## Abstrict There is described herein a method of obtaining a measure of flow
from an electromagnetic flow meter having at least one field generating
coil and potential sensing electrodes. A composite excitation waveform
is applied to the field-generating coil. The composite excitation
waveform comprises at least two frequency components and a plurality
of frequency components are simultaneously present for at least
a portion of the waveform. The potential sensed by the potential
sensing electrodes is sampled to produce a sampled output and the
sampled output is correlated with a composite waveform based on
the composite excitation waveform. The result of the correlating
is used to derive a measure of flow.
## Claims What is claimed is:
1. A method of obtaining a measure of flow from an electromagnetic
flow meter having at least one field generating coil and potential
sensing electrodes, the method comprising: applying, to the at least
one field generating coil, a composite excitation waveform comprising
at least two frequency components, wherein a plurality of frequency
components are simultaneously present for at least a portion of
the waveform; sampling a potential sensed by the potential sensing
electrodes to produce a sampled output; correlating the sampled
output with a composite waveform based on the composite excitation
waveform; and deriving a measure of flow based on the result of
the correlating.
2. A method according to claim 1 wherein the waveform comprises
a set of components, each having a pre-specified amplitude and frequency.
3. A method according to claim 1 wherein the composite waveform
is non-sinusoidal.
4. A method according to claim 1 wherein the composite waveform
is digitally synthesised.
5. A method according to claim 1 wherein correlation is performed
over a window which does not contain an integer number of periods
of all frequency components.
6. A method according to claim 5 wherein the window is shorter
than the period of the lowest frequency component.
7. A method according to claim 1 wherein correlating comprises
determining a measure of closeness of fit.
8. A method according to claim 1 further comprising deriving a
factor from said correlating, and deriving a measure of flow from
the factor.
9. A method according to claim 1 further comprising determining
a measure of a trend within a correlation window.
10. A method according to claim 9 further comprising subtracting
the measure of trend from the output sample.
11. A method according to claim 9 further comprising determining
a measure of measurement accuracy from the measure of trend.
12. A method of processing a signal, comprising correlating sampled
output data of the signal with a reference signal, and determining
both a measure of a physical quantity, and a measure of a trend
within the data over a measurement period based on the correlating.
13. A method according to claim 10 wherein the processing signal
is the output of an electromagnetic flow meter.
14. A method according to claim 10 wherein the physical quantity
is flow.
15. A method according to claim 10 further comprising determining
a measure of a linear trend.
16. A method according to claim 12 further comprising fitting
the sampled output data with reference data, wherein the reference
data comprises an expected signal multiplied by an unknown factor
and a trend of unknown gradient, determining values for the factor
and for the gradient which gives the best fit according to a predetermined
fitting method, determining a measure of physical quantity from
the value of the factor, and determining a measure of confidence
or accuracy from the gradient.
17. A method according to claim 16 wherein the physical quantity
is flow.
18. A method according to claim 16 wherein fitting further comprises
determining a sum of squares of differences between the reference
data and sampled output data.
19. A method according to claim 16 wherein the reference data
includes a constant unknown offset.
20. A method according to claim 19 further comprising determining
a value for the offset to improve the fit.
21. A method according to claim 20 wherein the offset value is
determined but the measure of accuracy or confidence is based primarily
on the value of the gradient.
22. A method according to claim 12 wherein calibration parameters
for the meter are stored, and the method further comprises adjusting
at least one calibration parameter for the meter based on a plurality
of measurements of at least one of trend, accuracy, and confidence.
23. A method of operating a flow meter, comprising: storing calibration
parameters for the meter; and adjusting at least one stored parameter
as successive flow measurements are derived based on a plurality
of measures of accuracy of the flow measurements.
24. A method according to claim 23 further comprising adjusting
at least one stored calibration parameter to reduce a measure of
trend or to improve a measure of accuracy or confidence based on
successive measurements.
25. A method according to claim 23 wherein the calibration parameters
include at least one of phase and amplitude response.
26. A method according to claim 25 wherein the calibration parameters
are stored for multiple frequency components.
27. A method according to claim 26 further comprising adjusting
at least one calibration parameter for a first frequency component
in response to measurements, and retaining at least one corresponding
calibration parameter for a second frequency component at an initial
setting.
28. A method according to claim 27 wherein the first frequency
component has a higher frequency than the second frequency component.
29. A method according to claim 28 wherein all calibration parameters
for the lowest frequency component are kept constant.
30. A method according to claim 23 further comprising performing
weighted filtering on measurements of flow based on the measure
of at least one of trend, accuracy, and confidence.
31. A method of determining error between a signal and a corresponding
reference signal, wherein each signal comprises a plurality of sampled
values in a sampling interval, the method comprising: defining a
plurality of sub intervals, each sub interval containing a respective
subset of the plurality of sampled values; determining an algebraic
sum for each sub interval of the difference between signal sample
values and reference signal sample values; and determining an absolute
sum of the algebraic sums for each sub interval as an error estimate
for the sampling interval.
32. A computer readable medium having a program for executing a
method of determining error between a signal and a corresponding
reference signal, wherein each signal comprises a plurality of sampled
values in a sampling interval, the method comprising: defining a
plurality of sub intervals, each sub interval containing a respective
subset of the plurality of sampled values; determining an algebraic
sum for each sub interval of the difference between signal sample
values and reference signal sample values; and determining an absolute
sum of the algebraic sums for each sub interval as an error estimate
for the sampling interval.
## Description CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is related to U.S. patent application Ser.
No. ______, Attorney Docket No. MATH2.001AUS, filed on the same
day as the present application, having the same inventor as the
present application, and entitled "ELECTROMAGNETIC FLOW METER".
The disclosure of the above-described filed application is hereby
incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to electromagnetic flow meters.
However, aspects of signal processing techniques disclosed herein
may be more broadly applied. The operating principles of Electromagnetic
Flow Meters are well known, discussed for example in GB-A-2380798.
[0003] Where the sensing electrodes are in contact with the fluid,
due to electrochemical or other effects, a DC potential is usually
present across the electrodes even when there is no coil excitation,
i.e. no field. That component of the signal is independent of the
flow. This inhibits the ability to determine the flow in a static
fashion. To overcome this some form of dynamic excitation to the
coils is typically provided in order to generate a dynamic component
at the electrodes that can be differentiated from the background
DC (or slowly varying) bias signal. This dynamic signal is normally
pulsed DC or an AC signal.
[0004] The bias signal will not generally be static. It may drift
randomly with time, flow and temperature. In some applications,
particularly for non-homogeneous fluids with inclusions, the signal
may contain large amplitude decaying exponential components, for
example in paper pulp and slurry applications, as discrete charged
particles occasionally touch the electrodes, changing the voltage
instantaneously and this voltage then discharges exponentially to
the (drifting) baseline.
[0005] The energy can be spread across a wide frequency range but
most applications have significant low frequency noise and this
is often more problematic due to the nature of the signal processing.
[0006] Therefore, one way to obtain flow measurements which are
less susceptible to such effects might be to use a high frequency
excitation, above most of the noise effects. It is found that a
frequency above about 1 kHz would for most practical purposes exclude
most bias effects. However, using such a frequency would introduce
its own problems. Most notably, the magnetic circuit of the flow
meter is less stable at the higher frequencies. One factor that
contributes to this is that the losses in the magnetic circuit,
which become more significant at higher frequencies, are quite temperature
dependent. Thus, for a given excitation, the field strength generated
may vary unpredictably. This can be exacerbated because the excitation
coils are usually positioned outside a steel shell of the flow meter.
A search coil can be used to measure the actual field generated
but this adds significant cost and manufacturing difficulties.
[0007] The `roll off` of the sensor head at these higher frequencies
leads to an uncertainty in the sensitivity of the sensor and to
variations in the phase between the field (and hence the electrode
signal) and the drive current. It is known to use a moderate frequency
(e.g. 70 Hz) sinusoidal excitation and to demodulate the electrode
signal synchronously with the excitation signal. Quite apart from
other considerations, the phase angle at which the demodulation
is (should be) carried out is not constant and requires either manual
or automatic adjustment.
[0008] To summarise the problems a lower drive frequency can give
much better sensor stability but measurements are more easily corrupted
by the bias drift and the effect of inclusions in the fluid. A further
important problem is that a low excitation frequency limits the
rate at which new measurements can be updated--it gives a low flow
measurement bandwidth. A higher frequency assists in distinguishing
wanted signals from unwanted and also allows a more acceptable higher
flow measurement bandwidth but the sensor characteristics will not
be so precisely defined and are less stable. The frequency chosen
is therefore normally a compromise for a particular set of circumstances.
[0009] These problems have been previously addressed and it has
been proposed in the assignee's earlier filed UK patent application
no. 0116168.6 to excite a meter with two frequencies simultaneously
or quasi-simultaneously. Each frequency component is separately
extracted and a combined measurement obtained in such a way as to
enhance the better properties of each measurement. A drawback is
that measurement rate is still limited by the lowest frequency,
as explained in more detail below.
SUMMARY OF CERTAIN INVENTIVE EMBODIMENTS
[0010] According to a first aspect the invention provides a method
of obtaining a measure of flow from an electromagnetic flow meter
comprising applying a composite excitation waveform comprising a
plurality of frequency components; receiving an output from the
meter; and correlating sampled output data from the meter with a
composite correlation waveform based on the composite excitation
waveform to derive a measure of flow.
[0011] In this method, by taking the novel step of correlating
with a composite waveform, rather than the conventional method of
correlating each frequency component with a sine wave, a number
of advantages can be obtained. Although the composite waveform will
effectively contain multiple frequency components, it has been found
that it is not necessary to process each component separately and
thus measurement rate is not limited by the lowest frequency component.
Furthermore, additional information is obtained from the combination
of the components (the shape of the waveform) as well as the components
themselves.
[0012] Preferably the meter is excited with a composite excitation
waveform obtained by combining at least two frequency components;
in this way the composite waveform can easily be selected to contain
frequency components which excite desired properties, for example
a relatively high and relatively low frequency. The composite waveform
will preferably not be completely sinusoidal. The composite waveform
preferably is substantially devoid of sharp turning points (these
are associated with numerous high frequencies which may behave unpredictably).
The composite waveform is preferably digitally synthesised. The
frequency components are preferably combined at pre-determined,
preferably similar, for example within a range of minimum to maximum
of 1 to 5 or less, preferably 1 to 3 or less, amplitudes. The amplitudes
(and phases) may be chosen to enhance the prominence of turning
points in the waveform.
[0013] The composite waveform preferably has a plurality of turning
points within a predetermined measurement window period; it is found
that multiple turning points or "features" may assist
in obtaining accuracy.
[0014] More than two components may be used and provision of three
or four components may enhance accuracy, by giving more features
to the waveform. However, it is preferable that the number of components
is limited, for example to less than about 10 preferably less than
5 components and/or that the highest frequency component with significant
amplitude has a frequency no greater than about 1 kHz. Diminishing
returns are achieved with greater than about 5 components, but in
some cases a few more components may be used.
[0015] Whilst an arbitrary waveform can theoretically be approximated
by an infinite number of sine and cosine waveforms, such approximations
tend to require a large number of harmonics to converge accurately
and this implies a large number of high frequencies which would
behave unpredictably in a real meter. By limiting the number of
components, most preferably by synthesising the composite waveform
from a discrete set of components, each having a chosen amplitude,
the effects of the individual components and the overall response
becomes more predictable.
[0016] Although the higher frequency may be an integral multiple
of the lower frequency, it is not necessary for the frequencies
to be harmonically related. Even when two frequencies are integral
multiples of each other, it is not necessary to include intervening
harmonics. Thus the composite waveform may comprise at least two
frequencies which are not harmonically related to each other. Alternatively,
the composite waveform may comprise two frequencies of which a higher
frequency is a harmonic of a lower frequency but in which at least
one intervening harmonic of the lower frequency is substantially
absent. Preferably, when the higher frequency is an odd harmonic,
at least one intervening odd harmonic may be substantially absent
and/or when the higher frequency is an even harmonic, at least one
intervening even harmonic may be substantially absent.
[0017] An advantageous feature is that correlation may be performed
over a window which does not contain an integer number of periods
of all (or any) frequency components. The window may be shorter
than the period of the lowest frequency component; this enables
measurement to be obtained with a higher bandwidth than the lowest
frequency.
[0018] Correlating preferably comprises determining a measure of
closeness of fit. A factor may be derived from said correlating
and a measure of flow may be derived from the factor. A measure
of a trend within a correlation window may be determined and a measure
of measurement accuracy may be determined from the measure of trend.
[0019] With traditional methods of measurement, it is difficult
to reduce sensitivity to trends in the baseline reading, e.g. due
to zero offsets. Pursuant to the invention, it has been appreciated
that in fact, particularly with the techniques disclosed herein
(but other techniques which give multiple measurement may be used),
trends (particularly baseline trends) in the meter data can usefully
be measured and can be used to determine or improve meter accuracy.
[0020] According to a further aspect, the invention provides a
method of processing the output of an electromagnetic flow meter
comprising correlating sampled output data with a signal to determine
a measure of flow and a measure of a trend within the data over
a measurement period.
[0021] The trend may provide data about the meter or may simply
account for interference during the measurement period.
[0022] A measure of a linear trend may be determined. Additionally
or alternatively a measure of an exponential trend (e.g. a decaying
exponential) may be determined. Advantageously an exponential or
linear trend may be approximated by a polynomial. In a preferred
arrangement a low order polynomial trend, preferably second or third
order, is fitted to the data--this can effectively remove linear
or exponential trends without interfering substantially with fitting
of the data. The sampled output data may be fitted with reference
data comprising an expected signal multiplied by an unknown factor
and a trend of unknown gradient (or polynomial coefficients) to
determine values for the factor and for the gradient (or polynomial)
which gives the best fit according to a predetermined fitting method,
preferably a least squares fitting method. Using higher order polynomials
to model trends trends leads to diminishing returns. Preferably
a measure of flow is determined from the value of the factor. Preferably
a measure of confidence or accuracy is determined from the gradient.
The predetermined fitting method may comprise determining a sum
of squares of differences between the reference data and sampled
output data. The reference data may include a constant unknown offset.
A value for the offset may be determined to improve the fit. However,
advantageously, the offset value may be determined but the measure
of accuracy or confidence is based primarily on the value of the
gradient. Calibration parameters for the meter may be stored, the
method further comprising adjusting at least one calibration parameter
for the meter based on a plurality of measurements of trend or accuracy
or confidence.
[0023] According to a further aspect, the invention may provide
a method of operating a flow meter comprising storing calibration
parameters for the meter and adjusting at least one stored parameter
as successive flow measurements are derived based on a plurality
of measures of accuracy of the flow measurements.
[0024] Preferably at least one stored calibration parameter is
adjusted to reduce a measure of trend or to improve a measure of
accuracy or confidence based on successive measurements.
[0025] Calibration parameters may include at least one of phase
and amplitude response. Preferably calibration parameters are stored
for multiple frequency components. At least one calibration parameter
for a first frequency component may be adjusted in response to measurements
whereas at least one corresponding calibration parameter for a second
frequency component may retained at an initial (e.g. factory calibration)
setting. The first frequency component may have a higher frequency
than the second frequency component. Preferably calibration parameters
for the lowest frequency component are all kept constant.
[0026] Weighted filtering may be performed on measurements of flow
based on the measure of trend or accuracy or confidence.
BRIEF DESCRIPTION OF THE DRAWINGS
[0027] An embodiment of the invention will now be described, by
way of example only, with reference to the accompanying drawings
in which:
[0028] FIG. 1 shows an example time window with two components
for the case of two frequency components and a good fit;
[0029] FIG. 2 shows another example of a good fit with four frequency
components;
[0030] FIG. 3 shows an example similar to FIG. 2 but exhibiting
a poor fit;
[0031] FIG. 4 illustrates removal of a trend from data;
[0032] FIG. 5 shows the expected "pure" signal from the
electrodes of an electromagnetic flow meter of an embodiment;
[0033] FIG. 6 is a schematic diagram of apparatus according to
an embodiment;
[0034] FIG. 7 illustrates error processing using an SSE approach;
[0035] FIG. 8 illustrates an enhanced method for determining errors;
[0036] FIG. 9 shows a flow signal as determined by an LSE fit algorithm;
[0037] FIG. 10 shows flow after filtering;
[0038] FIG. 11 shows a flow profile;
[0039] FIG. 12 shows the added noise zoomed in so the total window
is about 0.2 seconds long;
[0040] FIG. 13 shows derived flow values;
[0041] FIG. 14 shows the error estimates for each of several windows;
[0042] FIG. 15 shows noise added (over a 6 second window);
DETAILED DESCRIPTION OF CERTAIN INVENTIVE EMBODIMENTS
[0043] The method underlying the invention and a background method
will first be explained.
[0044] As noted above, single frequency measurement in an electromagnetic
flow meter is a compromise. To assist in understanding the invention,
an earlier technique will first be explained in more detail which
applies two frequencies simultaneously and then resolves the two
components of the electrode signal separately. This gives some of
the benefits of each frequency. Such a system is disclosed in the
assignees earlier filed UK patent application no. 0116168.6 hereby
incorporated by reference.
[0045] As a specific example, consider a system using 10 Hz and
70 Hz excitation simultaneously. At 10 Hz, the sensor characteristics
can be assumed to be stable but the results will be influenced by
noise. At 70 Hz, the signal is easier to recover but since the sensor
characteristics are less well defined, the flow signal is correspondingly
less well defined.
[0046] A basic system could use the zero measurement from the 10
Hz `channel` as the reference zero. The 70 Hz channel could then
be used to obtain a measurement with the benefits of the higher
frequency excitation and the zero would be `anchored` to the 10
Hz value.
[0047] Doing the 10 Hz correlation in the presence of the 70 Hz
component is not problematic; the higher frequency is an integral
multiple of the lower frequency (this is a constraint of the method)
and an integer number of cycles of an interfering frequency in the
correlation window does not cause a problem. However, performing
the 70 Hz correlation is problematic. It is necessary to arrange
that the correlation window to contain an integer number of both
the 70 Hz and the 10 Hz signals in order to get an accurate result.
This means that the window length for the 70 Hz signal should be
at least 0.1 seconds and hence measurement bandwidth is limited
to that of the lower frequency, 10 Hz. Thus, although some noise
may have been reduced and stability gained, the measurement bandwidth
is still limited by the lower frequency.
[0048] The assignee's earlier filed application in fact discloses
a more sophisticated technique with complementary high and low pass
filters but again the measurement bandwidth is limited by the lower
frequency.
[0049] In conventional multi-frequency analysis, the fact that
superposition applies (or is assumed to apply) is a useful basis
for simplifying calculations; it allows the components to be resolved
independently even if applied simultaneously as if the others were
not there (although this is subject to some limitations).
[0050] In the present invention, a composite waveform is applied,
and this can be considered to be applying multiple excitation frequencies
simultaneously (the coil excitation is the sum of a number of discrete
sine waves). An important difference between embodiments of the
invention and prior multi-frequency techniques is that the electrode
signal is analysed for all components simultaneously by correlating
the actual electrode signal with the expected electrode signal,
rather than by detecting each frequency component separately.
[0051] To assist in explaining the invention an example window
in time is shown in FIG. 1.
[0052] The "curve 1" line shows the expected electrode
signal, the "curve 2" noisy data is the actual electrode
signal. The magnitude of the correlation is then the magnitude of
the (curve 1) curve that gives the best fit to the (curve 2) data.
In the figure, the fit is already optimal.
[0053] Note that in this example, there are two frequency components
and both have an integer number of cycles in the window. In this
case, resolving the two frequencies separately would give similar
results to treating the composite waveform as one signal. In this
case, the inventive method may offer an advantage in the processing
but it is noted that the measurement should be similar to that obtained
by treating the components separately.
[0054] FIG. 2 shows another example where the inventive method
gives a significant advantage. In this example, there are four frequency
components, two of them containing less than one complete cycle
in the window.
[0055] Provided the expected signal is known then one of the great
benefits of this technique is that it does not depend on any or
all of the components having an integer number of cycles within
the window.
[0056] Conceptually, one may look for the `pattern` (curve 1) in
the data (curve 2). In principle, the more complex curve 1 the
more distinct a pattern being looking for.
[0057] Relative to the window above, the four frequency components
have frequencies 1 2 0.5 and 0.25. The four frequencies are 40
Hz (1 cycle in the window) 80 Hz, 20 Hz and 10 Hz. In this example,
the frequencies are harmonically related. In practice, using a digital
signal processor (DSP), it may often be convenient to produce frequencies
which are integer sub-multiples of a common frequency and this will
often mean that the higher frequencies are harmonics of lower frequencies
but it is not necessary for the components to be related.
[0058] The ability to fit without requiring a whole number of cycles
of all of the frequencies provides significant advantages.
[0059] It is advantageous from a `distinctiveness` point of view
to have several turning points in the waveform within the window,
hence the choice of frequencies and window length.
[0060] Ignoring zero offsets and noise for the moment then the
expected signal from the electrodes should be of the form shown
in FIG. 5 and the amplitude should be directly proportional to the
value of flow. For example, if FIG. 5 represents the received signal
at a flow of 1 m/s then a flow of 0.5 m/s should give half the amplitude,
a flow of 0 m/s would give a flat line and a flow of -1 m/s would
give the same signal as FIG. 5 but inverted.
[0061] Note that this waveform shape is not intended to be fixed
or indeed optimal. As noted above, the example happens to use harmonically
related frequencies. This is not necessary and may not be the most
advantageous arrangement. In any event it should be recognised that
the pattern being matched will change from window to window.
[0062] In this case of no zero offsets, the waveform can be fitted
using simple and well known Least Squares; the amplitude of the
red curve is the one that minimises the sum of the square of the
errors between the two sets of the data.
[0063] If the expected signal is P.sub.i and the received signal
is represented by Y.sub.i then one should find the factor F such
that:
.SIGMA.(Y.sub.i-F.multidot.P.sub.i).sup.2
[0064] is a minimum. In this case, the only degree of freedom is
F and one may simply choose F to minimise the SSE.
[0065] However, working with real world data, it has been recognised
that the signal being fitted is continually corrupted by a varying
offset and the offset may vary within the window being fitted.
[0066] Two extra degrees of freedom have been introduced, namely
a slope and an offset. Now the SSE equation that is to be minimised
becomes: 1 i ( Y i - F P i - M i - C )
[0067] Referring to FIG. 4 curve 1 represents the incoming data
with a clear trend on it. Curve 2 represents the same data after
fitting using the above equation to remove the trend.
[0068] This idea will seem deceptively simple on first inspection.
Indeed the technique could be applied to single frequency excitation
systems to achieve a certain amount of robustness to the incoming
signal having a superimposed trend.
[0069] However, trying to apply the technique to a multi-frequency
system where the signals are analysed separately would be problematic.
It would only work provided the expected signal does not have a
trend within the window. This means that there could only be whole
number of cycles of any applied frequencies within the window.
[0070] This technique works so well because the composite signal
is fit directly and simultaneously. Where it demonstrates its power
very effectively is on the `tails` of exponentials. As mentioned
earlier, the electrode signal could have a trend that is nothing
to do with the flow. Most frequently this would be either a lowish
frequency drift or the tail of an exponential. In the above graph,
the magenta curve is the measured data. It has a negative going
trend that would lead to a poor fit with the red reference curve.
However, by doing the fit with the slope and offset degrees of freedom,
a good fit is obtained (the blue data has the trend removed).
[0071] It should be noted that this is very different to just removing
any trend before the fit because even the expected signal has an
inherent trend by virtue of not having a whole number of cycles
of the waveforms in the window and so simply attempting to remove
a trend would corrupt the data.
[0072] In the mathematics, the scale factor that gives the best
fit (peak to trough) is the flow signal and the slope and offset
can be thought of as the best trend that can be applied to the signal
to make the peaks and troughs coincide.
[0073] The scale factor is F, the slope is M and the offset is
C. The offset C is thrown away, it offers little informational value.
However, M gives surprisingly useful information. Although at first
sight M would be expected to be no longer needed once the fit is
achieved, M in fact gives a very useful indication of the amount
of corruption seen by the system during the measurement window.
[0074] The difference between a poor fit (above) and a good fit
(the previous two graphs) is very apparent by eye. However, mathematically,
the quality can be much harder to judge in a reliable but computationally
simple manner. This is because there is a moderate level of random
noise on the data anyway and even a perfect fit has a moderate rms
error. A further aspect of this invention provides a method to determine
the quality of fit. This is done in a way that can be seen mathematically
to enhance the distinction between FIGS. 2 and 3.
[0075] We now consider a practical system. It is a sampled data
system. The sensor is being excited with 10 20 40 and 80 Hz (these
may be conveniently generated e.g. as submultiples of a 20 kHz or
20.48 kHz DSP sampling clock frequency with 250 or 256 samples respectively
for the 80 Hz signal and correspondingly more for the lower frequencies).
The acquisition system is acquiring samples continuously but the
processing is done on a window of data at a time.
[0076] The window length is one cycle of 40 Hz (25 mS) but the
window is moved along half a cycle at a time so the windows overlap
(it is an advantageous but optional feature that windows overlap,
although it is not necessary to use exactly half a window increment).
While this does not directly increase the bandwidth, it does give
a higher data rate making subsequent filtering easier.
[0077] From the result of each window is a flow value F, a slope
value M and an error estimate for the fit of the waveform within
that window. Sometimes, the M and error estimates will suggest that
the value of F is accurate and can be trusted highly. Other times
M and/or the error estimate will suggest that the value of F could
well be corrupt because there was excessive trend in the data or
the fit just was not very good.
[0078] This confidence value can be used to `weight` the data for
filtering purposes. Again, this filtering has proven to be very
effective on real world data. Different filtering and weighting
algorithms may be used, the choice may depend on application.
[0079] A simple algorithm is to hold the last value if the confidence
is too low. A monitor can be provided to ensure that the algorithm
adapts if the overall reading confidence for all the windows is
low.
[0080] In a more advanced algorithm, trend analysis is used to
give a better guess of the value if the confidence in the current
reading is low. In this respect, the filter could behave like a
Kalman filter.
[0081] Equally, the M value/error estimate can be used to give
a SEVAL like output e.g. clear, blurred, dazzled as proposed by
M. P. Henry et al.
[0082] The ability to fit the incoming signal and remove a trend
is a unique feature of this kind of system, which can be applied
to other measurements, but would not have an equivalent with a single
frequency excitation.
[0083] The system depends on knowing the amplitude and phase of
the incoming components. This information represents the frequency
response of the sensor. However, it is appreciated that this is
not necessarily constant. An algorithm will now be described that
can automatically adapt to changing sensor characteristics.
[0084] An outer loop is responsible for updating the matrix of
coefficients representing the frequency response. By suitable averaging
of the residual errors of each window, any error in one of the coefficients
becomes apparent.
[0085] The fit that gives the best possible fit while keeping the
amplitude ratio and phase of the components fixed is used. However,
if the fit could be improved by allowing the matrix coefficients
to be adjusted (preferably by a small amount below a threshold)
and the degree of adjustment is consistent over a number of windows
then the adjustment is made.
[0086] Preferably the lower frequency, here 10 Hz coefficients
are kept fixed (but in some cases may be subject to a very low limit
of adjustment). Limits can be placed on the amount by which the
other components can be adjusted. Limits may include a limit on
the maximum total deviation of a given coefficient from a starting
value and/or a maximum adjustment of a given coefficient in a given
adjustment interval and/or a maximum total or weighted combination
of adjustment of coefficients and/or a combination of the preceding
limits.
[0087] A method of determining measurement error will now be explained,
referring back to FIG. 1. It is clear by eye that there would be
no better fit than the one shown. However, the SSE (Sum of the Squared
Errors) is still significant because of the (relatively) high frequency
noise on the data being fitted. Now referring to FIG. 3 by eye,
it is clear that the fit is not very good. However, the SSE is not
very different from that for FIG. 1. For illustration, the SSE for
FIG. 1 is 0.121 while for FIG. 3 the SSE is 0.269 a little over
a factor of 2. Yet the fit is very much worse. This illustrates
the normal difficulty in measuring accuracy of measurement.
[0088] Since it is desired to use the measurement error as an aid
to weighted filtering, it is preferred that there be more `contrast`
(by which is meant a mathematically identifiable distinction) between
the error values for FIG. 1 and FIG. 3. This can be achieved by
substantially ignoring the high frequency residuals and considering
primarily the low frequency residuals. Conceptually therefore the
residuals could be filtered with a low pass filter before performing
the SSE calculations. Alternatively, it would be possible to do
an FFT of the residuals and measure only components below a certain
frequency. Both of these methods may be effective, but performing
an FFT at least is computationally intensive.
[0089] A computationally simple but highly effective method for
obtaining much more contrast will be described. This is based on
the recognition that the residual errors in FIG. 3 that are desired
to measure are low frequency and that, as a result, the error spends
a long time on the same side of the curve (ie either positive or
negative). In contrast, the high frequency residuals average to
zero over a very short interval.
[0090] Various embodiments of the method divide the window into
a plurality of intervals, preferably at least about 4 preferably
no more than about 20 typically 5-10 here 8 intervals. For each
of these intervals, the residual is summed algebraically. Referring
to FIG. 1 it is clear that this algebraic sum would be close to
zero over any of the intervals whereas for FIG. 3 it would be far
from zero (either large and negative or large and positive) over
most of the intervals.
[0091] To get a final error figure for the window, the absolute
value of each of the 8 interval errors is summed. This is because
the summation within any interval could be positive or negative
and an algebraic sum would largely cancel out.
[0092] There is thus provided a method of determining error between
a signal and a corresponding reference signal, each signal comprising
a first plurality of sampled values in a sampling interval, the
method comprising:
[0093] defining a second plurality of sub intervals, each sub interval
containing a respective subset of the first plurality of sampled
values;
[0094] determining an algebraic sum for each sub interval of the
difference between signal sample values and reference signal sample
values;
[0095] determining an absolute sum of the algebraic sums for each
sub interval as an error estimate for the sampling interval.
[0096] The calculation may include other filtering or weighting
and the error estimate may be further processed, but one point of
interest is that the step of algebraic summing comprises a calculation
or operation in which differences of opposite sign substantially
cancel and the step of absolute summing comprises an operation or
calculation in which the algebraic sums add constructively. In place
of an absolute sum, a sum of square might be used--this would increase
the effect of a single large error on the end result.
[0097] Although the units are different, the error using this technique
is 2.203 and 48.033 for FIGS. 1 and 3 respectively; a much higher
contrast (20:1 instead of 2:1).
[0098] Dividing the window into 8 intervals is very appropriate
in this example because of the frequencies present (ie ratios of
1 2 4 and 8). If different frequencies were chosen then these
intervals could be optimised accordingly.
[0099] FIG. 7 shows the SSE approach. The graph represents 6 seconds
worth of 25 ms windows. Although there is high contrast between
the peaks and the `baseline`, these peaks only represent the very
worst readings.
[0100] FIG. 8 shows the enhanced method for determining errors.
Here, the baseline is much lower and much better contrast exists
between good and bad readings.
[0101] On these two graphs, every point represents a processed
window. FIG. 9 shows the flow signal as determined by the LSE fit
algorithm. The final stage of the processing now is to use the error
measurement from graph 8 to filter the data in graph 9. Since it
is clear that the high peaks in FIG. 8 represent points with high
measurement errors, one can `filter out` these points with a suitable
algorithm.
[0102] FIG. 10 shows the flow after filtering.
[0103] FIG. 11 shows the flow profile used for the examples in
this example. FIG. 15 shows the noise added. Although the results
are partially simulated, the noise added to the data is from a real
flow meter in a real application.
[0104] FIG. 12 shows the added noise zoomed in (the total window
is about 0.2 seconds long).
[0105] FIG. 13 shows the derived flow values for approximately
the same interval. The intervals in FIG. 12 show the window numbers
and correspond to the x axis values of FIG. 13.
[0106] FIG. 14 shows the error estimates for each of the windows,
demonstrating a sensitive indicator of when the flow estimate is
not perfect. Note that the flow reading is sometimes good even though
the error indicator is high. This is logical because the error indicator
is really indicating the uncertainty in the flow reading, at least
in a qualitative way.
[0107] Apparatus embodying the method will now be described with
reference to FIG. 6.
[0108] The Microprocessor 10 maintains a `time` variable for the
purpose of calculating drive signals and expected signals. In this
embodiment, the microprocessor calculates a signal that is the sum
of four predetermined amplitude (here equal amplitude), distinct
frequency sinewaves. This signal is applied to the drive coil in
the sensor 3 via power amplifier 2. The electrode signals are amplified
4 and converted into discrete samples by ADC 5. Software modules
running on the microprocessor implements the method described.
[0109] The mathematical drive signal is transformed by the frequency
response coefficients in transformation module 9 in order to determine
the expected signal back from the sensor. In other words, knowing
the signal applied to the drive coil and knowing the transfer function
of the sensor, this module calculates the waveform expected back
from the sensor in the absence of perturbations.
[0110] Correlation module 6 performs the correlation or LSE fitting.
The results of this fitting are at least a flow signal and a `confidence`
value that can be used to assist in the weighted filter module 7.
As an enhancement, the results from the correlation module 6 can
also be used by an adaptive adjustment module 8. Such a module,
if present, monitors the quality of fit over a period of time and
decides whether the coefficients used by transformation module 9
need adjustment, subject to predetermined constraints.
[0111] Embodiments of the invention provide one or more of the
following novel features: Using multiple frequencies simultaneously,
fitting multiple frequencies simultaneously, weighted filtering
and adjusting coefficients dynamically.
[0112] Modifications of detail may be made and features disclosed
herein may be provided independently or in other combinations. |