CA2208452C - Method and apparatus for adaptive line enhancement in coriolis mass flow meter measurement - Google Patents

Abstract

An apparatus and method for determining frequency and phase relationships of vibrating flow tubes in a Coriolis mass flow meter. Adaptive line enhancement (ALE) techniques and apparatus are used in a digital signal processing (DSP) device to accurately determine frequency and phase relationships of the vibrating flow tube and to thereby more accurately determine mass flow rate of a material flowing through the mass flow meter. In a first embodiment, an adaptive notch filter is used to enhance the signal from each corresponding sensor signal on the vibrating flow tubes. In a second embodiment, a plurality of adaptive notch filters are cascaded to enhance the signal from each corresponding sensor signal. In both embodiments, an antialiasing decimation filter associated with each sensor signal reduces the computational complexity by reducing the number of samples from a fixed frequency A/D sampling device associated with each sensor signal. Computational adjustments are performed to compensate for spectral leakage between the fixed sampling frequency and the variable fundamental frequency of the vibrating flow tubes. Despite this added computational complexity, the present invention is simpler than prior designs and provides better noise immunity due to the adaptive notch filtration.
Heuristics are applied to the weight adaptation algorithms of the notch filters to improve convergence of the digital filters and to reduce the possibility of instability of the filters interfering with mass flow measurements.

Description

CA 022084~2 1997-06-13 ~ ~

METHOD AND APPARATUS FOR ADAPTIVE LINE ENHANCEMENT
IN CORIOLIS MASS FLOW METER MEASUREMENT

FIELD OF THE INVENTION
The present invention relates to mass fiow rate measurement and in particular to the use of digital signal processing adaptive filtration methods and apparatus in Coriolis mass flow meters.
PROBLEM
It is known to use Coriolis mass flowmeters to measure mass flow and other information for materials flowing through a conduit. Such flowmeters are disclosed in U.S. Pat. Nos. 4,109,524 of August 29, 1978, 4,491,025 of January 1, 1985, and Re. 31,450 of February 11, 1982l all to J. E. Smith et al. These flo~"~eler~ have one or more flow tubes of straight or curved configuration. Each 10 flow tube configuration in a Coriolis mass flowmeter has a set of natural vi~r~lio"
modes, which may be of a simple bending, torsional or coupled type. Each flow tube is driven to oscillate at resonance in one of these natural modes. Material~flows into the flowmeter from a connected conduit on the inlet side of the flowmeter, is directed through the flow tube or tubes, and exits the flowmeter 15 through the outlet side. The natural vibration modes of the vibrating, fluid filled system are defined in part by the combined mass of the flow tubes and the material within the flow tubes.
When there is no flow through the flowmeter, all points along the flow tube oscillate about a pivot point with identical phase due to an applied driver force.
20 As material begins to flow, Coriolis accelerations cause each point along the flow tube to have a different phase. The phase on the inlet side of the flow tube lags the driver, while the phase on the outlet side leads the driver. Sensors are placed on the flow tube to produce sinusoidal signals representative of the motion of the flow tube. The phase dif~erence between two sensor signals is proportional to the 25 mass flow rate of material through the flow tube.
A complicating factor in this measurement is that the density of typical process m~L~, ial varies. Changes in density cause the frequencies of the natural modes to vary. Since the flowmeter's control system maintains resonance, the oscillali~n frequency varies in response to changes in density. Mass flow rate in 30 this situation is proportional to the ratio of phase difference and oscillation frequency.
-~ ~CA 022084~2 1997-06-13 ~ The above-mentioned U.S. Patent No. Re. 31,450 to Smith discloses a Coriolis flowmeter that avoids the need for measuring both phase difference and - osc ~ iO, I frequency. Phase difference is determined by measuring the time delay between level crossings of the two sinusoidal sensor output signals of the flowmeter. When this method is used, the variations in the osc~ tion frequency cancel, and mass flow rate is proportional to the measured time delay. This - measurement method is hereinafter referred to as a time delay or ~t ~- measurement.
-- Measurements in a Coriolis mass flowmeter must be made with great -10 accuracy since it is often a requirement that the derived flow rate information have an accuracy of at least 0.15% of reading. The signal processing circuitry which receives the sensor output signals measures this phase di~re"ce with precision and generates the desired characteristics of the flowing process material to the" required accuracy of at least 0.15% of reading.
In order to achieve these accuracies, it is necessary that the signal - processi"y circuitry operate with precision in measuring the phase shift of the two signals it receives from the flowmeter. Since the phase shift between the two ~ output signals of the meter is the information used by the processing circuitry to derive the material characteristics, it is necessary that the processing circuitry not 20 introduce any phase shift which would mask the phase shift information provided by the sensor output signals. In practice, it is necessary that this processing circuitry have an extremely low inherent phase shift so that the phase of each input signal is shifted by less than .001~ and, in some cases, less than a few parts per million. Phase accuracy of this magnitude is required if the derived in~r",aLion 25 regarding the process material is to have an accuracy of less than 0.15%.
The frequencies of the Coriolis flowmeter output signals fall in the frequency range of many industrially generated noises. Also, the amplitude of the sensor output signals is often small and, in many cases, is not significantiy above theamplitude of the noise signals. This limits the sensitivity of the flowmeter and- . 30 makes the extraction of the useful information quite difficult.
There is not much a designer can do either to move the meter output signals frequency out of the noise band or to increase the amplitude of the output signals. Practical Coriolis sensor and flowmeter design requires compromises that ';
~ .

CA 022084~2 1997-06-13 result in the generation of output signals having a less than optimum signal to - noise ratio and dynamic range. This limitation determines the fiowmeter characteristics and specifications including the minimum and maximum flow rates which may be reliably derived from the flowmeter's output signals.
The magnitude of the minimum time delay that can be measured between ~ the two Coriolis flowmeter output signals at a given drive frequency is limited by various factors including the signal to noise ratio, the complexity of associaLe~
circuitry and hardware, and economic considerations that limit the cost and complexity of the associated circuitry and hardware. Also, in order to achieve a10 flowmeter that is economically attractive, the low limit of time delay measurement must be as low as possible. The processing circuitrv that receives the two output signals must be able to reliably measure the time delay between the two signals in order to provide a meter having the high sensitivity needed to measure the flowing characteristics of materials having a low densitv and mass such as, for example, gases.
- There are limitations regarding the extent to which conventional analogcircuit design can, by itself, permit accurate time delay measurements under allpossible operating conditions of a Coriolis flowmeter. These limitations are dueto the inherent noise present in any electronic equipment including the 20 imperfections of semi-conductor devices and noise generated by other circuit elements. These limitations are also due to ambient noise which similarly limits the measurement can be reduced to some extent by techniques such as shielding, guarding, grounding, etc. Another limitation is the signal to noise ratio of thesensor output signals themselves.
Good analog circuit design can overcome some of the problems regarding noise in the electronic equipment as well as the ambient noise in the environment.
However, an improvement in the signal to noise ratio of the output signals cannot be achieved without the use of analog fiiters. But analog filters alter the ar~plitu~e and phase of the signals to be processed. This is undesirable, since the time delay between the two signals is the base information used to derive charaoLerisLics of the process fluid. The use of filters having unknown or varying amplitude and/or phase characteristics can unacceptably alter the phase CA 022084~2 l997-06-l3 difference between the two sensor output signals and preclude the derivation of accurate information of the flowing material.
The flowmeter's drive signal is typically derived from one of the sensor output signals after it is conditioned, phase shifted and used to produce the 5 sinusoidal drive voltage for the drive coil of the meter. This has the disadvantage that harmonics and noise components present in the sensor signal are amplified and applied to the drive coil to vibrate the flow tubes at their resonant frequency.
- However, an undesirable drive signal can also be generated by unwanted mechanical vibrations and electrical interferences that are fed back to the meter 10 drive circuit and reinforced in a closed loop so that they create relatively high amplHude self-perpetuating disturbing signals which further degrade the precision - and accuracy of the time delay measurement.
There are several well known methods and circuit designs which seek to ~ reduce the above problems. One such successful technique to reduce some of 15 the above problems is described in U.S. Patent 5,231,884 to M. Zolock and U.S.
~ Patent 5,228,327 to Bruck. These patents describe Coriolis flowmeter signal - processing circuitry that uses three identical channels having precision intey,aL~
- as filters. A first one of these channels is permanently connected to one sensor signal, say, for example, the left. The other two channels ~second and third) are 20 alternately connected, one at a time, to the right sensor signal. When one ofthese, say the second channel, is connected to the right sensor signal, the third channel is connected, along with the first channel, to the left sensor signal. The - inherent phase delay between the first and third channel is measured by comparing the time difference between the outputs of the two cl~ai"~els now both25 connected to the left signal. Once this characteristic delay is determined, the role - of this third channel and the second channel connected to the right sensor signal is switched. In this new configuration, the second channel undergoes a calibration of its delay characteristics while the third calibrated channel is connected to the right sensor signal. The roles of second and third channels are alternately 30 switched by a control circuit approximately once every minute. During this one-minute interval (about 30 to 60 seconds), aging, temperature, and other effects have no meaningful influence on the phase-shift of the filters and therefore their phase relationship is known and considered defined.

CA 022084~2 1997-06-13 The precisely calibrated integrators used by Zolock provide a signal to noise ratio improvement amounting to about 6 db/octave roll-off in the amplitudetransfer function of the integrator. Unfortunately, this 6 db/octave improvementis not enough under many circumstances in which Coriolis flowmeters are 5 operated (such as light material or excessively noisy environments). The reason for this is that a single-pole filter, such as the Zolock integrator, has a relatively wide band width. As a result, noise signals generated by unwanted flow tube v;l.raLion modes, noisy environment, material flow noise, electromagnetic or radi frequency il ,l~lrerence and disturbances are not removed to the extent necess~ry 10 for high meter sensitivity required for precision. Depending on their frequency, their amplitude is reduced somewhat, but they can still interfere with the precision time delay measurement between the two sensor output signals when measuring low mass materials such as gases.
There is another source for errors in the Zolock and Bruck systems. The 15 integrator time delay measurements are made at three (3) certain well defined- points of the sinusoidal sensor signals. The two sensor signals are ideal onlywhen their shape is the same and is symmetrical around their peak values.
However, when the two magnetic circuits (sensors~ that generate the sensor signals are not identical, the resulting non-ideal wave forms contain dirrerenl 20 amounts of harmonics with possibly undefined phase conditions which can altertheir shape and poLe"Lial'y change their sym,l1eL,ical character. The result of such variations is such that when, during normal operations, a Zolock integrator is calibrated with one wave form and is subsequently used to measure another wave form, the difference in wave forms may produce an undefined and unknown 25 amount of error due to its harmonic content and its undefined and varying phase of its harmonics.
Other analog circuit design techniques suffer from similar problems of complexity, insufficient noise immunity, or insufficient harmonic rejection.
There are techniques currently available, such as digital signal processing 30 (hereinafter referred to as DSP) and associated digital filtering, to overcome the above-discussed problems and simultaneously improve the signal to noise ratio of the signals being processed. However, these alternatives have been more complicated and expensive than conventional analog circuit designs. In addition, CA 022084~2 l997-06-l3 these prior DSP designs have shown only modest improvement over conventional - analog circuit designs with respect to noise immunity and harmonic rejection.
United States Patent Number 4,934,196, issued June 19, 1990 to Romano, teaches a DSP design for computing the phase difference, ~\t, and correlated 5 mass flow rate. Romano's design alters the sampling frequency of an A/D
converter in an ~Len ~pl to maintain an integral number of sample times within each periodic cycle of the vibrating flow tubes. This need for variable frequency sampling complicates Romano's DSP design. Although this DSP design is structurally quite distinct from prior discrete analog circuit designs, it has proven 10 to provide only modest improvements over analog designs in meas~,rell~e"l accuracy because it provides significant improvement in filtration only at integer multiples of the fundamental frequency. However, many signal components result from mechanical vibration modes of the flow tubes whose resonant frequencies are not integer multiples of the fundamental frequency and are therefore poorly rejected by the prior DSP designs.
- Neither prior approach (analog nor prior DSP) effectively rejects non-harmonic or broadband noise. From the above discussion, it can be seen that there is a need for an improved method and apparatus for measuring mass flow rate in a Coriolis mass flow meter.
SOLUTION
The present invention solves the above identified problems and achieves an advance in the art by applying digital filtering and digital signal processing (DSP) methods and apparatus to improve the accuracy of mass flow measurements in a Coriolis mass flow meter. The present invention co"l,ulises a DSP design which includes adaptive notch filters to improve the accuracy of frequency and phase measurements used in the computation of mass flow rate.
The use of adaptive notch filtration in the present invention is one application of the technology commonly referred to as Adaptive Line Enhancement (ALE).
In the present invention, the signal from each vibrating flow tube sensor is sampled, digitized, and then processed by a digital adaptive notch filter which passes all noise signals outside a narrow frequency band (a notch) around the fundamental frequency. This digitized filtered signal is then subtracted from the original digitized signal to produce an enhanced signal representing the sensor -CA 022084~2 1997-06-13 output signal waveform at the fundamental frequency with virtually all noise signals eliminated. This method and apparatus eliminates harmonic as well as non-harmonic noise signals. Initially the width of the notch filter's "notch" is wide and is adapted over time to narrow as it converges on the fundamental frequency.
5 Adaptation algorithms rapidly adapt the notch frequency of the adaptive filter to ~ track changes over time in the fundamental frequency of the vibrating flow tubes.
The DSP design of the present invention uses a fixed sampling frequency as distinct from Romano's variable frequency design. This fixed sar~ li"y frequency approach permits rapid convergence of the adaptive notch filters on the 10 fundamental frequency of the vibrating flow tubes and simplifies the total circuit design. The fixed sampling rate eliminates the need exhibited in Romano to provide aLldilio~ ,al circuitry to vary the sampling rate. The present design pel rur, I Is cornr~ tional adjustments to compensate for spectral leakage between the fixed Salll,~iill~J frequency and the variable fundamental frequency of the vibrating flow 15 tubes. Despite this added computational complexity, the present invention is simpler than prior designs exemplified by Romano and provides better noise immunity due to the use of adaptive notch filtration.
The present invention provides superior noise immunity and harmonic rejection as compared to all known designs and simplifies aspects of the DSP
20 design disclosed by Romano. This permits improved accuracy of the flow rate measurements even in particularly noisy environments as well as applications with low density flow materials (such as gas).
Since the flow tubes vibrate at the same fundamental frequency, adaptation of the notch filters is de~er" ,i"ed by samples from only one of the two notch filters.
25 The ada~l~Lion ~J~ hL~ so determined are applied to both notch filters. Heuristics applied to the computations by the present invention prevent the notch filters from diverging from the fundamental frequency due to instability in the computations.Other heuristics restart convergence computations for the adaptation when the signal to noise ratio measured by the notch filter is too small. A small signal to 30 noise ratio indicates that the adaptive notch filter is not converged on the ~ fundall,e"Lal frequency. This may be due to a shift in the fundamental frequency of the vibrating flow tubes.

; CA 022084~2 l997-06-l3 ~
In a first embodiment of the present invention, the output signal from each vibrating flow tube sensor is sampled at a fixed frequency by a COI, es~onding A/D
converter. The sampled value generated by each A/D converter is then applied to a corresponding decimation filter to reduce computational complexity by - 5 reducing the number of samples used in subsequent computations. The decimation filters also provide a degree of anti-aliasing filtration to smooth the ~ sampled analog signals. The decimated signals are then each applied to a corl~sponding adaptive notch filter to further enhance the signal from each sensor.
- The enhanced output signal from each sensor, after being filtered of most noise and hallllo,~ -s, is then applied to a corresponding phase computation element to determine the phase difference between the two enhanced signals. The output of each phase computation element is applied to a computation element to determine the time dirr~r~rlce between the enhanced sensor signals and hence the~-- proportional mass flow rate.
In a second embodiment of the methods of the present invention, four adaptive notch filters are utilized, two in series on each of the left and right channel signals. The two filters on each of the left and right channels are "cascaded" in that the first filter utilizes a low-Q (wide notch) filter to supply limited signal enhancement but the ability to rapidly converge on changes in the fun.3a,l,e, llal frequency of the vibrating flow tubes. The signal output from the first c~c~er~
notch fiiter is then applied to a second cascaded notch filter. The second notch~ fiiter utilizes a high-Q (narrow notch) filter to provide superior noise and harmonic -.- rejection over that of previous solutions or over that of the first embodiment described above. Despite the narrow notch (high-Q) of the second notch filter, 25 it can still rapidiy adapt to changes in the fundamental frequency of the vibrating flow tubes due to the limited enhancement ffiltration) performed by the first notch - fiiter. The reduced noise and harmonic levels in the signal applied to the second notch filter allow it to also rapidly converge on changes in the fundamental frequency of the vibrating flow tubes.
An additional notch filter ffifth filter) having a notch shape even wider than - that of the first cascaded notch filter is used to provide an estimate of the ~ al l ,e, ILtll frequency of the vibrating flow tubes. This estimate is used by weight - adaptation computations to set the frequency parameter of the first c~sc~ed CA 022084~2 1997-06-13 notch filters for both the left and right channels. The output from the second cascaded notch filters is used by weight adaptation computations to adjust the frequency parameter of the second cascaded notch filters.
This combination of two (or more) cascaded adaptive notch filters to 5 enhance the output signal from each sensor further enhances both the rejectioncharacteristics of the filtration and the speed with which the adaptive filters converge on changes in the fundamental frequency of the vibrating flow tubes.
The term "adaptive notch filter" as used herein refers broadly to a filter with variable parameters. This definition contrasts with a more widely acce~led 10 definition which combines a variable parameter filter with a mechanism for automatically tuning the parameters of the filter based on the filter's own inputs and outputs. As used herein, the adaptation of some notch filters is computed based on the operation of other filters rather than each filters own inputs and outputs. In other words, some notch filters in the present invention are slaved to 15 the operation of other notch filter computations. For this reason, the detailed - discussions of the filters and the adaptation mechanisms are separated. One ac~a,ulalio,, computation may adjust the parameters for multiple notch filters based on inputs from a single filter.
The above and other aspects of the present invention will become apparent 20from the following description and the attached drawing.
Brief Description of the Dra~ g FIG. 1 shows a typical Coriolis mass flow meter attached to meter electronics which embody the apparatus and methods of the present invention;
FIG. 2 shows a block diagram of the computational elements within the 25meter electronics which determine mass flow rate through the flow meter in accordance with the present invention;
FIG. 3 shows additional detail of a first embodiment of the present invention shown in FIG. 2 wherein a single adaptive notch filter is used in conjunction with each sensor signal;
30FIGS. 4-12 show additional detail of the computational elements of the first ~ embodiment of the present invention shown in FIG. 3;

CA 022084~2 1997-06-13 FIG. 13 shows additional detail of a second embodiment of the present invention shown in FIG. 2 wherein two cascaded adaptive notch filters are used in conjunction with each sensor signal;
FIGS. 14-16 show additional detail of the computational elements of the 5 second embodiment of the present invention shown in FIG. 13;
FIG. 17 is a flowchart of a software implementation of the first embodiment of the present invention and depicts interrupt processing for servicing of an A/D
converter and associated decimation of the samples;
FIG. 18 is a flowchart of a software implementation of the first embodiment 10 of the present invention and depicts processing of decimated samples for purposes of filtering and determination of ~t phase difference;
FIG. 19 is a flowchart depicting additional detail of an element of FIG. 18 which determines updated filter parameters after each decimated sample is processed; and FIG. 20 is a block diagram of digital signal processing electronics sl ~it~hlQ
to perform the software methods of the present invention.
Detailed Description of the Preferred Embodiment A typical Coriolis mass flowmeter 10 is illustrated in FIG. 1 as having two cantilever mounted flow tubes 12, 14 affixed to a manifold body 30 so as to have20 su~latllial'y identical spring constants and moments of inertia about their respec-tive out-of-phase bending axes W-W and W -W' .
A drive coil and magnet 20 are mounted at a midpoint region between the top portion 130 and 130' of flow tubes 12, 14 to oscillate fiow tubes 12, 14 out of phase about axes W-W and W'-W'. Left sensor 16 and right sensor 18 are 25 mounted near the respective ends of the top portions of flow tubes 12, 14 to sense the relative movement of flow tubes 12, 14. This sensing may be done in many ways including by measuring the movement of the top ends of the flow tubes 12, 14 through their zero crossings or some other pre-defined point. Fiow - tubes 12 and 14 have left side legs 131 and 131 and right side legs 134 30 and 134' . The side legs converge downwardly toward each other and are affixed to surfaces 120 and 120' of manifold elements 121 and 121' . Brace bars 140R
and 140L are brazed to the legs of flow tubes 12, 14 and serve to define the axes W-W and W' -W' about which the flow tubes oscillate out of phase when driver 20 WO g7103339 PCTJUS96111280 is energized over path 156. The position of axes W-W and W-W is deler--,i-~ed by the placement of brace bars 140R and 140L on flow tube side legs 131 131 and 134 134 .
Temperature detector 22 is mounted on side leg 131 of flow tube 14 to 5 measure the flow tube s temperature and the approximate temperature of the material flowing therein. This temperature information is used to del~r,l,i-,e changes in the spring constant of the flow tubes. Driver 20, sensors 16 and 18 and temperature detector 22 are connected to mass flow instrumentation 24 by paths 156 157 158 and 159 respectively. Mass flow instrumentation 24 inc!llrles 10 at least one microprocessor which processes the signals received from sensors 16 18 and 22 to determine the mass flow rate of the material flowing through flowmeter 10 as well as other measurements, such as ",~lerial density and temperature. Mass flow instrumentation 24 also applies a drive signal over path 156 to driver 20 to oscillate tubes 12 and 14 out-of-phase about axes W-W
15 and W -W .
Manifold body 30 is formed of casting 150 150 . Casting elements 150, 150 are attachable to a supply conduit and exit conduit (not shown), by rla,lyes103, 103 . ManHold body 30 diverts the material flow from the supply condùit into flow tubes 12, 14 and then back into an exit conduit. When manifold flanges 103 20 and 103 are connected via inlet end 104 and outlet end 104 to a conduit system (not shown) carrying the process material to be measured the ",~lerial enters manifold body 30 and manifold element 110 through inlet orifice 101 in flange 103 and is connected by a channel (not shown) having a gradually changing cross-section in casting element 150 to flow tubes 12 14. The material is divided 25 and routed by manifold element 121 to the left legs 131 and 131 of flow tubes 14 and 12 respectively. The material then flows through the top tubes elements 130,130 and through the right side legs 134 and 134 and is recombined into a single stream within flow tube manifold element 121 . The fluid is thereafter routed to a channel (not shown) in exit casting element 150 and then to exit man~old element30 110 . Exit end 104 is connected by flange 103 having bolt holes 102 to the conduit system (not shown). The material exits through outlet orifice 101 to return to the flow in the conduit system (not shown).

CA 022084~2 l997-06-l3 Mass flow instrumentation 24 analyzes signals received on paths 157, 158, and 159 and generates standard output signals on path 155 to indicate mass flow rates utilized by a control system or operator for monitoring and control of themass flow rate through the associated conduit system (not shown).
OVERVIEW:
The present invention comprises digital signal processi"y methods operable within a digital signal processor (DSP) chip to perform the computational functions within mass flow instrumentation 24. Discrete samples are taken of the analog signals generated as output from each of the flow tube sensors. The discreLe samples from the left and right sensors are digitized by use of standard analog to digital conversion (A/D) devices. Once digitized, further processing of the samples is performed by digital signal processing methods within the DSP chip.
The processing of the digitized signal samples is expressed herein in two forms.In one form of expression, the DSP software flowcharts and equations used for the various filtering and processing functions are presented. To aid in the explanation - of the methods of the present invention, a second form of expression is utilized which depicts the computation of the various equations as pseudo-circuits (e.g.
block diagrams representing summing junctions, multiplication junctions, delay circuits, registers, multiplexors, etc.). Certain more complex mathematical operations are left as high level elements in the pseudo-circuit diagrams and are typically referred to herein as "computational elements". The two forms of explanation of the present invention are intended as equivalent descriptions, either of which fully specifies the methods and function of the present invention.
OVERVIEW- PSEUDO CIRCUITS:
FIG. 2 depicts the general structure of, and associated flow of information in, the flow meter electronics of the present invention. The meter electronics of the present invention is comprised of two essentially identical "channels": a first channel for processing the left flow tube sensor output signal and a second channel for processing the right flow tube sensor output signal. The two "channels" are identical except with respect to the weight adaptation of the notch filters as discussed below.
The description presented below is discussed in terms of a typical Coriolis flowmeter application in which the fundamental frequency of the vibrating flow -tubes is approximately 100 Hz. It will be readily recognized that the apparatus and methods of the present invention may be applied to any common flowmeter fundamental vibrating frequency.
Many of the computational elements discussed below operate 5 synchronously with clock signals associated with various samplings of the flow~ tube sensor output signals. CLOCK 214 of FIG. 2 provides clocking signals associated with the various sampling rates of the computational elements discussed below. First, CLOCK 214 supplies a periodic pulsed signal clock to A/D converters 200 over path 270 to determine the sampling rate of the raw 10 (unprocessed) signals generated by the flow tube sensors. Each A/D converter 200 samples its corresponding analog signal and converts the sampled value to digital form once for each signal pulse applied to path 270 by CLOCK 214. This clock signal applied to A/D converters 200 over path 270 must have a highly accurate frequency to permit sampling of the flow tube sensor output siy"als at 15 a fixed sampling rate as required for the processing of the present invention. This clock pulse accuracy is preferably achieved by use of a crystal controlled clock.
This same clock signal is also applied to 48:1 decimation filter elements 202 via path 270. The decimation filter elements 202 reduce the number of samples by a factor of 48 while providing significant anti-aliasing filtration of the sampled signal 20 values. One of ordinary skill in the art will recognize that the particular decimation ratio of 48:1 is a matter of engineering design choice depending upon the particular application environment.
CLOCK 214 also provides a signal CLK to other computational elernents ~iscussed below. The frequency of the CLK signal corresponds to the frequency 25 of sample values output by the decimation filter elements 202. In other words, the frequency of the CLK clock signal is 1/48th the frequency of the clock signal generated and applied to path 270. In the preferred embodiment of the present invention, the computational elements "clocked" by the CLK signal are implemented as software functions operable on a digital signal processing (DSP) 30 chip. As such, these functions perform their computations on the decimated discrete sampled sensor output signal values. The "clocking" of these functions corresponds to the availability of discrete sampled values. These values are preferably buffered in software implemented queues or FlFOs so that the functions 1~

- CA 022084~2 l997-06-l3 may actually operate asynchronously with respect to the fixed rate, crystal controlled, sampling frequency of the A/D converters 200. In the description of - the figures which follow, the CLK signal is representative of the frequency at which decimated, discrete, sampled sensor output signal values are made available for 5 further processing by the computational elements. The actual cor~p~lt~tion processing in software within the DSP chip proceeds generally asynchronously - with respect to the A/D sampling frequency of the clock signal on path 270.
The output signal from the right flow tube sensor ~8 of FIG. 1 is applied to A/D converter 200 over path 158 of FIG. 1. The output signal from the left flow 10 tube sensor 16 of FIG. 1 is applied to a second A/D converter 200 over path 157 of FIG. 1. A/D converter 200 samples and converts the analog signal from the right flow tube sensor to a digital value. A second A/D converter 200 samples and converts the analog signal from the left flow tube sensor to a digital value.
A/D converters 200 operates responsive to the fixed frequency periodic clock - 15 signal received on path 270 supplied by a system wide clock 214.
- The converted digital value is applied over path 252 to 48:1 decimation filter element 202. The 48:1 decimation filter element 202 is done in two stages, an 8:1 stage followed by a 6:1 stage. Both stages of decimation filter element 202 are ,ur~ l,ly implemented as finite impulse response (FIR) anti-aliasing filters. One 20 skilled in the art will recognize that an IIR filter may be used for the decimation stages. Use of FIR versus ilR filtration is a matter of design choice based on computational complexity and the relative power of the computational elements used in a particular design.
The first stage of decimation filter element 202 performs an 8:1 reduction 25 in the sample rate from 38.4 kHz to 4.8 kHz. The transfer function of the filter is:
G(z) = ~1 z-8)5 / (1 z-1)5 - Pole-zero cancellation yields an FIR filter of 36 taps. The filter has 5 zeros at each multiple of the subsampling frequency. This provides strong rejection of- those frequencies which alias into the passband of the second stage filter. This 30 first stage filter has small integer coefficients which may be represented in single precision computer arithmetic to thereby simplify computational complexities of the convolution and improve execution speed.

CA 022084~2 1997-06-13 WO 97/03339 PCT/US9611~280 The second stage filter of the decimation filter element 202 performs a 6:1 rer~l Iction in sample rate from 4.8 kHz to 800 Hz. The second stage filter is a 131 tap FIR filter designed using the well known Remez exchange algorithm. The passband is DC through 250 Hz and the stopband begins at 400 Hz. The 5 p~ssb~nd has weight 10-5 and the stopband has weight 1.
A high degree of anti-aliasing is provided by the two stage decimation filters. All aliasing components are reduced by over 120 dB, while ripple from DC
through 230 Hz is less than 1.5 dB.
The left channel, comprising A/D converter 200 and decimation filter 10 element 202 connected via path 250, operates identically to the above-~isc~ ~ssed right channel. The output of decimation filter element 202 for the left chani)elapplies its output signal to path 254.
The sample values from A/D converters 200 and the computations of the decimation stages preferably utilize 32-bit fixed point arithmetic to maintain the 15 computational accuracy and performance required. Subsequent computations for -- the notch filtration, phase computations, l~t computations, and mass flow rate computations are preferable performed using floating point arithmetic due to thewider range of computational scaling involved with the more complex functions.
The anti-aliased, decimated, digitized signal values are applied over path 20 256 to adaptive notch filter 204. Adaptive notch filter 204, discussed in detail below, enhances the signal values by effectively filtering all frequencies outside a band ce, llered about the fundamental frequency of the vibrating flow tubes. Theadaptive notch filter 204 eliminates a band of frequencies (a notch) centered about the fundamental frequency. The resultant signal is all noise outside the notch 25 ce~ r~ about the fundamental frequency of the vibrating flowtubes. This noisesignal is then subtracted from the signal applied as input to the notch filter 204 over path 256 which is the sum of the fundamental frequency and all noise not filtered by decimation filter element 202. The result of the subtraction, which represents the fundamental frequency of the vibrating flowtubes filtered of most30 noise signals, is then applied to path 262 as the output of the notch filter 204.
The parameters (weighting factors or coefficients and the ~e!-;~ci"g parameter) of the notch filter 204 determine the characteristics of the notch, namely the shape of the notch (bandwidth of frequencies rejected) and the ~:3 CA 022084~2 1997-06-13 fundamental frequency. ~The parameters are computed by weight adaptation element 210 and applied to notch filter 204 over path 258.
The left channel adaptive notch filter 204 accepts its input over path 254 and applies its output to path 260. As discussed below, signals generated as 5 ~~ Itr~ from left channel adaptive notch filter 204 are used by weight adapl~lion element 210 as feedback in determining the coeflicients of both notch filters (left and right channel adaptive notch filters).
The weighting factors (coefficients) of both notch filters 204 (left and right signal channels) are determined by operation of weight adaptation element 210.
10 Weight adaptation element 210 receives the filtered signal, the noise portion of the unfiltered signal, and a gradient of the filtered signal from the output of left channel adaptive notch filter 204. These signal values are used in the time-dependent (iterative) computations to determine the appropriate coefficients of the notch filters. The coefficients so determined control the characteristics of the notch.
15 Both the shape of the notch and the fundamental frequency are adapted to track - changes in the fundamental frequency. The shape of the notch deLer"~;. ,es thespeed with which the adaptive notch filters can converge on changes to the fundamental frequency. A wider notch provides less filtration but may be more rapidly adjusted to changes in the fundamental frequency. A narrower notch 20 converges more slowly to changes in the fundamental frequency but provides superior filtration of the input sensor signals.
It will be recognized that either the left or right channel output signals may be used as feedback to the weight adaptation element 210. Though it would be possible to utilize both the left and right channel output signals in weight 25 adaptation element 210, there is no clear benefit in so doing to outweigh theadded computational complexities. Regardless of the source of inputs to weight adaptation element 210, the weight adaptation parameters computed therein are applied to both the left and right channel adaptive notch filters 204 so that both sensor signal output channels are processed identically. Using a single set of 30 parameters applied to both the le~t and right channels serves to maintain thecritical phase relationship between the two channels, the fundamental value usedto compute the ~t value proportional to mass flow rate.

CA 022084~2 1997-06-13 WO 97/03339 ~CTIUS96111280 The values computed by the weight adaptation element 210 are also used, as discussed below, in the phase and ~t computations.
Element 212 receives coefficients from weight adaptation element 210 and delt:r, l li~ les the fundamental frequency of the vibrating flow tubes. Frequency and 5 Goertzel weight information are generated by frequency calculation element 212 and applied to path 268.
The filtered signal values generated by adaptive notch filter 204 are applied to phase computation element 206 over path 262. Phase computation element 206 receives Goertzel weight and frequency information over path 268 from 10 frequency c~lcu~tiQn element 212. Phase computation element 206 uses Fourier analysis techniques with two Hanning windows to determine the phase of the filtered signal. The length of a window is a function of the nominal or expectedflow tube fundamental frequency. The length of a window determines a number of oscillatory cycles of the flow tubes over which samples are gathered and 15 weighted to determine the phase of the flow tubes. The expected flow tube - frequency may be programmed into the electronics of the present invention at time of manufacture, or may be entered as a parameter at a particular installation/application site, or may be determined by operation of the flowmeter and appropriate measurements. The length of a window represents a tradeoff 20 between response time and rejection of signal noise and leakage. A larger number of cycles accumulated to determine the phase provides for additional rejection of noise but requires additional delay to achieve causality and therefore slows response to changes in the flow tube vibration phase relationship. Fewer samples reduces the delay and therefore improves the speed of response to flow 25 tube vibration phase changes, but provides inferior noise rejection. Eight flow tube cycles is selected as the preferred window length as measured in cycles.
Assuming a given expected frequency, the preferred window size ~2N) is determined as:
window_length = 2. floor(3200/expected_tube_frequency) 30 where floor(x) is the largest integer less than or equal to x.
The Hanning window is represented as a vector of weights to be applied to the discrete samples over the period of one Hanning window. Where 2N is the =~ CA 022084~2 1997-06-13 number of discrete samples within one period of the Hanning window, the weight for the k'th discrete sample where k ranges from 0 to 2N-1 is determined as:
h(k) = (l/2) ( 1 - COS ( ~k / ( 2N -1) ) ) A half window signal pulse is generated by CLOCK 214 of FIG. 2 and applied to path 274 of FIG. 2. every N discrete samples (where a complete Hanning window of the sampled sensor output signal has 2N discrete samples in a single period) for purposes discussed in detail below relating to parallel - computations of overlapping Hanning windows. In addition, CLOCK 214 of FIG.

2 applies SAMPNO, a counter value, on path 272. SAMPNO on path 272 counts (as a modulo N function of the CLK signal) from 0 to N-1. The SAMPNO counter on path 272 increments with each pulse of the CLK signal. When SAMPNO
reaches N-1 the next pulse of the CLK signal from CLOCK 214 resets SAMPNO
to 0. The half window signal corresponds to the SAMPNO counter being equal to zero. In the preferred embodiment of the present invention, the SAMPNO
counter is implemented in software which counts the number of discrete - decimated sampled sensor output signal values processed during a Hanning - window. The software implementation of the SAMPNO counter increments - asynchronously with respect to the fixed frequency, crystal controlled clock provided by CLOCK 214 of FIG. 2 on path 270.
The signal samples at the edges of each window are given lower weights than those toward the middle of the window. To more fully utilize the available data, two Fourier calculations are done simultaneously such that the windows ~ overlap by one half of a window length. New Fourier phase measurements are produced every half window of samples.
- 25 The use of a constant window size in the present invention allows the Hanning window weights to be pre-computed before flow measurements begin.
When used in conjunction with a discrete-time Fourier transform (DTFr), as in the - present invention, the window size determines the sharpness of the frequency discrimination characteristic of the DTFT filter output. It also increases the 30 rejection of noise and pseudo-harmonics. Unfortunately, a longer window size provides slower response of the filter to changes in phase. The window size as determined above therefore represents the best known approximation suited to balancing these competing goals (improved frequency discrimination and noise -CA 022084~2 l997-06-l3 - WO 97/03339 PCTlUS9~i/11280 rejection versus rapid response to phase changes). The preferred window size may be changed for different flow meter applications to optimize for certain environmental conditions.
Phase computation elements 206 sum the filtered discrete sampled values 5 to generate a complex number indicative of the phase of the sampled filtered sensor output signal. This complex number is applied to path 266 to be used in subsequent f~t computations. Specifically a Goertzel filter Fourier transform isapplied to each Hanning window of filtered discrete sampled sensor output signalvalues of both the right and left channels. The coefficients of the Goertzel filter are 10 determined by the frequency computation element 212 and supplied to phase computation elements 206 over path 268. The complex number output of phase computation element 206 is applied to path 266 and is used by the At computation.
The phase computation element 206 for the left channel operates identically 15 to the above-discussed right channel. The output of adaptive notch filter 204 for the left channel applies its output signals to path 260. Phase computation element 206 receives these signals and applies values indicative of the phase of the left channel signal to path 264.
Phase information for both the left and right channels is deLe"~,i"ed by 20 operation of phase calculation elements 206 and received by at c~lcul~tion ele~ "e"l 208 over path 264 for the left channel and path 266 for the right channel.
Frequency information determined by operation of frequency calculation element 210 is received by ~t calculation element 208 over path 268. ~t c~lclJI~tion element 208 determines the time delay resultant from the phase difference 25 between the left and right sensor output signals which in turn is approximately proportional to the mass flow rate of the material flowing through the flow tubes of the Coriolis flowmeter.
The Fourier transform of the left channel is multiplied by the conjugate of the Fourier transform of the right channel. The angle of the complex result is then 30 computed. This phase difference angle is divided by the tube frequency of thevibrating flow tubes (converted to appropriate units to match the phase measurements) to produce a ~t value.

-; CA 022084~2 1997-06-13 --OVERVIEW- SOFT\NARE:
- The flowcharts of FIGS. 17-19 provide an overview of the operation of a software implementation of the methods of the present invention. FIG. 17 depictsthe operation of a portion of the software which operates in real time in response 5 to an interrupt from the A/D converters 200 (of FIG. 2). FIG. 18 depicts the operation of a portion of the software implementation which performs further rlllr~lion and processing on the decimated samples produced by operation of the software depicted in FIG. 17. Decimated samples produced by operation of the - -software depicted in FIG. 17 are buffered so that the softNare of FIG. 18 may ~ 10 operate asynchronously with respect to the accurately timed samples from the - A/D converters 200. FIG. 19 provides additional detail of an element in FIG. 18 which includes heuristic methods to help assure stability and accuracy of the resultant measurements of mass flow rate.
The software of FIGS. 17-19 is operable on mass flow instrumentation 24 shown in greater detail in FIG. 20. Digital signal processor 2000 of FIG. 20 is a computing device much like any common microprocessor but with special purpose functions tuned for application to signal processing tasks. Many such DSP processor devices are known to those skilled in the art. One exa"".le of such a device is the Texas Instruments TMS 320C50-57. This device is a fixed -~ 20 point arithmetic signal processor. Software emulation libraries are provided for precision floating point computations. This exemplary device provides 32-bit ,urt:c;si~n required for the sampling and decimation operations. The floating point ~mulation software provides adequate performance for most flow meter applications though other processor devices may be used if additional floating point computational performance is required for a particular flow meter application.
Processor 2000 reads program instructions from program ROM 2002 over bus 2052 and manipulates data and buffers in RAM 2004 over bus 2054. One of ordinary skill will recognize that depending upon several cost and performance factors, it may be preferable under certain circumstances to copy the program instructions from ROM 2002 to RAM 2004 to improve the pe, rur" ,a"ce of processor 2000 in fetching instructions.
A/D converters 200 each receive an analog signal from their respective flow tube sensor output signals applied to paths 157 and 158 respectively. Processor 2000 applies control signals to A/D converters 200 over paths 250 and 252, respectively, and receives digitized sample values from the A/D converters 200 over paths 250 and 252, respectively. Processor 2000 applies control signals over path 2050 to clock 214 to determine the sampling frequency of A/D converters 200. In response, clock 214 applies a sample frequency clock signal to A/D
converters 200 over path 270. In this manner, processor 200 initially sets the sample frequency of A/D converters 200 to the desired rate.
In the preferred embodiment, A/D converters 200 are embodied within a single integrated circuit with multiple converters and a single communication bus 10 connection to the DSP processor. This helps assure that the phase relationship behNeen the ~NO sampled signals is due to the Coriolis effects of the vibrating flow tubes rather than effects of imbalances between physically se,c ~ aLe A/D converter circuits. Many such stereo A/D converter chips are known to those skilled in theart. One example of such a chip is the Crystal Semiconductors CS5329, a 2-15 channel stereo A/D converter device.
Processor 2000 determines the appropriate fundamental frequency at whichthe flow tubes are vibrated and applies a proportional signal to path 2058. Driver circuit 2008 converts the signal applied to path 2058 into a signal appro~,riaLe to drive the flow tubes to vibrate and applies the signal to path 156. Many methods20 and a~.~aralus to drive the flow tubes to vibrate are well known in the art and need not be discussed here in further detail.
Processor 2000 also determines a ~t value from the phase dirr~re,)ce between the sampled channels and applies a signal proportional to ~\t to path 2056. D/A converter 2006 converts the signal value applied to path 20~6 into an 25 analog signal applied to path 155 proportional to mass flow rate. The signal on path 155 is applied to utilization means (not shown) appropriate to the particular flow meter measurement application.
OVERVIEW - SOFT\NARE (REAL TIME INTERRUPT PROCESSING):
As noted above, the A/D converters 200 operate at a fixed frequency to 30 provide accurately timed sample values of the sensor output signals from the left and right flow tubes. As shown in FIG. 17, the raw sample values are decimated by a two-stage, 48:1 decimation filter. The decimation filtration provides some smoothing (anti-aliasing) of the sampled data while reducing the sample rate and CA 022084~2 1997-06-13 thus the computational power required to apply the notch filters and to determine phase differences and the resulting ~t measurement. Well known software techniques may be applied to permit the nesting of interrupts during certain less critical computational processing to thereby avoid any possible loss of data due5 to complex computations while an A/D converter 200 sample interrupt is being rr, processed. For example, circular buffering as in the use of FIFO memory techniques can be applied to retain additional data while previous samples are being processed. These buffering techniques and others are well known to those of ordinary skill in the art and need not be addressed further.
Element 1700 of FIG. 17 represents the occurrence of an interrupt - generated by the A/D converters 200 to signify the availability of a digitized sample for both each of the left and right flow tube sensor signal outputs. Elements 1702 then operates in response to the interrupt to read the sampled, digitized valuesfrom the A/D converters 200 for each of the left and right flow tube sensor siyl l~ls 15 (also referred to herein as the left and right channels). The sampled, digitized - - values read from the A/D converters 200 are stored in a first stage circular buffer associated with each of the left and right channels. Each channel's first stage - circular buffer is of sufficient size to store the sampled values of the FIR filter. The - first stage filter is preferably a 36 tap filter and therefore requires at least 36 entries 20 in the circular buffer for each channel.
Element 1704 is operable to determine if eight new samples have been stored in the first stage circular buffer since the last convolution of the sample -- values read from the A/D converters 200 by operation of element 1702. If eight new samples have not yet been so read, then processing of this A/D converter 25 200 interrupt is complete. If eight new samples have been stored in the first stage circular buffer since the last filter convolution, then element 1706 is operable to determine the convolution of the 36 sampled values currently stored in the first- stage circular buffer for each channel. The convolved value for each channel is ~ then stored in a second stage circular buffer associated with each channel. Each -- 30 channel's second stage circular buffer is of sufficient size to store the sampled values of the FIR filter. The second stage filter is preferably a 131 tap filter and therefore requires at least 131 entries in the circular buffer for each channel.

WO 97/03339 PCTlUS96lll280 Element 1708 is operable to determine if six new values have been stored in the second stage circular buffer by operation of element 1706. If six new values from the first stage convolution have not yet been stored in the second stage ~ circular buffer, then processing of this A/D converter 200 interrupt is complete.
5 If six new values have been stored in the second stage circular buffer, then element 1710 is operable to determine the convolution of the 131 values stored in the second stage circular buffer for each channel. The second stage filter sum (convolution) of the second stage circular buffer values for each channel is then stored in a decimated sample circular buffer associated with each channel. Each 10 I channel's decimated sample circular buffer holds decimated values for its associated left or right channel samples. The buffers are used to hold the dec;,nalecl values until the asynchronous processing described below with respect to FIG. 18 can retrieve the values for further filtering and processing. The decimation computations are simple enough that they can be pr~cessed within the 15 interrupt processing software of this FIG. 17. Further processing to apply the -- notch filter, to determine phase di~Ference and ~t values, and to adapt the notch filter parameters, is more complex and therefore operates asynchronously with respect to the real time processing required for reading sample values from the A/D converters 200. One of ordinary skill in the art will recognize that the division 20 of tasks between the interrupt processing of FIG. 17 and the asynchronous processing of FIG. 18 is a matter of design choice depending upon the performance characteristics of the selected DSP chip and desired performance goals as measured by A/D converter sampling frequency. A number of equivalent software and associated data structures are within the spirit and scope of the 25 present invention.
The software structure summarized herein with reference to FIGS. 17-19 are described below in ~pseudo-circuits" to aid in understanding of the present invention. In these pseudo-circuit descriptions, a signal referred to as CLK is pulsed for each decimated sample generated by the operations described above 30 in FIG. 17. In other words, the CLK signal is 1/48th the sample frequency. As~ can be seen in the software description depicted in FIGS. 17-19 the CLK signal indicates simply that a decimated sample value is available in the decimated sampie circular buffers (more precisely a pair of decimated values, one for the left CA 022084~2 l997-06-l3 channel and one for the right). The computationally more complex notch rilL,~Iion - and ~t determinations are performed asynchronously with respect to the accurately timed sample frequency clocked A/D conversions and associated two-stage decimations. In other words the CLK signal discussed below is preferably 5 no more than an indication that a decimated sample is available in the decimated sample circular buffer.
- OVERVIEW - SOF~WARE (ASYNCHRONOUS DIGITAL SIGNAL
~ PROCESSING):
FIG. 18 is a flowchart depicting the asynchronous portion of the software --~ 10 which is operable in response to the real time san~ li"g and decimation ~.eralions ~iscllssed above with respect to FIG. 17. Element 1800 of FIG. 18 represents allprocessing required to initialize the circular buffers ffirst stage, second stage, and - decimated sample) used to pre-process the sampled data for both channels. In ' addition, element 1800 initializes any required hardware associated with the A/D
15 converters 200 of FIG. 2 to setup the fixed sampling frequency of the converters - - (i.e. ciock 214) and to enable the A/D converters 200 to interrupt the DSP
operation when a sampled value is available from the A/D converters 200.
Element 1802 is operable to wait until a pair of decimated sample values is available in each of the decimated sample circular buffers (one for the left channel 20 and one for the right). When a pair of decimated sample values is available element 1804 is operable to apply the notch filter function to the dee;."~L~.I, sampled value to thereby enhance the signal. The signal is enhanced by - removing unwanted noise and harmonics of the signals frequency.
Element 1806 is next operable to update the parameters of the notch filters.
25 The a~la,ul~Lio" methods of the present invention adapt the notch filter parameters to account for changes in the fundamental frequency of the vibrating flow tubes.In the process of the notch filter adaptations, heuristics are utilized to help assure stability of the flow measurements made by meter instrumentation 24. These heuristics are discussed in further detail below. The updated filter parameters are 30 applied to the notch filters.
Element 1812 of FIG. 18 is next operable to determine if the sample is the first sample at the start of a new half window period (i.e. SAMPNO = 0 indicating that all samples in the previous half window have been processed). If the sample _ ~ ==

CA 022084~2 1997-06-13 WO g7/03339 PCTtUS96111280 is not the first sample at- the start of a half window period, then processing continues with elements 1808 and 1810 to update the Goertzel filter parameters and to accumulate the signai and noise energy values. If the sample is the firstsample in a new half window period, then processing which relates to completion 5 of the previous half window is performed by operation of element 1814 discussed ~ below.
Element 1814 is operable at the end of a half window period (the start of a new half window period) to determine the signal to noise ratio (SNR) given theaccumulated enhanced sample energies and accumulated enhanced noise 10 component energies generated by operation of element 1810 discussed below.
The accumulated energy sums generated by operation of element 1810 are also reset by operation of element 1814 to prepare the accumulation for the start of the next Hanning half window period of samples. Element 1816 then tests whether the SNR is above an acceptable threshold. In the present invention, a pr~r~
15 SNR threshold for many common applications is five. One of ordinary skill in the art will recognize that the preferred SNR threshold may vary accorcJi.lg to the needs of each particular flow measuring environment and application. If the SNR
value drops below the predetermined threshold value then an SNR fault condition is said to exist for the previous half window period (the just completed half 20 window). If element 1816 determines that there was an SNR fault in the previous half window, then processing continues with element 1818. Otherwise, processing continues with element 1820. Element 1818 is operable to reset the computEions involved in the weight adaptation of the notch filters. Specifically, the debiasing parameter (a), the forgetting factor Q\), and the covariance matrix (P) are all reset 25 to states which restart the computations to converge the notch filter on the fundamental frequency of the vibrating flow tubes.
Element 1820 is next operable to determine ~t from the complex numbers indicative of phase of the signal on each channel during the period of the immediately preceding sample values. In other words, after each Hanning window 30 of sample values (which occurs every half window as discussed below), a /~t value is computed from the immediately preceding Hanning window samples reduced to a complex number indicative of phase for each channel. Element 1820 is further operable to determine the Goertzel filter coefficients for the next period from CA 022084~2 l997-06-l3 the accumulated parameters generated by element 1808. The paran ,eler accumulation of element 1808 is also reset to begin a new period. Processing then continue with elements 1808 and 1810 to update the Goertzel filter parameters and accumulate the signal and noise energies.
Element 1808 is operable to update the Goertzel filter by accumulating the average notch filter weights over a half window period. At boundaries of the half window periods, the Goertzel filter weights are updated in preparation for processing of the samples during the next half window period. Eiement 1808 is also responsive to the generation of the enhanced sampled values and applies theenhanced sample values to a complex Goertzel filter. The Goertzel filter, as discussed above, produces a complex number, accumulated over a series of waveform sample values, representative of the phase of the waveform. This phase value is accumulated for both the left and right channels.
As discussed above, the Goertzel filters are used to accumulate a complex number indicative of the phase of the enhanced sampled signal of each channel.
The accumulation continues through a number of samples equal to the length of a Hanning window (said length denoted 2N). The samples in a Hanning window approximately span eight full vibration cycles of the associated flow tube sensor signal. To maximize the utilization of the sampled data, two Goertzel filter computations are performed in parallel on the samples of a channel (totaling four computations, 2 each on the left and right channel). The two parallel computations on a channel are performed on the same enhanced sample values of the channel but one computation begins one half Hanning window length after the other (i.e. delayed by N samples). In other words, the two parallel Goertzel2~ filter computations applied to samples of a channel are separated from one another in time by the one half the Hanning window period of the vibrating flow tube sensor signal samples.
Element 1810 is operable to accumulate the enhanced signal energy and to accumulate the noise energy of the sampled values. The accumulated values are checked at the end of a half window (as discussed above with respect to element 1814) to determine if the signal to noise ratio is within desired limits.
Processing of the method then continues by looping back to element 1802 to await the receipt of another decimated sample value.

CA 022084~2 1997-06-13 WO 97/03339 PCTIUS9611~8~

FIG. 19 provides additional detail of the operation of element 1806 which - updates the filter parameters in preparation for processing another decimated sample value. In addition to the SNR testing discussed above with respect to FIG.
18, another heuristic test is applied in the methods of the present invention to help 5 prevent any instability in the notch filter calculations.
A heuristic test depicted in FIG. 19 checks the computed notch filter weights for stability within a predetermined acceptable range. The newly computed filterweights will not be used for the next sample if they fall outside the acce~la~lerange. In such a case, the previous values of the weights, computed from the 10 previous sample values, will be used until a subsequent computation results in acceptable filter weights.
Elements 1902-~908 are operable to determine the updated forgetting factor, the updated gain vector, the updated debiasing parameter, and the updated covariance matrix from the current sample values. Element 1910 is next 15 operable to determine the updated notch filter weights given the previous wei~l ,Ls -(computed from the previous sample processing), the gain vector, and debiasing parameter values determined by operation of elements 1902-1908. As discussed above with respect to FIG. 18, when an error is sensed by testing the el,hal,cedsignal to noise ratio, the computations associated with the updated coefficients are 20 reset to restart the convergence o~ the notch on the shifted fundamental frequency of the flow tubes.
Element 1912 is operable to evaluate the stability of the newly computed weights against a predetermined range of acceptable values. If the newly computed weights are in the acceptable range, element 1914 operates to apply 25 the new weights to the notch filters in preparation for the processing of the next decimated samples. If the newly computed weights are outside the acceptable range, the new weights are not applied to the filters, but rather, the previous weights (computed from the processing of the previous sample) are used again -~ for the next decimated sample.
30 A FIRST PREFERRED EMBODIMENT:
In a first exemplary preferred embodiment of the present invention, two adaptive notch filters are utilized, one for filtering discrete digitized samples from the left channel and a second for the right channel. The weight adaptation CA 022084~2 l997-06-l3 -computations adjust the notch parameters for both adaptive notch filters by sampling the signals associated with the left channel processing.
FIG. 3 decomposes elements of FIG. 2 to show additional detail regarding the flow of information between computational elements of FIG. 2. Computational 5 elements 204 are the adaptive notch filters first depicted in FIG. 2. Left channel adaptive notch filter 204 receives decimated sensor output signal samples (xL) from path 254 (of FIG. 2). Weight coefficients (W) of the notch filter transfer function are received from weight adaptation element 210 over path 258.
- Debiasing parameter (a), which determines the shape of the notch, is also 10 received from weight adaptation element 210 over path 258. Right channel -- adaptive notch filter 204 receives decimated sensor output signal samples (XR) from path 256 (of FIG. 2) but otherwise operates identically to left channel adaptive notch filter 204. Both the left and right channel adaptive notch filters receive the ~ same adaptation parameters (W and a) over path 258 from weight acJa,ul~lion - 15 element 210.
- Both the left and right channel adaptive notch filters 204 generate an Iha"ced signal represented by di~cr~Le sample values applied to their respectiveoutput paths 260 and 262 respectively. The enhanced signal, denoted eL and eR
for the left and right channels respectively, represents the associated input signal 20 samples filtered of all noise signals but for a narrow band of frequencies near the fundamental frequency of the vibrating flow tubes.
Left channel adaptive notch filter 204 applies a signal re~resel ,lir~g the noise portion of the input signal samples (nL) and a value indicating the gradient vector of the input signal sample values ~ ) to its output path 260. These signal values 25 (eL, nL, and ~IJ) are used by weight adaptation element 210 to determine the weight adapl~lion parameters for the next adjustment of the notch filter. Both left and right channel adaptive notch filters 204 compute the same functions, however, the noise and gradient values from the right channel adaptive notch filter are not used in the methods and apparatus of the present invention. In practice, the 30 unused signals for the right channel adaptive notch filter 204 are not computed by the DSP software of the preferred embodiment. The functions computed by adaptive notch filters 204 are discussed in detail below.

- WO 97/03339 PCT/US~6/11280 The enhanced signal values from the left and right channel adaptive notch filters 204 are received over paths 260 and 262, respectively, by phase computation elements 206. Phase computation elements 206 d~L~ e the phase of the sinusoidai signais represented by the enhanced discrete sample signals 5 applied to their respective inputs on paths 260 and 262.
~ The Fourier transform phase computation elements 206 utilize a Hanning window we;~hliny method to sum 2N discrete weighted samples on each channel which represent eight cycles of the corresponding sinusoidal input signals. As discussed below, various computational elements in the present invention apply 10 their respective computations to data received during half of the Hanning window period (samples O..N-1). The value SAMPN0 indicative of the particular sample of the present half window cycle (sample O..N-1) is received as an input over path 272 to phase computation elements 206 The SAMPN0 value is used as an index to a vector of weights applied to the enhanced sampled signal values for the first 15 and seconds halves of the Hanning window. These weighting methods are employed by the phase computation elements 206 discussed below.
Phase computation elements 206 apply a Goertzel filter Fourier L,~r,sror", to the filtered discrete sampled signal values to determine the phase of the sinusoidal signal on each channel of the system. The coefficients of the Goertzei 20 filter (B - a complex number) are supplied to phase computation elements 206 by frequency computation element 212 over path 268. The Goertzel filter processes the samples in each Hanning window to generate a complex number representing the phase of the sampled sinusoidal sensor output signals.
The complex number values generated by the phase cornr~ tion elements 25 206 are applied to paths 264 and 266 for the left and right channels, respectively.
~t computation element 208 receives the complex numbers indicative of the phase of the sampled signals on paths 264 and 266 corresponding to the left and right channel signals, respectively. ~t computation element 208 receives a number (Q) indicating the current the fundamental frequency of the vibrating flow tubes from 30 frequency computation element 212 over path 268.
To more fully utilize the data available from each channel, the phase, frequency, and ~t computations are performed every half window (half the Hanning window length as determined above). Two parallel phase computations CA 022084~2 l997-06-l3 are performed on the filtered discrete sampled input values on each channel.
Each of the two parallel computations completes once for ever,v full window of filtered discrete sample values. The parallel computations are offset from one another in time by the period corresponding to a number of samples equal to half5 the length of the Hanning window. Since the two computational elements are offset from one another by one half of the length of the Hanning window, one of the two parallel computations completes its computation every half window periodon each channel. Therefore, every half window period of time, a new phase, frequency, and ~t computation is completed and utilized for mass flow rate 1 0 measurements.
Weight adaptation element 210 of FIG. 2 is shown decomposed into four sub-elements, namely SNR fault detection element 300, notch filter weight computation element 302, gain vector computation element 304, and debiasing parameter computation element 306.
SNR fault detection element 300 receives the enhanced signal values (eL) and the noise component of the unfiltered sample values (nL), both generated by the left channel notch filter 204 and applied to path 260. SNR fault detection element 300 determines whether the energy ratio of the enhanced signal values (eL) to the noise component of the unfiltered sample values (n ~ is below a 20 threshold level. When the signal to noise ratio drops below a pre~ L~r",i"ed lower limit, it typically indicates that the notch filter 204 is not converged on the fundamental frequency of the vibrating flow tubes. When the signal to noise ratio is found to be deficient, an SNR FAULT signal is generated and applied to the output of SNR fault detection element 300 on path 350 of FIG. 3. As ~iscllssed below, the SNR FAULT signai applied to path 350 is used by other computational elements within weight adaptation element 210 to restart the computations used to adapt the notch filter and to converge the notch on the fundamental frequencyof the vibrating flow tubes. The precise computation and details of SNR fault detection element 300 are presented below with respect to FIG. 7.
Notch filter weight computation element 302 receives the noise component of the unfiltered sample values (nL) generated by the left channel notch filter 204 and applied to path 260. Element 302 also receives the gain vector values (K - atwo element vector) generated by gain vector computation element 304 and -WO 97/03339 PCTIUS96J11~80 applied to path 352. In addition, element 302 receives the updated debiasing parameter (a') generated by debiasing parameter computation element 306 and ap,l~ to path 354. Notch filter weight computation element then computes the updated values of the notch filter weights (W) and applies them to path 258 for 5 use by notch filters 204 and frequency calculation element 212. The prec;~e - computation and details of notch filter computation element 302 are prese~L~d below with respect to FIG. 6.
Gain vector computation element 304 receives the gradient ~) generated by left channel notch filter 204 and applied to path 260. Element 304 also receives 10 the SNR FAULT signal generated by SNR fault detection element 300 and appliedto path 350. In addition, element 304 receives forgetting factor ~) generated bydebiasing parameter computation element 306 and applied to path 356. Gain vector computation element 304 then computes the updated values of the gain vector (K) and applies them to path 352 for use by notch filter weight computation 15 element 302. The precise computation and details of gain vector computation ~element 304 are presented below with respect to FIG. 5.
Debiasing parameter computation element 306 receives the SNR FAULT
signal generated by SNR fault detection element 300 and applied to path 350.
Del~iasi"y pa,~ Ler computation element 306 then computes the updated values 20 of the debiasing parameter (a) and applies it to path 258 for use by notch filters 204. Debiasing parameter computation element 306 also computes an updated ~le~ c "y parameter (a ') and applies it to path 354 for use by notch filter weight computation element 302. In addition, debiasing computation element 306 computes an updated forgetting factor ~) and appiies it to path 356 for use by 25 gain vector computation element 304. The precise computation and details of .~el~i~s: ,g parameter computation element 306 are presented below with respect to FIG. 8.
Frequency c~lGul~tion element 212 of FIG. 2 is shown decomposed into two sub-elements, namely Goertzel filter weights computation element 308 and half 30 window coefficient pipeline 310.
Goertzel filter weights computation element 308 accepts the notch filter rei~ i deter,r,i"ed by operation of weight adaptation element 210 and applied topath 258. Goertzel filter weights computation element 308 then determines the CA 022084~2 1997-06-13 Goertzel filter weights (B') as a complex number and also determines the frequency (Q') of the sinusoidal flow tube sensor output signal represented by the dis(;reLe sampled signal values and as contained in the weights of the notch filter.
Both values so determined are computed at the end of each half window period 5 as indicated by the half window signal applied to path 274 by CLOCK 214 of FIG.
2. The Goertzel weights and frequency so determined are applied to path 358 for use by half window coefficient pipeline 310. The precise computation and detailsof Goertzel filter weights computation element 308 are presented below with respect to FIG. 9.
Half window coefficient pipeline 310 receives the Goertzel filter weights (B') and the frequency (n') both computed as above by Goertzel filter weights computation element 308. Half window coefficient pipeline 310 then adjusts the timing of the computed values (B' and Q') to associate them with one of the two parallel computations for the overlapping half windows. The precise computation 15 and details of half window coefficient pipeline 310 are presented below with respect to FIG. 10.
As noted previously, the computations performed by the elements depicted in FIG. 3 (and other detailed figures discussed below) are preferably performed using floating point arithmetic to maintain accuracy over a broad scale of numeric 20 precision. Floating point computation functions may be performed by hardware within the signal processor 2000 of FIG. 20 or may be emulated by processor 2000 using software libra~ functions. Performance and cost factors will deler",i,)e - the choice between floating point hardware and software as appropriate for each application of the present invention.
25 A FIRST EXEMPLARY EMBODIMENT - NOTCH FILTER:
FIG. 4 shows additional detail regarding the function and computations performed within adaptive notch filters 204 of FIG. 3. Both adaptive notch filters 204, one associated with the left channel and the other with the right channel, are identical in structure and the computations performed. The left channel adaptive30 notch filter 204 receives decimated discrete time sample sensor values as input from path 254 and applies its filtered output to path 260. The right channel adaptive notch filter 204 receives decimated discrete time sample sensor values as input from path 256 and applies its filtered output to path 262.

- WO 97/03339 PcTJus96/1128U

Adaptive notch filter-204 also receives current weights (W a two element vector represented as W1,W~ and the debiasing parameter (a) from weight adaptation element 210 of FIG. 3 over path 258. Adaptive notch filter 204 yener~ s the square of the debiasing parameter (~ ) by applying it from path 2585 to both inputs of multiplication junction 446 the output of which is applied to path 488.
A portion of the elements within adaptive notch filter 204 of FIG. 4, denoted by the dashed line box within the adaptive notch filter 204, are used to computethe gradient of the input signal samples ~ a two element vector represented as 10 ~ ~ ) 2) The gradient value so computed is applied to path 260 in the adaptive notch filter 204 of the left channel. The gradient is used by the weight ~pt~tion element 210 of FIG. 3 to compute updated notch filter weights for the ne~* sample received on path 254. The elements in the dashed box of FIG. 4 used to compute the gradient are not used in the adaptive notch filter 204 of the right cl la",1el.
The adaptive notch filter 204 of FIG. 4 determines the noise present in the ~isc, ele sample input values. Subtracting the noise signal values from the input sample values yields the enhanced filtered value for output on path 260. The adaptive notch filter 204 determines the enhanced signal value e by a second order filter polynomial and matrix arithmetic as follows (where variable(t) as used 20 in the equations below indicates the value of variable corresponding to sample period "t"):
x(t)the input signal value received on path 254 (256 for the right channel) A(t) = diag(a(t),a(t)2) the debiasing diagonal matrix W(t) = [W1(t),W2(t)~ theweightsvector Y(t) = [y(t-1 ),y(t-2)] the recursive filter state vector y(t) = x(t) + W(t)A(t)Y(t) intermediate computation n(t) = y(t) - W(t)Y(t) the noise signals isolated from the input signal e(t) = x(t) - n(t) the enhanced signal, input signal x - noise signals n The pseudo-circuits of FIG. 4 describe these equations in the form of circuit and computational elements. Summing junction 400 sums the input signal value x on path 254 (256 for the right channel) and the intermediate computation value35 on path 452 (representing WAY as above) to generate y = x + WAY as above which is applied to path 450. The value of y on path 450 is applied as input to : CA 022084~2 1997-06-13 delay circuit 408 to delay it one sample clock period (CLK) then apply it to output - path 460. The once delayed value of y on path 460 is input to delay circuit 436 to delay it a second sample clock period (CLK) then apply it to output path 468.The once delayed value of y on path 460 and the twice delayed value of y on path= 5 468 represent the vector Y as above.
- The debiasing diagonal matrix A is comprised of the debiasing parameter and its square (a and ~ ) on paths 258 and 488, respectively. The vector Y on paths 460 and 468 is multiplied by the debiasing diagonal matrix A applied to - paths 258 and 488 through muitiplication junctions 406 and 434, respectively, to produce AY on paths 458 and 470, respectively. This product is in turn multiplied by tne weights vector W applied to path 258 through multiplication junctions 404and 432, respectively, to produce intermediate computational values on paths 456and 454, respectively. The two intermediate values on paths 456 and 454, respectively, are applied to summing junction 402 to produce the scalar value 15 WAY on path 452 as described above.
- The vector Y on paths 460 and 468 is also multiplied by the weights vector W on path 258 through multiplication junctions 414 and 438, respectively, to produce intermediate values on paths 464 and 466. The two intermediate values on paths 464 and 466 are summed through summing junction 416 to produce the 20 value WY on path 462.
Summing junction 412 subtracts the value WY on path 462 from the value y on path 4~0 to produce the noise value n = y - WY on path 470. In the adaptive notch filter 204 of the left channel, this value representing the noiseportion n of the input sample values x is applied to path 260 for use in the weight 25 a.ia~,lalion element 210 of FIG. 3.
Summing junction 410 subtracts the noise value n on path 470 from the input sample value x on path 254 (256 for the right channel) to produce the enhanced signal value e = x - n on path 260 (262 for the right channel). The enhanced signal value is used in subsequent phase computation elements 206 30 and in weight adaptation element 210 as discussed below.
In addition to the noise value, n, and the enhanced signal value, e, the adaptive notch filter 204 computes the gradient vector ~1) as ~ 1, and ~ 2 on path -260. The adaptive notch filter 204 determines the gradient vector ~1~ by a second order filter polynomial and matrix arithmetic as follows:
F(t) = [f(t-1),f(t-2)]T recursive filter state vector f(t) = n(t) + W(t)A(t)F(t) intermediate computation 5 ~ (t) = Y(t) - A(t)F(t) gradient vector Summing junction 418 adds the noise value n on its input path 470 to the intermediate computation value WAF on its input path 474 to produce f = n +
WAF on path 472. The value f on path 472 is applied as input to delay circuit 420 to delay it one sample clock period (CLK) then apply it to output path 476. The 10 once delayed value of f on path 47~ is input to delay circuit 430 to delay it a second sample clock period (CLK) then apply it to output path 484. The once delayed value of f on path 476 and the twice delayed value of f on path 484 represent the vector F as above.
The vector F on paths 476 and 484 is multiplied by the debiasing diagonal 15 matrix A applied to paths 258 and 488 through multiplication junctions 426 and 442, respectively, to produce AF on paths 478 and 486 respectively. This productis in turn multiplied by the weights vector W applied to path 258 through multiplication junctions 424 and 440, respectively, to produce intermediate computational values on paths 480 and 482, respectively. The two intermediate 20 values on paths 480 and 482, respectively, are applied to summing junction 422 to produce the scalar value WAF on path 474 as described above.
The intermediate product AF on paths 478 and 486 is subtracted from the Y vector on paths 460 and 468 through summing junctions 428 and 444 to produce the gradient vector ~ ~ 1 ~ 2) = Y - AF and apply it path 260. The 25 gradient vector on path 260 is used by weight adaptation element 210 of FIG. 3 to compute the updated notch filter weights.
Both the left and right channel adaptive notch filters 204 operate as described above. The computation of the gradient vector ~ and the noise value n on path 260 is unnecessary in the right channel and so may be skipped as a 30 computational step in the right channel. The weight adaptation element 210 utilizes only the values from the left channel applied to path 260 to adjust theweights for both adaptive notch filters 204. Only the enhanced signal value e isused from the right channel and is applied to path 262 for use by the phase computation elements 206.

:
CA 022084~2 l997-06-l3 A FIRST EXEMPLARY EMBODIMENT - WEIGHT ADAPTATION:
The weight adaptation element 210 of FIG. 3 receives the enhanced signal value eL, the noise portion of the unfiltered input signal nL, and the gradient ~ all ye"er~Led by the adaptive notch filter 204 of the left channel and applied to path 260. Weight adaptation element 210 then determines the weights vector W and the ~ Ie~ "g parameter a and applies them to path 258 to adjust notch filters ofboth channels for the next discrete sampled value to be processed in adaptive notch filter 204. To simplify this description of the weight adaptation functions, weight adaptation element 210 is decomposed into four sub-elements each performing portions of the total computation, namely SNR fault detection element300, notch filter weight computation element 302, gain vector computation element 304, and debiasing parameter computation element 306.
SNR fault detection element 300, depicted in additional detail in FIG. 7, receives the enhanced signal values (eL) and the noise component of the ~ ered sample values (nL), both generated by the left channel notch filter 204 ~nd applied to path 260. SNR fault detection element 300 detenl".les whether theenergy ratio of the enhanced signal values (eL) to the noise component of the unfiltered sample values (nL) is below a threshold level as discussed above. SNRfault detection element 300 is depicted in additional detail in Fl5. 7.
The SNR fault detection element 300 of FIG. 7 determines the signal to noise ratio by summing the noise energy and summing the noise canceled energy, then comparing the ratio of the two values against a pre-determined threshold values. SNR fault detection element receives the enhanced signal value eL and the noise signal nL from the left channel over path 260.
The noise signal value is applied to both inputs of m~ lic;-liol) junction 700 to produce the square of the noise signal n2 and apply it to path 750. The n2 value on path 750 is applied to one input of a 2:1 mux 704 and to one input of summing junction 706. The output of mux 704 is applied to the input of register 712 via path 758. Register 712 stores the value on its input when clocked by theCLK sample clock. The current value in register 712 is applied to its output through path 764 to the other input of summing junction 706. The sum output of summing junction 706 is applied over path 754 to the other input of mux 704. At the start of each half window period, as signaled on path 274, mux 704 selects its input connected to the n2 value on path 750 to restart the summing of the noise energy for a new half window period. For all other samples in the half window period, mux 704 selects its input connected to path 754 to accumulate the noise energy. The accumulated noise energy is accumulated in register 712 for each 5 s~",~.le in the half window period and the current accumulated sum is applied to the output of register 712 on path 764. The accumulated sum is resL~,led on each new half window period.
The noise-canceled signal energy is accumulated in like f~si - ~ ~ by squaring and accumulating the enhanced signal value received on path 26û. The noise-10 canceled energy is accumulated by operation of multiplication junction 702,summing junction 710, mux 708, and register 714, over paths 752, 756, 760, and 762 in a similar manner to that described above for accumulation of noise energy.
The noise-canceled energy accumulated through each half window period of sampled values is applied to the output of register 714 to path 762.
Computational element 716 receives the accumulated noise energy over path 764 and the accumulated noise-canceled energy over path 762 and compares the values to pre-determined threshoid values. The ratio of the accumulated noise-canceled value and the accumulated noise value is the signal to noise ratio. If the ratio drops below a pre-determined threshold, then a signal 20 to noise ratio fault condition is detected and a signal so indicating is applied to the output of computational element 716.
Fault timing element 718 receives the fault condition signal on path 766 generated by computational element 716 and receives the half window signal on path 274. When a fault condition is sensed on input path 766, fault timing element 25 718 applies a pulse signal to SNR FAULT on path 350. The SNR fault signal on path 350 is sensed by other sub-elements within weight adaptation element 210 to force a reset of various notch parameter computations. Following ~ lic~tion of a signal to SNR FAULT, fault timing element 718 enforces a grace period during which no further signals are applied to the SNR FAULT signal on path 350. The 30 grace period is intended to allow the notch filter parameters a period of time to re-converge on the fundamental frequency of the vibrating flow tubes. The fault timing element 718 also enforces a grace period during power-on iniLi~ oll to permit the notch filters to converge on the fundamental frequency. The grace . .

period during power-on initialization is preferably approximately 100 half window - periods. The grace period following the detection of an SNR FAULT is prerera~ly approximately 66 half window periods.
Notch filter weight computation element 302, depicted in ~d~itional detail in 5 FIG. 6, receives the noise component of the unfiltered sample values (nL) generated by the left channel notch filter 204 and applied to path 260. Element 302 also receives the gain vector values (K) generated by gain vector computation element 304 and applied to path 352. In addition, element 302 receives the updated debiasing parameter (a') generated by debiasing parameter computation 10 element 306 and applied to path 354. Notch filter weight computation element 302 then computes the updated values of the notch filter weights ~W) and applies them to path 258 for use by notch filters 204 and frequency calculation element 212.
The notch filter weight computation element 302 determines the weights W
for the adaptive notch filters 204 by matrix arithmetic as follows:
~5 W'(t) = W(t) + n(t)K(t) the updated w~ L~ vector if stable, otherwise, W'(t) = W(t) weights not updated if unstable Ml lltiplic~tion junctions 602 and 604 multiply the gain vector K (K1, K2) on path 352 by the noise component (n) of the signal sample received on path 260 to produce the product nK on paths 650 and 656. The product on path 650 is 20 applied to summing junction 606. The other input to summing junction 606 is the - previously computed W1 weight on path 652. The output of summing junction 606 is W1 + nK1 and is applied to the normally selected input of mux 616 over path 654. The output of mux 616 is applied over path 670 to the normally selected input of mux 624. This input value is normally passed through mux 624 onto 25 output path 674 to the input of delay circuit 620, and to bus 258 as the nextupdated value of W1' (where Wx' indicates the value of Wx to be used for the next received sample value) for use in computation of the Goertzel weights in element 308. The once delayed coefficient (W1) from delay circuit 620 is appliedto bus 258 as W1 for use by the notch filters 204. The normally deselected input30 of mux 624 on path 676 is selected by a system RESET signal to apply the zero value (0) as the initial value of the W1 weight.
The other partial product on path 656 is applied to summing junction 608.
The other input to summing junction 608 is the previously computed W2 weight W097/03339 PCTnUS96111280 on path 666. The output of summing junction 608is W2 + nK2 and is applied to the normally selected input of mux 618 over path 660. The output of mux 618 is applied over path 672 to the normally selected input of mux 626. This input value - is normally passed through mux 626 onto output path 676 to thé input of delay 5 circuit 622, and to bus 258 as the next updated value of W2' for use in corTr~ tiQn of the Goertzel weights in element 308. The once delayed coefficient(W2) from delay circuit 622iS applied to bus 258 as W 2for use by the notch filters 204. The normally deselected input of mux 626 on path 678 is selected by a system RESEI signal to apply the negative one value (-1) as the initial value of the 10 W2 weight.
Multiplication junction 600 receives the updated debiasing parameter a' (where a ' indicates the value of a to be used for the next received sample value) on path 354 as both inputs and produces the square value a' on its output path 658. Multiplication junction 610 receives debiasing parameter a' on path 354 as 15 one input and the updated weight W1 on path 654 as the other input and produces the producta'W1 on its output 662. Multiplication junction 612 receivesthe squared debiasing parameter a ~2 on path 658 as one input and the updated weight W2 on path 660 as the other input and produces the product a'2W2 on its output 664. Stability test element 614 receives a first parameter X = ~'W1 on path 20 662 and a second parameter Y = a'2W2 on path 664. The stability test element 614 evaluates the X and Y parameters and generates a one output signal if the conditions of the test are satisfied. The stability test outputs a one signal if and only if:
IYI < 1 and IXI < (1 -Y) 25 This test constrains the poles of the notch filter to be within the unit circle to assure the stability of the notch filters 204 and thereby the validity of the resultant mass flow measurements. The output of stability test element 614 is applied to the select inputs of muxes 616 and 618 over path 668. The normally deselected input of muxes 616 and 618 receive the previously computed value of W1 and W2 30 respectively. If the updated notch filter weights fail the stability test performed by element 614, a zero output signal is generated by test element 614 on its outputpath 668. In response to the zero output signal on path 668, muxes 616 and 618 apply their respective normally deselected inputs on paths 652 and 666, CA 02208452 l997-06-l3 respectively, to their output paths 670 and 672, respectively, so that the previous computed value of the corresponding coefficient is re-used for the next samples value to be processed. In other words, the weight vector will not be changed from the last stable computed values so long as the stability test element 614 in~Jical~s 5 instability of the computations. This test eliminates the numerical problems associated with an unstable notch filter weight computation and also helps prevent grossly erroneous flow rate computations during a period of brief instability of the notch filters as they converge on a change in the fundamental frequency of the vibrating flow tubes.
Gain vector computation element 304, shown in additional detail in FIG. 5, receives the gradient ~ ) generated by left channel notch filter 204 and applied to path 260. Element 304 also receives the SNR FAULT signal generated by SNR
fault detection element 300 and applied to path 350. In addition, element 304 receives forgetting factor Q\) generated by debiasing parameter cor~r~lPtion 15 ele,l,er,l 306 and applied to path 356. Gain vector computation element 304 then computes the updated values of the gain vector (K) and applies them to path 352 for use by notch filter weight computation element 302.
Gain vector computation element 304, shown in additional detail in FIG. 5, receives the gradient vector ~IJ) on path 260, the forgetting factor Q\) on path 356 20 and the SNR FAULT signal on path 350, computes the gain vector (K1,K2) and applies the computed gain vector to path 352 for further processing. The comp(~L~Lio, lal elements depicted in FIG. 5 generally perform matrix manipulations on their various inputs to produce an output computed scalar value or vector. The gain vector computation element 304 determines the gain vector K using matrix 25 arithmetic as follows:
K(t) = QT(t) / ~(t) + ~(t)TQ(t)) the updated gain vector Q(t) = P(t)~ (t) intermediate computation vector P'(t) - (P(t) - Q(t)K(t)) / A(t) the next covariance matrix Computational element 500 receives the gradient vector ~ over path 260 30 and receives the current covariance matrix (P) over path 552 from delay circuit 514. As can be seen in FIG. 5, paths which carry the signals representing the covariance matrix (P) are shown with three signals. This indicates the symmetricnature of the 2X2 covariance matrix. The two off-diagonal elements of the 2X2 covariance matrix (P) are always equal. Therefore only three values need be represented in the implemelltation of the present invention (whether in the pseudo circuit of FIG. 5 or in the DSP software preferred embodiment). Computational element 500 then calculates the intermediate product Q = P~ and applies the Q
~ vector to path 550. Computational element 502 receives the intermediate Q vector 5 on path 550, receives the gradient vector ~ on path 260, receives the forgetting factor A on path 356, calculates the gain vector K (K1 ,K2), and applies the gain vector to path 352 for further processing.
Element 504 receives the current value of the current covariance matrix P
on path 552, receives the current gain vector K on path 352, receives the current 10 Q vector on path 550, calculates a new covariance matrix P' = (P - QK)/A, andapplies the new covariance matrix P' to path 554 for use as P in processing the next sample received. Muxes 508 and 512 are used to reset the computations performed by element 504 when a system reset occurs or when an SNR FAULT
condltion is detected. Mux 508 normally applies the new covariance matrix on its15 input path 554 to its output path 558. When an SNR FAULT signal is applied to~ath 350, mux 508 selects its other input path 556 to apply an initial matrix value (PSNR) to its output path 558. Mux 512 normally applies the value on its input path 558 to its output path 562 as input to delay register 514. When a system reset is applied, mux 512 selects its other input path 560 to apply an initial matrix 20 value (PINlT) to its output path 562. In other words, if either a system reset or an SNR FAULT condition is sensed, covariance matrix computation is reset.
Otherwise, the computation of the next covariance matrix (P' to be used with thenext sample received) is a function of the previous covariance matrix (P) ~pplie~
to path 5~4 through muxes 508 and ~12 onto path 562. Delay circuit 514 delays 25 application of its input on path 562 until the next sample value is received for processing as signaied by a CLK pulse, then applies its stored value onto its output path 552 as input to the covariance computational element 504.
Debiasing parameter computation element 306, shown in additional detail in FIG. 8, receives the SNR FAULT signal generated by SNR fault detection 30 element 300 and applied to path 350. Debiasing parameter computation element 306 then computes the updated values of the debiasing parameter (a) and applies it to path 258 for use by notch filters 204. Debiasing parameter computation element 306 also computes an updated debiasing parameter for the next sample -CA 02208452 l997-06-l3 W097/03339 PCT~S96tll280 -(~') and applies it to path 354 for use by notch filter weight computation element i- 302. In addition, debiasing computation element 306 computes an updated - roryeLLi,~g factor ~) and applies it to path 356 for use by gain vector computation - - element 304.
= 5 The debiasing parameter computation eiement 306 determines the ~ debiasing parameters and the forgetting factor as follows:
- - a'(t) = a(t)~DECAy + aADDER the updated debiasing parameter A(t) = A'(t-1~DEcAy + AADDER the updated forgetting factor . - 10 computation - Registers 800, 802, 804, and 806 each contain values used in the computation of the forgetting factor A. 2:1 mux 818 receives one input from path 356 on which is applied the previous value of the forgetting factor A. Mux 818 is ., -~ normally selected to pass this value through to output path 872 and onto one = 15 input of 2:1 mux 820. Mux 820 is normally selected to pass this value through to output path 874 and onto the input of register 826. Register 826 contains this previous value of the forgetting factor A until its clock line is pulsed by the CLK
- signal. The value in register 826 is applied to its output on path 858 to one input of r~ tirlir~lion junction 828. The other input of multiplication junction 828 is path 852 which receives the ADECAy value stored in register 802. The product of multiplication junction 828,AADEcAy,is applied to its output path 860 and onto one input of summing junction 830. The other input of summing junction 830 is path 850 which receives the AADDER value stored in register 800. The sum result ~- of summing junction 830iS applied to path 356 as the updated forgetting factor A = A-A DECAY + AADDER-When SNR FAULT signal is applied to path 350, mux 818 selects its input from path 854 which receives the ASNR stored in register 804. This value is thenapplied to the output of mux 818 to path 872 and substitutes for the previoùs - forgetting factor normally used in the normal computation of the next value. This pre-defined value resets the computation of the forgetting factor A on path 356 whenever an SNR FAULT condition is recognized as discussed above. This pre-determined forgetting factor restarts the computations of the adaptive notch filter for purposes of forcing convergence on the fundamental frequency of the vibrating flow tubes.
-~ 42 . . _ When a system wide~RESEr is applied to mux 820, the mux selects its input from path 856 which receives the AINlT stored in register 806. This value is then applied to the output of mux 820 to path 874 and substitutes for the previous ~ forgetting factor used in normal computation of the next value. This pre-5 determined forgetting factor starts the computations of the adaptive notch filter for purposes of forcing convergence on the fundamental frequency of the vibrating flow tubes.
Registers 808, 810, 812, and 832 each contain values used in the computation of the debiasing parameter a. 2:1 mux 834 receives one input from 10 path 354 on which is applied the previous vaiue of the debiasing parameter a.Mux 834 is normally selected to pass this value through to output path 878 and onto the input of mux 814. Mux 814 is, in turn, normally selected to pass this vaiue through to output path 868 and apply it to the input of register 816. Register 816 contains this previous value of the debiasing parameter a until its clock line 15 is pulsed by the CLK signal. The value in register 816 is applied to its output on ~ath 2~8 to one input of multiplication junction 822 and to adaptive notch filters 204 of FIG. 3. The other input of multiplication junction 822 is path 864 which receives the aDECAy value stored in register 810. The product of multiplication junction 822, a.a DECAY~ is applied to its output path 866 and onto one input of20 summing junction 824. The other input of summing junction 824 is path 862 which receives the aADDER value stored in register 808. The sum result of summing junction 824 is applied to path 354 as the updated debiasing parameter a' =
a'aDECAY + aADDER
When SNR FAULT signal is applied to path 350, mux 834 selects its input 25 from path 876 which receives the a SNR stored in register 832. This value is then applied to the output of mux 834 to path 878 and substitutes for the previous ~ie!~i~c ,-g parameter normally used in the normal computation of the next value.
This pre-defined value resets the computation of the debiasing parameter a on path 354 whenever an SNR FAULT condition is recognized as discussed above.
30 This pre-determined debiasing parameter restarts the computations of the adaptive notch filter for purposes of forcing convergence on the fundamental frequency ofthe vibrating flow tubes.

When a system wide RESET is applied to mux 814, the mux selects its input from path 870 which receives the a INIT stored in register 812. This value is then applied to the output of mux 814 to path 868 and substitutes for the previous debiasing parameter used in normal computation of the next value. This pre-: 5 determined debiasing parameter starts the computations of the adaptive notch filter for purposes of forcing convergence on the fundamental frequency of the vibrating flow tubes.
A FIRST EXEMPLARY EMBODIMENT - FREQUENCY CALCULATIONS:
Frequency c~lcul~tisn element 212 of FIG. 3 is shown deco,~ osed into two sub-elements, namely Goertzel filter weights computation element 308 and han window coefficient pipeline 310.
Goertzel filter weights computation element 308, shown in additional detail in FIG. 9, accepts the notch filter weights determined by operation of weight adapL~Lion element 210 and applied to path 258. Goertzel filter ~ JhLs computation element 308 then determines the Goertzel filter weights (B') as a -complex number and also determines the frequency (Q') of the sinusoidal flow tube sensor output signal represented by the discrete sampled signal values and as conLai,led in the weights of the notch filter. Both values so deLer~ ed are computed at the end of each half window period as indicated by the half window - 20 signal applied to path 274 by CLOCK 214 of FIG. 2. The Goertzel weights and frequency so deler",i, led are applied to path 358 for use by half window coefficient pipeline 310.
Summing junction 900 receives next notch filter weight W1' as one input over path 2~8 and receives its other input from path 966 as the output of r~yi~ler 916. The sum produced is applied to path 950 as one input to 2:1 mux 904. The other input of mux 904 on path is the next weight (W1') on bus 258. Mux 904 is normally selected to pass through the sum on path 950 from its input and apply the value to its output on path 954. 2:1 mux 912 is normally selected to pass through the value on it input path 954 to its output on path 962. The value on path 962 is applied to register 916 as an input value which is loaded on each pulse of the sample clock CLK. The current value stored in register 916 is the accumulating sum of weights (W1') as just described. At the start of a new half window period, a signal is applied to half window on path 274 by CLOCK 214 of = =

CA 02208452 l997-06-l3 WO 97/03339 PCT/U~16J11~8 FIG. 2. At the start of a half window period, mux 904 is changed for one period to select its other input from path 258 to restart a new accumulation of the ~
received. During power-on initialization, a system wide RESET signal is applied to mux 912 causing it to select its input from path 958 which receives the initial 5 weight value of zero (0). This starts a new accumulation of the weights received on path 258.
Summing junction 902 receives notch filter weight W2' as one input over path 258 and receives its other input from path 968 as the output of register 918.
The sum produced is applied to path 952 as one input to 2:1 mux 906. The other 10 input of mux 906 is the next weight (W2') on bus 258. Mux 906 is normally selected to pass through the sum on path 952 from its input and apply the value to its output on path 956. 2:1 mux 914 is normally selected to pass through the value on it input path 956 to its output on path 964. The value on path 964 is applied to register 918 as an input value which is loaded on each pulse of the 15 sampie clock CLK. The current value stored in register 918 is the accumulating sum of wei~hL~ ( V2') as just described. At the start of a new half window period, a signal is applied to half window on path 274 by CLOCK 214 of FIG. 2. At the start of a half window period, mux 906 is changed for one period to select its other input from path 258 to restart a new accumulation of the w~ hL~ received. During20 power-on i,lil:e' ,~lion, a system wide RESEr signal is applied to mux 914 causing it to select its input from path 960 which receives the initial weight value negative one (-1). This starts a new accumulation of the weights received on path 258.
The sum of the weights ~N1') received on path 258 is applied to the X input of computation element 920 over path 966. The sum of the weights ~\/V2') 25 received on path 258 is applied to the Y input of computation element 920 over path 968. Computation element 920 computes the real part of the Goertzel filter wei~l lls (B 0) as:
B'o = X / (2 sqrt(-YN)) where X and Y are the inputs to element 920 as above and N is the number of 30 samples in a half window period. More specifically, the real part of the filter weight is equal to:
B'o = avg(W1') / (2 sqrt(-avg(W2))) CA 022084~2 l997-06-l3 where avg(x) is the average value of x over the previous half window period of samples. The real part of the Goertzel filter weights (B~o) computed by computational element 920 is applied to path 358 for use by half window coefficient pipeline 310 discussed below. The real part of the Goertzel filter 5 weights is also applied to the X input of computational element 922 which computes the imaginary part of the Goertzel filter weights (B'1) as:
B'1 = sqrt(1-X2) where X is the real part of the filter weight as computed above. The imaginary part of the Goertzel filter weights (B'1) computed by computational element 922 10 is applied to path 358 for use by half window coefficient pipeline 310 disc~lsse~
below. In addition, the real part of the Goertzel filter weights is applied to the X
input of computational element 924 which computes the fundamental frequency (Q') of the vibrating flow tubes as:
n = cos~1 x 15 where X is the real part of the filter weight as computed above. The fundamental -frequency (~'~ computed by computational element 924 is applied to path 358 foruse by half window coefficient pipeline 310 discussed below.
It may be noted that the computations performed by comp~,L~lio- ,al elements 920, 922, and 924 are undefined when their respective inputs are 20 outside certain appropriate ranges. The output values of these computations are utilized only on the boundaries of Hanning windows at which time the inputs are assured to be appropriate to the respective computations. For this reason, the undefined computations suggested by the diagram of FIG. 9 are of little practical relevance. The computations may be invalid at half window boundaries under 25 certain error conditions of the notch filters. However, such filter errors are ~eL~;L~d and corrected within a few half window periods as discussed above. As a practical matter, the effect of these errors in the Goertzel filter weight computations may be ignored. In a production use of the present invention, such a condition may be detected and flagged to indicate that flow measurement values30 are temporarily unusable. As discussed above, the pseudo circuits of FIG. 9 are intended only as an aid in understanding the methods and related computations of the present invention.

-Half window coefficient pipeline 310, shown in additional detail in FIG. 10, receives the Goertzel filter weights (B' = B'ol B' 1) and the frequency (n') both computed as above by Goertzel filter weights computation element 308. The ~ values computed by operation of element 308 correspond to the half window 5 period samples which were used to compute the weights and frequency. Half window coefficient pipeline 310 then adjusts timing of the computed values (B' and Q') to associate them with one of the two parallel phase computations for the overlapping half windows. The Goertzel filters are used to compute a windowed DTFr every half window period of samples. However, computing a windowed 10 DTFr requires that the summation of sampled valued be done for an entire window. As discussed elsewhere in this document, two Goertzel filters are therefore computed in parallel. The first filter performs the required c~lc~ tions for the first half of a window. When the first half of a window is completed, and a new filter computation must start, the state of the first half is transferred to the 15 second filter which is then responsible for completing the computation by filtering ~or the second half of a window. In this manner, a complete window conlrut~tion may be completed at each half window boundary. The half window coefficient pipeline 310 aligns the computation of full window filter \~e;!JhLs with the assoc;aLed haif window pipelined portion of the computation so that the first half window and 20 the seco, l~ half window are accumulated using the same full window filter wei.JI IL~.
Delay circuits 1000, 1002, 1004, 1010, 1012, and 1014 operate by applying the value on their respective inputs to their respective outputs delayed by one pulse of their respective clock input lines. Each of delay circuits 1000, 1002, 1004, 1010, 1012, and 1014 as well as muxes 1006, 1008" 1016, and 1018, receive their 25 respective input clock pulses or select signals from the output of AND gate 1020 on path 1062 (labeled "X"). AND gate 1020 receives the sample clock CLK as one input, and the half window signal on path 274 as its other input. At the start of each half window period, the values in the respective registers are loaded with the input values connected to their respective input buses. This loading is 30 s~"-;l "onous with the CLK pulse at the start of a half window. The Goertzel filter weight B~o is applied over path 358 to the input of delay circuit 1000 and to one input (normally not selected) of mux 1006. The once delayed Goertzel filter weight B~o is applied over path 1050 to the other input (normally selected) of mux 1006, CA 022084~2 l997-06-l3 ., - to the input of delay circuit 1010 and to one input (normally not selected) of mux ' 1016. The once delayed Goertzel filter weight B~o is applied through mux 1006 onto path 268 as Goertzel filter weight Bo1 for further processing by phase computation elements 206 corresponding to a first of two parallel half window ~ - ~ phase computations discussed in further detail with respect to FIG. 11 below. The twice delayed Goertzel filter weight B'o is applied over path 1056 to the other input -= (normally selected) of mux 1016. The twice delayed Goertzel filter weight B'o is applied through mux 1016 onto path 268 as Goertzel filter weight Bo2 for furtherprocessing by phase computation elements 206 corresponding to a second of two parallel half window phase computations discussed in further detail with respectto FIG. 11 below. When the half window signal is applied to path 274 (also =
~-' labelled "A" in FIG. 10), mux 1006 is selected to apply the signal on its input path ; 3~8 onto path 268 for further processing as Goertzel filter weight Bo1, an ~- undelayed copy of the input value B'o from input path 358. Similarly, when the half window signal is applied to path 274 (also labelled "A" in FIG. 10), mux 1016 is selected to apply the signal on its input path 1050 onto path 268 for furtherprocessing as Goertzel filter weight Bo2~ a once delayed copy of the input valueB'o from input path 358.
- Goertzel filter weight B'1 is applied over path 358 to the input of delay circuit 1002 and to one input (normally not selected) of mux 1008. The once delayed Goertzel filter weight B'1 is applied over path 1052 to the other input (normally selected) of mux 1008, to the input of delay circuit 1012 and to one input (normally not selected) of mux 1018. The once delayed Goertzel filter weight B'1is applied through mux 1008 onto path 268 as Goertzel filter weight B11 for further processing by phase computation elements 206 corresponding to a first of two parallel half window phase computations discussed in further detail with respectto FIG. 11 below. The twice delayed Goertzel filter weight B'1 is applied over path 1058 to the other input (normally selected) of mux 1018. The twice delayed Goertzel filter weight B'l is applied through mux 1018 onto path 268 as Goertzelfilter weight B12 for further processing by phase computation elements 206 --- corresponding to a second of two parallel half window phase computations discussed in further detail with respect to FIG. 11 below. When the half window signal is applied to path 274 (also labelled "A" in FIG. 10), mux 1008 is selected . .
-. .

- WO 97103339 PCT/USg6111280 to apply the signal on its input path 358 onto path 268 for further processing as Goertzel filter weight B1 1, an undelayed copy of the input value B'1 from inputpath 358. Similarly, when the half window signal is applied to path 274 (also labelled ~A~ in FIG. 10), mux 1018 is selected to apply the signal on its input path 5 1052 onto path 268 for further processing as Goertzel filter weight B12, a once delayed copy of the input value B'1 from input path 358.
Fundamental frequency n~ is applied over path 358 to the input of delay circuit 1004. The once delayed frequency Q' is applied over path 1054 to the input of delay circuit 1014. The twice delayed frequency Q' is applied by delay 10 circuit 1014 to path 268 as frequency n for further processing by ~t computation element 208.
A FIRST EXEMPLARY EMBODIMENT- PHASE CALCULATIONS:
Phase calculation elements 206, shown in additional detail in FIG. 11, process the filtered discrete sample values to generate a complex number 15 i~,di~li~/e of the phase of the sampled, filtered sensor output signal. The complex number is applied to path 266 (and to path 264 by phase computational element 206 for the left channel) to be used in subsequent /\t computations. Specifically, a Goertzel filter Fourier transform is applied to the each Hanning window of filtered, discrete sampled sensor output signal values of both the right and left 20 channels. The coefficients of the Goertzel filter are determined by the frequency computation element 212 and supplied to phase computation elements 206 over path 268. The complex number output of phase computation element 206 is applied to path 266 (and to path 264 by phase computational element 206 for the left channel) and is used by the ~t computation.
To more effectively utilize the available sample data, two computations are performed in parallel, a first on each window of sample data, and a second on each window of sample data starting with a sample one half window length later than the first parallel computation. At each half window period boundary, the partial Fourier sum for the first half of a window is transferred from the first parallel 30 computation element to initialize the second partial computation. Simultaneously, the completed computation from the second parallel computation element, representing the complex phase value for the preceding full window period of samples, is transferred to the subsequent ~t computations.

-CA 022084~2 1997-06-13 Elements 1100 and- 1102 receive the current sample number within the current half window (SAMPNO) on path 272 and apply on their output paths (1150 and 1152 respectively) the corresponding pre-computed weight value. The weight value is retrieved from a vector (WINDOW) indexed by the SAMPNO index value.
5 Element 1102 adds the value N (half the length of the Hanning window) to the SAMPNO value received on path 272 in indexing in the WINDOW vector to offset the weight values by a number of samples corresponding to half the Hanning window size. The weight values on paths 1 150 and 1152 are applied to an input of multiplication junctions 1104 and 1106, respectively. The other input of 10 mllltiplic~tion junctions 1104 and of 1106 is the next enhanced sample value (e) on path 260 (or path 262 for the right channel). Multiplication junctions 1104 and 1106 apply their products (Hanning window weighted enhanced sample values) to output paths 1 154 and 1 156, respectively, as inputs to computational element 1108 and 1 1 10, respectively.
Computational elements 1108 and 1 1 10 each apply a Goertzel filter to the !Neighted samples to form a complex number representing the phase of the sampled signal values. The weighted samples are processed on each pulsed sample clock signal applied to the CLK path for the duration of one half window length of samples. Computational element 1108 receives the weighted sample 20 value (wsamp) on path 1154, receives the Goertzel filter coefficients for the first half window (Bo1,B11) on path 268, receives the previous filter state on path 1158, and calculates the new filter state as the complex sum Y' = wsamp + BY. The new state is applied to output path 1162 on the next clock pulse applied to the CLK path. Computational element 1110 receives the weighted sample value 25 (wsamp) on path 1156, receives the Goertzel filter coefficients for the second half window (Bo2~B12) on path 268, receives the previous filter state on path 1160, and c~c~ tes the new filter state as the complex sum Y' = wsamp + BY. The new filter state is applied to output path 264 as RL,QL ffor the left channel, and on path 266 as RR,QR for the right channel). At each pulse of the CLK signal, indicating30 a new sample to be processed, computational elements 1108 and 1110 perform their respective computations. The newly computed output value (Y') of element 1108 and 1110 is applied to its output path, 1162 and 264, respectively (266 forthe right channel) on the clock pulse (CLK) for the next sample period. The -clocked output values are applied over path 1162 and 264 to the normally selected zero input of mux 1112 and 1114, respectively. Mux 1112 and 1114 apply their respective normally selected input value to their respective outputs 1158 and 1160 and thereby to the Y input of element 1 108 and 1 1 10 for use in the next Goertzel 5 filter computation.
~ On receipt of a pulsed half window signal on path 274, both computational elements 1108 and 1110 are restarted for a Goertzel filtration over the period of the next half window period. Normally mux 1112 is selected to apply the complex value on it input path 1162 to its output path 1158 as the current state in 10 computational element 1 108 for the present half window period. At the start of the half window period (the end of the previous half window period), the half windowsignal applied to path 274 selects mux 11 12 to apply a zero value on its input path 1164 to its output path 1158. This resets the filter in the first compuLaLiGnal element 1108 to begin a new half window period. Normally mux 1114 is selected 15 to apply the complex value on it input path 264 (266 for the right channel) to its output path 1160 as the state of computational element 1110 for the present halfwindow period. At the start of the half window period, the half window signal applied to path 274 selects mux 1114 to apply filter state from the previous half window period, computed as the current output of element 1108, on its input path20 1162 to its output path 1160. This causes computational element 1110 to begina new half window period with a partial Goertzel result computed for the preceding half window by operation of element 1108. In other words, computational element 1108 processes the first half of each full window of samples while element 1110 processes the second half and combines it with the first half to produce a complex 25 number indicative of phase at each half window period for the previous full window length of samples. At each half window boundary, a completed phase computation is generated as the output of element 1110 on bus 264 (266 for the right channel) which represents the phase of the previous full window period of samples. As discussed above, at each half window boundary, half window 30 coefficient pipeline 310 shifts the Goertzel filter coefficients for the first half window parallel computation element 1108 (Bo1, B1~ to the coefficients used in the second half window parallel computation element 1110 (Bo2~ B12). This assures that the same Goertzel filter weights are applied to the first half window parallel -CA 022084~2 1997-06-13 partial computation as to the corresponding second half window parallel partial computation.
A FIRST EXEMPLARY EMBODIMENT - ~t CALCULATIONS:
~t caiculation element 208, shown in additional detail in FIG. 12, receives 5 phase information for both the left and right channels as determined by operation of phase ~lcl ~I?tiQn elements 206 and applied to path 264 for the left channel and path 266 for the right channel. Frequency information determined by operation of frequency calculation element 212 and is received by ~t c~lcl ll?tion element 208 over path 268. ~t c~lcul~tiQn element 208 determines the time difference between10 the two sampled sinusoidal signals resultant from the phase difference between the left and right flow tube sensor output signals. The ~t value is approximately proportional to the mass flow rate of the material flowing through the flow tubes of the Coriolis flowmeter. Other factors, well known in the art, are used to correct the calclJl~ted mass flow rate to adjust for temperature variations and other 15 factors.
- The Fourier transform of the left channel is multiplied by the conjugate of the Fourier l,~ rur", of the right channel. The angle of the complex result is then computed. This phase difference is divided by the tube frequency of the vibrating flow tubes to give a ~t value.
The real and imaginary parts of the left channel phase value (RL~ QL
respectively) are received from left channel phase calculation element 206 over path 264. The real and imaginary parts of the right channel phase value (RR~ QR
respectively) are received from right channel phase calculation element 206 overpath 266. Multiplier junction 1200 receives RL over path 264 and R R over path 266 as inputs to produce the product R~RR and applies the product to path 1250.
Multiplier junction 1202 receives QL over path 264 and Q Rover path 266 as inputs to produce the product QLQR and applies the product to path 1252. Multiplier junction 1204 receives QL over path 264 and RR over path 266 as inputs to produce the product QLRR and applies the product to path 1254. Multiplier junction 1206 receives RL over path 264 and QR over path 266 as inputs to produce the product RLQR and applies the product to path 1256.
Summing junction 1208 receives the product RLRR over path 1250 and the product Q~QR over path 1252 to generate the sum R LR R+ Q ~? Rand applies WO 97/03339 PCT~US96111280 the sum over path 1268 to the X input of computational element 1212. Summing junction 1210 receives the product QLRR over path 1254 and the product R~QR
over path 1256 to generate the sum QLRR - RLQR and applies the sum over path 1270 to the Y input of computational element 1212 - Computational element 1212 accepts its X input from path 1268 and its Y
input from path 1270 and determines the phase difference angle between the sinusoid signal on the left channel flow tube sensor and the sinusoidal signal on the right channel flow tube sensor from the argument (phase) of the complex number represented by its X and Y inputs as ~+iY) (i.e. ARG(X+iY)). The phase angle difference so computed by operation of computational element 1212 is applied over path 1258 to the X input to computational element 1214. The frequency (n) computed by operation of frequency c~lclJI~tion element 212 of FIG.

3 is applied over path 268 to the Y input of computational element 1214.
Computational element 1214 then computes the ratio X/Y (phase ~ erence /
frequency) and applies the computed ratio value to its output on path 1260.
M~ iplic~tion junction 1218 receives the computed ratio value on one input over path 1260 and receives the value N stored in register 1216 over path 1262 re,u,ese,,Lirlg the fixed sampling period (inverse of the sampling frequency). The product of the two inputs to multiplication junction 1218 is ~t and is applied over path 1264 to the input of register 1222. Register 1222 loads the current value on its input when clocked by a pulse on path 1266. And gate 1220 receives the sample frequency clock CLK on one input and the half window signal indicating the start of a new half window sampling period on its other input. The output ofAND gate 1220 is the half window signal pulse synchronized with the sample frequency clock pulses CLK generated by CLOCK 214 of FIG. 2. The ~t value stored in register 1222 is indicative of the mass flow rate of material through the flowmeter and is applied to path 294 for use by mass flow computation element 290. As is well known in the art, the ~t value is only approximately proportional to the mass flow rate in the flow tubes. Mass flow computation element 290 30 corrects the ~t value to generate the mass flow rate and apply it to utilization 292 of FIG. 2 over path 155. Element 290 performs appropriate corrections and scaling to compensate for the effects of temperature and other environmental factors.

WO 97/03339 CA 0 2 2 0 8 4 5 2 l 9 9 7 - 0 6 - l 3 PCTIUS96/11280 The embodiment described above utilizes a number of constant values to reset the computations associated with the notch filter. The debiasing parameter(a), the r.r~elLi,lg factor ~\), and the covariance matrix (P) are all reset under error conditions to restart the computational processing for adapting the notch filter5 parameters to changes in the fundamental frequency. The debiasing p~r~n,eler (a) and the forgetting factor Q\) are adjusted and initialized as described above.
One of ordinary skill in the art will recognize that these values may be adapted to any particular flow tube application and environmental parameters. Useful valuesfor these constants may be computed as a function of the expected nominal 10 fundamental frequency ffreq) of the vibrating flow tubes as follows:
- O ,9~0freq/100 aLIMIT = 0.98freq/ , ~DECAY ~- SN

AI~T97=fre~q9/~i00 ~ ALIMIT 0 995 ~ ADECAY 0 99 ~ AsNR
15 aADDER ~LIM11~ aDEC~Y) T~e covariance matrix (P~)lEs Inltlalized under various conditions discussed above as follows:

20 PINITR _ 10-4 1 w~ere "I" is the identity matrix.
A SECOND EXEMPLARY EMBODIMENT tBEST KNOWN MODE):
- The best presently known mode for implementing the present invention is depicted in FIGS. 13-16 as a second embodiment of the m~thods of the present 25 invention. As above in the first embodiment, adaptive notch filters are used to : enhance the signal represented by the decimated sampled values of the left and right channels and applied to paths 254 and 256, respectively. In this second embodiment four adaptive notch filters are utilized, two in series on each of the left and right channel signals. The two filters on each of the left and right channels 30 are "cascaded" in that the first filter utilizes a low-Q (wide notch) filter to supply Iimited signal enhancement but the ability to rapidly converge on changes in thefundamental frequency of the vibrating flow tubes. The signal output from the first -cascaded notch filter is then applied to a second cascaded notch filter. The second notch filter utilizes a high-Q (narrow notch) filter to provide superior noise 35 and harmonic rejection over that of previous solutions or over that of the first -WO 97/03339 PCT/US96tll280 embodiment described abave. Despite the narrow notch (high-Q) of the second notch filter, it can still rapidly adapt to changes in the fundamental frequency of the vibrating flow tubes due to the limited enhancement ffiltration) performed by the first notch filter. The reduced noise and harmonic levels in the signal applied to 5 the second notch filter allow it to also rapidly converge on changes in the fundamental frequency of the vibrating flow tubes.
An ~rl~litional notch filter having a notch shape even wider than that of the first cascaded notch filter is used to provide an estimate of the fundamental frequency of the vibrating flow tubes This estimate is used by weight adaptation10 computations to set the frequency parameter of the first cascaded notch filters for both the left and right channels. The output from the second cascaded notch filters is used by weight adaptation computations to adjust the frequency parameter of the second cascaded notch filters.
The first embodiment discussed above attempts to balance the width of the 15 notch to provide a narrow notch (high-Q) for better signal enhancement while -a!lowing for rapid convergence on changes in the fundamental frequency of the vibrating flow tubes through use of a wide notch (low-Q). In attempting to balance this aspect of the notch filters, the debiasing parameter (a) is modified at each sample period to adjust the notch width for the next sampled signal value. This 20 second embodiment uses a plurality of notch filters within fixed notch shapesffixed Q values) to provide an optimal solution to both requirements for rapid tracking of frequency changes and for superior noise rejection. This second embodiment provides better accuracy and repeatability than the first embodiment for three reasons. First, the second cascaded notch filter remains steady with a25 fixed narrow notch shape (high-Q) for superior noise and harmonic rejection. This improved noise rejection alone provides improved accuracy as compared to other solutions. Second, the improved tracking of the cascaded filters to changes in the fundamental frequency of the vibrating flow tubes improves the repeatability of the enhance",e. IL~ of the sampled signal values. And third, the cascaded notch filters 30 provide a more accurate estimate of the flow tube frequency for subsequent l~t computations in element 208.
lllese improvements are derived at the cost of computational complexity.
The individual computational elements of this second embodiment are somewhat CA 02208452 l997-06-l3 simpler than for the first embodiment (scalar arithmetic versus matrix). However, this second embodiment increases the total computational complexity by applying five notch filters and two weight adaptation computations at each sample.
Although somewhat more complex computationally, this second embodiment is 5 well within the computational power of commercially available digital signal processors.
A SECOND EXEMPLARY EMBODIMENT - OVERVIEW:
FIG. 13 decomposes elements of FIG. 2 to show additional detail regarding the flow o~ ur~, ~alion between computational elements of FIG. 2. Computational 10 elements 1300 are the first cascaded adaptive notch filters. Left channel first cascaded adaptive notch filter 1300 receives decimated input sensor output signal samples from path 254 (of FIG. 2). Weight coefficient (~(t)) of the notch filterIsrer function is received from weight adaptation element 1302 over path 1360.
Debiasing parameter (a1), which determines the shape of the notch, is received 15 from register file 1306 over path 1364 (also labelled "E"). P~ight channel first c~c~cled adaptive notch filter 1300 receives decimated input sensor output signal samples from path 256 (of FIG. 2) but otherwise operates identically to left channel first cascaded adaptive notch filter 1300. Both the left and right channel firstled adaptive notch filters receive the same adaptation parameter ~3 (t)) from 20 weight adaptation element 1302 over path 1360 and receive the same debiasing parameter (a1) over path 1364 from register file 1306.
An additional adaptive notch filter 1308 receives the decimated signal sample values from the left channel over path 254. This notch filter receives a ~iehi~lng parameter (~0) from register file 1306 over path 1364. This debiasing 25 parameter (aO) defines a broad notch (low-Q) to permit this notch filter to rapidly track changes in the fundamental frequency of the vibrating flow tubes. The enhanced output signal of this notch filter is not utilized (the filter provide very little effective enhancement due to its broad notch shape). Instead, the error factor (n) and gradient ~) are generated as output and applied to weight a.la,uLalion 30 element 1302 over path 1358 for computation of the weight parameters (0(t-1) and ~(t)). The newly computed weight parameters (~(t-1) and 0(t)) are applied by weight adaptation element 1302 to notch filters 1300 and 1308 over path 1360 in preparation for receipt of the next decimated sampled signal.

WO 97/03339 PCTIUS96~11280 The enhanced signal value of each decimated sample input processed by notch filters 1300 for the left and right channels are applied to a corresponding second cascaded notch filters 1310 over paths 1350 and 1352 as YL and yRfor the left and right channels, respectively. Second cascaded notch filters 1310 5 receive identical weight parameters (~(t-1) and ~(t)) from weight adapLaLion element 1312 over path 1362. Debiasing parameter (a2), which deter",i,les the shape of the notch, is received from register file 1306 over path 1364 (also labelled "E"). The error factor (n) and gradient ~) are generated as an output of leK
channel second cascaded notch filter 1310 is applied to weight adaptation element 10 1312 over path 260 for computation of the weight parameters ~9(t-1) and ~(t)).
The newly computed weight parameters (~ (t-1) and 0 (t)) are applied by weight adaptation element 1312 to notch filters 1310 over path 1362 in preparation for receipt of the next decimated sampled signal value as enhanced by the first c~c~led notch filters 1300.
Both the left and right channel second cascaded adaptive notch filters 1310 -generate an enhanced signal represented by discrete sample values applied to their respective output paths 260 and 262 respectively. The enhanced signal, denoted eL and eR for the left and right channels respectively, represents the ~sr~r ~le~:~ input signal samples filtered of all noise signals but for a narrow notch 20 of frequencies near the fundamental frequency of the vibrating flow tubes.
Ail notch filters discussed above with respect to FIG. 13 (1300, 1308, and 1310) compute the same functions to generate the same output values, namely:
an enhanced signal value (y or e), an error factor (n), and a gradient ~).
However, the noise (error factor) and gradient values from the right channel 25 second cascaded adaptive notch filter 1310 and from both of the first cascaded adaptive notch filters are not used in the methods and apparatus of the present invention. Similarly, the enhanced signal value output of the frequency trackingadaptable notch filter 1308 is not used in the methods of the present invention.The functions computed by all adaptive notch filters 1300, 1308, and 1310 are 30 discussed in detail below. The error factor is essentially the noise component of the sampled values. It is known to those of ordinary skiil in the art that when applying a recursive least-squares algorithm, as here, that an a posteriori prediction error improves the convergence rate of the filter (see Arye Nehoral "A

CA 02208452 l997-06-l3 i."al Parameter Adaptive Notch Filter With Constrained Poles and Zero", IEEE
Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-33, No. 4, August 1985 at page 987).
The enhanced signal values from the left and right channel second 5 c~c~ed adaptive notch filters 1310 (eL and eR) are received over paths 260 and262, respectively, by phase computation elements 206. Phase computation elements 206 and ~t computation element 208 are identical to the elements discussed above with respect to the first embodiment and FIGS. 3-12.
Frequency calculation element 1304 receives the filter weight ~3~t)) from 10 weight a~apl~Lion element 1312 over path 1362 and computes the weights (B') for the Goertzel fiiter computations of phase computation elements 206 and computes - the frequency (n') of the vibrating flow tubes. These output values are applied to half window multiplexor half window coefficient pipeline 310 over path 358. Halfwindow coefficient pipeline 310 is discussed above with respect to the first 1~ ernbodiment and FIGS. 3-12.
- -A SECOND EXEMPLARY EMBODIMENT - NOTCH FILTERS:
FIG. 14 depicts additional detail of the adaptive notch filters 1300, 1308, and 1310 of this second embodiment. AS discussed above, certain output values and associated input values are not used for certain of the otherwise identical 20 ~c1art~hle notch filters of this second embodiment of the present invention. The description of FIG. 14 discusses operation of the depicted notch filter as though - all inputs and outputs are utilized (as in the left channel second cascaded adaptable notch filter 1310). For simplicity, the notch filter discussed in detail . below will be referred to by reference number 1310 (left channel) to represent all - - 2~ five adaptable notch filters of this second embodiment (1300, 1308, and 1310).
Left channel filter 1310 receives its input on path 1350 and applies its outputs to path 260. Other notch filters receive their respective inputs from paths 254 (1300 left channel and 1308), 256 (1300 right channel), and 1352 (1310 right channel).-~ Other notch filters apply their respective output signals to paths 1350 (1300 left 30 channel), 1352 (1300 right channel), 1358 (1308), and 262 (1310 right channel).
One of ordinary skill will recognize the similarity between the operation of all five notch filter computational elements.

, ~, WO 97/03339 PCTrUS96111280 The adaptive notch filter 1310 (left channel) of FIG. 14 determines the noise present in the discrete sample input values u(t) received on its input path 1350(where (t) as used in the equations below indicates the value corresponding to sample period "t"). Debiasing parameter (denoted as a in the equations below) 5 is feceivcd on path 1364 (as a2). The coefficient of the notch filter for the current sample period (~ (t)) and for the previous sample period (~ (t-1)) are received over path 1362. Subtracting the noise signal values e from the input sample values u yields the enhanced filtered value e for output on path 260. The adaptive notch filter 1310 determines the enhanced signal value e(t) by a second order filter 10 polynomial as follows:
u(t) sample values e(t) = u(t) - e(t) 2 enhanced sample values e(t) = u(t) + u(t-2) - a e(t-2) - (p (t)~ (t) noise component of sample values ~(t) = -u(t-1) + ae(t-1) In addition, adaptive notch filter 1310 determines the gradient ~ (t)) as follows:
~1) (t) = ~ (t) - a 2ll) (t-2) - a~ (t-1)~ (t-1) Finally, adaptive notch filter 1310 also determine the error estimation (n(t)) as 20 follows:
n(t) = u(t) + u(t-2)-cx2e(t-2)-q)(t,~(t-1) Adaptive notch filter 1310 applies the input value (u(t) or v(t) - the sample value to be applied to the notch filter) received over path 1350 to delay circuit 1408.
The once delayed input sample value u(t-1) generated as the output of delay 25 circuit 1408 is applied over path 1454 to delay circuit 1410 and its twice delayed input sample value u(t-2) is applied to path 1456. Delay circuits 1408 and 1410 delay the value applied to their respective inputs by one pulse of the sample clock signal applied to the CLK path as discussed above. Delay circuits 1426, 1428 1440, and 1442 operate in like manner to delay their respective input values by 30 one sample clock period as indicated by the CLK signal path. Debiasing parameter a received on path 1364 is applied to both inputs of multirlic~tion junction 1412 and its output producta2 is applied to path 1468.
The debiasing parameter a on path 1364 and the once delayed intermediate value e(t-1) on path 1462 (discussed below) are applied as inputs to 35 multiplication junction 1416 and its output product a e(t-1) is applied to pEh 1460.

-CA 022084~2 l997-06-l3 The debiasing parameter squared a2 on path 1468 and the twice delayed - intermediate value e(t-2) on path 1464 (discussed below) are applied as inputs to multiplication junction 1420 and its output product a~e(t-2) is applied to path 1466.
- The once delayed input sample value u(t-1) is subtracted from the 5 intermediate value ae(t-1) on path 1460 by summing junction 1414 to produce intermediate value ~(t) = -u(t-1) + ae(t-1) and apply that intermediate value topath 1458. The intermediate value a2e(t-2) on path 1466 is subtracted from twice- delayed input sample value u(t-2) on path 1456 by summing junction 1418 and the ~: resultant intermediate value u(t-2) - a2e(t-2) is applied to path 1486. Intermediate 10 valueq)(t) on path 1458 and the filter coeKicient~(t) on path 1362 are applied to multiplication junction 1422 to produce the intermediate value ~ (t)~(t) and apply that product to path 1472. Intermediate value ~(t) on path 1458 and the filter coefficient ~(t-1) on path 1362 are applied to multiplication junction 1424 to produce the intermediate value ~(t)~(t-1) and apply that product to path 1470.
The notch filter 1310 determines the noise estimate e(t) of the input sample - -value u(t) by first applying the input sample value u(t) on path 1350 and the i~,L~r")ediate value u(t-2) -a~e(t-2) on path 1486 to the inputs of summing junction 1400 to produce the sum u(t) + u(t-2) - a~e(t-2) and apply that sum to path 1450.
~ The intermediate value ~ (t)~ (t) on path 1472 is subtracted from the intermediate 20 value u(t) + u(t-2) - a~e(t-2) on path 1450 by summing junction 1404 to d~ e the noise estimate e(t) of the input sample value u(t) and apply the noise e~lil,l~Le e(t) to path 1452. The noise estimate e(t) on path 1452 is subtracted from inputsample value u(t) on path 1350 by summing junction 1406 and the resultant enhanced signal value e(t) is applied to the notch filter s output path 260. The25 noise estimate e(t) on path 1452 is applied to delay circuit 1426 to produce a once delayed noise estimate e(t-1~ on path 1462. The once delayed noise esli"lale e(t-1) on path 1462 is applied to delay circuit 1428 to produce twice - delayed noise estimate e(t-2) on path 1464. These delayed noise esli~,ale values on paths 1462 and 1464 are utilized in intermediate computations as discussed 30 above.
~; In addition to the enhanced signal e(t) generated by the notch filter 1310 an a priori noise estimation n(t) is determined for use in the weight adaptationcon~pl~tions discussed below. The intermediate value~(t)~(t-1) on path 1470 is -wo 97/03339 PCTIUS96/11280 subtracted from the interrnediate value u(t) + u(t-2) - cx2e(t-2) on path 1450 by summing junction 1402 to determine the estimation error n(t) of the input samplevalue u(t) and apply the estimation error to path 260 for use by weight adapLaLion computational element 1312 as discussed below.
L~stly, the notch filter 1310 recursively computes a gradient ~1) (t) for use inthe weight adaptation computations discussed below. The current gradient value ~I)(t) on path 260 is applied to delay circuit 1440 to produce a once delayed gradient value ~ (t-1) on path 1474. The once delayed gradient value ll)(t-1) onpath 1474 is applied to delay circuit 1442 to produce twice delayed gradient value ~1) (t-2) on path 1480. The once delayed gradient value ~ (t-1) on path 1474 andthe weight coefficient ~ (t-1) on path 1362 are multiplied by multiplication junction 1434 which applies the intermediate product to path 1476. This intermediate product on path 1476 and the debiasing parameter a on path 1364 are applied to multiplication junction 1432 to produce the intermediate producto~6(t-1)~(t-1) on path 1478. The twice delayed gradient ~ (t-2) on path 1480 and the square of -the debiasing parameter o,2 on path 1468 are applied to multiplication junction1438. The product of multiplication junction 1438 is applied to path 1482 and issubtracted from the intermediate value ~ (t~ on path 1458 by summing junction 1436 to produce the intermediate value ~(t) - a2~(t-2) on path 1484. The i, ll~rlnec~iale value on path 1478 is subtracted from the intermediate value on path 1484 by summing junction 1430 to produce the new gradient:
~IJ (t) = ~ (t) - a 2~ (t-2) - a~ (t-1)~J (t-1) and apply it to path 260.
A SECOND EXEMPLARY EMBODIMENT - WEIGHT ADAPTATION:
FIG. 15 provides additional detail regarding the structure and operation of weight adaptation computational elements 1302 and 1312 of FIG. 13. Weight ~;a~L~lion computational elements 1302 and 1312 perform identical computations but receive unique input values from register file 1306 of FIG. 13 and from their associated adaptive notch filters 1308 and 1310, respectively. Weight adaptationcomputational element 1302 receives the error factor n and the gradient ~IJ fromnotch filter 1308 over path 1358 and receives forgetting factorA1 from register file 1306 over path 1364. Weight adaptation computational element 1302 applies the current weight ~(t) to notch filters 1300 and 1308 over path 1360. The once CA 02208452 l997-06-l3 W097/03339 PCT~S96/11280 - delayed weight ~(t-1) is applied to notch filter 1308 over path 1360. Weight :~ - adaptation computational element 1312 receives the noise estimate n and the gradient ~1) from left channel notch filter 1310 over path 260 and receives forgetting factorA2 from register file 1306 over path 1364. Weight adaptation compùtational~- 5 element 1312 applies the current weight~(t) and the once delayed weight~(t-1) - to notch filters 1310 and applies the current weight ~ (t) to frequency c~lc~ tion - element 1304 over path 1362. Since both weight adaptation computational element 1302 and 1312 operate identically, the description below refers only theoperation of element 1302.
Weight adaptation computational element 1302 determines the next weight coer~icie,lL for its associated notch filters using scalar arithmetic as follows (where (t) as used in the equations below indicates the value corresponding to sample - period"t"):
~(t) = ~(t-1) + P(t)~(t)n(t) the u~2dated weight coefFicient P(t) = (P(t-1) - ((P(t-1)~(t)2P(t-1)) / ~ + (~J(t) P(t-1)))) /A
the covariance variable VVeight adaptation computational element 1302 determines an updated weight -- ~ coefficient ~ (t) on path 1360 (as discussed below) and applies it to the input of delay circuit 1500 to produce a once de!ayed weight coefficient ~(t-1) on path 1360.
Weight adaptation computational element 1302 determines the updated = covariance variable P(t) with each new sampled value as a function of the - previously computed covariance variable on path 1556, the supplied gradient ~1) on path 1358 and the forgetting factorA1 from register file 1306 over path 1364.The current covariance variable P(t) on path 1554 is applied to delay circuit 1508 to produce a once delayed covariance variable P(t-1) applied to path 1556.
-- Multipiication junction 1512 receives the once delayed covariance variable P(t-1) ~;- on path 1556 and the gradient ~1) on path 1358 and applies to path 1558 the product P(t-1)~ (t). Multiplication junction 1514 receives this product on path 1558 and receives the gradient ~ on path 1358 and applies to path 1560 the product P(t-l)~l)(t)2. Multiplication junction 1516 receives this product on path 1560 and . . ~
~ receives the once delayed covariance variable P(t-1) and applies to path 1562 the -~ i product P(t~ 1J(t)2P(t-1) (the numerator in the covariance variable computation ~- given above). Summing junction 1510 receives the product P(t-1)~ (t)2 on path . .
~ 62 1560 and the forgetting factor Al on path 1364 and applies to path 1568 its sum:A1 + P(t~ (t)2 (the denominator in the covariance computation given above).
Comrllt~tional element 1518 divides the numerator applied to its input path 1562by the denominator applied to its input path 1568 to produce an output quotient 5 on path 1564. Summing junction 1520 then subtracts this quotient on path 1564 from the once delayed covariance variable on path 1556 and applies the result topath 1566. Computational element 1522 divide the numerator on its input path 1566 by the denominator forgetting factor A 1 on its input path 1364 to produce the updated covariance variable P(t) and apply it to output path 1554.
Ml~ Lc~lion junction 1502 receives the error ~actor n on path 1358 and the gradient ~ on path 1358 and applies to path 1550 the product ~ n. M
junction 1504 receives the product ~IJ (t)n(t) on path 1550 and the update covariance variable P(t) on path 1554 and applies to path 1552 the product P(t)~ (t)n(t). Summing junction 1506 then receives this product on path 1552 and15 the once delayed weight coefficient ~ (t-1) on path 1360 and applies to path 1360 -the updated weight coefficient ~ (t).
A SECOND EXEMPLARY EMBODIMENT - FREQUENCY CALCUIATION:
In addition to adaptive notch filters 1310, frequency calculation element 1304 receives the updated weight coefficient ~ (t) from weight adaptation 20 computational element 1312 over path 1362. Frequency calculation element 1304, shown in additional detail in FIG. 16, accumulates the weight coefficients ~(t) values received over path 1362 to compute the Goertzel filter weights B' (B~o and B'1) and the frequency Q' and apply them to path 358. Frequency c~lclJl~tion element 1304 of FIG. 16 operates in a manner similar to element 308 of FIG. 9 in25 the first embodiment discussed in detail above. Summing junction 1600 receives the previous accumulated sum on path 1652 and the updated weight ~ (t) on path 1362 and applies the sum to an input of mux 1602 over path 1654. Mux 1602 is normally selected to apply the accumulated sum on its input path 1654 onto its output path 1650. The accumulated sum on path 1650 is applied to the input of 30 register 1604 to store the accumulated sum when the sample clock signal CLK is pulsed for each new weight value applied to path 1362. When the half window signal (discussed above with respect to the first embodiment and FIGS. 3-12) is applied to mux 1602 over path 274, the accumulation is reset by applying the -- CA 022084~2 1997-06-13 newly received weight value on input path 1362 to output path 1650 through mux 1602. This resets the accumulated sum in register 1604 and begins the new accumulation for another half window period of sampled values.
The sum of the weights received on path 1362 is applied to the X input of 5 corrr~tion element 1606 over path 1652. Computation element 1606 computes the real part of the Goertzel filter weights (B'o) as:
B~o = -X / 2N
where X is the input to element 1606 as above and N is the number of samples in a ha~ window period. The real part of the Goertzel filter weights (B'o) computed 10 by computational element 1606 is applied to path 358 for use by half window coefficient pipeline 310 discussed above. The real part of the Goertzel filter weights is also applied to the X input of computational element 1608 which computes the imaginary part of the Goertzel filter weights (B'1) as:
B'1 = sqrt(1-X2) 15 where X is the input to element 1608 as above. The imaginary part of the Goertzel -filter ~ L~ (B'1) computed by computational element 1608 is applied to path 3~8 - for use by hat,f window coefficient pipeline 310 discussed above. In addition, the real part of the Goertzel filter weights is applied to the X input of computational element 1610 which computes the fundamental frequency (~2') of the vibrating flow - 20 tubes as:
-~ n~ = cos~1 x where ~C is the input to element 1610 as above. The fundamental frequency (Q') computed by computational element 1610 is applied to path 358 for use by half - window coefficient pipeline 310 discussed above.
It may be noted that the computations performed by computational elements 1606, 1608, and 1610 are undefined when their respective inputs are o~ cle certain appropriate ranges. The output values of these computations are utilized only on the boundaries of Hanning windows at which time the inputs are assured to be appropriate to the respective computations. For this reason, the undefined computations suggested by the diagram of FIG. 16 are of no practical relevance. As discussed above, the pseudo circuits of FIG. 16 are intended only as an aid in understanding the methods and related computations of the present invention.

- WO 97/03339 PCT/US96111~80 It will be readily apparent to one of ordinary skill in the art that heuristic tests simiiar to those described above with respect to the first embodiment may be employed in the second embodiment. These heuristics help to prevent erroneous flow rate measurement generated by erroneous computations caused 5 by loss of frequency convergence of the notch filter adaptation methods. Such - heuristics generally update computations at each sample (or at half windôw boundaries) only if the new values are within reasonable ranges for the particular application of the flow meter. If the computations result in unexpected values, the updated values will not be used and the previous values will be re-used.
It is expressly understood that the claimed invention is not to be limited to the description of the preferred embodiment but encompasses other modifications and alte,~Lions within the scope and spirit of the inventive concept. For ex~,,,,ule, the invention has been described in conjunction with the flowmeter of FIG. 1. Itis to be understood the invention is not limited in its application to flowmeters of 15 the type shown in FIG. 1 It may be used with any type of flowmeter that operates or the Corio~,s principle, ir,cludi"g thost: having single tubes, dûub;~ iubes, straight tubes, tubes of irregular configuration, etc. Also, the flowmeter with which the invention is utilized need not have the specific flange and hole configuration shown on FIG. 1 and, instead, may be mounted by any suitable means to the 20 conduit to which the flowmeter is connected. Or, for example, the adaptive notch filters depicted in the present invention may receive sampled input signal values with other forms of decimation or even without decimation as appropriate for theparticular sampling rates and the particular application. In addition, the weight adaptation computations may be based on signal values other than the left 25 channel sampled signal values. One of ordinary skill in the art will recognize a wide variet,v of modifications to the embodiments described herein which are within the scope and spirit of the claimed invention.

Claims (34)

What is claimed is:

1. Apparatus for measuring mass flow rate of a material in a Coriolis mass flow meter having flow tube means and having sensors associated with said flow tube means for generating output signals indicative of the oscillatory movement of said flow tube means, said apparatus comprising:
means for periodically sampling said sensor output signals and for converting sampled sensor output signals to digital form to generate a sequence of discrete sampled values representative of said output signals, including any undesirable components, of said first and second sensors;
digital notch filtration means, responsive to the generation of said sequence of discrete sampled values for generating a sequence of discrete enhanced values, each discrete enhanced value corresponding to a sample of said sequence of discrete sampled values with said undesirable components removed;
phase determination means, responsive to the generation of said sequence of discrete enhanced values for determining a phase difference between the output signals of said first and second sensors; and mass flow measurement means, responsive to the determination of phase difference, for determining a mass flow rate value of the material flowing through the flow tube means.

2. The apparatus of claim 1 further comprising:
notch adaptation means, cooperative with said digital notch filtration means, for altering filter parameters of said digital notch filtration means to affect the notch capability to reject undesirable components of the output signals of said first and second sensors.

3. The apparatus of claim 2 wherein said filter parameters comprise variable polynomial coefficients applied to said discrete sampled values to enhance said discrete sampled values, wherein said variable polynomial coefficients determine the center frequency of the notch of said digital notch filtration means.

4. The apparatus of claim 3 wherein said notch adaptation means further comprises weight adaptation means for adjusting said variable polynomial coefficients applied to said discrete sampled values in enhancing said discrete sampled values to after the center frequency of said digital notch filtration means.

5. The apparatus of claim 4 further comprising:
means for detecting that the ratio of a discrete enhanced value to a corresponding noise signal has fallen below a predetermined threshold value and for generating a fault signal responsive to said detection; and means responsive to generation of said fault signal for adjusting said variable polynomial coefficients.

6. The apparatus of claim 4 further comprising:
stability test means for detecting instability in the adjustment of said variable polynomial coefficients and for generating an instability signal to indicate detection of the instability; and means responsive to generation of said instability signal to adjust said variables polynomial coefficients to reduce said instability.

7. The apparatus of claim 2 wherein said filter parameters comprise a variable debiasing parameter applied to said discrete sampled values in enhancing said discrete sampled values, wherein said variable debiasing parameter determines the frequency spectrum width of the notch of said digital notch filtration means.

8. The apparatus of claim 7 wherein said notch adaptation means further comprises weight adaptation means for adjusting said variable debiasing parameter applied to said discrete sampled values in enhancing said discrete sampled values.

9. The apparatus of claim 8 further comprising:
means for detecting that the ratio of a discrete enhanced value to a corresponding noise signal has fallen below a predetermined threshold value and for generating a fault signal responsive to the detection; and means responsive to said fault signal for adjusting said variable debiasing parameter.

10. The apparatus of claim 1 wherein said phase determination means further comprises:
windowing means for defining a window comprising a plurality of sequential ones of said discrete enhanced values; and Goertrel filtration means for decimating the discrete enhanced values in said window to determine a phase value for said window.

11. The apparatus of claim 10 further comprising Hanning windowing means for weighting each of said plurality of discrete enhanced values in said window wherein the weights are determined as:
h(k) = (1/2) (1 - cos (2~k / (2N -1))) where:
N is half the number of discrete enhanced values in the window, and k is the index of the value to which the weight h(k) is applied.

12. The apparatus of claim 1 wherein said phase determination means further comprises:
windowing means for defining a plurality of windows, each of said plurality of windows comprising a plurality of sequential ones of said discrete enhanced values; and Goertzel filtration means for decimating said plurality of discrete enhanced values in each of said plurality of windows to determine a phase value for said each of said plurality of windows, wherein each of said windows comprises an equal number of said discrete enhanced values and wherein each of said windows is offset from an earlier window by an equal number of said discrete enhanced values.

13. The apparatus of claim 12 further comprising Hanning windowing means for weighting each of said plurality of discrete enhanced values in each of said windows wherein the weights are determined as:

h(k) = (1/2) (1 - cos (2~k / (2N -1))) where:
N is half the number of discrete enhanced values in the window, and k is the index of the value to which the weight h(k) is applied.

14. The apparatus of claim 1 wherein said digital notch filtration means further comprises:
first digital notch filtration means, responsive to the generation of said sequence of discrete sampled values, for generating an intermediate sequence of discrete values, each intermediate discrete value corresponding to a sample of said sequence of discrete sampled values with signals representative of said undesirable components partially removed; and second digital notch filtration means, responsive to the generation of said intermediate sequence of discrete values, for generating said sequence of discrete enhanced values, each discrete enhanced value corresponding to an intermediate discrete value of said intermediate sequence of discrete values with signals representative of said undesirable components removed.

15. The apparatus of claim 14 further comprising:
first notch adaptation means, cooperative with said first digital notch filtration means for altering filter parameters of said first digital notch filtration means which are determinative of the characterization of signals as representative of noise; and second notch adaptation means, cooperative with said second digital notch filtration means for altering filter parameters of said second digital notch filtration means which are determinative of the characterization of signals as representative of noise.

16. The apparatus of claim 15 wherein said filter parameters comprise variable polynomial coefficients applied to said discrete sampled values to enhance said discrete sampled values.

17. The apparatus of claim 16 wherein said first notch adaptation means further comprises weight adaptation means for adjusting said variable polynomial coefficients applied to said discrete sampled values to generate said intermediate sequence of discrete values, and wherein said second notch adaptation means further comprises weight adaptation means for adjusting variable polynomial coefficients applied to said intermediate sequence of discrete values to generate said sequence of discrete enhanced values.

18. In a Coriolis mass flow meter having a flow tube means and having first and second sensors associated with the flow tube means for generating output signals indicative of the oscillatory movement of the flow tube means, a method for measuring the mass flow rate of a material flowing through said flow tube means of said flow meter comprising the steps of:
periodically converting analog output signals generated by the first and second sensors into digital form to generate a sequence of discrete sampled values representative of said output signals, including any undesirable components, of each of said first and second sensors;
applying said sequence of discrete sampled values to digital notch filtration means to generate a sequence of discrete enhanced values, each discrete enhanced value corresponding to a sample of said sequence of discrete sampled values with signals representative of noise removed;
applying said sequence of. discrete enhanced values to phase value determination means to determine phase information regarding the oscillatory movement of the flow tube indicated by said sequence of said discrete enhanced values;
applying said phase information to phase difference computation means to determine a phase difference between the output signals of said first and second sensors; and determining the mass flow rate of the material flowing through said flow meter responsive to the determination of phase difference.

19. The method of claim 18 further comprising:
altering filter parameters of said digital notch filtration means to adjust the digital notch filtration means to compensate for changes in the frequency of oscillations of the flow tube.

20. The method of claim 19 wherein said filter parameters comprise variable polynomial coefficients applied to said discrete sampled values to enhance said discrete sampled values, wherein said variable polynomial coefficients determine the center frequency of the notch of said digital notch filtration means.

21. The method of claim 20 wherein the altering step further comprises adjusting said variable polynomial coefficients applied to said discrete sampled values in enhancing said discrete sampled values to alter the center frequency of said digital notch filtration means.

22. The method of claim 21 further comprising:
determining a ratio of a discrete enhanced value to a corresponding noise signal;
determining whether said ratio has fallen below a predetermined threshold value;
generating a fault signal responsive to the determination that said ratio has fallen below said predetermined threshold value; and adjusting said variable polynomial coefficients responsive to generation of said fault signal.

23. The method of claim 21 further comprising:
determining whether said variable polynomial coefficients are outside an acceptable range of stable values;
generating an instability signal responsive to a determination that said variable polynomial coefficients are unstable; and adjusting said variable polynomial coefficients responsive to generation of said instability signal to reduce said instability.

24. The method of claim 19 wherein said filter parameters comprise a variable debiasing parameter applied to said discrete sampled values in enhancing said discrete sampled values, wherein said variable debiasing parameter determines the frequency spectrum width of the notch of said digital notch filtration means.

25. The method of claim 24 wherein said step of altering said parameters further comprises adjusting said variable debiasing parameter applied to said discrete sampled values for enhancing said discrete sampled values.

26. The method of claim 25 further comprising:
determining a ratio of a discrete enhanced value to a corresponding noise signal;
determining whether said ratio has fallen below a predetermined threshold value;
generating a fault signal responsive to the determination that said ratio has fallen below said predetermined threshold value; and adjusting said variable debiasing parameter responsive to generation of said fault signal.

27. The method of claim 18 wherein the application of said phase values to said phase difference computation means further comprises:
defining a window comprising a plurality of sequential ones of said discrete enhanced values; and decimating the discrete enhanced values in said window through a Goertzel filtration to determine a phase value for said window.

28. The method of claim 27 further comprising:
determining a Hanning window weight for weighting each of said plurality of discrete enhanced values in said window wherein the weights are determined as:
h(k) = (1/2) (1 - cos (2~k / (2N -1))) where:

N is half the number of discrete enhanced values in the window, and k is the index of the value to which the weight h(k) is applied.

29. The method of claim 18 wherein the application of said phase values to said phase difference computation means further comprises:
defining a plurality of windows, each of said plurality of windows comprising a plurality of sequential ones of said discrete enhanced values; and decimating the discrete enhanced values in each of said plurality of windows through a Goertzel fitter to determine a phase value for said each of said plurality of windows, wherein each of said windows comprises an equal number of said discrete enhanced values and wherein each of said windows is offset from an earlier window by an equal number of said discrete enhanced values.

30. The method of claim 29 further comprising:
determining a Hanning window weight for weighting each of said plurality of discrete enhanced values in each of said plurality of windows wherein the weights are determined as:
h(k) = (1/2) (1 - cos (2~k / (2N -1))) where:
N is half the number of discrete enhanced values in the window, and k is the index of the value to which the weight h(k) is applied.

31. The method of claim 18 wherein the step of applying said discrete sampled values to said digital notch filtration means further comprises:
operating a first digital notch filtration means to generate an intermediate sequence of discrete values, each intermediate discrete value corresponding to a sample of said sequence of discrete sampled values with signals representative of noise partially removed; and operating a second digital notch filtration means responsive to the generation of said intermediate sequence of discrete values to generate a sequence of discrete enhanced values, each discrete enhanced value corresponding to an intermediate discrete value of said intermediate sequence of discrete values with signals representative of noise removed.

32. The method of claim 31 further comprising:
operating first notch adaption means to alter filter parameters of the first digital notch filtration means to adjust the first digital notch filtration means to compensate for changes in the frequency of oscillations of the flow tube; and operating second notch adaption means to alter filter parameters of the second digital notch filtration means to adjust the second digital notch filtration means to compensate for changes in the frequency of oscillations of the flow tube.

33. The method of claim 32 wherein said filter parameters comprise variable polynomial coefficients applied to said discrete sampled values to enhance said discrete sampled values.

34. The method of claim 33 wherein said step of altering said first notch adaptation means further comprises operating weight adaptation means for adjusting variable polynomial coefficients applied to said discrete sampled values to generate said intermediate sequence of discrete values and wherein said step of operating said second notch adaptation means further comprises operating weight adaptation means for adjusting variable polynomial coefficients applied to said intermediate sequence of discrete values to generate said sequence of discrete enhanced values.