Response Time and Drift Testing

Off-line calibration of the zero and span of measurement was the topic of the previous section. In this section, the on-line methods of response time determination and calibration verification will be described for sensors that have already been installed in operating processes. As in Section 1.8, the discussion here will also focus on temperature and pressure sensors. FUNDAMENTALS OF RESPONSE TIME TESTING The response time of an instrument is measured by applying a dynamic input to it and recording the resulting output. The recording is then analyzed to measure the response time of the instrument. The type of analysis is a function of both the type of instrument under test and on the type of dynamic input applied, which can be a step, a ramp, a sine wave, or even just random noise. The terminology used in connection with time response to a step change was defined in Figure 1.3z. The time constant (T ) of a first-order system was defined as the time required for the output to complete 63.2% of the total rise (or decay) resulting from a step change in the input. Figures 1.9a and 1.9b show the responses of instruments to both step changes and 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 instrument that responds as a first-order system equals its response time and it is determined by measuring, after a step change in the input, the time it takes for the output to reach 63.2% of its final value. The response of a first-order system is mathematically 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 equation by calculating the output when the time equaling the time 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, their response time is often determined as if they were, and as if their response time were synonymous with their time constant. However, if the system is of higher than first order, there is a time constant for each first-order component in the system. In spite of this, in the field, the definition of the firstorder time constant is often also used in connection with higher-order systems. The ramp response time is the time interval by which the output lags the input when both are changing at a constant rate. For a ramp input, the response time (τ) is defined as the delay shown in Figure 1.9b. This is also referred to as ramp time delay and can be measured after the initial transient, when the output response has become parallel with the input ramp signal. For a first-order system, the ramp time delay, response time, and time constant are synonymous. The ramp time 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 Output Sensor Response τ Time 63.2% of A

1.9 Response Time and Drift Testing

H M HASHEMIAN (2003)

Off-line calibration of the zero and span of measurement was

the topic of the previous section In this section, the on-line

methods of response time determination and calibration

ver-ification will be described for sensors that have already been

installed 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 applying

a dynamic input to it and recording the resulting output The

recording is then analyzed to measure the response time of

the instrument The type of analysis is a function of both the

type of instrument under test and on the type of dynamic

input applied, which can be a step, a ramp, a sine wave, or

even just random noise

The terminology used in connection with time response

to a step change was defined in Figure 1.3z The time constant

(T) of a first-order system was defined as the time required

for the output to complete 63.2% of the total rise (or decay)

resulting from a step change in the input Figures 1.9a and

1.9b show the responses of instruments to both step changes

and 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 response

time and it is determined by measuring, after a step change in

the input, the time it takes for the output to reach 63.2% of its

final value The response of a first-order system is

mathemat-ically described by a first-order differential equation,

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 the

time 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, their response time is often determined as if they were, and as if their 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 the system In spite of this, in the field, the definition of the first-order time constant is often also used in connection with higher-order systems

The ramp response time is the time interval by which the output lags the input when both are changing at a constant rate For a ramp input, the response time (τ) is defined as the delay shown in Figure 1.9b This is also referred to as ramp time delay and can be measured after the initial transient, when the output response has become parallel with the input ramp signal For a first-order system, the ramp time delay, response time, and time constant are synonymous The ramp time 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.

Sensor

63.2% of A

A

1.9 Response Time and Drift Testing 115

where C is the ramp rate of the input signal The derivations

of Equations 1.9(1) through 1.9(3) and the topic of Laplace

transformation 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 using

a step input, whereas the response time of pressure sensors is

usually detected by using ramp input signals This is because

obtaining a step change in temperature is easier and more

repeatable than obtaining a step change in pressure Ramp

inputs 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 the

response time of a temperature sensor This experiment is

called the plunge test At the beginning of the test, the sensor

is held by a hydraulic plunger, and its output is connected to

a recorder The heated sensor is then plunged into a tank of

water at near-ambient temperature This step change in

tem-perature determines the type of transient in its output, as was

illustrated in Figure 1.9a To identify the response time of

the temperature sensor, the time corresponding to 63.2% of

the full response is measured

Because the response time of a temperature sensor is a function of the type, flow rate, and temperature of the media

in which the test is performed, the American Society for Testing and Material (ASTM) has developed Standard E644 (Reference 2), which specifies a standard plunge test This document specifies that a plunge test should be performed in water that is at near room temperature and is flowing at a velocity of 3 ft/sec (1 m/sec) A plunge test can therefore be performed by heating the sensor and then plunging it into a rotating tank that contains water at room temperature By controlling 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 and plunged into warm water Although the actual temperatures have an effect on response time, this effect is usually small; therefore, the response time is not significantly different if the water is at a few degrees above or below room temperature

Testing of Pressure Sensors

The response time of pressure sensors is usually determined

by using hydraulic ramp generators, which produce the ramp test input signals A photograph of a hydraulic ramp generator

is provided in Figure 1.9d This equipment consists of two pressure bottles, one bottle filled with gas or air and the other

FIG 1.9b

Illustration of ramp response and calculation of ramp time delay.

Sensor

Time

Response Time

Input Output

τ

FIG 1.9c

Plunge test setup.

Channel 2

Channel 1

Response Time

Timing Signal

Test Transient

Trigger

Signal Conditioning Sensor Hot Air Blower

Rotating Tank Timing Probe

Multimeter

Data Recorder

ω

0.632 × AΑ Water

r

116 General Considerations

with water, as shown in Figure 1.9e In the outlet from the

gas bottle, an on–off and a throttling valve is provided The

setting of the adjustable valve determines the flow rate of the

gas into the water bottle Therefore, the desired ramp pressure

rate can be generated by adjusting the throttling valve

The water pressure is detected simultaneously by two

sensors, a high-speed reference sensor and the sensor under

test, as shown in Figure 1.9f The outputs of the two sensors

are recorded on a two-pen recorder, and the time difference

(delay) between the two outputs is measured as the response

time of the sensor being tested This delay time measurement

is taken after the pressure in the water bottle has reached a

predetermined setpoint or after the input and output curves

have become parallel

The pressure setpoint is based on the requirements of the

process where the sensor is going to be used For example, if

a full process shutdown is initiated, and if the pressure exceeds

a certain upper limit, then this pressure is likely to be used as

the setpoint pressure at which the response time of the

pres-sure sensor is meapres-sured When testing differential-prespres-sure sensors (serving the measurement of level or flow), the set-point pressure can be selected to correspond to the low level

or flow alarm setpoint of the process In such cases, a decreas-ing ramp input signal is used durdecreas-ing the response time test and the setpoint that initiates the test reading corresponds to the low d/p pressure setting at which the alarm or shutdown

is triggered in the process

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

The laboratory testing methods described earlier are useful for testing of sensors if they can be removed from the process and brought to a laboratory for testing, but this is often not the case For testing installed sensors, a number of new tech-niques have been developed as described below They are referred to as in situ, on-line, or in-place testing techniques

To measure the in-service response time of a temperature

response time of a temperature sensor always is a function

of the particular process temperature, process pressure, and process 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 the process pressure and flow rate is because they affect the heat transfer of the film of the temperature-sensing surface of the detector In contrast, the process temperature affects not only the heat transfer of the film but also the properties of the sensor internals and sensor geometry

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

FIG 1.9d

Photograph of pressure ramp generator for response time testing of

pressure sensors.

FIG 1.9e

Simplified diagram of pressure ramp generator.

Gas Supply

Gas

Signal Rate Adjust

Signal Initiate Solenoid

Reference Sensor

Sensor Under Test

Data Recorder Water

1.9 Response Time and Drift Testing 117

of process pressure and flow rate are easier This is because

we know that, as the process pressure or flow rate increases,

the heat transfer coefficient on the sensor surface also

increases and causes a decrease in the response time, and

vice versa In contrast, an increase in process temperature

can cause either an increase, or a decrease in the response

time of a sensor This is because, on the one hand, an increase

in process temperature can result in an increase in the heat

transfer coefficient, which reduces sensor response time On

the other hand, an increase in process temperature can also

expand or contract the various air gaps in the internals of the

temperature sensor, causing dimensional changes or altering

material properties, which can increase or decrease the

response 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 testing

is based on considering the convenience of in situ testing and

less on the basis of the accuracy of the test results Therefore,

one can measure the response time of an installed pressure

sensor without removing it from the process by taking the ramp

test generator (Figure 1.9d) to the installed sensor (if this can

be done efficiently and safely) In fact, this operation is often

tedious, time consuming, and expensive, especially in

hazard-ous locations or in processes such as exist in nuclear power

plants Still, if one can afford it, using an in situ technique to

measure the response time of a pressure sensor is preferred

Testing of Temperature Sensors

The in situ response time testing of temperature sensors is

referred to as the loop current step response (LCSR) test LCSR

is performed by electrically heating the temperature sensor by

sending electric current through the sensor extension leads

This causes the temperature of the sensor to rise above the

ambient temperature Depending on the sensor involved, the

amount of current and the amount of temperature rise used in

the LCSR test can be adjusted When testing resistance

tem-perature detectors (RTDs), the use of 30 to 50 mA of DC

current is normally sufficient This amount of current raises

the internal temperature of the RTD sensor by about 5 to 10°C

(8 to 18°F) above the ambient temperature, depending on the

RTD and the process fluid surrounding it

For thermocouples, a higher current (e.g., 500 mA) is typically required This is because the electrical resistance of

a thermocouple is distributed along the length of the thermo-couple leads, but the resistance of an RTD is concentrated at the tip of the sensing element In the case of thermocouples, the LCSR current heats the entire length of the thermocouple wire, not only the measuring junction Because, in testing thermocouples, we are interested only in heat transfer at the measuring junction, it is preferred to heat up the thermocou-ple first and measure its output only after the heating current has been turned off Also, for LCSR testing of thermocouples,

AC current is used instead of DC to avoid Peltier heating or cooling, which can occur at the thermocouple junction if DC current is used The direction of the DC current determines whether the measuring junction is cooled or heated

is used in the LCSR testing of RTDs The RTD is connected

to one arm of the bridge, and the bridge is balanced while the electrical current in the circuit is low (switch is open) Under these conditions, the bridge output is recorded, and the current

is then switched to high (switch closed) to produce the bridge output for the LCSR test shown in Figure 1.9h In preparing for the LCSR test, the power supply is adjusted to provide a low current within the range of 1 to 2 mA and a high current

in the range of 30 to 50 mA The actual values depend on the RTD and on the environment in which the RTD is operating

In addition, the amplifier gain is adjusted to give an output in the 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 an operating power plant In some plants, because of process

FIG 1.9f

Ramp test setup.

Pressure

Test Signal

Time

Test Sensor Reference Sensor

Output

Time τ

FIG 1.9g

Wheatstone bridge for LCSR test of RTDs.

RRTD

R1

RS

LCSR Transient

Variable Resistor Fixed

Resistors

Switch

DC Power Supply

Amplifier

118 General Considerations

temperature fluctuations, the LCSR transient is not as smooth

as shown in Figure 1.9i In such cases, the LCSR test is repeated several times on the same RTD, and the results are averaged to obtain a smooth LCSR transient as in Figure 1.9i The LCSR test duration is typically 30 sec for RTDs mounted

in fast-response thermowells and tested in flowing water The LCSR test duration, when the sensor is detecting the temper-ature of liquids, typically ranges from 20 to 60 sec but is much longer for air or gas applications

ther-mocouples includes an AC power supply and circuitry shown

in the schematic in Figure 1.9j The test is performed by first applying 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 cools down to the ambient temperature (Figure 1.9k) The millivolt output records a transient representing the cooling of the thermocouple junction alone The rate of cooling is a function

of the dynamic response of the thermocouple

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

FIG 1.9h

Principle of LCSR test.

FIG 1.9i

In-plant LCSR transients for RTDs.

Time

0.0

0.2

0.4

0.6

0.8

1.0

Single Transient

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Time (sec)

Averaged Transient

FIG 1.9j

Simplified schematic of LCSR test equipment for thermocouples.

V

Sensor Output

Power Supply

Test Medium

Thermocouple

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 be

removed by electronic or digital filtering

test cannot be interpreted easily into a response time reading

This is because the test data is the result of step change in

temperature inside the sensor, whereas the response time of

interest should be based on a step change in temperature

out-side the sensor Fortunately, the heat from inout-side the sensor to

the ambient fluid is transferred through the same materials as

the heat that is transferred from the process fluid to the sensor

(Figure 1.9m) Therefore, the sensor response due to internal

temperature 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 LCSR test is valid for an RTD or a thermocouple, laboratory tests using both plunge and LCSR methods should be performed

on each sensor design to ensure that the two tests produce the same results

Because, for most sensors, the heat transfer path during LCSR and plunge tests is usually the same, one can use LCSR test data to estimate the sensor response of a plunge test where 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 laboratory tests (see References 3 through 5) Therefore, it can be con-cluded that the test results gained from internal heating of a sensor (LCSR) can be analyzed to yield the response time of

a sensor to a step change in temperature that occurred in the medium outside the sensor

One can mathematically prove the similarities between the transient outputs, which are generated by the same temperature sensor, when evaluated by the plunge and the LCSR tests For the plunge test, the sensor output response T(t) to a step change

in the temperature of the surrounding fluid is given by

1.9(4)

Each of the three (or more) elements in Equation 1.9(4) is referred to as a mode, while the terms τ1 and τ2 are called the modal time constants, and the terms (A0, A1, A2,…) are called the modal coefficients. For the LCSR test, the sensor output response T′(t) to a step change in the temperature inside the sensor is given by

1.9(5)

Note that the exponential terms in the above two equations are identical; only their modal coefficients are different The response 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.

Time

Time Ambient Temperature

0

1

Time (sec)

1/16" Dia K-Type

FIG 1.9m

Heat transfer process in plunge and LCSR tests.

Heat Transfer:

Surrounding Fluid

to Sensor

Heat Transfer: Sensor

to Surrounding Fluid

LCSR

Plunge

T t( )=A +A e−t/ +A e−t/ +

1

T t( ) B0 B e1 t/τ 1 B e2 t/τ 2 L

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 might

list the steps required in the LCSR test to obtain the response

time 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 (τ1, τ2,…)

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 for

determining the response times of both RTDs and

thermo-couples, both in laboratory and in situ applications As a

result, it has been demonstrated that the LCSR test can

deter-mine the response time of a temperature sensor within about

10% of the conclusions of a plunge test if both were

per-formed under the same conditions

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 Regulatory

Commission (NRC) for in situ measurement of the response

also been used in aerospace applications to correct transient

temperature data and in solid rocket motors to determine the

quality of the bonding of thermocouples with the solid

mate-rials such as the nozzle liners.7

In addition to response time measurements, the LCSR

test 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 is

to check if the resulting LCSR signal is normal This

test is especially useful if a reference set of baseline

LCSR data is available, representing the test results

on normal thermocouples so that gross

nonhomoge-neities can be easily noted

2 Determining if “strap-on” RTDs are properly bonded

to pipes or tubes In case of the Space Shuttle main

engine,7 in an experiment, the LCSR test was used to

verify the quality of “strap-on” RTD bonding within

the 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 resulting

from LCSR tests change as a function of the strength

of RTD bonding to the pipe Therefore, the LCSR test

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

Figures 1.9p and 1.9q illustrate the commercial equipment used in LCSR testing of RTDs and thermocouples In Figure 1.9p, an LCSR test system includes six channels for RTD response time measurements so that six RTDs can be simultaneously tested This system automatically performs the LCSR test, obtains and analyzes the LCSR data, and

τ

τ τ





− −























 1

2 1

3 1

FIG 1.9n

LCSR test to verify the attachment of a temperature sensor to a solid surface.

FIG 1.9o

LCSR test to verify the attachment of a strain gauge to a solid surface.

FIG 1.9p

RTD response time test equipment.

0 1

Time (sec)

LCSR Response (Normalized) Good Bond

75% Bonded

25% Bonded

Unbonded

0 1

Time (sec)

Good Bond Medium Bond

Partial Bond

1.9 Response Time and Drift Testing 121

determines the response times for each RTD The system can

send the data to a printer and print a table of RTD response

times A response time test transient display of a thermocouple

is 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 technique

is called noise analysis and is based on the monitoring of the

normally present fluctuations of the pressure transmitter output

signals In Figure 1.9r, such an output signal is shown at a

steady state that corresponds to the normal process pressure

This steady-state value is referred to as the DC reading When

magnified, it displays some small fluctuations This magnified

signal is called the noise or the AC component of the signal

sources The first source is the fluctuation of the process

pres-sure caused by turbulence, random heat transfer, vibration, and

other effects Second, there is electrical noise superimposed

on the pressure transmitter output signal Fortunately, these

two phenomena occur at widely different frequencies and thus

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

Figure 1.9s illustrates how the noise can be extracted from

a raw signal that includes both the DC and the AC components The first step to remove the DC component is by adding a

negative bias or by highpass electronic filtering Next, the

signal is amplified and passed through a lowpass filter, which

removes 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 The computer 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 includes the information required to determine the response time of the pressure sensor that generated the steady-state (DC) signal The raw noise data is a small portion of a noise record, which

is normally about 30 to 60 min

For noise data analysis, the two techniques available are the frequency-domain analysis and the time-domain analysis The first uses the power spectral density (PSD) technique involving fast Fourier transform (FFT) The PSD is obtained

by bandpass filtering the raw signal in a narrow frequency band and calculating the variance of the result This variance

is divided by the width of the frequency band, and the results are plotted as a function of the center frequency of the band pass This procedure is repeated from the lowest to the highest expected frequencies of the raw signal to obtain the PSD In

Figure 1.9u, the frequency spectrum of the noise signal from

a pressure transmitter in an operating power plant is shown against PSD If the pressure transmitter is a first-order system, its response time can be determined on the basis of measuring the break frequency of the PSD as shown in Figure 1.9v

FIG 1.9q

Thermocouple response time test analyzer.

FIG 1.9r

Principle of noise analysis technique.

Noise

DC Signal

Time

FIG 1.9s

Block diagram of the noise data acquisition equipment.

FIG 1.9t

Raw noise data from a flow sensor in a power plant.

Data Sampling and Storage Device Low-Pass

Filter

High-Pass Filter

or Bias

Isolated Plant Signal

Amplifier

−4.0

−2.0 0.0 2.0 4.0

Time (sec)

122 General Considerations

However, pressure sensors are not necessarily first order,

and PSD plots for actual process signals are not smooth

enough to allow the accurate measurement of the break

fre-quency In addition, PSDs often also contain resonance and

other disturbances that further complicate the response-time

analysis Therefore, both experience and a validated dynamic

model of the sensor are needed to obtain the sensor response

time by analyzing a PSD plot The model, which usually is

a frequency-domain equation, is fit to the PSD to yield the

model parameters, which are then used to calculate the

response time of the pressure sensor A PSD for a flow sensor

in an operating power plant and its model fit are shown in

Figure 1.9w

Autoregressive (AR) modeling is used for noise data

analysis 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 paramparam-eters are then used to cal-culate the response time of the sensor.9 Time-domain analysis

is generally simpler to code in a computer and therefore

is preferred for automated analysis However, in time-domain analysis, it is often difficult to remove noise data components that are unrelated to the sensor response time For example, if the noise data contains very low-frequency process fluctuations, the AR model will take them into account In such a case, it gives an erroneously large response time value In contrast, in frequency-domain analysis, it is easier to ignore low-frequency process fluctuations and to fit the PSD to that portion of the data that most accurately represents the sensor

Commercial, off-the-shelf equipment is available for both the frequency-domain and the time-domain analysis

of noise data A number of companies provide spectrum ana-lyzers (also called FFT anaana-lyzers), which take the raw noise data from the output of a sensor and provide the necessary conditioning and filtering to analyze it and calculate the sen-sor response time However, because of resonance and other influences, simple FFT analysis does not always yield the correct response time reading This is not a shortcoming of the FFT equipment but a consequence of the inherent nature

of the input signal with which they must work

ON-LINE VERIFICATION OF CALIBRATION

The calibration of installed instruments such as industrial pressure sensors involves (1) the decision whether calibration

is needed at all and (2) the actual calibration, when necessary The first step can be automated by implementing an on-line drift monitoring system This system samples the steady-state output of operating process instruments and, if it is found to have drifted, it calls for it to be calibrated Conversely, if there is no (or very little) drift, the instrument is not calibrated

at 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 that occurs in the process from instrument drift before a reference limit of “allowable drift” can be defined For example, if redundant sensors are used to measure the same process parameter, their average reading can be assumed to closely represent the process and used as the reference This is done

by first sampling and storing the normal operating outputs of the redundant instruments and then averaging these readings for each instant of time These average values are then sub-tracted from the corresponding individual readings of the redundant instruments to identify the deviation of each from the average

FIG 1.9u

Pressure sensor PSD

FIG 1.9v

First-order system PSD.

FIG 1.9w

Flow 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

Frequency (Hz)

1

Frequency (Hz)

b

Fb= Break Frequency

Fb

1.0E−06

1.0E −04

1.0E −02

1.0E+00

1.0E+02

Frequency (Hz)

1.9 Response Time and Drift Testing 123

In Figure 1.9x, the results of on-line monitoring of four

steam-generator level transmitters in a nuclear power plant

are shown The difference between the average of the four

transmitters and the individual readings are shown on the

y axis as a function of time in months The data are shown

for a period of about 30 months of operation, and the four

signals 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 be

recalibrated If it is suspected that all four transmitters are

drifting in an identical manner (drifting together in one

direc-tion), the data for deviation from the average would not reveal

the drift Therefore, to rule out any systematic or common

drift, one of the four transmitters can be recalibrated

detecting systematic drift is to obtain an independent estimate

of the monitored process and track that estimate along with

the indication of the redundant sensors Both empirical and

physical modeling techniques are used to estimate systematic

drift They each monitor various related process variables

and, based on their values, evaluate the drift in the monitored

parameter For example, in a process involving the boiling

of water (without superheating of the steam), temperature

and pressure are related Thus, if temperature is measured,

the corresponding saturated steam pressure can be easily

determined, tracked, and compared with the measured

pres-sure as a reference to identify systematic drift The use of this

method of drift detection does not require the use of multiple

sensors, and individual sensors can also be tracked and their

calibration drift evaluated on line

The relationship between most process variables is much

more complex than the temperature–pressure relationship of

saturated steam Therefore, most process parameters cannot

be 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 models use empirical equations, neural networks, pattern recognition, and sometimes a combination of these, including fuzzy logic for 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 under

a variety of operating conditions As shown in Figure 1.9y,

if the output parameter (y) is to be estimated on the basis of measuring the input parameters x1, x2, and x3, then, during the training period, weighting factors are applied to the input variables These factors are gradually adjusted until the dif-ference between measured output and the output of the neural network is minimized Such training can continue while the neural network learns the relationship between the three inputs and the single output, or while additional input and output signals are provided to minimize the error in the empirical model Training of the model is completed when the 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 or control purposes

An on-line calibration monitoring system might use a combination of averaging of redundant signals (averaging can be both straight and weighted), empirical modeling, physical modeling, and calibrated reference sensor(s) in a configuration similar to the one shown in Figure 1.9z In such

a system, the raw data is first screened by a data-qualification algorithm and then analyzed to provide an estimate of the process parameter being monitored In the case of averaging analysis, a consistency algorithm is used to make sure that a reasonable agreement exists among the redundant signals and that unreasonable readings are either excluded or weighted less that the others before the signals are averaged Such systems as the one illustrated in Figure 9.1z can be consid-ered for both power plants and chemical industry applications for the on-line verification of the calibration requirements of process sensors

The data for on-line monitoring can be obtained from the plant 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 for each instrument from a process estimate and a listing of instruments that have drifted The data acquisition system

FIG 1.9x

On-line monitoring data for steam generator level transmitters.

−3.0

−1.5

0.0

1.5

3.0

Time (Month)

SG D Level

15

FIG 1.9y

Illustration of training of a neural network

X1

Y output

X2

X3

Figure 1.9aa illustrates a data acquisition system used in a