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Description  |
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BACKGROUND OF THE INVENTION
This invention relates to the continuous surveillance of sensors used for
monitoring changes in the various parameters of a system. More
particularly, the invention provides a method and apparatus for on-line
detection of degradation or undesirable changes in the time constants of
sensors used in monitoring the flow rate, temperature, pressure, level,
radiation, etc., of a system.
Heretofore, evaluation and calibration of sensors used in monitoring a
process or system, typically took place during periodic maintenance or
when the system was completely shut down. However, as industrial processes
have become more continuous and complex, it is often undesirable and very
expensive to shut down an industrial process as often as would be
necessary to provide adequate periodic calibration and evaluation of the
sensors monitoring the process. In addition, some industrial processes and
systems operations, including nuclear power plant operations, represent
such potential danger that any degradation or reduced performance of
sensors used in monitoring the process or system could be critical.
Therefore, it is of great importance that any such degradation be brought
to the attention of the person responsible for the systems opration.
The use of fluctuating output signals to obtain information about the
dynamic characteristics of a system or process in itself is not new. For
example, refer to "Random Data: Analysis and Measurement Procedures" by J.
S. Bendat and A. G. Piersol which was published by John Wiley and Sons,
Inc., New York, 1971; and "Random Noise Techniques in Nuclear Reactor
Systems" by R. E. Uhrig which was published by the Ronald Press company,
New York, 1970. Typically, these available methods as discussed in the
above references include evaluation of spectral densities or time series
models. According to these methods, however, it is necessary to perform
extensive calculations on the raw data to obtain the desired results. In
addition, methods have been devised which continually monitor and use the
statistical properties of a sensor output to detect degradation. A
discussion of some of the methods may be found in "Two On-Line Methods for
Routine Testing of Neutron and Temperature Estimates of Power Reactors" by
M. Eldemann, a Kernforschungszentrum Karlsruhe Report, KFK, 2316, July,
1976 Karlsruhe, Germany; and "In-Situ Response Time Testing of Platinum
Resistance Thermometers" by T. W. Kerlin et al. a EPRI Report, NP-459,
January, 1977, Palo Alto, Calif. Unfortunately, as was mentioned above,
the presently available methods and apparatus are typically very complex
and expensive and require such extensive calculation on the raw data that
a computer is usually necessary for implementation. However, the previous
methods and techniques were more powerful than necessary for simply
monitoring the sensor response characteristics. Therefore, as will become
clear hereinafter, the zero crossing method used in the sensor response
time degradation monitor of this invention uses a technique which is,
therefore, less demanding than the presently available methods and
techniques which require a detailed computer analysis.
SUMMARY OF THE INVENTION
Therefore, it is an object of the present invention to provide a simple and
inexpensive method and apparatus for monitoring the degradation of a
sensor used in monitoring a process or system.
It is another object of the invention to provide a method and apparatus for
monitoring the performance of a sensor used in a process or system while
it is functioning or operating in the system.
It is still another object of the invention to provide a simple and
inexpensive method and apparatus for monitoring a system while it is
on-line.
These and other objects are achieved by the methods and apparatus of the
present invention which provides for evaluating changes in the response
time of a sensor, used to monitor changes in a selected system parameter.
According to this invention, a signal generated by the sensor being
evaluated and normally used to indicate the changes in a selected system
parameter is received by circuitry for monitoring when the value of the
sensor signal crosses a selected signal level such as for example the
level predetermined to be the average level. Also included, is circuitry
for determining the number of times that the sensor signal crosses the
selected level during a selected time period such that a crossing rate may
be obtained. The crossing rate obtained is then compared with a nominal
crossing rate to determine whether a change has taken place in the
response time of the monitored sensor. For example, the crossing rate is
compared with a preselected acceptable rate such that when the determined
crossing rate does not achieve the preselected acceptable rate a warning
or alarm will be provided to the operator of the system.
The above mentioned objects as well as other objects will be more clearly
understood by reference to the detailed description of this invention and
the drawings wherein:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a sensor response time degradation monitor
incorporating the features of this invention;
FIG. 2 is a part pictorial and part schematic drawing of an alternate
embodiment of the time degradation monitor of the present invention;
FIG. 3 is a graph illustrating the actual fluctuations of a system or
process parameter;
FIG. 4 is a graph illustrating the fluctuations of a system or process
parameter of FIG. 2 as sensed by a theoretical sensor having a zero time
constant;
FIGS. 5 and 6 are graphs illustrating the fluctuations of a system or
process parameter as sensed by a typical sensor having different time
constants. The graph of FIG. 5 having a faster time constant than that of
FIG. 6; and
FIG. 7 is a circuit diagram of a specific embodiment of the present
invention.
DESCRIPTION OF THE INVENTION
Referring now to FIG. 1 there is shown a block diagram of a Sensor Response
Time Degradation Monitor incorporating the features of this invention. As
is shown, system or process 10 is of a type having various parameters that
are monitored by a sensor 12. It will be appreciated that most processes
or systems will include many parameters which need such monitoring, but
for purposes of explanation a single sensor is shown. For example, sensor
12 could be a sensor suitable for monitoring such conditions as flow rate,
temperature, pressure, radiation, etc. It will become clear hereinafter,
that the degradation monitor of this invention is suitable for use with
all such types of sensors. The output of sensor 12 on line 14 is shown as
being provided to the Sensor Using Circuitry 16 which may simply be a
recorder or a meter for visual observation of the fluctuations of the
system parameter being monitored. The output of sensor 12 is also provided
to the sensor response Time Degradation Monitor 18 of this invention.
Thus, the Sensor Response Time Degradation Monitor Circuitry 18 may be
considered separately from Sensor Using Circuitry 16. The sensor output on
line 14 is received by the Sensor Response Time Degradation Monitor
Circuitry 18 of this invention at Bandpass Filter 20. Bandpass Filter 20
removes the low frequencies, such as for example frequencies of 0.001 Hz
to 0.1 Hz and below as well as, of course, the DC components of a signal.
In addition, Bandpass Filter 20 is selected to eliminate the effects of
extraneous electrical signals having a higher frequency. For example,
Bandpass Filter 20 will eliminate frequencies above a selected frequency
such as 1 Hz or 30 Hz. Thus, it will be appreciated that 60 Hz electrical
noise will be eliminated. It will also be appreciated, of course, that the
high frequency selected and the low frequency selected for Bandpass Filter
20 is determined by the specific type of the sensor and its output. For
purposes of explanation and to aid in the understanding of this invention,
there is shown at FIG. 3 a graph representing the actual variations of a
process parameter such as, for example, temperature, pressure, etc.
According to this graph the process crosses the average or "zero" level
nine times as is indicated by arrows 23. FIG. 4 illustrates a theoretical
filter output as might be provided on line 22 through Bandpass Filter 20
from a perfect sensor having a zero time constant or instantaneous
response. The graph of FIG. 4 is substantially identical to the graph of
FIG. 3, and also crosses the average or zero level nine times as indicated
by arrows 23. Referring now to FIGS. 3 and 4, it can be assumed that a
random signal of approximately 10 Hz is illustrated. It should be
understood, however, that the frequency of the illustrated output of FIG.
3 was not intended to be a steady periodic signal or is it in any way
limited to a frequency of around 10 Hz since the frequency of the random
signal could vary significantly, such as, for example, between 5 and 20
Hz. As can be seen from FIG. 3, the illustrated output is shown as varying
around a zero voltage level. It will be appreciated, however, that the
signal might well have varied around a positive or negative average
voltage level of say 5 volts and also could have included a high frequency
component such as 60 cycle electrical noise.
It is understood, of course, that such a perfect sensor as illustrated in
FIG. 4 does not exist and in actuality the response time of the sensor may
be substantially slower than instantaneous. FIGS. 5 and 6 which will be
discussed in detail hereinafter show a more realistic or typical sensor
output signal which has passed through Bandpass Filter 20 such that the
low frequency (including DC) and high frequency components have been
removed.
As will be discussed in detail, hereinafter, FIGS. 5 and 6, which are
provided for explanation purposes only, represent the output signal of a
typical sensor 12 on line 22. The time constant of the sensor illustrated
by the graph of FIG. 5 was selected to be "fast" such as, for example, on
the order of a few hundred milliseconds, whereas the time constant of the
sensor illustrated by the graph of FIG. 6 was selected to be slow, as, for
example, on the order of a few seconds.
The output of Bandpass Filter 20 on line 22 is provided to Detector 24 on
line 22. Detector 24 provides an indication at output 26 each time the
signal input on line 22 crosses a preselected reference level such as, for
example, a predetermined average signal level which will be referred to
hereinafter as the zero level. This output on line 26 is then provided to
a Monitor Circuitry 28. It will be appreciated, that the Monitor Circuitry
28 may be a counter, or a register but in either event it is preferably
recorded such that a continuous monitoring of the zero crossing rate per a
selected time period can be evaluated. Further, as will be discussed
below, monitor 28 could simply be the read-out on a counter used in the
Rate Comparison Circuitry 30. In addition to the output provided to
Monitor Circuitry 28, the present embodiment also illustrates that the
Detector 24 (hereinafter referred to as Zero-Crossing Detector) output is
also provided to Rate Comparison Circuitry 30 for comparing the zero
crossing rate as detected by Zero-Crossing Detector 24 with a
predetermined acceptable zero crossing rate. Rate Comparison Circuitry 30
which receives the output from Zero-Crossing Detector 24 may be of any
suitable type but will include a counter, means for providing an
electrical signal when a selected count occurs, and a timer. According to
the embodiment of FIG. 1, a selected count is set in Counter 32 by the
"Count Preset" Controls 34. During operation Counter 32 continuously
receives an input from Zero-Crossing Detector 24. Therefore, to start a
comparison cycle, a reset/start signal is shown being received by both
Counter 32 and Timer 36 on line 38. The output of Timer 36 on line 40 is
connected to Control Switch 42 such that when a selected time period
elapses a signal can be supplied through Control Switch 34 via line 40A
and 40B to Alarm 44. However, Timer 36 may also provide the selected time
period mentioned above with respect to Monitor Circuitry 28 by means of
line 40C. However, Counter 32 is also connected to Control Switch 42 such
that an output from Counter 32 on line 46, will interrupt the path between
line 40A and 40B. Although the embodiment of FIG. 1 discloses discrete
components such as Monitor 28, Counter 32, Preset Controls 34, and Control
Switch 42, it will be appreciated that readily available units having all
the above mentioned components provided as an integral unit are available.
For example, the Veeder-Root Company of Hartford, Connecticut manufactures
a "Minicontroller Predetermining Counter," part no. 799204-246 which is
particularly suitable for use with this invention. FIG. 2 shows a part
pictorial and part schematic of an embodiment similar to that of FIG. 1
employing such a predetermining counter.
Thus, referring again to FIG. 1; as Zero-Crossing Detector 24 provides a
pulse on line 26 to Counter 32, Counter 32 will be incremented (or
decremented if a "down" counter is used) for each zero crossing. If the
number of counts received by counter 32 does not equal or exceed the
preselected number selected by Preset Counter 34, before Timer 36
completes its timing cycle, the path between Timer 36 and Alarm 44 will
not be interrupted, and Timer 36 will provide an output on line 40A
through Control Switch 42 to line 40B and on to Alarm 44 which in turn
will provide a warning. However, if Counter 32 provides a signal to
Control Switch 42, the signal from Timer 36 to Alarm 42 will be
interrupted and no alarm given. Control Switch 42 could be any suitable
electronic or electrical switch, including a relay as is illustrated in
FIG. 1 wherein line 40A and 40B between the Timer 36 and Alarm 44 are
connected to the relay normally closed contacts, and line 46 from the
Counter is connected to the relay coil. Typical counting durations could
range from a minute to several hours depending, of course, on the type of
signal being monitored.
The number of zero crossings that indicates acceptable performance and
which should be set in Counter 32 may be determined by obtaining the time
constant of the sensor when first installed (i.e. .tau..sub.new). The
number of zero crossings during a selected time period for the newly
installed sensor is then obtained (i.e. N.sub.new). A value for the
maximum allowable time constant (.tau..sub.max) is then selected and may
be determined because of safety consideration or minimum acceptable system
performance. From this information the minimum number of acceptable zero
crossings N.sub.c may be determined from the following equation:
N.sub.c =N.sub.new (.tau..sub.new)/.tau..sub.max (1)
Although the operation of the Sensor Response Time Degradation Monitor of
this invention as discussed above and the form of equation (1) have been
demonstrated by emperical data, and may be intuitively understood, such an
understanding and emperical data can be shown to be correct by the
following mathematial proof which was developed by a unique combination of
previously known theories. For example, the power spectral density of an
output signal from a system has been shown by J. S. Thie in his
publication, "Reactor Noise" by Rowman and Littlefield, Inc. New York,
1963 to be:
PSD.sub.o =.vertline.G.vertline..sup.2 PSD.sub.1 (2)
where PDS.sub.o =the power spectral density of a fluctuating output signal
from the system; PSD.sub.1 =the power spectral density of a fluctuating
input disturbance to a system; and .vertline.G.vertline..sup.2 =the square
modulas of a system transfer function.
Now, since all the three quantities of equation (2) are functions of
frequency, it will be appreciated that a change in PSD.sub.o would
indicate a change in either PSD.sub.1 or in .vertline.G.vertline..sup.2.
And, since it seems appropriate to assume that PSD.sub.1 is white noise
and is, therefore, substantially constant at all frequencies, it will be
appreciated that a measurable change in PSD.sub.o would probably indicate
a change in the response characteristics of .vertline.G.vertline..sup.2.
Thus, since the PSD.sub.o function can be determined from a fluctuating
output signal using Fourier analysis method, it will be appreciated that
if value of .vertline.G.vertline..sup.2 is known, a transfer function
having a specific form can be made to fit the PSD.sub.o function by the
least squares fitting method. Once the transfer function of PSD.sub.o is
known, the response to any time dependent input such as a step or ramp
function can also be determined. Finally, of course, by using a step
response the time constant can be determined.
Now, it will be appreciated by those skilled in the art, that the system
transfer function for thermocouples and resistance thermometers may be
expressed as:
##EQU1##
It has previously been shown by experts in the field, such as A. Papoulis
in his publication, "Probability, Random Variables and Stochastic
Processes," published by McGraw Hill Book Company, New York, in 1965, that
the number of zero crossings N, per unit time of a random signal is given
by the equation:
##EQU2##
wherein R=autocorrelation function of the signal,
d=differential operator
t=time
R(.tau.)=autocorrelation function of the signal at a lag of .tau.,
R(0)=autocorrelation function of the signal at a lag of 0.
The autocorrelation function R can further be expressed according to the
integral function:
##EQU3##
wherein: T=Time period of the sample.
According to the Thie publication previously discussed, a relation exists
between the power spectral density of the signal and the autocorrelation
function of that signal. Accordingly, this function may be expressed as:
PSD=F[R] (6)
R=F.sup.-1 [PSD] (7)
wherein:
F=Fourier transform operator
F.sup.-1 =inverse Fourier transform operator
Now, if we assume white noise such that the term PSD.sub.1 is a constant,
we can combine equations (2) and (3) to obtain the function:
##EQU4##
Now, if according to equation (7) we take the inverse Fourier transform of
equation (8) we obtain:
##EQU5##
Then by substituting the value of R(.tau.) into the equation (4),
simplifying and reducing terms we obtain the equation:
##EQU6##
Since p.sub.1 and p.sub.2 are reciprocals of time constants, equation (10)
may be rewritten as:
##EQU7##
Equation (11) itself can in turn be rewritten in the form:
(.tau..sub.1 .tau..sub.2).sup.1/2 =1/.pi.N (12)
It can be shown that .tau..sub.2 =(1/.alpha.).tau..sub.1 when .alpha. is
greater than 1, and therefore we can obtain:
##EQU8##
Thus, since
.tau..congruent..tau..sub.1 +.tau..sub.2, (15)
it will be appreciated that:
##EQU9##
Inspection of equation (16) quickly reveals that the zero crossing rate for
a typical temperature sensor is approximately inversely related to the
sensor time constant. Also, it should be appreciated that even though some
assumptions were made and that the relationship of equation (16) is not
exact, it is certainly believed to be exact enough to show that an N-fold
increase in the sensor time constant will cause approximately an N-fold
decrease in the zero crossing rate.
Thus, in addition to emperical data which shows that a decrease in the
number of zero crossings is indicative of the sensor response time
degradation there has been shown by the above discussed proof, a
mathematical or theoretical bases of the operation of the response time
degradation monitor. Finally, although the example of the mathematical
proof was with respect to a thermocouple and resistance thermometer sensor
which have a simple transfer function, it is believed that this proof is
sufficient to show that a similar proof would be available for sensors
having mechanical linkages that include energy storing components such as
springs, and which consequently would require a second order transfer
function with complex poles.
It will also be appreciated that Rate Comparison Circuitry 30 was described
with respect to a particular embodiment. However, Rate Comparison
Circuitry 30 could include any type of circuitry or arrangement of
components which would have the overall effect of comparing the present
zero crossing rate with a predetermined acceptable zero crossing rate.
Also, of course, the Timer 36 could be of two types, one which runs for a
selected duration and then stops until reset such as is indicated by
Switch 47 or Timer 36 could run for a selected duration and then reset
itself as is indicated by dashed line 48. It will also be appreciated that
Counter 32 could be an electro-mechanical counter for sensors having a
slow zero crossing rate, when an electronic counter might be necessary for
sensors having a high zero crossing rate.
Alarm 44 could actually be an audible alarm, some visual indicator such as
a flashing red light, or nothing more than a readout on a recorder.
However, it will be appreciated that the purpose of the Alarm 44 is to
indicate to the operator of a system that the number of zero-crossings of
the monitored signal has decreased below the level that indicates an
acceptable sensor time constant.
Also shown are Recorders 49 and 50 which could be connected to Monitor
Circuitry 28 or Rate Comparison Circuitry 30 for providing a permanent and
continuous record of the zero crossing rate and excessive degradation of
the time constant of the sensor.
Referring again to FIGS. 3 and 4, it can be seen that the number of actual
zero crossings of the system fluctuations after being filtered by Bandpass
Filter 20, and as would be sensed by the perfect sensor having zero
response time would be approximately 9. However, as was mentioned
heretofore, such perfect sensors are not available and in fact are not
necessary. FIG. 5 shows the output of a "fast" sensor which would monitor
system fluctuations of the type shown in FIG. 3. Thus, there is
illustrated in FIG. 5 the approximate representation of the signal of FIG.
3 around a zero level by a sensor having a time constant on the order of a
few hundred milliseconds. As can be seen from FIG. 5, a sensor of this
type will result in a different shaped graph than that of the theoretical
signal of FIG. 3. In the graph of FIG. 5, there are still nine
zero-crossings, however, it will be noted that the curve is somewhat
smoother and just barely crosses the zero level at arrows 51 and 52. It
should also be appreciated that even a "fast" sensor may eventually miss
one or more zero crossings. Now referring to FIG. 6, there is shown a
graph of a sensor similar to that discussed with respect to FIG. 5 except
that the response time has been substantially increased above the response
time of the graph shown in FIG. 5, such as for example, to several
seconds. In this graph, it can be seen that the curve is even smoother
than the curve of FIG. 5, and that the number of zero crossings has
decreased to only five. Thus, FIGS. 5 and 6 graphically illustrate that an
increase in the time constant of a sensor will result in the decrease in
the number of zero crossings. It is this relationship between the number
of zero crossings and the increase in time constants that provides a basis
for the unique method and apparatus of this system. That is, the Sensor
Response Time Degradation Monitor of this invention exploits the
dependancy and the statistical properties of the sensor output with
respect to its response characteristics. This is because, the normal
fluctuations that occur in a process or the operation of the system cause
fluctuations in the output of the sensors that monitor these variables.
Fast sensors, of course, respond more exactly to these process variables
than do slow sensors. Thus, if the monitored parameter variable crosses an
average value 10 times per second, then the output of a perfect sensor
(i.e. one having a response time of zero) also crosses the average value
10 times per second. However, it will be appreciated those skilled in the
art that all sensors have a finite response time such that they cannot
follow the process variables exactly and, therefore, there will always be
a lag. As a result, some of the crossings of the average value will not be
observed by the sensor. Furthermore, the number of crossings monitored by
the sensor will decrease continuously as the sensor response time
increases. A faster sensor will track fluctuations in a monitored
parameter better than a slower sensor, and a faster sensor will pass
through its average value more frequently than a slower sensor.
Referring now to FIG. 5, there is shown a specific embodiment of a Bandpass
Filter 20 and Zero Crossing Detector 24 suitable for use with the present
invention. According to this embodiment, Bandpass Filter 20 was designed
to have a low frequency cut-off value of around 4 Hz. Operation amplifiers
54 and 56 have a standard identifying number 356. Operational Amplifier 58
has a standard identifying number 741. Capacitors 64, 66, and 68 have
values of 4, 0.22 and 0.22 micro farads respectively. Resistors 70, 72,
74, 76, 78, 80, 82, 84 and 86 have values of 1.2 meg-ohms, 1.2 meg-ohms
200 kilo-ohms, 200 kilo-ohms, 360 kilo-ohms, 1 kilo-ohm, 10 kilo-ohms, 900
ohms and 5.1 kilo-ohms, respectively.
Zero-Crossing Detector 24 includes a comparator identified as number 339.
Feed-Back Resistor 94 is a 1 meg-ohm resistor.
Thus, although the present invention has been described with respect to
specific methods and apparatus for monitoring degradation of the response
time of a sensor, it is not intended that such specific references be
considered as limitation on the scope of this invention except insofar as
is set forth in the following claims.
* * * * *
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