GB2391313A

GB2391313A - Processing sampled data to obtain an integral number of samples for a complete cycle of measured periodic physical quantity

Info

Publication number: GB2391313A
Application number: GB0217396A
Authority: GB
Inventors: Troy Wray
Original assignee: ABB Ltd Great Britain
Current assignee: ABB Ltd Great Britain
Priority date: 2002-07-26
Filing date: 2002-07-26
Publication date: 2004-02-04
Anticipated expiration: 2022-07-26
Also published as: GB2391313B; GB0217396D0

Abstract

Sampled data is processed to provide a processed set of data in which a complete cycle of the measurement frequency corresponds to an integral number of sample periods. The method comprises determining a measurement frequency of vibration of periodic data, setting a desired integral value for a number of samples for a complete cycle of the measurement frequency periodic data, and processing (by interpolation) the sampled data to derive processed sample values at the set of desired sample instants. The resampled data, having a whole number of samples per cycle of the periodic data, lends itself more readily to data processing algorithms eg cross-correlation. The method finds application in field of Coriolis flowmeters 10.

Description

, - 1 Deriving Measurements from Periodic Data The present invention

relates to the processing of periodic data which contains information about a physical quantity. There are many instances where a 5 periodically varying signal, typically a sinusoidal signal, contains information about a physical quantity to be measured. For example, in a coriolis-type flow meter, a sinusoidal signal is produced as a result of oscillation of a part of the meter. The amplitude of the sinusoid is used to control the excitation amplitude, the frequency gives a measure of the density of the sample and the phase of oscillation gives a 10 measure of mass flow. In an electromagnetic flow meter which has AC excitation, a sinusoidal output signal is produced and phase-sensitive detection of that signal may be used to improve noise tolerance. There are numerous other instances where periodic, typically sinusoidal, signals convey information about physical quantities to be measured in one or more of amplitude, frequency and phase.

There are numerous well-documented analogue techniques for processing periodic signals to extract the desired information. More recently, digital signal processing (DSP) techniques have come into widespread use. In such digital techniques, an analogue signal is sampled to obtain a series of values representing 20 the amplitude of the sample at each of a sequence of (normally equally) spaced points in time and the values are processed numerically using a computer or dedicated processor.

Because digital samples comprise one of a discrete set of possible values for 25 amplitude and are taken at a series of discrete time intervals, there is potential for loss of accuracy in the sampling process. However, 16 bit analog-to-digital converters (giving approximately +/- 32,000 values) are readily available and 24 bit (giving approximately +/- 8,000, 000 values) are available if high accuracy is required. Thus, obtaining a desired amplitude resolution is rarelya serious problem.

30 As far as sampling interval is concerned, high speed converters are available so it is normally also possible to obtain samples at a desired sampling interval. Thus, on the face of it, a desired accuracy can be obtained simply by using an appropriate

( - 2 conversion resolution and sample frequency.

However, as the number of samples increases, the cost both in terms of the converter speed and, often more significantly in terms of memory required to store 5 the samples and processing power and the time required to process a large number of samples may become excessive. This is particularly the case for some processing operations which may vary as a greater-than-first-order function of the total number of samples.

10 Thus, while inaccuracies which can arise due to quantisation errors can be reduced by increasing the sample frequency and/or by sampling over a number of sample periods, both of which are common conventional "fixes", such fixes do not solve all problems. Also, increasing the number of samples or the number of sampling periods imposes requirements in terms of memory and processing time.

15 It is also possible to filter results, but this degrades bandwidth and again increases processing requirements.

The invention seeks to provide an improved method and apparatus for processing sampled periodic data.

According to a first aspect, the invention provides a method of processing sampled periodic data representing a physical quantity, the method comprising: determining a measurement frequency of variation of the periodic data; setting an integral value for a number of samples for a complete cycle of the 25 measurement frequency periodic data; processing the data to provide a processed set of sample data in which a complete cycle of the measurement frequency substantially exactly occupies the set integral number of samples.

30 Pursuant to the invention, it has been appreciated many data processing algorithms work significantly more accurately if the period of the measurement frequency is substantially exactly a whole number of sampling periods. A potential

( - 3 solution therefore was positively to control the system so the signal and sampling frequency are constrained so that this requirement is met. In many applications, however, this is not practical so would not represent a generic solution.

5 The conventional approach to improving measurement accuracy is to concentrate on improving measurement acquisition; once data are acquired, although noise can be reduced by processing, processing and only decrease or at best maintain the "real world" information content of the data. It has been appreciated by the inventorthat, although one would therefore normally be reluctant 10 to process the data in any way which might lose "real world" information, it may nonetheless be beneficial to process the data to produce a processed data set with more favourable characteristics. Thus, somewhat unexpectedly in the case of extracting a measurement from data, the raw data are "discarded" in favour of a processed set of data in which, in many cases, all "samples" are synthetic. It has 15 been found that this processing need not lead to any significant loss of useful information or accuracy and an overall improvement in accuracy may be attained.

Thus, in the invention, a processed data set in which the signal is conveniently sampled is produced; the effect is equivalent to having sampled the data at a sampling frequency (and appropriate phase) that was an exactly desired multiple of 20 the (previously imprecisely known) measurement frequency.

In a practical example, the signal is unlikely to be a pure sinusoid but may contain many different frequency components. However, the important consideration is the period of the measurement frequency, that is the frequency of 25 primary interest. It will be noted that complete cycles of other frequencies present in the data will not necessarily occupy an integer number of samples, but that is not critical. Processing the data may comprise interpolating the received data to derive 30 processed sample values at instants offset in time from received sample values.

Processing the data may comprise defining a set of desired sample instants, preferably equally spaced (this may facilitate many forms of processing), and

( - 4 interpolating processed sample values at the desired sample instants from the received sample data.

Processing may comprise determining the closest received sample in time 5 to a desired sample time and interpolating a value for a processed sample at the desired sample time based on the closest received sample and at least one other received sample.

Interpolating may comprise interpolating, preferably linearly, based on two 10 received sample values but more preferably comprises performing a second order interpolation based on three received sample values. Preferably, processing the data comprises selecting a base received sample closest in time to a desired sample time and eadier and later samples, preferably respectively immediately preceding and subsequent to the base sample. Preferably a second order 15 interpolation is applied based on the desired sample time, the received sample times and the received sample values to arrive at a single value for a processed sample at the desired sample time.

The invention is particularly beneficial when the data is subsequently to be 20 processed by cross-correlation. Cross-correlation comprises correlating a signal with a sinusoidal signal of the same frequency, desirably over an integral number of cycles. Whilst a sinusoidal signal can be synthesised at a desired frequency to match the sample frequency even when the period of this frequency is not an exact number of sample periods, problems may still arise due to the fact that a cycle does 25 not exactly occupy an integral number of sample periods. Thus integration cannot normally readily be performed over an exact period but results in either slightly more or slightly less than a complete cycle being taken into account. With the invention, integration over a substantially exact integral number of periods can be performed.

30 The desired number of samples may be selected to be close to the actual number of samples in a data period. For example, the desired number of samples may be selected to be the nearest integer number of samples, or may be selected

( - 5 to be the nearest integer below the number of sample periods. Having the desired number of sample periods lower than the actual number of samples may simplify interpolation. Alternatively the data may be oversampled with more than one interpolated value corresponding to a received sample value; although this does not 5 create information, it may simplify calculation and/or may smooth noise.

In a particularly advantageous embodiment, the desired number of sample periods may be selected to correspond to a predetermined number. Having a fixed number may simplify code and/or allow code and/or hardware to be optimised - the 10 number may be based on computational considerations (powers of two, or whole multiples of data words used by a processor may be particularly convenient) and may be based on (preferably equal to) the number of samples in a period of a waveform to correlate with the samples. For example, a synthetic sinusoidal waveform may be stored in a look-up table of a fixed number of (for example, 128 15 or 256) samples and the data may be sampled to provide data in which a period of the measurement frequency of the sample data occupies exactly the same number of samples as the stored waveform. This facilitates correlation of the two waveforms and avoids having to interpolate the synthetic waveform. Highlyoptimised code may be used to process the data. Use of optimised code may facilitate application of 20 known techniques such as "windowing" where samples are taken substantially continuously and a "window" on the data is advanced, for example by half a cycle each time a batch of new data is acquired. For example, with a signal of the order of 100 Hz, the correlation may be performed sufficiently rapidly for a new calculation to be performed every half cycle and the results of successive calculations can then 25 be filtered to reduce noise but still retain a high bandwidth.

The invention extends to apparatus for perforrning any of the above methods and to a computer program or computer program product comprising instructions for performing any such method, as well as to a measurement device, preferably a 30 flow meter, most preferably a mass flow meter incorporating processing apparatus according to any aspect and means for extracting from the processed samples a measure of a physical quantity, preferably a measure of flow rate, preferably a

( - 6

measure of mass flow rate from a measure of phase obtained by cross correlation.

Further aspects and preferred features are set out in the claims.

An embodiment will now be described, by way of example, with reference to 5 the accompany drawings in which: Fig. 1 is a schematic overview of apparatus embodying the invention; Fig. 2 is a graph showing sampled data.

10 Referring to Fig. 1, a typical application will be explained. In this embodiment, a coriolis flow meter 10, having a metering tube 12, sensors 14a and 14b and driver 16 provides two substantially sinusoidal output signals to digital signal processor (DSP) 20. The processor 20 may also supply an excitation signal (not shown) to the driver 16 of the flow meter, for example from output interface 30.

15 The details of the coriolis flow meter may be largely conventional, for example as described in WO-A-00/71979 and referenced document, the entire disclosure of

which including all documents referenced therein is incorporated herein by reference for the purpose of description of known meters which will not be described further.

The operation of the processor will now be described; these remain substantially 20 unchanged if the meter 10 is replaced by another source of signal(s) to be processed; the invention is primarily directed to the core of operation and no limitation to any specific application should be inferred.

The DSP 20 comprises a processor 24, a dynamic store (RAM) 22, an input 25 interface 26 (here shown as two-channels, but a single channel or more channels may be employed), a stored program 28 (for example in ROM, Flash, disk or other (preferably non-volatile) memory) and an output interface 30. Under the operation of the stored program 30, the processor performs the steps outlined in the method described above and below. Specifically, the processor 24 controls the input 30 interface 26 to store samples in the store 22, processes the samples to re-sample them as described herein, and then further processes the processed samples to derive a measure of flow, in this example by correlating the signals and determining

( - 7 a measure of phase difference between the signals.

The method will be further explained with reference to a worked example, the details of which are illustrative and non-limiting.

For test purposes, a synthetic sample signal fy(t) is generated according to the following parameters: freq:= 100.37 - signal frequency Amp:=1.0 signal amplitude 10 Phase:= 15 - signal phase in degrees tJ:= Mop i<] fq t + --36-o-- 2 it) A sampling frequency is defined.

15 Fs:= 10X10^3 -Sampling frequency The frequencies of the signal and sampling frequency are here deliberately chosen so that the latter is not an exact multiple of the former.

20 The signal frequency is determined based on zero-crossing detection (but other techniques can be used). The point of zero crossing can be estimated, assuming it is known to occur between samples n and fn+1) as ncross = -y(n) / (y(n+1) - y(n The number of samples which exactly occupies a signal period is calculated.

Nexact:= Fs / freq - exact number of samples for 1 period of signal Nexact = g9.63136 30 N:= int(Nexact + 0.5) - nearest integer number of samples for 1 period N = 100

( - 8 A cross-correlation is performed on the sampled data in an attempt to deduce the original phase and amplitude, by correlating with sine and cosine functions, as depicted in Fig. 2. The following pseudo code outlines this process.

j:= 1N - a counter over samples Sl:= sin t -I- --) start these arrays at index 1 Cl:= colt 2 7; - -I-

10 J Nexact) m:= 0..Nt3 Y = firm -l-) generate more points ready for interpolation algorithm later SumSine:= An, S I. Y. J SurnCo:= LOCI Y. J J Ampex = 2,:9WmSmc SumC02) SumCos Eta' Phone t:=-S=nSinc 360 2x 25 This results in this example in an Amplitude estimate of 0.99698 (1.000 was theactualvalueforthetestsignal)and a Phase Estimate of 15.121 (15. 000wasthe actual value for the test signal). The error in the Amplitude is thus of the order of 0.3% and the error in the phase is over 0.8%. In the case of, for example, a mass meter where phase must be determined accurately to determine flow rate, such an 30 error can lead to noticeable errors.

The re-sampling of data according to an embodiment will now be described.

( - 9 - s v=r 3.113 3

- 1 3.B92 _

no = 4 467 6

10 7 B 15 The first table of values above, v gives the first few 'exact' sampling times needed in order to have data in which one period exactly occupies the desired number of samples (here 128 is the chosen desired number as this is convenient for processing and can be directly correlated with a table of 128 sine values).

20 From this a second index table of values, nv, is generated in which the numbers in the left hand column represent the index number of samples in the processed data set and the right hand column gives the index number of the "nearest sample (in this case by rounding down) in the original data set which is used as the basis for interpolation. This can be used with one other sample the 25 other "side" of the target sample (in this case simply the next sample) to interpolate linearly. In this embodiment, however, second order interpolation with three sample points is used to generate a processed sample. Higher order interpolation can be 30 used but it is found that second order interpolation gives very good results, significantly better than first order, and yet is computationally simpler and fasterthan higher order interpolation with little discernible decrease in accuracy.

( - 10 The convention used herein is that there will be 3 consecutive points in the raw data array a(O), a(1) and a(2) and we will fit the equation to those 3 points but always interpolate only over the interval 0,1. For example, the first point in the 128 point array is 0, and there is no need for interpolation but the formula does not need 5 to treat it as a special case, the indexing formula automatically guarantees Z(O) = y(o) A suitable procedure for generating the new data set is: Determine the "exact" timing of the desired sample value v e.g. O. 778.

10 Determine the base sample timing, e.g. int(O.778) is 0, the centre sample, so the samples to work with are Y(-1) Y(O) and Y(+1) Determine polynomial coefficients CO, C1 and C2 that fin the samples, here Y(-1) Y(O) and Y(+1), (offing Y(x) where x = -1 0 and +1) Use the curve which fits the samples to calculate a processed sample value by 15 interpolating a value for Y at a time value corresponding to the time of the desired sample (X=desired sample time-base sample time), here (O. 778- 0) The signal can be re-sampled so that the re-sampled signal goes from zero-

crossing to zero-crossing in the processed samples but this is not necessary as 20 highly accurate results can be obtained with the processed samples at an arbitrary phase starting point, provided a complete cycle is used, as described herein.

In this example, the program does not work with indices less than O so the function definition fy is used to calculate Y(-1); this could have been achieved 25 by offsetting the indices but that might have made the code of the example more confusing. It will be noted that some values are repeated because sometimes two consecutive Z (processed sample) values will be calculated from the same set of Y 30 (received sample) values (but at different interpolation points). This should be expected because in this example the data is over sampled (generating 128 data points from 100 original values). The mathematics for the above procedure are

( outlined below.

nvi:- n 1 v;) SP:= I

fraCj:- Vj -- noO196) C.Oj:= nv' SP) fYLtov' t l) SPA - ftnVj- 1) SP1 fy(n,; + I) SP| + fY[( i) 1 _ CO; Z;;= On; Cl j film C2j {fi2 SumSuc:= 2, S-Z i SumCos:= >,Cj Z (SumSinc2 SumCos2) AmpEat:= 2 1282 SumCa' PhneeE _ 'am SUmS o) 360 2rc This example gave an Amplitude estimate of 1.00000 and a Phase Estimate of 14.99941. Thus, within the limits of calculation accuracy, the amplitude was determined exactly accurately and the phase was determined to an accuracy of 25 approximately 0.004% (as compared to 0.8%) - a very significant improvement in accuracy. The small residual error is presumed to be at least in part attributable to the use of a second order approximation to interpolate the data - it can be seen that such an approximation in generating the processed samples therefore leads to negligible degradation of accuracy (40ppm total error). Furthermore, 30 although an additional step of interpolation is required, although highly accurate, this is computationally simple to implement and the resulting processed data set having exactly a desired number of sample points can be processed more efficiently than

- 12 the original sampled data set so in fact there was only a minimal increase in overall processing requirement but this is offset by the significantly greater accuracy attainable from processing a single cycle.

5 it will be noted that the processed data does not have a predetermined frequency ratio to the original data and the ratio itself is not important other than that it is indirectly chosen to fit the measurement conveniently into the processed samples. 10 It will further be noted that the re-sampling means that the time period represented by a sample in the processed samples does not correspond to that of the original data. This is, however, very simply taken into account in processing the data (it merely requires multiplication by the known correction factor). In particular, in frequency determination, the time spacing of the processed samples is used 15 rather than the time spacing of the original samples.

Although significant improvements have been demonstrated when cross correlation is used to process the data, the applicability of the invention is not limited

to such processing. For example, even simple techniques such as averaging the 20 data over a whole number of cycles to determine a mean value may benefit from having the data aligned with samples more precisely.

For the avoidance of doubt, it should be appreciated that in any real world measurements, values cannot be truly "exact". In this specification, reference is

25 made to the number of samples substantially exactly matching the number required for a period of the signal. In the prior art, the number of samples may have differed

by +/- 0.5 samples, which is clearly not exact. According to the invention, this is deliberately reduced to a much smaller number, which will typically be zero within the limits of calculation accuracy performed. References to a cycle substantially 30 exactly occupying an integral number of samples imply that any mismatch is significantly less than one sample, typically less than one tenth of a sample period and preferably substantially zero within the limits of calculation accuracy performed

( - 13 or target accuracy.

Modifications of detail may be made and the invention may be applied to other measurement problems and techniques. Features disclosed in the 5 embodiment may be provided independently of the other features of the embodiment unless otherwise stated.

Claims

- 14 Claims

1. A method of processing sampled periodic data representing a physical quantity, the method comprising: 5 determining a measurement frequency of variation of the periodic data; setting an integral value for a number of samples for a complete cycle of the measurement frequency periodic data; processing the data to provide a processed set of sample data in which a complete cycle of the measurement frequency substantially exactly occupies the set 10 integral number of samples.

2. A method according to Claim 1 wherein processing the data comprises interpolating the received data to derive processed sample values at instants offset in time from received sample values.

3. A method according to any preceding claim wherein processing the data includes defining a set of desired sample instants.

4. A method according to Claim 3 wherein the desired sample instants are 20 equally spaced.

5. A method according to any preceding claim wherein processing includes determining the closest received sample in time to a desired sample time.

25

6. A method according to Claim 5 wherein processing further comprises interpolating a value for a processed sample at the desired sample time based on the closest received sample and at least one other received sample.

7. A method according to Claim 6 wherein interpolating comprises interpolating 30 based on two received sample values.

8. A method according to Claim 6 wherein interpolating comprises performing

- 15 a second order interpolation based on three received sample values.

9. A method according to Claim 6 wherein processing the data comprises selecting a base received sample closest in time to a desired sample time and 5 earlier and later received samples and wherein a second order interpolation is applied based on the desired sample time, the times of the base, earlier and later received samples and the values of the received samples to arrive at a single value for a processed sample at the desired sample time.

10 10. A method according to any preceding claim wherein the processed samples are subsequently processed by cross-correlation.

1 1. A method according to any preceding claimwherein the numberof processed samples is selected based on the actual number of samples in a period of the 15 measurement frequency.

12. A method according to Claim 1 1 wherein the number of processed samples is an integer adjacent to the actual number of samples in a period of the measurement frequency.

13. A method according to any of Claims 1 to 10 wherein the number of processed samples is selected to correspond to a predetermined number.

14. A method according to Claim 13 wherein the predetermined number is based 25 on the number of samples of a waveform to correlate with the samples.

15. A method according to any preceding claim wherein the number of processed samples is greater than the number of received samples in a period of the measurement frequency.

16. A method according to any of Claims 1 to 14 wherein the number of processed samples is less than the number of received samples in a period of the

- 16 measurement frequency.

17. A method according to any preceding claims wherein the number of processed samples is a power of two.

18. Digital signal processing apparatus arranged to perform a method according to an preceding claim.

19. A computer program or computer program product comprising instructions 10 for performing a method according to any of Claims 1 to 17.

20. Digital signal processing apparatus comprising: memory for storing sampled periodic data representing a physical quantity, a processor arranged for 15 determining a measurementfrequencyof variation of the periodic data; setting an integral value for a number of samples for a complete cycle of the measurement frequency periodic data; processing the data to provide a processed set of sample data in which a complete cycle of the measurement frequency substantially exactly 20 occupies the set integral number of samples.

21. A flow meter comprising: metering apparatus for providing a periodic signal which varies as a function of a flow rate to be measured; 25 means for sampling said periodic signal to provide sampled data; means for processing the sampled data by a method according to any of Claims 1 to 17 to produce processed sampled data; means for determining a measure of flow rate from the processed sampled data.

22. Apparatus or a method substantially as any one herein described.