HK1116535B

HK1116535B - High speed frequency and phase estimation for flow meters

Info

Publication number: HK1116535B
Application number: HK08106567.2A
Authority: HK
Inventors: Mark James Bell; Richard L. Maginnis; Craig B. Mcanally
Original assignee: Micro Motion, Inc.
Priority date: 2004-12-29
Filing date: 2005-12-05
Publication date: 2010-07-23

Description

High speed frequency and phase estimation for flow meters

Technical Field

The invention relates to meter electronics and methods for processing one or more sensor signals in a flow meter.

Background

It is known to use coriolis mass flowmeters to measure mass flow, density and volumetric flow of material flowing through a pipeline, along with other information, as disclosed in U.S. patent No.4,491,025 to j.e.smith et al, 1/1 1985, and re.31,450 to j.e.smith, 2/11 1982. These flow meters have one or more flow tubes of different configurations. Each conduit configuration can be viewed as having a set of natural vibration modes including, for example, simple bending, torsional, radial, and coupled modes. In a typical coriolis mass flow measurement application, a conduit configuration is excited in one or more vibration modes as material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit.

The vibration modes of the system of packing material are defined in part by the combined mass of the flow tube and the material within the flow tube. Material flows into the flow meter from the connecting line on the inlet side of the flow meter. The material then flows through one or more flow tubes and exits the flow meter to a line connected on the outlet side.

The driver applies a force to the flowtube. This force causes the flow tube to oscillate. When no material flows through the flowmeter, all points along the flow tube oscillate with the same phase. As material begins to flow through the flow tube, coriolis accelerations cause each point along the flow tube to have a different phase relative to other points along the flow tube. The phase on the inlet side of the flow tube lags the driver and the phase on the outlet side leads the driver. Sensors are placed at different points on the flow tube to produce sinusoidal signals representative of the motion of the flow tube at the different points. The phase difference between the two sensor signals is proportional to the mass flow rate of the material flowing through the one or more flow tubes. In one prior art approach, a Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) is used to determine the phase difference between the sensor signals. The phase difference and the vibrational frequency response of the flow tube assembly are used to obtain the mass flow rate.

In one prior art approach, an independent reference signal is used to determine the cutoff (pickoff) signal frequency, for example by using the frequency sent to the vibration driver system. In another prior art approach, the frequency may be determined by concentrating the vibrational response frequency generated by the cut-off sensor in a notch filter, where the prior art flow meter attempts to maintain the notch in the notch filter at the cut-off sensor frequency. This prior art works very well in a quiescent state where the fluid material in the meter is uniform and the resulting cutoff signal frequency is relatively stable. However, the prior art phase measurement suffers from problems when the fluid material is not homogeneous, such as in the case of a two-phase flow in which the fluid material comprises a liquid and bubbles in a solid or liquid flow material. In such cases, the prior art determined frequency may fluctuate rapidly. During conditions where frequency transitions are fast and large, the cutoff signal may move outside the filter bandwidth, resulting in incorrect phase and frequency measurements. This is also a problem in empty-full-empty batch processes, where the flow meter is repeatedly operated in alternating empty and full conditions. Likewise, if the frequency of the sensor is moving rapidly, the demodulation process will not be able to keep up with the actual or measured frequency, resulting in demodulation at an incorrect frequency. It should be appreciated that if the determined frequency is incorrect or inaccurate, then the subsequently derived values for density, volumetric flow rate, etc. will also be incorrect and inaccurate. In addition, errors may be compounded in subsequent flow characterization determinations.

In the prior art, the cut-off signal can be digitized and digitally manipulated to implement a notch filter. The notch filter accepts only narrow band frequencies. Therefore, when the target frequency changes, the notch filter may fail to track the target signal for a period of time. Typically, a digital notch filter implementation takes 1-2 seconds to track a fluctuating target signal. Because of the time required to determine the frequency in the prior art, the result is that not only does the frequency and phase determinations contain errors, but the error measurements include time intervals that exceed the time intervals over which the errors and/or two-phase flow actually occur. This is due to the relative slowness of the response achieved by the notch filter.

The result is that prior art flowmeters fail to accurately, quickly, or satisfactorily track or determine the cutoff sensor frequency during two-phase flow of the fluid material in the flowmeter. Therefore, the phase determination is also slow and error prone, since the prior art uses a determined cut-off frequency to derive the phase difference. Therefore, any error in the frequency determination is mixed into the phase determination. The result is increased error in the frequency determination and the phase determination, resulting in increased error in determining the mass flow. Furthermore, because the density value is determined using the determined frequency value (the density is approximately equal to one-square of the frequency), errors in the frequency determination may be repeated or mixed in the density determination. This is also true for the determination of the volume flow, which is equal to the mass flow divided by the density.

Prior art meter electronics are given in U.S. patent No.5,578,764 to Yokoi et al. The Yokoi patent discloses a hilbert transformer 21 and trigonometric function calculator 31 that receive the upstream and downstream cut-off sensor signals and use the two signals to calculate the phase difference between the signals. The hilbert transformer 21 phase-shifts the two cut-off sensor signals by 90 degrees, and uses the two phase-shifted signals in the phase difference calculation. In Yokoi, the phase difference thus obtained is used in conjunction with independently measured external frequencies to calculate mass flow. The prior art technique of Yokoi therefore does not quickly and accurately derive the frequency components needed to calculate a highly accurate mass flow. Furthermore, Yokoi cannot generate mass flow quickly because Yokoi has to wait for the frequency determination.

Disclosure of Invention

The above and other problems are solved and an advance in the art is obtained by providing meter electronics and methods for processing sensor signals in a flow meter.

Meter electronics for processing sensor signals in a flow meter are provided according to embodiments of the invention. The meter electronics includes an interface for receiving the first sensor signal and the second sensor signal and a processing system in communication with the interface and configured to generate a 90 degree phase shift from the first sensor signal and to use the 90 degree phase shift to calculate the phase difference.

Meter electronics for processing sensor signals in a flow meter are provided according to embodiments of the invention. The meter electronics includes an interface for receiving the first sensor signal and the second sensor signal and a processing system in communication with the interface and configured to generate a first 90 degree phase shift from the first sensor signal and calculate a frequency using the first 90 degree phase shift.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a 90 degree phase shift from the first sensor signal, and calculating a phase difference using the 90 degree phase shift.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a 90 degree phase shift from the first sensor signal, and calculating a frequency using the 90 degree phase shift.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a 90 degree phase shift from the first sensor signal, and using the 90 degree phase shift to calculate a phase difference, and using the 90 degree phase shift to calculate a frequency.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a 90 degree phase shift from the first sensor signal and using the 90 degree phase shift to calculate a phase difference, using the 90 degree phase shift to calculate a frequency, and calculating one or more of a mass flow, a density, or a volumetric flow.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a first 90 degree phase shift from the first sensor signal and a second 90 degree phase shift from the second sensor signal, and calculating a frequency using one of the first 90 degree phase shift or the second 90 degree phase shift.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a first 90 degree phase shift from the first sensor signal and a second 90 degree phase shift from the second sensor signal, calculating a frequency using one of the first 90 degree phase shift or the second 90 degree phase shift, and calculating one or more of a mass flow, a density, or a volume flow.

A method for processing sensor signals in a flow meter is provided according to an embodiment of the invention. The method includes receiving a first sensor signal and a second sensor signal, generating a first 90 degree phase shift from the first sensor signal and a second 90 degree phase shift from the second sensor signal, calculating a frequency using one of the first 90 degree phase shift or the second 90 degree phase shift, calculating a phase difference using the first 90 degree phase shift and the second 90 degree phase shift, and calculating one or more of a mass flow, a density, or a volumetric flow.

Drawings

Like reference numerals refer to like parts throughout the several views of the drawings.

Fig. 1 illustrates a coriolis flow meter in an example of the invention.

FIG. 2 shows meter electronics in accordance with an embodiment of the present invention.

FIG. 3 is a flow chart of a method for processing sensor signals in a flow meter according to an embodiment of the invention.

FIG. 4 shows meter electronics in accordance with an embodiment of the present invention.

FIG. 5 is a flow chart of a method for processing first and second sensor signals in a flow meter according to an embodiment of the invention.

FIG. 6 is a block diagram of a portion of a processing system according to an embodiment of the present invention.

Fig. 7 shows details of a hilbert transform block according to an embodiment of the present invention.

Fig. 8 and 9 are block diagrams of two independent branches of an analysis block, according to an embodiment of the invention.

FIG. 10 is a power spectral density plot of a cutoff sensor signal of a flow meter under normal conditions.

Fig. 11 shows a hilbert transform block in accordance with a single phase shift embodiment.

Fig. 12 shows an analysis block for a single phase shift embodiment.

Fig. 13 shows the sensor processing of the present invention compared to the prior art, wherein the respective time difference (Δ t) values are compared.

Detailed Description

Fig. 1-13 and the following description depict specific examples to teach those skilled in the art how to make and use the best mode of the invention. For the purpose of teaching inventive principles, some conventional aspects have been simplified or omitted. Those skilled in the art will appreciate variations from these examples that fall within the scope of the invention. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of the invention. Accordingly, the present invention is not limited to the specific examples described below, but only by the appended claims and their equivalents.

Fig. 1 shows a coriolis flow meter 5 that includes a meter assembly 10 and meter electronics 20. The meter assembly 10 is responsive to the mass flow and density of the process material. The meter electronics 20 is connected to the meter assembly 10 via wires 100 to provide density, mass flow and temperature information, as well as other information not relevant to the present invention, on path 26. A coriolis flowmeter structure is described, although it will be apparent to those skilled in the art that the present invention may be practiced as a vibrating tube densitometer without the additional measurement capability provided by a coriolis mass flowmeter.

The meter assembly 10 includes a pair of manifolds 150 and 150 ', flanges 103 and 103' having flange necks 110 and 110 ', a pair of parallel flow tubes 130 and 130', a drive mechanism 180, a temperature sensor 190, and a pair of speed sensors 170L and 170R. Flow tubes 130 and 130 'have two substantially straight inlet legs 131 and 131' and outlet legs 134 and 134 'that converge toward each other at flow tube mounting blocks 120 and 120'. The flow tubes 130 and 130' are bent at two symmetrical locations along their length and are substantially parallel throughout their length. The support rods 140 and 140 'serve to define axes W and W' about which each flow tube oscillates.

The lateral legs 131, 131 ' and 134, 134 ' of the flow tubes 130 and 130 ' are fixedly connected to the flow tube mounting blocks 120 and 120 ', and these blocks are in turn fixedly connected to the manifolds 150 and 150 '. This provides a continuous closed material path through coriolis meter assembly 10.

When flanges 103 and 103 ' having apertures 102 and 102 ' are connected via inlet end 104 and outlet end 104 ' into a process line (not shown) carrying the process material being measured, the material inlet end 104 of the meter passing through port 101 in flange 103 is directed through manifold 150 to flow tube mounting block 120 having surface 121. Within manifold 150, material is diverted and passed through flow tubes 130 and 130'. Upon exiting the flow tubes 130 and 130 ', the process material is recombined into a single stream within the manifold 150 ' and thereafter sent to the outlet end 104 ' connected by the flange 103 ' having bolt holes 102 ' to a production line (not shown).

Flow tubes 130 and 130 ' are selected and suitably mounted to flow tube mounting blocks 120 and 120 ' so as to have substantially the same mass distribution, moment of inertia, and young's modulus about bending axes W-W and W ' -W ', respectively. These bending axes pass through the support rods 140 and 140'. Since the young's modulus of the flow tube changes with temperature and this change affects the flow and density calculations, a Resistance Temperature Detector (RTD)190 is mounted to the flow tube 130' to continuously measure the temperature of the flow tube. The temperature of the flow tube, and thus the voltage appearing across the RTD for a given current flowing, is controlled by the temperature of the material flowing through the flow tube. In a known approach, the meter electronics 20 uses the temperature-dependent voltage present across the RTD to compensate for changes in the modulus of elasticity of the flow tubes 130 and 130' due to any changes in the flow tube temperature. The RTD is connected to the meter electronics 20 by lead 195.

The driver 180 drives the two flow tubes 130 and 130 'in opposite directions about the respective bending axes W and W' and is said to be in the first out of phase bending mode of the meter. This drive mechanism 180 may comprise any of a number of well known arrangements, such as mounting a magnet to the flow tube 130' and a counter-acting coil to the flow tube 130, and vibrating both flow tubes with alternating current. An appropriate drive signal is applied to the drive mechanism 180 by the meter electronics 20 via a wire 185.

Meter electronics 20 receives the RTD temperature signal on lead 195 and receives the left and right velocity signals appearing on leads 165L and 165R, respectively. The meter electronics 20 generates a drive signal appearing on the lead 185 to drive the member 180 and vibrate the tubes 130 and 130'. The meter electronics 20 processes the left and right velocity signals and the RTD signal to calculate the mass flow rate and density of the material flowing through the meter assembly 10. The meter electronics 20 uses this information along with other information on the path 26 to the application 29.

Fig. 2 shows meter electronics 20 according to an embodiment of the invention. The meter electronics 20 may include an interface 201 and a processing system 203. The meter electronics 20 receives a first sensor signal and a second sensor signal, such as a cutoff/speed sensor signal, from the meter assembly 10. The meter electronics 20 may operate as a mass flow meter or may operate as a density meter, including operating as a coriolis flow meter. The meter electronics 20 processes the first sensor signal and the second sensor signal to obtain a fluid characteristic of the fluid material flowing through the meter assembly 10. For example, the meter electronics 20 may determine one or more of, for example, phase difference, frequency, time difference (Δ t), density, mass flow rate, and volume flow rate from the sensor signals. In addition, other fluid characteristics may also be determined in accordance with the present invention. These determinations are discussed below.

The phase difference determination and frequency determination are much faster, accurate and reliable than such determinations in the prior art. In one embodiment, the phase difference determination and the frequency determination are derived directly from the phase shift of only one sensor signal without any frequency reference signal. This advantageously reduces the processing time required to calculate the fluid characteristics. In another embodiment, the phase difference is derived from the phase shift of the two sensor signals, while the frequency is derived from the only phase shifted signal. This increases the accuracy of the two fluid characteristics and allows them to be determined much more quickly than in the prior art.

The prior art frequency determination methods typically take 1-2 seconds to perform. In contrast, frequency determination according to the present invention may be performed in as little as 50 milliseconds (ms). Even faster frequency determination is contemplated depending on the type and configuration of the processing system, the sampling rate of the vibrational response, filter size, decimation rate, etc. At a frequency determination rate of 50ms, the meter electronics 20 according to the present invention may be approximately 40 times faster than the prior art.

The interface 201 receives a sensor signal from one of the speed sensors 170L and 170R via the conductor 100 of fig. 1. The interface 201 may perform any necessary or desired signal conditioning, such as formatting, amplifying, buffering, etc. in any manner. Alternatively, some or all of the signal conditioning may be performed in the processing system 203.

Further, the interface 201 may also enable communication between the meter electronics 20 and external devices. The interface 201 is capable of any manner of electronic, optical, or wireless communication.

The interface 201 in one embodiment is coupled to a digitizer 202, wherein the sensor signal comprises an analog sensor signal. Digitizer 202 samples and digitizes the analog sensor signal and generates a digital sensor signal. Digitizer 202 may also perform any required decimation, where the digital sensor signal is decimated to reduce the amount of signal required to be processed and to reduce processing time. Decimation will be discussed in more detail below.

The processing system 203 directs the operation of the meter electronics 20 and processes fluid measurements from the meter assembly 10. The processing system 203 executes one or more processing routines and processes the fluid measurements accordingly to generate one or more fluid characteristics.

The processing system 203 may comprise a general purpose computer, a micro-processing system, a logic circuit, or another general purpose or customized processing device. The processing system 203 may be distributed among multiple processing devices. The processing system 203 may include any manner of integrated or stand-alone electronic storage media, such as storage system 204.

The processing system 203 processes the sensor signal 210 to determine one or more fluid characteristics from the sensor signal 210. The one or more fluid characteristics may include, for example, phase difference, frequency, time difference (Δ t), mass flow rate, and/or density of the fluid material.

In the illustrated embodiment, the processing system 203 determines the fluid characteristic from the two sensor signals 210 and 211 and the single sensor signal phase shift 213. The processing system 203 may determine at least a phase difference and a frequency from the two sensor signals 210 and 211 and the single phase shift 213. As a result, the first phase-shifted sensor signal or the second phase-shifted sensor signal (e.g., one of the upstream or downstream cutoff signals) may be processed by the processing system 203 according to the present invention to determine a phase difference, a frequency, a time difference (Δ t), and/or a mass flow rate of the fluid material.

The storage system 204 may store flow meter parameters and data, software routines, constant values, and variable values. In one embodiment, the storage system 204 includes routines executed by the processing system 203. In one embodiment, the memory system 204 stores a phase shift routine 212, a phase difference routine 215, a frequency routine 216, a time difference (Δ t) routine 217, and a fluid characterization routine 218.

In one embodiment, storage system 204 stores variables used to operate a flow meter (e.g., coriolis flow meter 5). The memory system 204 in one embodiment stores variables such as the first sensor signal 210 and the second sensor signal 211 that are received from the speed/cut-off sensors 170L and 170R. Further, the storage system 204 stores the 90 degree phase shift 213 generated to determine the fluid characteristic.

In one embodiment, the storage system 204 stores one or more fluid characteristics obtained from fluid measurements. The storage system 204 in one embodiment stores fluid characteristics such as phase difference 220, frequency 221, time difference (Δ t)222, mass flow 223, density 224, and volume flow 225, all of which are determined from the sensor signal 210.

The phase shift routine 212 performs a 90 degree phase shift on the input signal, i.e., a 90 degree phase shift on the sensor signal 210. The phase shift routine 212 in one embodiment implements a hilbert transform (discussed below).

Phase difference routine 215 determines the phase difference using a single 90 degree phase shift 213. Additional information may also be used in order to calculate the phase difference. The phase difference in one embodiment is calculated from the first sensor signal 210, the second sensor signal 211, and the 90 degree phase shift 213. The determined phase difference may be stored in phase difference 220 of storage system 204. When the phase difference is determined from the 90 degree phase shift 213, the phase difference can be calculated and acquired much faster than in the prior art. This can provide a critical difference in flowmeter applications with high flow rates or where multi-phase flow occurs. In addition, the phase difference may also be determined independently of the frequency of the sensor signal 210 or 211. Furthermore, because the phase difference is determined independent of frequency, the error component in the phase difference does not include the frequency determined error component, i.e., there is no kurtosis error in the phase difference measurement. Therefore, the phase difference error is reduced to be superior to the phase difference of the related art.

The frequency routine 216 determines the frequency (e.g., represented by the first sensor signal 210 or the second sensor signal 211) based on the 90 degree phase shift 213. The determined frequency may be stored in the frequency 221 of the storage system 204. When the frequency is determined from the 90 degree phase shift 213, it can be calculated and acquired much faster than in the prior art. This can provide a critical difference in flowmeter applications with high flow rates or where multi-phase flow occurs.

The time difference (Δ t) routine 217 determines the time difference (Δ t) between the first sensor signal 210 and the second sensor signal 211. The time difference (Δ t) may be stored in the time difference (Δ t)222 of the storage system 204. The time difference (Δ t) essentially comprises the determined phase divided by the determined frequency, and thus the time difference (Δ t) is used to determine the mass flow.

The fluid characterization routine 218 may determine one or more fluid characterizations. The fluid characterization routine 218 may use, for example, the determined phase difference 220 and the determined frequency 221 to achieve these additional fluid characterizations. It should be understood that additional information may be necessary for such determinations as mass flow or density. The fluid characterization routine 218 may determine the mass flow rate from the time difference (Δ t)222 and, therefore, may determine the mass flow rate from the phase difference 220 and the frequency 221. The formula for determining mass flow is given in U.S. patent No.5,027,662 to Titlow et al, which is incorporated herein by reference. The mass flow rate is related to the mass flow rate of the fluid material in the meter assembly 10. Likewise, the fluid characterization routine 218 may also determine the density 224 and/or the volumetric flow rate 225. The determined mass flow, density, and volume flow may be stored in mass flow 223, density 224, and volume 225, respectively, of storage system 204. Additionally, the fluid characteristics may also be transmitted to an external device by the meter electronics 20.

Fig. 3 is a flow chart 300 of a method for processing sensor signals in a flow meter according to an embodiment of the invention. In step 301, a first sensor signal and a second sensor signal are received. The first sensor signal may comprise an upstream or downstream cutoff sensor signal.

In step 302, the sensor signals may be adjusted. In one embodiment, the conditioning may include filtering to eliminate noise and unwanted signals. In one embodiment, the filtering may include band pass filtering centered around an expected fundamental frequency of the flow meter. In addition, other adjustment operations may also be performed, such as amplification, buffering, and the like. If the sensor signal comprises an analog signal, this step may also include any manner of sampling, digitizing, and decimation performed to produce a digital sensor signal.

In step 303, a single 90 degree phase shift is generated. The 90 degree phase shift comprises a 90 degree phase shift of the sensor signal. The 90 degree phase shift may be performed by any manner of phase shift mechanism or operation. In one embodiment, the 90 degree phase shift is performed using a hilbert transform operating on digital sensor signals.

In step 304, the phase difference is calculated using a single 90 degree phase shift. Additional information may also be used in order to calculate the phase difference. In one embodiment, the phase difference is determined from the first sensor signal, the second sensor signal, and the single 90 degree phase shift. The phase difference includes a phase difference in the response signal (i.e., in the cut-off sensor) seen due to the coriolis effect in the vibrating meter assembly 10.

The resulting phase difference can be determined without any frequency value in the calculation. The resulting phase difference can be acquired much faster than the phase difference calculated using the frequency. The resulting phase difference has greater accuracy than the phase difference calculated using the frequency.

In step 305, a frequency is calculated. The frequency according to the invention is advantageously calculated on the basis of the 90-degree phase shift. The frequency in one embodiment uses a 90 degree phase shift and the corresponding sensor signal from which the 90 degree phase shift is derived. The frequency is the vibrational response frequency of one of the first sensor signal and the second sensor signal (in operation the frequencies of the two sensor signals are substantially the same). The frequency comprises a vibrational frequency response of the one or more flow tubes to vibrations generated by driver 180.

The thus derived frequency is obtained without any separate frequency reference signal. In operation much faster than the prior art, the frequency is acquired from the 90 degree phase shift 213. The resulting frequency has greater accuracy than the frequency calculated in the prior art.

In step 306, the mass flow rate of the fluid material is calculated. The mass flow rate is calculated from the phase difference and the frequency calculated in steps 304 and 305. In addition, the mass flow rate calculation may calculate a time difference (Δ t) from the phase difference and the frequency, and finally calculate the mass flow rate using the time difference (Δ t).

In step 307, the density may optionally be determined. The density may be determined as one of the characteristics of the fluid and may be determined from, for example, frequency.

In step 308, the volumetric flow rate may optionally be determined. The volumetric flow rate may be determined as one of the characteristics of the fluid and may be determined based on, for example, mass flow rate and density.

Fig. 4 shows meter electronics 20 according to an embodiment of the invention. Parts common to fig. 2 share the same reference numerals.

The meter electronics 20 in this embodiment includes a first sensor signal 210 and a second sensor signal 211. The processing system 203 processes the first 210 and second 211 (digital) sensor signals to determine one or more fluid characteristics from the signals. As discussed previously, the one or more fluid characteristics may include phase difference, frequency, time difference (Δ t), mass flow rate, density, and/or volume flow rate of the fluid material.

In the illustrated embodiment, the processing system 203 determines the fluid characteristic from only the two sensor signals 210 and 211 without any external frequency measurement and without an external frequency reference signal. The processing system 203 may determine at least a phase difference and a frequency from the two sensor signals 210 and 211.

As previously discussed, the memory system 204 stores a phase shift routine 212, a phase difference routine 215, a frequency routine 216, a time difference (Δ t) routine 217, and a fluid characterization routine 218. The storage system 204 stores a first sensor signal 210 and a second sensor signal 211. The storage system 204 also stores the first 90 degree phase shift 213 and the second 90 degree phase shift generated from the sensor signal in order to determine the fluid characteristic. As previously discussed, storage system 204 stores phase difference 220, frequency 221, time difference (Δ t)222, mass flow 223, density 224, and volume flow 225.

The phase shift routine 212 performs a 90 degree phase shift on the input signal, including a 90 degree phase shift on the first sensor signal 210 and on the second sensor signal 211. The phase shift routine 212 in one embodiment implements a hilbert transform (discussed below).

The phase difference routine 215 determines the phase difference using the first 90 degree phase shift 213 and the second 90 degree phase shift 214. Additional information may also be used in order to calculate the phase difference. The phase difference in one embodiment is calculated from the first sensor signal 210, the second sensor signal 211, the first 90 degree phase shift 213, and the second 90 degree phase shift 213. As previously discussed, the determined phase difference may be stored in phase difference 220 of storage system 204. When the phase difference is determined using the second 90 degree phase shift 213, the phase difference can be calculated and obtained much faster than in the prior art. This can provide a critical difference in flowmeter applications with high flow rates or where multi-phase flow occurs. In addition, the phase difference may also be determined independently of the frequency of the sensor signal 210 or 211. Furthermore, since the phase difference is determined independently of the frequency, the error component in the phase difference is not affected by the error component of the frequency determination, i.e. there is no mixing error in the phase difference measurement. Therefore, the phase difference error is reduced to be superior to the phase difference of the related art.

The frequency routine 216 determines a frequency (e.g., as represented by the first sensor signal 210 or the second sensor signal 211) based on the first 90 degree phase shift 213 and the second 90 degree phase shift 214. As previously discussed, the determined frequency may be stored in the frequency 221 of the storage system 204. When determining the frequency from the first and second 90 degree phase shifts, the frequency can be calculated and retrieved much faster than in the prior art. This can provide a critical difference in flowmeter applications with high flow rates or where multi-phase flow occurs.

The time difference (Δ t) routine 217 determines the time difference (Δ t) between the first sensor signal 210 and the second sensor signal 211. As previously discussed, the time difference (Δ t) may be stored in the time difference (Δ t)222 of the storage system 204. The time difference (Δ t) essentially comprises the determined phase divided by the determined frequency, and thus the time difference (Δ t) is used to determine the mass flow.

As previously discussed, the fluid characterization routine 218 may determine one or more of mass flow, density, and/or volumetric flow.

Fig. 5 is a flow chart 500 of a method for processing first and second sensor signals in a flow meter according to an embodiment of the invention. In step 501, a first sensor signal is received. In one embodiment, the first sensor signal comprises an upstream or downstream cutoff sensor signal.

In step 502, a second sensor signal is received. In one embodiment, the second sensor signal comprises an upstream or downstream cutoff sensor signal (i.e., a signal opposite the first sensor signal).

In step 503, the sensor signals may be adjusted. In one embodiment, the conditioning may include filtering to eliminate noise and unwanted signals. In one embodiment, the filtering may comprise bandpass filtering, as discussed previously. In addition, other adjustment operations may be performed, such as amplification, buffering, and the like. If the sensor signal comprises an analog signal, this step may also include any manner of sampling, digitizing, and decimation performed to produce a digital sensor signal.

In step 504, a first 90 degree phase shift is generated. The first 90 degree phase shift comprises a 90 degree phase shift of the first sensor signal. The 90 degree phase shift may be performed by any manner of mechanism or operation. In one embodiment, the 90 degree phase shift is performed using a hilbert transform operating on digital sensor signals.

In step 505, a second 90 degree phase shift is generated. The second 90 degree phase shift comprises a 90 degree phase shift of the second sensor signal. The 90 degree phase shift may be performed by any manner of mechanism or operation, as in the first 90 degree phase shift.

In step 506, a phase difference between the first sensor signal and the second sensor signal is calculated using the first 90 degree phase shift and the second 90 degree phase shift. Additional information may also be used in order to calculate the phase difference. In one embodiment, the phase difference is determined from the first sensor signal, the second sensor signal, the first 90 degree phase shift, and the second 90 degree phase shift. The phase difference includes the phase difference in the response signal (i.e., in the two cut-off sensors) seen due to the coriolis effect in the vibrating meter assembly 10.

In step 507, a frequency is calculated. The frequency according to the invention is advantageously calculated on the basis of the first 90-degree phase shift and the second 90-degree phase shift. The frequency in one embodiment uses a 90 degree phase shift and the corresponding sensor signal from which the 90 degree phase shift is derived. The frequency is the vibrational response frequency of one of the first sensor signal and the second sensor signal (in operation the frequencies of the two sensor signals are substantially the same). The frequency comprises a vibrational frequency response of the one or more flow tubes to vibrations generated by driver 180.

The thus derived frequency is obtained without any separate frequency reference signal. In operation much faster than the prior art, the frequency is taken by the 90 degree phase shift 213. The resulting frequency has greater accuracy than the frequency calculated in the prior art.

In step 508, the mass flow rate of the fluid material is calculated. The mass flow rate is calculated from the phase difference and the frequency calculated in steps 506 and 507. Further, the mass flow calculation may calculate a time difference (Δ t) from the phase difference and the frequency, and finally calculate the mass flow using the time difference (Δ t).

In step 509, the density may optionally be determined, as previously discussed.

In step 510, the volumetric flow rate may optionally be determined, as previously discussed.

Fig. 6 is a block diagram 600 of a portion of the processing system 203 according to an embodiment of the present invention. In the drawings, a block represents a processing circuit or a processing action/routine. The block diagram 600 comprises a stage 1 filter block 601, a stage 2 filter block 602, a hilbert transform block 603 and an analysis block 604. The LPO and RPO inputs include a left cutoff signal input and a right cutoff signal input. The LPO or RPO may include a first sensor signal.

In one embodiment, stage 1 filter block 601 and stage 2 filter block 602 comprise digital Finite Impulse Response (FIR) polyphase decimation filters implemented in processing system 203. These filters provide an optimal method for filtering and decimating one or both sensor signals, where the filtering and decimation are performed at the same timing time (stochastic time) and at the same decimation rate. Alternatively, stage 1 filter block 601 and stage 2 filter block 602 may comprise Infinite Impulse Response (IIR) filters or other suitable digital filters or filter processes. However, it should be understood that other filtering processes and/or filtering embodiments are contemplated and are within the scope of the description and claims.

Fig. 7 shows details of the hilbert transform block 603 according to an embodiment of the present invention. In the embodiment shown, the hilbert transform block 603 comprises an LPO branch 700 and a PRO branch 710. The LPO branch 700 includes an LPO delay block 701 in parallel with an LPO filter block 702. Likewise, the RPO branch includes an RPO delay block 711 in parallel with the RPO filter block 702. The LPO delay block 701 and RPO delay block 711 introduce a sampling delay. The LPO and RPO digital signal samples selected by the LPO delay block 701 and the RPO delay block 711 are therefore later in time sequence than the LPO and RPO digital signal samples filtered by the LPO filter block 702 and the RPO filter block 712. The LPO filter block 702 and the RPO filter block 712 perform a 90 degree phase shift on the input digital signal samples.

The hilbert transform block 603 is the first step in providing the phase measurement. The hilbert transform block 603 receives the filtered and decimated LPO and RPO signals and performs a hilbert transform. The hilbert transform produces a 90 degree phase shifted version of the LPO and RPO signals, i.e., it produces the quadrature (Q) component of the original in-phase (I) signal component. The output of the hilbert transform block 603 thus provides new quadrature (Q) components LPO Q and RPO Q, along with the original in-phase (I) signal components LPO I and RPO I.

The input to the hilbert transform block 603 may be expressed as:

LPO＝A_lpo cos(ωt) (2)

RPO＝A_rpo cos(ωt+φ) (3)

using the hilbert transform, the output becomes:

LPO_hilbcrt＝A_lpo sin(ωt) (4)

RPO_hllbert＝A_rpo sin(ωt+φ)] (5)

combining the original term with the output of the hilbert transform yields:

LPO＝A_lpo[cos(ωt)+isin(ωt)]＝A_lpoe^j(ωt) (6)

RPO＝A_rpo[cOS(ωt+φ)+isin(ωt+φ)]＝A_rpoe^j(ωt+φ) (7)

fig. 8 and 9 are block diagrams of two separate branches of the analysis block 604 according to embodiments of the present invention. The analysis block 604 is the final stage of frequency, phase difference, and delta T (at) measurements. Fig. 8 is a phase section 604a comprising a first branch determining a phase difference from in-phase (I) and quadrature (Q) components. Fig. 9 is a frequency portion 604b that determines frequency from in-phase (I) and quadrature (Q) components of a single sensor signal. The single sensor signal may comprise an LPO signal as shown or may comprise an RPO signal.

In the embodiment of fig. 8, phase portion 604a of analysis block 604 includes addition blocks 801a and 801b, conjugation block 802, complex multiplication block 803, filter block 804, and phase angle block 805.

The add blocks 801a and 801b receive the in-phase (I) and quadrature (Q) components of the sensor signal and pass them on. The conjugation block 802 performs complex conjugation on the sensor signal (here the LPO signal) and forms the negative of the imaginary signal. The complex multiplication block 803 multiplies the RPO signal and the LPO signal, thereby realizing the following equation (8). The filter block 804 implements a digital filter, such as the FIR filter discussed above. The filter block 804 may include a polyphase decimation filter for removing harmonic content and decimation of the signal from the in-phase (I) and quadrature (Q) components of the sensor signal. The filter coefficients may be selected to provide decimation, e.g., by a factor of 10, of the input signal. The phase angle block 805 determines the phase angle from the in-phase (I) and quadrature (Q) components of the LPO and RPO signals. The phase angle block 805 implements equation (11) shown below.

The phase section 604a shown in fig. 8 performs the following equation:

LPO×RPO＝A_lpoe^-j(ωt)×A_Rpoe^j(ωt+φ)＝A_lpo×A_Rpoe^{j(-ωt+ωt+φ)} (8)

wherein LPO is the complex conjugate of LPO. Suppose that:

A_Rpo＝A_LPo＝A (9)

then:

LPO×RPO＝A²e^j(φ)＝A²[cos(φ)+isin(φ)] (10)

the differential phase angle thus obtained is:

fig. 9 is a block diagram of the frequency portion 604b of the analysis block 604 according to the present invention. The frequency portion 604b may operate on the left or right cutoff signal (LPO or RPO). The frequency portion 604b in the illustrated embodiment includes an add block 901, a complex conjugate block 902, a sample block 903, a complex multiplication block 904, a filter block 905, a phase angle block 906, a constant block 907, and a division block 908.

As discussed previously, the add block 901 receives the in-phase (I) and quadrature (Q) components of the sensor signal and passes them on. The conjugation block 902 performs complex conjugation on the sensor signal (here the LPO signal) and forms the negative of the imaginary signal. Delay block 903 introduces a sampling delay to frequency portion 604b and thus selects digital signal samples that are older in time. This older digital signal sample is multiplied with the current digital signal in a complex multiplication block 904. The complex multiplication block 904 multiplies the LPO signal and the LPO conjugate signal, thereby realizing the following equation (12). The filter block 905 implements a digital filter, such as the FIR filter discussed previously. The filter block 905 may include a polyphase decimation filter for removing harmonic content and decimation of the signal from the in-phase (I) and quadrature (Q) components of the sensor signal. The filter coefficients may be selected to provide decimation, e.g., sampling by a factor of 10, of the input signal. The phase angle block 906 determines the phase angle from the in-phase (I) and quadrature (Q) components of the LPO signal. The phase angle block 906 performs a portion of equation (13) below. The constant block 907 provides a constant including a sampling rate F as shown in equation (14)_sDivided by a factor of 2 pi. The division block 908 performs the division operation of equation (14).

The frequency part 604b performs the following equation:

the angle between two consecutive samples is therefore:

this is the angular frequency of the left cut-off. Conversion to Hz:

wherein "F_s"is the rate of the hilbert transform block 603. In the example discussed previously, "F_s"about 2 kHz.

FIG. 10 is a power spectral density plot of a cutoff sensor signal of a flow meter under normal conditions. The fundamental frequency of the meter is the highest peak of the curve and is located at about 135 Hz. The figure also shows a number of other large peaks in the frequency spectrum (the first non-fundamental mode is a torsional mode at a frequency of about 1.5 times the frequency of the fundamental mode). These peaks include the harmonic frequencies of the flow meter, as well as other undesirable sensor modes (i.e., torsional mode, second bending mode, etc.).

Fig. 11 shows an alternative hilbert transform block 603' in accordance with a single phase shifting embodiment. In this embodiment, the hilbert transform block 603' comprises an LPO branch 1100 and a PRO branch 1110. The LPO branch 1100 includes a delay block 701 in parallel with an LPO filter block 702. The RPO branch 1110 in this embodiment includes only the delay block 701. As before, delay block 701 introduces a sampling delay. As before, the filter block 702 performs a 90 degree phase shift on the input digital signal samples. It should be appreciated that alternatively the hilbert transform block 603' may perform a phase shift only on the RPO signal.

This process embodiment uses the hilbert transform/phase shift of only one sensor signal to derive the frequency and phase difference on one side (see fig. 2-3). This significantly reduces the number of calculations required to perform the phase measurements and significantly reduces the number of calculations required to obtain mass flow.

In this embodiment, the output of the hilbert transform block 603' will provide the quadrature (Q) component of either the left or right sensor signal, rather than both. In the examples below, phase shifting is performed on the LPO signal.

LPO＝A_lpo cos(ωt) (26)

RPO＝A_rpo cos(ωt+φ) (27)

Using the hilbert transform, the output becomes:

LPO_hilben＝A_lpo sin(ωt) (28)

RPO＝A_rpo cos(ωt+φ) (29)

combining the LPO original term with the output of the hilbert transform (i.e., with a 90 degree phase shift) yields:

LPO＝A_lpo[cos(ωt)+isin(ωt)]＝A_lpoe^j(ωt) (30)

while RPO remains the same:

fig. 12 shows an analysis block 604 a' for a single phase shift embodiment. The analysis block 604 a' in this embodiment comprises an addition block 801, a complex multiplication block 803, a low pass filter block 1201 and a phase angle block 805. The analysis block 604 a' in this embodiment implements the following formula:

the low-pass filter block 1201 includes a low-pass filter that removes high-frequency components generated by the complex multiplication block 803. The low pass filter block 1201 may implement any manner of low pass filtering operation. The result of the multiplication produces two terms. The (- ω t + ω t + Φ) terms combine and reduce to the phase phi (the result of DC) only, since the (- ω t) and (ω t) terms cancel each other out. At twice this frequency, (ω t + ω t + Φ) is simplified to the (2 ω t + Φ) term. Since the result is the sum of the two terms, the high frequency (2 ω t + Φ) term can be removed. The only signal of interest here is the DC term. A low pass filter may be used to filter out the high frequency (2 ω t + Φ) terms from the result. The cut-off of the low-pass filter can be made anywhere between zero and 2 omega.

After filtering, the result is:

thus, the differential phase angle is:

by performing the hubert transform on one cutoff signal instead of two, the computational load required to perform phase and frequency estimation in a coriolis mass flowmeter is advantageously reduced. It is thus possible to determine the phase and frequency using two sensor signals but only one 90 degree phase shift.

Fig. 13 shows the sensor processing of the present invention compared to the prior art, where the respective time difference (Δ t) values are compared. The figure shows a fluid material comprising a gas flow, i.e. e.g. bubbles. In this case, the fluid noise is substantially reduced in the new algorithm due to the rate of phase and frequency calculations. It can be seen from the figure that the results obtained by the present invention do not show the large peaks and large valleys reflected in the prior art (Δ t) measurements.

The present invention is different from the prior art. First, the prior art typically uses a cutoff signal and a separate frequency source, such as a driver signal sent to the driver system, to determine the cutoff frequency in order to determine the vibration response frequency. Instead, the present invention determines the frequency by shifting the phase of one of the two sensor signals. The prior art does not determine the vibration response frequency from the phase shift of the sensor signal.

Second, most prior art flow meters use prior art frequency determinations to determine the phase difference between the cutoff signals. Thus, any error included in the prior art frequency determination is included in the prior art phase difference determination, thereby blending the total error into the prior art mass flow determination. In contrast, the present invention determines the phase difference directly from one or both phase shifted sensor signals without using any frequency determination. As a result, any error term is only the result of the phase operation and phase measurement of the phase difference determination, and is not affected by any frequency determination error.

Third, the prior art uses an independently determined external frequency to determine mass flow. Typically, the prior art also utilizes phase differences acquired using independently determined external frequencies. Thus, in the prior art, the mass flow rate may double the effect of any error in the frequency determination and is therefore not satisfactorily accurate and reliable. In contrast, in the present invention, the frequency determination and the phase difference determination are derived independently. The frequency determination and the phase difference determination in the present invention therefore contain a much smaller error component. As a result, the amount of error in mass flow determination is greatly reduced using the meter electronics and methods of the present invention. The density and the volume flow according to the invention are therefore also improved in terms of accuracy and reliability.

Fourth, the frequency determination of the prior art takes a relatively long time. Where the fluid material comprises a two-phase or three-phase fluid (e.g. a liquid comprising entrained solids and/or entrained gases (e.g. bubbles)), the prior art frequency determination may take as long as 1-2 seconds to provide a stable and relatively accurate frequency measurement. Instead, the frequency and phase difference determinations according to the present invention may be acquired more quickly, e.g., on the order of milliseconds or hundreds of milliseconds. All fluid characteristics derived from the frequency and phase difference can also be acquired in less time.

The meter electronics and method for processing sensor signals according to the invention can be implemented according to any of these embodiments in order to obtain a number of advantages when required. The present invention can calculate the phase difference from the two phase shifted sensor signals. The present invention may provide for greater accuracy and reliability of phase difference determination. The invention may provide a faster phase difference determination than the prior art while consuming less processing time.

The invention can calculate the frequency from the sensor signal with only one phase shift. The present invention may provide frequency determination with greater accuracy and reliability. The invention may provide faster frequency determination than the prior art while consuming less processing time.

The present invention may calculate, for example, mass flow, density, and/or volume flow from only one or two sensor signals. The present invention may provide a more accurate and reliable determination of mass flow. The invention may provide a faster determination of mass flow while consuming less processing time than the prior art. The present invention thus provides substantially better performance for airborne conditions, empty-full-empty conditions, gas applications and steady state conditions.

Claims

1. Meter electronics (20) for processing sensor signals in a coriolis flow meter, the meter electronics comprising an interface (201) for receiving a first sensor signal and a second sensor signal and a processing system (203) in communication with the interface (201), the meter electronics (20) characterized by:

the processing system (203) is configured to generate a 90 degree phase shift from the first sensor signal and to calculate a frequency from the first sensor signal and the 90 degree phase shift.

2. The meter electronics (20) of claim 1, with the interface (201) comprising a digitizer (202) configured to digitize the sensor signal.

3. The meter electronics (20) of claim 1, with the meter electronics (20) further configured to adjust the first sensor signal and the second sensor signal prior to generating the 90 degree phase shift from the first sensor signal.

4. The meter electronics (20) of claim 1, with the meter electronics (20) further configured to calculate a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal.

5. The meter electronics (20) of claim 1, with the processing system (203) further configured to calculate one or more of a mass flow, a density, or a volume flow.

6. The meter electronics (20) of claim 1, with the processing system (203) being further configured to calculate a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal, and to calculate a mass flow from the phase difference and from the frequency.

7. Meter electronics (20) for processing sensor signals in a coriolis flow meter, the meter electronics (20) comprising an interface (201) for receiving a first sensor signal and a second sensor signal and a processing system (203) in communication with the interface (201), the meter electronics (20) characterized by:

the processing system (203) is configured to generate a first 90 degree phase shift from the first sensor signal, calculate a frequency from the first sensor signal and the first 90 degree phase shift, and calculate a phase difference from the first sensor signal, the first 90 degree phase shift, and the second sensor signal.

8. The meter electronics (20) of claim 7, with the interface (201) comprising a digitizer (202) configured to digitize the sensor signal.

9. The meter electronics (20) of claim 7, with the meter electronics (20) further configured to adjust the first sensor signal and the second sensor signal prior to generating the 90 degree phase shift from the first sensor signal.

10. The meter electronics (20) of claim 7, with the processing system (203) further configured to calculate one or more of a mass flow, a density, or a volume flow.

11. The meter electronics (20) of claim 7, with the processing system (203) being further configured to calculate a mass flow rate as a function of the phase difference and as a function of the frequency.

12. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

generating a 90 degree phase shift from the first sensor signal; and

calculating a frequency from the first sensor signal and the 90 degree phase shift.

13. The method of claim 12, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the 90 degree phase shift.

14. The method of claim 12, wherein the calculating further comprises calculating a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal.

15. The method of claim 12, further comprising:

calculating a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal; and

one or more of mass rate, density, or volumetric flow rate is calculated.

16. The method of claim 12, further comprising calculating the 90 degree phase shift using a hilbert transform.

17. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

generating a 90 degree phase shift from the first sensor signal;

calculating a frequency from the first sensor signal and the 90 degree phase shift; and

calculating a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal.

18. The method of claim 17, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the 90 degree phase shift.

19. The method of claim 17, further comprising:

one or more of mass rate, density, or volumetric flow rate is calculated.

20. The method of claim 17, further comprising calculating the 90 degree phase shift using a hilbert transform.

21. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

generating a 90 degree phase shift from the first sensor signal;

calculating a phase difference from the first sensor signal, the 90 degree phase shift, and the second sensor signal;

one or more of mass rate, density, or volumetric flow rate is calculated.

22. The method of claim 21, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the 90 degree phase shift.

23. The method of claim 21, further comprising calculating the 90 degree phase shift using a hilbert transform.

24. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

generating a first 90 degree phase shift from the first sensor signal and a second 90 degree phase shift from the second sensor signal; and

calculating a frequency from the first sensor signal and the first 90 degree phase shift or calculating the frequency from the second sensor signal and the second 90 degree phase shift.

25. The method of claim 24, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the first 90 degree phase shift and the second 90 degree phase shift.

26. The method of claim 24, further comprising calculating a phase difference from the first sensor signal, the first 90 degree phase shift, and the second sensor signal, or calculating the phase difference from the first sensor signal, the second sensor signal, and the second 90 degree phase shift.

27. The method of claim 24, further comprising:

one or more of mass rate, density, or volumetric flow rate is calculated.

28. The method of claim 24, further comprising calculating the first 90 degree phase shift and the second 90 degree phase shift using a hilbert transform.

29. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

generating a first 90 degree phase shift from the first sensor signal and a second 90 degree phase shift from the second sensor signal;

calculating a frequency from the first sensor signal and the first 90 degree phase shift or calculating the frequency from the second sensor signal and the second 90 degree phase shift; and

one or more of mass rate, density, or volumetric flow rate is calculated.

30. The method of claim 29, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the first 90 degree phase shift and the second 90 degree phase shift.

31. The method of claim 29, further comprising calculating a phase difference from the first sensor signal, the first 90 degree phase shift, and the second sensor signal, or calculating the phase difference from the first sensor signal, the second sensor signal, and the second 90 degree phase shift.

32. The method of claim 29, further comprising calculating the first 90 degree phase shift and the second 90 degree phase shift using a hilbert transform.

33. A method for processing sensor signals in a coriolis flow meter, the method comprising receiving a first sensor signal and a second sensor signal, the method characterized by:

calculating a frequency from the first sensor signal and the first 90 degree phase shift or calculating the frequency from the second sensor signal and the second 90 degree phase shift;

calculating a phase difference from the first sensor signal, the first 90 degree phase shift and the second sensor signal, or calculating the phase difference from the first sensor signal, the second sensor signal and the second 90 degree phase shift; and

one or more of mass rate, density, or volumetric flow rate is calculated.

34. The method of claim 33, further comprising adjusting the first sensor signal and the second sensor signal prior to the step of calculating the first 90 degree phase shift and the second 90 degree phase shift.

35. The method of claim 33, further comprising calculating the first 90 degree phase shift and the second 90 degree phase shift using a hilbert transform.