Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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PLANT PARAMETER DETECTION BY MONITORING OF
POWER SPECTRAL DENSITFES
FIELD OF THE INVENTION
This invention relates to process control systems, and more
particularly, to a system for determining whether a process
parameter is in a steady or unsteady state through a use of
the parameter's power spectral density.
BACKGROUND OF THE INVENTION
In controlling dynamic plant processes, it is often
necessary to knc>w whether process variables are in a steady
state or in an unsteady state . While, many process control
systems monitor plant variables and compare them against
predetermined set points, it is often more important to
know whether deviations of a plant variable, over time,:
away from a setpoint are significantly different from
normal. It is also important to be able to predict
whether a plant: parameter output exhibits an incipient
condition which may lead to an unsteady state.
The prior art contains many teachings concerning plant
parameter monitoring for process control applications. In
U.S. Patent 4,744,041 to Strunk et al., the steady state
speed of a do motor is detected through the use of fast
Fourier transform analysis. Strunk et al employ a current
sensor which measures the current in a test motor and sends
the sampled current signal as data to a computer. The
computer then samples and stores measured instantaneous
current values at plurality of discrete times and performs
a fast Fourier transform on the steady state current to
determine its power spectral density. Based on the
computed power spectral density, the speed of the motor is
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determined by detecting the frequency at which maximum
power is used.
Kato et al., in U.S. Patent 4,303,979, disclose a system
for monitoring frequency spectrum variations in output
i
signals. The system initially determines an RMS average
frequency value for an input signal. In addition, it
determines RMS values for each of a plurality of frequency
subranges within the input signal. The system then
monitors an input test signal and obtains its RMS value and
the average frequency of the overall input signal. If the
determined reference and test frequencies differ
substantially in their RMS and average frequency values,
the RMS value and average frequency bf an anomalous
frequency component peak is calculated. The average of the
anomalous frequency component is then compared to boundary
frequency values to determine in which frequency range the
anomalous value lies. The RMS value of the thus determined
frequency range and the average frequency are then employed
to determine correction parameters.
Grassart, in U.S. Patent 4,965,757 discloses a process and
device for decoding a received, encoded signal. The
received signal is first filtered, sampled and digitized
before being stored. Digitized samples of each successive
signal block are transposed to the frequency domain by a
fast Fourier transform. The thus computed spectra are
compared with stored theoretical values for each possible
code signal in order to identify the received encoded
signal.
Schmidt, in U. S . Patent 3 , 883 , 726 , discloses a fast Fourier
transform algorithm computer that utilizes an attenuated
input data window. An input buffer receives input time
samples, a cosine square attenuator superimposes a cosine
squared shape on the input data samples, and then the
resultant signal is passed to the fast Fourier analysis
computer. A delay device, adders and an output buffer are
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provided for removing the effect of, the attenuating input
data window.
Toda et al, in U.S. Patent 4,975,633, disclose a spectrum
analyzer that displays spectrum data and power values of an
RF or optical signal. An input signal is directed down one
path where it is subj ected to a spectrum analysis, and down
a second path where its power value is determined. Display
means indicates both the spectrum data and the power value.
Murphy et al. , in U.S. Patent 5, 087, 873, disclose apparatus
for detecting a corrosion state of buried metallic pipe.
In Figs. 4-7, a spectrum analyzer receives input signals
from a pair of magnetometers. The magnetic field, as a
function of frequency, is determined by conducting a fast
Fourier transform on the received signals, with the
resulting spectrum indicating the amplitude and phase of
the magnetic field. Those values are used to determine the
condition of the buried pipe.
Demjanenko et al. in U.S. Patent 4,980,844 teach a method
for diagnosing mechanical conditions of a machine. The
Demjanenko et al. procedure is computationally complex and
involves the creation of one or more sets of reference
signatures (those reference signatures may be power
spectrum data). Similar test data is then acquired and a
comparison action occurs. The procedure averages the test
and reference signatures, determines a distance
therebetween (i.e. the Euclidean distance), compares that
calculated distance against a computed threshold value, and
classifies the distance as being normal or abnormal based
upon the comparison. The threshold is established as a
function of the mean reference distance and reference and
test standard deviations.
Toshiba Japanese patent application S62-245931 describes a
procedure for determining abnormalities in a rotating pump.
A plurality of reference frequency spectra are stored in
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memoxy (called restriction patterns), each reference
frequency spectrum indicative of an operational state of
the pump under different load cond~.tions. To cQn.serve
memory, a "bias" procedure i.s employed to modify a closest
reference frequency spectrum to bring it into the load
(i.e. power) range of a test fx'equency spectrum taken from
the pump , rf the test frequency spectrum exceeds l~.m~.ts
determined from the 'biased" reference frequency spectrum,
an alarm is given. The Toshiba system thus requires
1Q storage of a plurality of reference frequency spectra and
accurate modification of a chosen spectrum by application
of a bias va~.ue thereto to enable its comparison with a
test spectrum. Misadjustment of the bias can negate.the , ,
effectiveness of the test system.
Hartusiak ,et al. in PCT published Application wo 94/22025
describe a process signal detection technique that is
dependent upon power spectral densities. Reference data is
accumulated while a plan.t.operates at a steady state and
p includes the energy content of each of a plurality of
frequency components. A current operational database is
then established by sampling a process variable when the
' plant is in operation. The sampled current output signal is
analyzed to derive current data that includes the energy
content of each of a plurality of frequency components. For
each common frequency component of the reference data_and
' current data, the system makes a comparison of the energy
contents and issues a non-steady state signal if a
difference between the compared energy contents exceeds a
predetermined limit.
_..
.A.ccordingly, it is an object of this invention to provide
a method for determining when a process variable output
signal is in a steady state condition.
zt is another object of this invention to provide a method
for analysis of a parameter output signal to indicate an
incipient unsteady state.
,~~1ENDED SHEET
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It is still another of this invention to provide a plant
parameter output signal detection technique that is
dependent upon power spectral densities.
SUMMA1~Y OF THE INVENTION
A method for determining whether a current state of a
process variable output signal is within acceptable limits
includes the fo3.lowing steps: establishing reference data
1C by sampling a plant's pxocess variable output signal when
the plant is operating at steady State and analyzing the
sampled output szgnal to derive normalised reference data
including an energy content of each of a plurality of .
frequency components of the sampled output signal. The
procedure establishes a current operational data base by
sampling a process variable signal when the plant is in'
operation. The sampled current output signal is analyzed
to derive current data including a normalized energy
Content of each of a plurality of ~.ts frequency components.
40 For each common frequency component of the reference data
and the current data, the procedure compares their
normalized energy contents and issues a non-steady state
signal if the comparison indicates that the difference
between the compared energy contents exceeds a
predetermined limit.
DESGRIPTT_QN OF THE DRAWINGS
3C Fig. 1 zs a block diagram of a system for performing the
_~.
-- method of the invention;
Figs. 2a anal 2b are high level flow diagrams illustrating
the method of the invention;
Fig. 3 is a plot of a variation in flow over time in an
exemplary plant;
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Fig. ~ is a semi-log plot a~ er_ergy versus frequency
derived from the signal shown in Fig. 3;
Fig. 5 is a plot of flog vs. time showing a negative-going
ramp disturbance;
Fig. 5 is a semi-log plot of energy vs. frequency of the
plot of Fig. 5 indicating' the that the ramp disturbance
produces the most severe violation of plotted energy
10' thresholds in the low frequency range;,
Fig. 7 is a plot of flow vs. time showing a "U" type
disturbance in the f7.ow signal;
Fig. 8 ~.s a semi-log plot of energy vs. frequency of the
plot of Fia. 7 indicating, at one energy threshold, that.
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disturbance exceeds the threshold.
DETATLED DESCRIPTION OF THE IIv'VENTIdN
The system and method for carrying out the invention
determine whether a plant process is operating within a
steady state or a non steady state condition. Irz brief,
the system determines a reference power spectral density
(PSD) of a process variable, during' a time that the ~prflcess
a vaxiable is in a steady state . A power spectral. density is
a representation of an energy content of a sigxial as a
function of its component frequencies and is computed via
a fast ~Fourier transform (FFT) which converts a time-domain - -
s~.gnal into its frequency-domain representation.
I. 5
The signal from which the reference PsD is deriv~cl is .,
subjected to a first normalization procedure to derive a
zero mean basis fox the signal. This normalization is
accomplished by subtracting the mean process variable value ~ .
20 of a time series of sample data values from each time
series sample data value. A second normalization procedure
is performed or_ the spectral data by di.~iding each power
value in the spectrum by the number of time series signal
' samples used to compute the spectrum. The first
normalization procedure enables a single stored reference
PSD .to be used as a reference in all subsequent test
procedures. and eliminates the need for plural reference
spectra ar for a biasing procedure to adjust the reference
spectra. The second normalisation procedure enables the
3p reference PsD to be compared. to a current PSD, even in the
event that the time windows differ during win,a.ah the current
and reference PS1~'s are der~.ved. -
The reference PSD is compared with a current PSD derived
3S when the process variable is in operatiozx_ The current 15SD
i.s also subjected to the first and second normalization
4
procedures described above with respect to the reference'
PSD. If the current FSD is too energetic (either with
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respect to slow changes like ramps or with respect to fast
changes like spikes) relative to the reference PSD, the
process variable i.s determined to be unsteady and such
condition is signaled.
Turning to Fig. 1, flow monitors 10 and 12 continuously
monitor the state of flow in a pair of pipes 14 and 16,
respectively. Pipes 14 and 16 form portions of a plant
whose process variables are continuously monitored to
determine if any one has moved from a steady state to a
unsteady state. Those skilled in the art will realize that
the representation of inputs from pipes 14 and 16 is merely
exemplary and that a plurality of other types of system
variables (e.g. pressure, volume, temperature, etc.) can be
monitored. The outputs from each of flow monitors 10 and
12 are fed to respectively connected analog to digital
converters (A/D) 18, 20 whose outputs are, in turn,
connected to a bus 22 that forms the main communication
pathway in a control data processing system.
A central processing unit (CPU) 24 is interconnected with
bus 22 and also is connected to A/D converters 18 and 20 to
enable timed, sample signals to be derived therefrom. A
read only memory (ROM) 25 is connected to bus 22 and
contains a procedure for operating CPU 24 to monitor
sensors 10, 12 and a procedure for enabling CPU 24 to
perform a fast Fourier transform (FFT) of input data
received from A/D converters 18 and 20. A random access
memory (RAM) 26 is connected to bus 22 and contains
allocated memory for storing: raw input data from A/D
converters 18 and 20; reference PSD data determined during
a time that a process variable being monitored is in a
steady state; and current PSD data that is determined when
the process variable is being currently monitored.
The operation of the system of Fig. 1 will now be described
in conjunction with the flow diagram shown in Figs. 2a and
2b. Initially, a steady state (i.e. reference) PSD is
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determined for a monitored process variable. The steady
state PSD is derived by initially time sampling a process
variable output signal when the plant is operating in a
steady state condition (box 30) . To avoid contamination of
the steady state PSD, the time sampled output signal is
filtered to remove aperiodic signals therefrom (box 32).
The filtered output samples are then normalized to a zero
mean basis by subtracting the mean process variable value
of a time series of sample data values from each time
series sample data value. This eliminates any bias that is
operating-state dependent (box 33).
The filtered, normalized periodic sample signals are then
subjected to an FFT analysis by central processor 24, under
control of a procedure read out from ROM 24 (box 34). A
second normalization procedure eliminates any bias that
results from the time window during which the time series
samples were detected. The second normalization procedure
divides each spectral frequency data value by the number of
time samples so as to achieve a "time" normalization of the
frequency data.
The result of the PSD analysis is a series of normalized
energy values at frequencies (c~~) for the filtered steady
state signal, each normalized energy value at a frequency
(off) having an attribute associated therewith that is
proportional to the energy contained in the particular
frequency signal. Those frequencies. and energy value
attributes are stored in RAM 26 as steady state (or
reference) PSD data.
At this point, a user-supplied multiplier factor is
accessed that is to be applied to each energy value
attribute of the steady state PSD. The multiplier factor
enables the derivation of an energy threshold which is the
amount that a process variable's current PSD must exceed a
reference PSD to be considered in an unsteady state (box
36) .
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The system of Fig. 1 now switches to a "current" monitor
state wherein it monitors the outputs of sensors 10, 12,
etc. During the time that any one sensor is monitored, iJts
output is converted by an FFT procedure to a PSD
representation which is then compared with the previously
' derived steady state PSD for the same sensor (i.e. is
stored in RAM 26). CPU 24 commences the current monitor
state by sampling output signals from a sensor (e.g. 10)
during operation of the plant (Box 38). After sufficient
samples have been accumulated, CPU 24 filters the sampled
current output signal to remove aperiodic components (box
39), normalizes the filtered output signal to a zero-mean
basis (identically as with the reference PSD) (box 40) and
then computes a PSD(o~) for the sampled current output
signal using an FFT procedure (box 41). Each spectral
frequency data value is now divided by the number of time
series samples to achieve a "time" normalization of the
frequency data. Time normalizing of both reference and
current PSD data enables those data to be compared even if
different time windows are used during their detection.
It is now determined whether any current PSD (o~) is
greater than its corresponding steady state PSD (~~),
multiplied by the user-inputted multiplier factor (boxes
42,44). If yes, the system outputs the value of o~ at
which the maximum energy ratio is found and a signal is
issued that the process variable is in a non steady state
condition (box 46).
If the decision indicated in decision box 44 is that no
current PSD(c~~) exceeds the multiplier factor times the
steady state PSD(o~), then it is determined that the
sampled current output signal is in a steady state
condition and no further action is required. At this
' 35 point, the procedure terminates and CPU 24 may then monitor
another current process variable signal and the procedure
is repeated.
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Figs. 3-8 contain examples of the procedure described
above.- In Fig. 3, a process variable (flow) is plotted
over a period of several hours (126 minutes). Each dot on
the plot trace evidences a sampled flow value that is input
5 to the system. Prior to monitoring the current flow
values, a reference flow during steady state of the same '
process variable was monitored and a reference PSD was
derived (e.g. dotted trace 100 in Fig. 4). Reference PSD
trace 100 has been quantized into ten "bins" so as to
10 enable averaged comparisons to be made. The PSD for the
signal of Fig. 3 is then calculated (trace 102) and is seen
to exhibit considerable variations in power over the
frequency spectrum.
Turning to Fig. 5, a ramp disturbance 103 is plotted (flow
vs. time). Furthermore, for exemplary purposes only, it
is assumed that two multiplier factors (e.g. 1.0 and 1.5 )
have been utilized to derive energy PSD thresholds 108 , 110
respectively. The conversion of ramp signal 103 to a PSD
results in energy versus frequency trace 106 shown in Fig.
6. Note that the ramp disturbance 103 produces the most
severe violation of both PSD energy thresholds 108 and 110
in the low frequency range. Under such conditions, an
alarm is generated. The system may be adjusted such that
an alarm is inhibited from issuance if only energy
threshold 108 is exceeded, however the frequencies at which
the energy exceeds threshold 108 may be output for user
monitoring of a possibly incipient instability mode.
In Fig. 7, a "U" disturbance 113 is depicted in a plot of
flow versus time. Over the span of the time during which
the flow is monitored in Fig. 7, the flow difference is not
large and yet it is clear that a disturbance does occur. -
As shown by Fig. 8, such disturbance is picked up by
comparison of the peak corresponding PSD trace 112 with
energy threshold 114.
It should be understood that the foregoing description is
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only illustrative of the invention. Various alternatives
and modifications can be devised by those skilled in the
art without departing from the invention. Accordingly, the
present invention is intended to embrace all such
alternatives, modifications and variances which fall within
' the scope of the appended claims.
