. Once the training is completed,the output of the model can be used for drift evaluation orcontrol purposes.

An on-line calibration monitoring system might use acombination of averaging of redundant signals (averagingcan be both straight and weighted), empirical modeling,physical modeling, and calibrated reference sensor(s) in aconfiguration similar to the one shown in Figure 1.9z. In sucha system, the raw data is first screened by a data-qualificationalgorithm and then analyzed to provide an estimate of theprocess parameter being monitored. In the case of averaginganalysis, a consistency algorithm is used to make sure that areasonable agreement exists among the redundant signals andthat unreasonable readings are either excluded or weightedless that the others before the signals are averaged. Suchsystems as the one illustrated in Figure 9.1z can be consid-ered for both power plants and chemical industry applicationsfor the on-line verification of the calibration requirements ofprocess sensors.

The data for on-line monitoring can be obtained from theplant computer or from a dedicated data acquisition system.

power plant for on-line calibration monitoring purposes.The computer applies the on-line calibration algorithms and,based on the sampled data from a variety of process instru-ments, provides such information as plots of deviation foreach instrument from a process estimate and a listing ofinstruments that have drifted. The data acquisition system

FIG. 1.9xOn-line monitoring data for steam generator level transmitters.

−3.0

−1.5

0.0

1.5

3.0

Time (Month)

Dev

iatio

n fr

om A

vera

ge (

% L

evel

)

0 30

SG D Level

15

FIG. 1.9yIllustration of training of a neural network.

X1

Y outputX2

X3

© 2003 by Béla Lipták

Figure 1.9aa illustrates a data acquisition system used in a

124 General Considerations

includes its own calibration signals so that test equipmentdrift can be isolated from the drift that occurs in processinstruments. If on-line monitoring data is already availablein the plant computer, it can be stored or analyzed to providecalibration verification results.

On-line calibration monitoring identifies calibrationproblems at the monitored point (i.e., the process operatingconditions). As such, the above approach may be labeled as

a one-point calibration check. To verify the calibration ofinstruments over their entire range, on-line monitoring datashall also be collected during plant startup and shutdownepisodes. With data from these episodes, the instrument cal-ibration can be verified for a wide range.

According to research data on pressure transmitters innuclear power plants,14 about 70% of the time, the one-pointcalibration monitoring can reveal calibration problemsthroughout the instrument range. This is because the drift inpressure transmitters is usually due to a zero shift, whichdoes affect the entire operating range of the transmitter.

References

1. Hashemian, H. M. et al., Effect of Aging on Response Time of NuclearPlant Pressure Sensors. U.S. Nuclear Regulatory Commission,NUREG/CR-5383, 1989.

2. American Society for Testing and Materials (ASTM), Standard Meth-ods for Testing Industrial Resistance Thermometers, Standard E 64478, Annual Book of ASTM Standards, Part 44, Philadelphia, PA, 1979.

3. Hashemian, H. M., New Technology for Remote Testing of ResponseTime of Installed Thermocouples, United States Air Force, ArnoldEngineering Development Center, Report No. AEDC-TR-91–26, Vol.1, Background and General Details, 1992.

FIG. 1.9zConceptual design of an on-line monitoring system.

Straight orWeightedAveraging

ConsistencyChecking

DataQualification

Flow Signal S1

Flow Signal S2

Flow Signal S3

Pressure (P)

Temperature (T)

Level (L)

DataQualification

EmpiricalModel

PhysicalModel

F1

F2

F3

ConsistencyChecking

&Averaging

S

Time

S1 = S1 − FS2 = S2 − F

S3 = S3 − F

Deviations

21

3

REDUNDANT SIGNALS

DIVERSE SIGNALS

DataQualification F4

REFERENCE CHANNEL

F1 + F2 + F3 + F4F =4

F is theBest Estimateof the Process

F

∆∆∆

∆

FIG. 1.9aaDedicated system.

SignalIsolation

Computer

Short CalibrationSignals

MULTIPLEXER

(Optional)

Plan

t Sig

nals

5 VDCReference

Results

Plots

Tables

Etc.

© 2003 by Béla Lipták

1.9 Response Time and Drift Testing 125

4. Hashemian, H. M. and Petersen, K. M., Loop current step responsemethod for in-place measurement of response time of installed RTDsand thermocouples, in Proceedings of American Institute of Physics,Seventh International Symposium on Temperature, Vol. 6, 1151–1156,Toronto, Can., 1992.

5. Hashemian, H. M. et al., Advanced Instrumentation and MaintenanceTechnologies for Nuclear Power Plants, U.S. Nuclear Regulatory Com-mission, NUREG/CR-5501, August 1988.

6. NUREG-0809, Review of Resistance Temperature Detector TimeResponse Characteristics, U.S. Nuclear Regulatory Commission,Washington, D.C., 1981.

7. Hashemian, H. M., Shell, C. S., and Jones, C. N., New InstrumentationTechnologies for Testing the Bonding of Sensors to Solid Materials,National Aeronautics and Space Administration, Marshall Space FlightCenter, NASA/CR-4744, 1996.

8. Hashemian, H. M. and Petersen, K. M., Measurement of performanceof installed thermocouples, in Proceedings of Aerospace Industriesand Test Measurement Divisions of The Instrument Society of America,37th International Instrumentation Symposium, 913–926, ISA Paper#91–113, San Diego, CA, 1991.

9. Glocker, O. and Upadhyaya, B. R., Results and Interpretation of Mul-tivariate Autoregressive Analysis Applied to Loss-of-Fluid Test ReactorProcess Noise Data, SMORN-V, Vol. 21, Progress in Nuclear Energy,Pergamon Press, Burlington, MA, 447–456, 1988.

10. Hashemian, H. M., On-Line Testing of Calibration of Process Instru-mentation Channels in Nuclear Power Plants, U.S. Nuclear RegulatoryCommission, NUREG/CR-6343, 1995.

11. Upadhyaya, B. R., Glocker, O., and Eklund, J. J., Multivariate statis-tical signal processing technique for fault detection and diagnostics,ISA Transactions, 29(4), 79–95, 1990.

12. Tsoukalas, L. H. and Uhrig, R. E., Fuzzy and Neural Approaches inEngineering, John Wiley & Sons, New York, 1997.

13. Fantoni, P. F., Figedy, S., and Papin, B., A Neuro-Fuzzy ModelApplied to Full Range Signal Validation of PWR Nuclear PowerPlant Data, Second OECD Specialist Meeting on Operator Aidsfor Severe Accident Management (SAMOA-2), Lyon, France,1997.

14. EPRI Topical Report, On-line Monitoring of Instrument Channel Per-formance, TR-104965-R1 NRC SER, Electric Power Research Insti-tute, Final Report, Palo Alto, CA, September 2000.

© 2003 by Béla Lipták