Title: Control system and method for detecting plugging in differential pressure cells
Abstract: A method and control system is disclosed that monitors the high frequency or commonly referred to as the "noise" component of a measurement signal to detect plugging conditions in fluid flow systems monitored by DP-cell based sensors. This high frequency component has contributions from the process factors like disturbances, user actions and random effects like turbulence. A test statistic θ(t) has been developed that monitors the proportion of variance introduced by process factors and random effects. By monitoring this proportion, it is possible to detect a frozen sensor that is characterized by a dramatic reduction in the variance due to process factors over a sufficiently long detection window. The method works with measurements sampled at frequencies commonly achievable in a process environment.
Patent Number: 6,904,386 Issued on 06/07/2005 to Mylaraswamy
| Inventors:
|
Mylaraswamy; Dinkar (Saint Anthony, MN)
|
| Assignee:
|
Honeywell International Inc. (Morristown, NJ)
|
| Appl. No.:
|
265988 |
| Filed:
|
October 7, 2002 |
| Current U.S. Class: |
702/183; 73/61.73; 340/608; 702/47; 702/50 |
| Intern'l Class: |
G01L 015/00 |
| Field of Search: |
702/183,45,47,50,51,55,75,100,114,124,138,140,182,185,189,198
73/116,117,135,157,159,163,173,40,405.R,617.3,861.02,861.03,861.356,195,196,861.52,86142-86146,861.61,521,861.64,708,712
340/606,607,608,611,612,614,626
137/557-559,551,554
|
References Cited [Referenced By]
U.S. Patent Documents
| 2057767 | Sep., 1936 | Collins.
| |
| 4231262 | Nov., 1980 | Boll et al.
| |
| 4528847 | Jul., 1985 | Halmi.
| |
| 4654813 | Mar., 1987 | Edlund et al.
| |
| 5442551 | Aug., 1995 | Denz et al.
| |
| 5461912 | Oct., 1995 | Gohara.
| |
| 5680109 | Oct., 1997 | Lowe et al.
| |
| 5708211 | Jan., 1998 | Jepson et al.
| |
| 5739429 | Apr., 1998 | Schmitkons et al.
| |
| 5763764 | Jun., 1998 | Mieczkowski et al.
| |
| 5905208 | May., 1999 | Ortiz et al.
| |
| 6021677 | Feb., 2000 | Hepner.
| |
| 6526358 | Feb., 2003 | Mathews, Jr. et al.
| |
| 6654697 | Nov., 2003 | Eryurek et al.
| |
| Foreign Patent Documents |
| 04328435 | Nov., 1992 | JP.
| |
| 06109511 | Apr., 1994 | JP.
| |
| 08136386 | May., 1996 | JP.
| |
| 08166309 | Jun., 1996 | JP.
| |
| WO 97/4571/6 | Dec., 1997 | WO.
| |
Other References
Taya et al., "Detecting blockage in process connections of differential pressure
transmitters", Jul. 26-28, 1995, IEEE, SICE'95, Proceedings of the 34th SICE Annual
Conference, pp. 1605-1608.
|
Primary Examiner: Wachsman; Hal
Attorney, Agent or Firm: Ohlandt, Greeley, Ruggiero & Perle, L.L.P.
Claims
1. A method for detecting a plugging condition in lines that provide a signal
in a system, said method comprising:
(a) developing a variance factor from a sensor signal;
(b) signaling an occurrence of said plugging condition in response to changes
in said variance factor; and
(c) processing said sensor signal to detect a zero mean velocity condition,
wherein step (b) signals said occurrence of said plugging condition when said
variance factor and said zero mean velocity condition are developed simultaneously.
2. The method of claim 1, wherein said lines are impulse lines of a differential
pressure cell, wherein said sensor signal is proportional to pressure and velocity
of a fluid, and wherein said variance factor measures the relative proportion between
variance imposed by turbulence and variance imposed by process dynamics at a current
time t, with respect to a baseline value and a predetermined threshold.
3. The method of claim 2, wherein step (a) uses a current value of said sensor
signal, and wherein said baseline value is based on a value of said sensor signal
that is earlier in time than said current value.
4. The method of claim 3, wherein said current value is based on a window of
a number of samples of said sensor signal, wherein said window of said number of
samples advances at least one sample at a time to provide a plurality of windows
and wherein step (a) is repeated for each of said plurality of windows.
5. The method of claim 4, wherein said baseline value is dynamically updated
based on a value of said baseline developed prior to said window of said current value.
6. The method of claim 5, wherein said baseline value is updated during each
of said windows over a detection window that spans a plurality of said windows
of said number of samples.
7. The method of claim 6, wherein said baseline value is updated using an exponentially
weighted moving average of said plurality of sample windows.
8. The method of claim 4, wherein said number is selected to minimize the effect
of slow process dynamics.
9. The method of claim 8, wherein said developing step (a) compares said baseline
value and said threshold to a ratio of high frequency components of said sensor
signal due to turbulence effects and to process effects so as to substantially
eliminate effects due to working conditions of said system.
10. The method of claim 2, wherein said baseline value is dynamically updated.
11. A control system for detecting a plugging condition in lines that provide
a sensor signal in a process system, said control system comprising:
a sensor that generates a sensor signal;
a controller that detects said sensor signal from said sensor and develops a
variance factor from said sensor signal; and
an indicator that signals an occurrence of said plugging condition in response
to changes in said variance factor,
wherein said controller processes said sensor signal to detect a mean velocity
condition, and wherein said indicator signals said occurrence of said plugging
condition when said variance factor and said zero mean velocity condition are developed
simultaneously.
12. The control system of claim 11, wherein said lines are impulse lines of a
differential pressure cell, wherein said sensor signal is proportional to pressure
and velocity of a fluid, and wherein said variance factor measures the relative
proportion between variance imposed by turbulence and variance imposed by process
dynamics at a current time t, with respect to a baseline value and a predetermined threshold.
13. The control system of claim 12, wherein said baseline value is dynamically updated.
Description
FIELD OF THE INVENTION
This invention relates to a control system and method for detecting plugging
in differential pressure cells.
BACKGROUND OF THE INVENTION
Sensors that provide accurate and reliable measurements are crucial in today's
world of highly automated and integrated operations. Sensor failure is one of the
biggest nightmares of an operator. A sensor failure is defined as the loss of proper
sensing action, that is, the sensor fails to respond correctly to changes in the
measurement variable it is sensing. Often a sensor failure goes undetected until
it escalates into a process problem. It may then be too late to take any preventive
action. The process industry is filled with real-life case studies, in which a
catastrophic incident can be traced back to a failed sensor.
A differential pressure cell (DP-cell) is commonly used to measure process variables
like flow and level. The DP-cell is often located close to the ground for ease
of maintenance and, hence, is connected to the process through long impulse lines.
These impulse lines are easily blocked by accumulation of suspended particles in
the process fluid, or by uneven steam flow during tracing, or by poor insulation.
As used herein, the term "frozen sensor" is used to indicate the state of a sensor
(either flow or level) that contains a blocked DP-cell. A blocked DP-cell measures
incorrect pressure and, thus, provides an incorrect indication of flow or level.
Unlike the failure of a temperature sensor that results in the measurement reading
either pegged at a constant value or widely oscillating between lower and upper
limits of a range of the instrument, a frozen sensor is more subtle to detect.
Traditionally, there are two ways of detecting a frozen sensor. First,
an operator may suspect a frozen sensor based on his or her experience. Second,
a spectral analysis may be performed to monitor changes in the high-frequency component
of a measurement signal. Pressure p(t) described at a molecular level measures
the net energy transferred by random impact of atoms and molecules at any point.
The pressure p(t) at any time t is given by:
where, p′(t)represents fluctuations introduced because of turbulence
and electrical interference and {overscore (p)}(t) represents the ensemble average
of the instantaneous pressure calculated over a very small measurement volume.
These fluctuating components of a measurement signal can often provide valuable
insights into the state of the measuring device. Although the use of spectral analysis
to monitor these fluctuations and deduce diagnostic states has been successful
in laboratory setups, most methods require measurement frequencies in the range
of 200-1000 Hz, which is rarely practical in process industries.
Thus, there is a need for an automated and predictive plugging detection system
and method.
SUMMARY OF THE INVENTION
The method of the present invention detects a plugging condition in the impulse
lines of a DP-cell. The DP-cell provides a sensor signal proportional to the pressure
drop and, hence, the velocity of a fluid in a system. A variance factor is developed
for the variance of a fluctuating component of the sensor signal that is mainly
due to turbulence effects of the fluid; compared with a baseline value using a
predetermined threshold. An occurrence of the plugging condition is signaled in
response to the change in this variance factor.
The method of the invention works with well-established and prevalent sampling
rates as compared to frequency based methods that require high sampling rates.
Thus, the method can be deployed within established distributed control systems
without changing sampling rates or data collection frequency.
According to one embodiment of the method of the invention, the sensor
signal is also processed to detect a zero mean velocity condition of the fluid.
The occurrence of the plugging condition is signaled when the variance factor and
a non-zero mean velocity condition are developed simultaneously.
According to another embodiment of the method of the invention, the comparison
is with a current value of the sensor signal, and a baseline value based on a value
of the sensor signal that is calculated earlier in time than the current value.
Preferably, the baseline value is dynamically updated.
According to another embodiment of the method of the invention, the current
value is based on a window of N samples of the sensor signal that advances at least
one sample at a time to provide a plurality of windows. The comparison of the current
value and the baseline value is repeated for each of the plurality of windows.
The baseline value is dynamically updated preferably based on a value of the baseline
developed prior to the window of the current value. More preferably, the baseline
value is updated during each of the windows over a detection window that spans
a plurality of the sample windows. Most preferably, the baseline value is updated
using an exponentially weighted moving average of the plurality of sample windows.
According to another embodiment of the method of the present invention,
the variance factor uses only the high frequency component of the sensor signal.
Preferably, the variance factor closely corresponds to turbulence effects and substantially
eliminates effects due to low frequency process effects. Comparing the variance
factor with the baseline value substantially eliminates effects due to working
conditions of the system.
According to another embodiment of the method of the invention, the variance
factor is compared to with a baseline value and a predetermined threshold. An occurrence
of the plugging condition is signaled in response to the variance factor. The baseline
value is dynamically updated.
The control system of the present invention includes a controller that comprises
a processor, a memory and a program that causes the processor to perform a plurality
of operations that correspond to the steps of the method of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
Other and further objects, advantages and features of the present invention
will be understood by reference to the following specification in conjunction with
the accompanying drawings, in which like reference characters denote like elements
of structure and:
FIG. 1 is a schematic diagram of a control system of the present invention for
measuring fluid flow and/or level;
FIG. 2 is a schematic diagram of a control system for measuring and/or maintaining
liquid level in a process vessel;
FIG. 3 is a schematic diagram showing more detail of the control system of FIG. 2;
FIGS. 4 and 5 depict traces of normal and frozen temperature sensors;
FIGS. 6-9 depict traces of normal and frozen DP-cell based sensors;
FIG. 10 is a schematic diagram showing more detail of the control system of
FIG. 2;
FIG. 11 depicts in graphical form a sample comparison step of the method of
the present invention;
FIG. 12 is a flow diagram of the frozen sensor detection program of the control
system of FIG. 2;
FIGS. 13-16 depict traces of the test statistic for normal sensors;
FIG. 17 depicts traces of the test statistic for a normal and a frozen sensor;
FIG. 18 depicts a scatter plot for a normal sensor; and
FIG. 19 depicts a scatter plot for a frozen sensor.
DESCRIPTION OF THE PREFERRED EMBODIMENT
According to the present invention, a test statistic is developed that
measures the variance of fluctuating (high frequency) components of a sensor signal
that is monitored to provide insights into the diagnostic state of the sensor.
Unlike conventional statistical hypothesis testing, domain knowledge in terms of
the actual sensor model is used. A 2×2 covariance matrix is constructed for
the measurement of the variance introduced due to turbulence and process effects.
The eigen values of this covariance matrix are monitored to provide diagnostic
information. By way of example, the method of the invention is illustrated using
historical data from a level sensor in a petrochemical plant. For this example,
the method of the invention is capable of detecting a frozen level sensor hours
before it results in a process upset.
Referring to FIG. 1, a measurement system
20 includes a DP-cell
22 that is connected via a pair of impulse lines
24 and
26
to a pair of spaced apart points on a pipe
28 to measure the flow of a fluid
therethrough. A flange arrangement
30 is disposed on pipe
28 to facilitate
the connection of impulse lines
24 and
26 to pipe
28. For
the indicated flow direction, impulse line
24 is a high-pressure line and
impulse line
26 is a low pressure line. The fluid pressure, velocity and
elevation on the high pressure side are denoted by p
1, u
1 and z
1,
respectively. The fluid pressure, velocity and elevation on the low-pressure side
are denoted by p
2, u
2 and z
2, respectively. First and second
flange arrangements each disposed on a respective impulse line
24 and
26
flank DP-cell
22. The first and second flange arrangements operate to facilitate
the service of DP-cell
22. DP-cell
22 is operative to provide a pressure
signal that is a difference between p
1 and p
2. According to Bernoulli,
the pressure drop p
1-p
2 can be modeled as:
where ρ is the average density.
Referring to FIG. 2, another test setup
40 includes a DP-cell
22
that is connected via impulse lines
24 and
26 to a pair of spaced
apart points on a process vessel
42 for the measurement of a level of liquid
44 contained in process vessel
42. Impulse line
24 is connected
to process vessel
42 in the liquid containing portion of thereof, and preferably
near the bottom of process vessel
42. Impulse line
26 is connected
to a vapor containing portion of process vessel
22.
Referring to FIG. 3, a level maintenance system
50 includes a liquid
distillation column
52 (or any drum for that matter) that is interconnected
with a sensor
54, a level controller
56 and a drain valve
58
for the maintenance of the level of liquid
44 at a desired level in distillation
column
52. Sensor
54 is a DP-cell based sensor that provides an output
signal proportional to a difference in pressure between the liquid containing portion
and the vapor containing portion of column
52. It also converts the pressure
difference signal to a level signal. Level controller
56 compares the level
signal from the level transmitter
54 to a level set point. Level controller
56 provides an output signal to valve
58 to control drainage of liquid
44 from column
52 to maintain the level of liquid
44 at the
set point level. The level set point is provided by a user or an advanced control
application. Level controller
56 includes a computer with a processor, a
memory and a plugging detection program that controls either the valve opening
or the set point for a low-level flow regulatory controller. It also provides an
indication of the plugging state of the DP-Cell contained in sensor
54.
Referring to FIGS. 4 and 5, traces are shown for a normal and a frozen
temperature sensor (a resistance thermocouple in this case), respectively. The
x-axis represents sample numbers collected at a 1-minute frequency. As shown in
the FIGS. 4 and 5, there is a marked difference between a normal and a malfunctioning
temperature sensor, thereby making detection of a frozen temperature sensor rather easy.
Referring to FIGS. 6 and 7, the traces of the output of level sensor
54
are shown under normal and frozen conditions, respectively (the conclusion that
the sensor was frozen was deduced from what happened later on in the process).
The x-axis represents sample numbers collected at a 1-minute frequency. Unlike
the temperature sensor traces shown in FIGS. 4 and 5, detecting problems in a level
sensor is more difficult as there is very little difference between the normal
and frozen conditions. To a casual observer, the trace under normal conditions
appears to be more flat-lined. A small transient around sample numbers
500-
700
in FIG. 7 provides contradictory evidence to the fact that the sensor is indeed
frozen. This is because the frozen DP-cell may respond to changes in upstream or
downstream static pressure changes, albeit incorrectly.
Referring to FIGS. 8 and 9, traces of the output of level sensor
54
and the output of level controller
56, respectively, show the subtlety of
the frozen sensor detection problem. FIGS. 8 and 9 are continuations of FIGS. 6
and 7, respectively. From FIGS. 8 and 9, it is clear that level controller
56
starts to windup as a result of the frozen sensor around sample number
4250.
This process continues and leads to a loss of level and subsequent process upset.
It is at this point, that the operator realizes that the level sensor was frozen.
This is a commonplace occurrence in the process industry, wherein an apparently
small sensor problem leads to major upsets.
Referring to FIGS. 3 and 10, a separate level sensor translator
60
is provided to translate or convert the output of sensor
54, which is the
DP-cell signal p(t). Level sensor translator
60 converts the differential
pressure signal p(t) into a level signal L(t), which is provided to level controller
56. Level sensor translator may also include an analog to digital converter
to convert level signal L(t) to a digital signal for use by level controller
56.
Level controller
56 then operates on the level signal L(t) to provide an
output signal m(t). The controller output signal m(t) is proportional to the error
between the actual measurement L(t) and the set point Lset(t). Under a condition
of a constant set point, the level-to-flow relationship can be described using
the following set of model equations:
Unless stated explicitly, L(t), m(t) refer to appropriately scaled values,
typically with respect to the nominal range of the instrument. Since pressure is
a gross effect of randomly colliding atoms and molecules, the instantaneous value
of p(t) consists of two components as given by equation (1). These fluctuations
in the pressure introduce corresponding fluctuations in the level measurement and
the controller output as given by:
The component {overscore (L)}(t), {overscore (m)}(t) is an ensemble average and
corresponds to a net effect of measured/unmeasured disturbances acting on the process
and user initiated set point changes. These disturbances are collectively called
process factors herein. The rate of change of this component is relatively slow
compared to the sampling rate Δt. The component L(t)′, m(t)′
is a net effect of turbulent flows and transducer noise. The rate of change of
this component is relatively fast compared to the sampling rate. The method of
the present invention monitors the variance introduced by process effects compared
to that introduced due to turbulence effects. A frozen sensor is signaled by a
drastic change in their relative proportions.
A test statistic θ(t) that monitors various statistical properties of these
fluctuations is derived below. This test statistic forms the basis of either accepting
or rejecting the frozen sensor hypothesis. Mathematically, the frozen level sensor
test is formulated as:
where, θ(t) is a function of L(t), m(t) and δ
f is the
threshold for acceptance.
The method of the invention monitors the variance introduced by process factors
and turbulence by comparing their statistical properties. This is done by applying
a high-pass filter in the form of a first difference to the measurement signal.
Although, the first difference may not completely remove the effect of process
factors, it will reduce its influence considerably and thus make it statistically
comparable to the variance introduced by turbulence. Secondly, the first difference
has the effect of statistically amplifying the variance introduced by turbulence
(The variance is doubled). Let ΔL(t) and Δm(t) denote the first difference,
which is defined as follows.
##EQU1##
where, t-1 denotes the instantaneous value at the previous sample. Similarly,
Let S
L2(t), S
m2(t) denote the variance
calculated using N previous samples. Thus:
where, the var(·) of a uniformly sampled time series variable y(t) is
defined by:
##EQU2##
Suppose N is chosen such that statistically:
##EQU3##
In order to establish this criterion, with about 90% confidence, a minimum of
10 samples must be collected within Tmin/3 time windows, where Tmin is the smallest
process time constant. For example, if the process time constant is of the order
of an hour, then sampling every minute will satisfy the above criterion. For this
example, 10 samples are collected every 20 minutes (one hour/3 time windows) so
that at least one sample is collected every two minutes. Substituting equation
(12) in the definition of S
2, L(t) and S
2
m(t) gives:
##EQU4##
##EQU5##
Equations (13) and (14) clearly show that, for an appropriate number of
samples N and a sampling interval Δt, the variance of the first difference
of a sampled times series measurement y(t) is composed of two components:
- 1. The first component, S{overscore (y)}2(t),
corresponds to a variance introduced as a result of process effects. In other words,
over a window of N samples,
##EQU6##
- represents the fraction of the variance that is accounted by process factors.
- 2. The second component, Sy′2(t), corresponds
to a variance introduced as a result of turbulence and transmitter circuits. In
other words, over a window of N samples, Sy′2(t),
corresponds to a variance introduced as a result of turbulence and transmitter
circuits. In other words, over a window of N samples, Sy′2(t)
represents the fraction of the variance that is accounted by random effects like turbulence.
In addition to the physical interpretation, the two components are different
mathematically.
Although, the occurrence of process factors cannot be determined once they occur,
the net effect on the process is systematic. The effect of turbulence, on the other
hand, is random. This mathematical difference is exploited in the formulation of θ(t).
Define X(t)=└S
L2(t) S
m2(t)┘
T
and the 2×2 covariance matrix cov X(t) as follows:
##EQU7##
where, M is called the frozen sensor detection window and M>>N.
Typically, M is an order of magnitude larger than N.
Consider a principal component analysis (PCA) of the covariance matrix of
equation (15). A PCA decomposition of cov X(t) gives:
Eigen Values: Σ(t)=[σ
1(t) σ
2(t)]
Eigen Vectors: V(t)=[ν
1(t) ν
2(t)]
Finally, define the test statistic θ(t) as follows:
##EQU8##
At every instant, X(t) is made up of four components:
##EQU9##
S
L′2(t), S
m′2(t),
of which two of these components
##EQU10##
are due to process effects and the remaining two components (S
L′2(t)
and S
m′2(t)) are due to random turbulence effects.
The singular values of the covariance matrix are a composite measure of these four
components over the detection window M.
Consider the case such that the over the entire detection window M, Δ{overscore
(L)}(t), Δ{overscore (m)}(t)≈0, thus making
##EQU11##
From the sensor model equation (4 & 5) we get,
or
That is, the sample-to-sample variation in p(t), and hence in L(t) and m(t),
is solely due to random turbulence effects.
Now let us examine the covariance matrix under above mentioned condition.
##EQU12##
This makes cov X(t) singular (σ
2(t)→0) and θ(t)→∞.
This key result, upon which the frozen detection test is based, is re-stated formally
as follows:
- Theorem: Frozen sensor test statistic.
- For level sensor translator 60 of FIG. 10, if {overscore (p)}(t)→0,
then {overscore (L)}(t), {overscore (m)}(t)→0. The test statistic θ(t)
is given by equation (17)→∞.
- However, if the sensor were not frozen and was responding to process
factors, each element of the covariance matrix will have contributions from
##EQU13##
- making it non-singular and resulting in a smaller value for θ(t).
The theorem provides a sufficient condition under which a frozen sensor results
in
##EQU14##
- and, hence, θ(t)→∞.
The frozen sensor theorem is interpreted physically as: over the entire detection
window M, there was insignificant contribution to the overall variance due to process
effects. If M is chosen to be large enough, then this is very unlikely to occur,
unless there is some loss in the sensor response. In other words, the detection
window M is chosen to ensure that the process is subjected to a minimum of one
disturbance within MΔt time interval. This puts a minimum bound on the detection
window M. The question that needs to be answered before choosing M is: how often
do process disturbances occur? A typical value of 4-6 times the dominant time constant
is a good first guess.
The next question to be asked is whether the frozen detection theorem provides
the necessary condition. A zero value for
##EQU15##
does not necessarily imply that the sensor is frozen. Consider the following
example of a uniform ramp y(t)=kt:
##EQU16##
Therefore, the above mentioned trivial case needs verification before
applying the frozen detection theorem.
The principle of the detection algorithm is described graphically in FIG.
11.
Referring to FIG. 11, the test statistic θ(t) at current time t is
calculated over a window
62 consisting of N sensor signal samples. This
is compared with the baseline statistic developed based on a window
64 of
samples taken at an earlier time T. As stated earlier, the comparison is of a ratio
of a variance contribution due to process effects and a contribution due to turbulence
effects with those established by the baseline. Ideally the baseline is established
in a laboratory by careful calibration. However, in practice, the baseline value
is preferably updated to take into account the natural aging of the physical device
and associated pipes. Thus, when window
62 slides right upon arriving of
a new reading, the baseline calculation is also updated using a exponential weighted
moving average window scheme. Thus, the frozen sensor detection comparison is relative
to baseline established T samples ago.
According to the method of the invention, the sliding baseline calculation
is implemented using a recursive covariance matrix. The recursive formula is given
by:
##EQU17##
The ramp test given by equation (21) is done using a z-statistic, which tests
whether the mean of the first difference is statistically non-zero.
Referring to FIG. 12, a plugging detection program
70 at step
72
obtains a series of N samples of the DP-cell sensor. Consecutive windows advance
by at least one sample. Step
74 calculates a mean of the N samples of a
window. Step
76 tests the mean to determine a zero velocity condition. That
is, step
76 determines whether the fluid velocity is zero. For this determination,
step
78 generates a Z statistic and step
80 tests the Z statistic
for the zero velocity condition.
Step
82 calculates the variance of the N samples collected over the window.
Step
86 updates the baseline based on the output of step
82, a frozen
detection window M provided by step
88 and a previous baseline provided
by step
90 by using equation (22). Step
92 implements the frozen
detection theorem. That is, it develops a variance factor using the most recent
N values of the sensor signal, compares it with an updated baseline value and a
specified threshold. If the result of this comparison exceeds the threshold, the
variance factor or yes flag is generated. Step
94 develops the eigen values
by using equation (16). Step
96 uses the eigen values in equation (17) to
develop the test statistic θ(t). Step
98 compares the test statistic
θ(t) with the threshold and if greater, generates the variance factor flag.
Step
100 gives a frozen sensor notice or alert when the zero fluid velocity
condition and the variance factor flag are simultaneously developed.
During the frozen sensor development phase, the decisions about the following
parameters are made:
- 1. The number of samples, N, used in the calculation of the sample variance
given by equations (13) and (14)
- 2. The detection window size, M. As mentioned earlier, the larger the
size, the less likely of false positives.
- 3. The detection threshold, δf.
The method of the invention was applied to an example of a petrochemical plant,
with a sampling rate of 1 min. For this example, N=10 and a detection window of
M=50×N=500 samples was chosen. In order to determine the detection threshold,
δ
f, the test statistic θ(t) was calculated using data segments
over a two year period for which the operator reported no anomalies.
FIGS. 13-16 show traces of the test statistic θ(t) for four normal modes
of operation for the level sensor. As shown in FIGS. 13-16, θ(t) is relatively
the same for the four traces. A threshold of 1.6 was chosen based on visual inspection.
The traces of FIGS. 4-7 were developed from this same example. As shown in FIGS.
4-7 and discussed above, it was quite a challenge for the operator to detect a
frozen sensor.
Referring to FIG. 17, traces
110 and
112 of the test statistic
θ(t) for the same sensor is shown under normal and frozen conditions, respectively,
for the same value of N, M. Trace
112 demonstrate that the test statistic
θ(t) for the sensor is approaching a frozen condition as its magnitude for
the frozen condition is an order of magnitude higher than trace
110 for
a normal sensor (remember that the test statistic uses a logarithmic scale). Using
a threshold of 1.6, the problem could have been detected at least a day in advance.
As discussed earlier, frozen sensor detection is a very subtle problem. Heretofore,
the operator was able to detect this only when the controller wound-up completely.
In other words, for about a day, the process was operating with an incipient problem,
oblivious to the operations team.
As mentioned earlier, the method and control system of the present invention
monitors
the relative proportion between the variances introduced due to process effects
and due to turbulence. If the sensor is responding to process effects, additional
variance is added to the covariance matrix making it less singular. This is evident
from the scatter plot shown in FIG.
18. There is no dominant direction along
which the variance is scattered indicating that the covariance matrix is not singular.
On the other hand, as explained earlier, the covariance matrix for a frozen sensor
approaches singularity. This implies that there a dominant direction along which
the variance can be explained, making the columns of the covariance matrix redundant.
This can be seen in FIG. 19, which clearly shows a dominant direction and hence
absence of any cross-directional scatter that is normally introduced when the sensor
is responding to changes in the process factors.
The present invention having been thus described with particular reference to
the preferred forms thereof, it will be obvious that various changes and modifications
may be made therein without departing from the spirit and scope of the present
invention as defined in the appended claims.
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