CN101819056B - Instrument electronic device for checking and diagnosing flow meter and method - Google Patents

Abstract

Meter electronics and methods for calibration diagnostics of flow meters. An embodiment in accordance with the present invention provides meter electronics (20) for a flow meter (5). The meter electronics (20) includes an interface (201) for receiving a vibratory response from the flow meter (5), which is a response to flow at a fundamental resonant frequency, and a processing system (203) in communication with the interface (201). The response of the gauge (5) to vibration. The processing system (203) is arranged to receive the vibration response from the interface (201), determine the frequency (ω ₀ ) of the vibration response, determine the response voltage (V) and drive current (I) of the vibration response, measure the flowmeter (5 ), and determine the stiffness parameter (K) from the frequency (ω ₀ ), response voltage (V), drive current (I) and decay characteristic (ζ).

Description

Meter electronics and method for calibration diagnostics of a flow meter

This application is a divisional application of the application number 200580051626.4, the application date is September 19, 2005, and the invention title is "Meter Electronic Devices and Methods for Calibration and Diagnosis of Flow Meters".

technical field

The present invention relates to a meter electronics device and method for calibration diagnosis of a flow meter.

Background technique

statement of problem

Vibrating pipe sensors, such as Coriolis mass flow meters or vibrating tube densitometers, generally work by detecting the motion of a vibrating pipe containing flowing material. Properties related to the material in the pipeline, such as mass flow, density, etc., can be determined by processing the measurement signals received from motion transducers associated with the pipeline. The stiffness and damping properties generally affect the modes of vibration of a vibrating material filled system through the combined mass of the containing pipe and the material contained therein.

The piping of a vibratory flow meter may include one or more flow tubes. The flow tube is forced to vibrate at a resonant frequency, which in this case is proportional to the density of the fluid in the flow tube. Sensors positioned on the inlet and outlet sections of the tube measure the relative vibration between the ends of the tube. During flow, the vibrating tube and flowing mass are coupled together due to Coriolis forces, causing a phase shift in vibration between the ends of the tube. This phase shift is directly proportional to mass flow.

A typical Coriolis mass flow meter includes one or more conduits that are connected internally in a pipeline or other transport system and transport materials, such as fluids, slurries, etc. in the system. Every pipe can be viewed as having a set of natural modes of vibration including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, as material flows through the pipe, the pipe structure is excited in one or more modes of vibration and the motion of the pipe is measured at points spaced along the pipe. Excitation is typically provided by an actuator, for example an electromechanical device, such as a voice coil type driver, which disturbs the tubing in a periodic fashion. Mass flow can be determined by measuring the time delay or phase difference between motions at the transducer locations. Two such sensors (or pick-off sensors) are typically employed, measuring the vibrational response of the flow conduit or conduit, and are typically positioned at locations upstream and downstream of the actuator. Via cables, the two pickoff sensors are connected to the electronics. The device receives signals from two pickup sensors and processes the signals in order to obtain mass flow measurements.

The phase difference between the two sensor signals relates to the mass flow rate of material flowing through the flow tube or tubes. The mass flow rate of the material is proportional to the time delay between the two sensor signals, and thus the mass flow rate can be determined by multiplying the time delay by the Flow Calibration Factor (FCF, Flow CalibrationFactor), in this case the time delay includes the phase difference Divide by frequency. FCF reflects the material properties and cross-sectional properties of the flow tube. In the prior art, the FCF is determined through a calibration procedure prior to installation of the flowmeter into a pipeline or other conduit. In the calibration step, fluid is passed through the flow tube at a given flow rate, and the phase difference and characteristics between the flow rates are calculated.

One advantage of Coriolis flow meters is that the accuracy of the measured mass flow is not affected by wear and tear of the moving parts of the flow meter. Flow is determined by multiplying the phase difference between two points in the flow tube by the flow calibration factor. The only input is a sinusoidal signal from the sensor, representing an oscillation at two points on the flow tube. Calculate the phase difference from these sinusoidal signals. There are no moving parts in a vibrating flow tube. Therefore, measurements of phase difference and flow calibration factors are not affected by wear and tear of moving parts in the flow.

FCF may relate to the stiffness characteristic of a flow meter device. If the stiffness characteristics of the flowmeter device change, then the FCF also changes. The changes thus affect the accuracy of the flow measurement produced by the flow meter. Material changes and changes in the cross-sectional properties of the flow tube can be brought about, for example, by corrosion or erosion. Therefore, it is highly desirable to be able to detect and/or quantify any changes to the stiffness of the flow meter arrangement in order to maintain a high level of accuracy of the flow meter.

Contents of the invention

In accordance with an embodiment of the present invention, meter electronics for a flow meter are provided. The meter electronics includes an interface for receiving a vibration response from the flowmeter and a processing system in communication with the interface. The vibrational response includes a response to vibrations of the flowmeter at the fundamental resonant frequency. The processing system is arranged to receive the vibration response from the interface, determine the frequency (ω ₀ ) of the vibration response, determine the response voltage (V) and drive current (I) of the vibration response, measure the damping characteristic (ζ) of the flowmeter, and Stiffness parameter (K) is determined from frequency (ω ₀ ), response voltage (V), driving current (I) and damping characteristic (ζ).

According to an embodiment of the present invention, a method for determining a stiffness parameter (K) of a flow meter is provided. The method includes receiving a vibratory response from a flow meter. The vibrational response includes a response to vibrations of the flowmeter at the fundamental resonant frequency. The method further includes determining a frequency (ω ₀ ) of the vibratory response, determining a response voltage (V) and drive current (I) of the vibratory response, and measuring a damping characteristic (ζ) of the flowmeter. The method further includes determining a stiffness parameter (K) from the frequency (ω ₀ ), the response voltage (V), the drive current (I) and the damping characteristic (ζ).

According to an embodiment of the present invention, a method for determining a change in stiffness (ΔK) of a flow meter is provided. The method includes receiving a vibratory response from a flow meter. The vibrational response includes a response to vibrations of the flowmeter at the fundamental resonant frequency. The method further includes determining a frequency (ω ₀ ) of the vibratory response, determining a response voltage (V) and drive current (I) of the vibratory response, and measuring a damping characteristic (ζ) of the flowmeter. The method further includes determining a stiffness parameter (K) from the frequency (ω ₀ ), the response voltage (V), the drive current (I) and the damping characteristic (ζ). The method further includes receiving a second vibration response from the flow meter at a second time t ₂ , generating a second stiffness characteristic (K ₂ ) from the second vibration response, comparing the second stiffness characteristic (K ₂ ) to the stiffness parameter (K ), and detecting a change in stiffness (ΔK) if the second stiffness characteristic (K ₂ ) differs from the stiffness parameter (K) by more than a predetermined tolerance.

In accordance with an embodiment of the present invention, meter electronics for a flow meter are provided. The meter electronics includes an interface for receiving three or more vibration responses from the flowmeter. The three or more vibration responses include a fundamental fundamental frequency response and two or more non-fundamental frequency responses. The meter electronics further includes a processing system in communication with the interface, and the processing system is arranged to receive three or more vibration responses from the interface, from which a pole-residue frequency response is generated function, and at least one stiffness parameter (K) is determined from the pole-residue frequency response function.

According to an embodiment of the present invention, a method for determining a change in stiffness (ΔK) of a flow meter is provided. The method includes receiving three or more vibration responses including a fundamental fundamental frequency response and two or more non-fundamental frequency responses. The method further includes generating a pole-residue frequency response function from the three or more vibration responses, and determining at least one stiffness parameter (K) from the pole-residue frequency response function.

According to an embodiment of the present invention, a method for determining a stiffness parameter (K) of a flow meter is provided. The method includes receiving three or more vibration responses including a fundamental fundamental frequency response and two or more non-fundamental frequency responses. The method further includes generating a pole-residue frequency response function from the three or more vibration responses and determining at least one stiffness parameter (K) from the pole-residue frequency response function. The method further includes receiving a second set of three or more vibratory responses from the flow meter at a second time _t , from which a second stiffness characteristic (K ₂ ) is generated , comparing the second stiffness characteristic (K ₂ ) with the stiffness parameter (K), and detecting a stiffness change (ΔK) if the second stiffness characteristic (K ₂ ) differs from the stiffness parameter (K) by more than a predetermined tolerance.

Aspects of the invention

In one aspect of the meter electronics, measuring the damping characteristic (ζ) further includes allowing the vibration response of the flow meter to damp down to a predetermined vibration target.

In another aspect of the meter electronics, the processing system is further arranged to measure the damping characteristic (ζ) by de-energizing the flow meter, and allowing the vibration response of the flow meter to decay down to a predetermined vibration target while measuring the damping characteristic .

In another aspect of the meter electronics, the stiffness parameter (K) includes K=(I*BL _PO *BL _DR *ω ₀ )/2ζV.

In one aspect of the method, measuring the damping characteristic (ζ) further includes allowing the vibration response of the flow meter to damp down to a predetermined vibration target.

In another aspect of the method, measuring the damping characteristic (ζ) further includes removing excitation of the flow meter, and allowing the vibration response of the flow meter to decay down to a predetermined vibration target while measuring the damping characteristic.

In another aspect of the method, the stiffness parameter (K) comprises K=(I*BL _PO *BL _DR *ω ₀ )/2ζV.

In another aspect of the method, generating a second stiffness characteristic (K ₂ ) from a second vibrational response includes generating a second stiffness characteristic (K 2 ) from a second frequency, a second response voltage, a second drive current, and a second damping characteristic. ₂ ).

In another aspect of the method, the method further includes detecting a stiffness change (ΔK) if the second stiffness parameter (K ₂ ) differs from the stiffness parameter (K) by more than a predetermined stiffness tolerance.

In another aspect of the method, the method further comprises quantifying the change in stiffness (ΔK) from the comparison of _K2 and K.

In an embodiment of the meter electronics, the processing system is further arranged to determine the damping parameter (C) from the pole-residue frequency response function.

In a further embodiment of the meter electronics the processing system is further arranged to determine the quality parameter (M) from the pole-residue frequency response function.

In a further embodiment of the meter electronics the processing system is further arranged to calculate the pole (λ), the left residue ( _RL ) and the right residue ( _RR ) from the pole-residue frequency response function.

In another embodiment of the meter electronics, the three or more vibration responses include at least one tone above the fundamental frequency response and at least one tone below the fundamental frequency response.

In another embodiment of the meter electronics, the three or more vibration responses include at least two tones above the fundamental frequency response and at least two tones below the fundamental frequency response.

In another embodiment of the meter electronics, the pole-residue frequency response function comprises a first order pole-residue frequency response function.

In another embodiment of the meter electronics, the pole-residue frequency response function comprises a first-order pole-residue frequency response function comprising

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

In another embodiment of the meter electronics, the pole-residue frequency response function comprises a first-order pole-residue frequency response function comprising And wherein the stiffness parameter (K), damping parameter (C) and mass parameter (M) are determined according to the equations M=1/2jRω _d , K=(ω _n ) ² M and C=2ζω _n M .

In another embodiment of the meter electronics, the pole-residue frequency response function includes a second order pole-residue frequency response function.

In another embodiment of the meter electronics, the pole-residue frequency response function includes a second-order pole-residue frequency response function that includes

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; jC\&omega;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; .</span>$

并且其中依据

确定刚度参数(K)，依据M＝K/(ω_n)²确定质量参数(M)，以及依据

确定阻尼参数(C)。In another embodiment of the meter electronics, the pole-residue frequency response function includes a second-order pole-residue frequency response function that includes

and based on

Determine the stiffness parameter (K), determine the quality parameter (M) according to M=K/(ω _n ) ² , and determine the quality parameter (M) according to

Determine the damping parameter (C).

In one embodiment of the method, said determining comprises further determining a damping parameter (C) from a pole-residue frequency response function.

In another embodiment of the method, said determining comprises further determining a quality parameter (M) from a pole-residue frequency response function.

In another embodiment of the method, said determining further comprises calculating the pole (λ), left residue ( _RL ) and right residue ( _RR ) from the pole-residue frequency response function.

In another embodiment of the method, the three or more vibration responses include at least one tone above the fundamental frequency response and at least one tone below the fundamental frequency response.

In another embodiment of the method, the three or more vibration responses include at least two tones above the fundamental frequency response and at least two tones below the fundamental frequency response.

In another embodiment of the method, the pole-residue frequency response function comprises a first order pole-residue frequency response function.

In another embodiment of the method, the pole-residue frequency response function comprises a first-order pole-residue frequency response function comprising

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

并且其中依据等式M＝1/2jRω_d，K＝(ω_n)²M和C＝2ζω_nM确定刚度参数(K)，阻尼参数(C)和质量参数(M)。In another embodiment of the method, the pole-residue frequency response function comprises a first-order pole-residue frequency response function comprising

And wherein the stiffness parameter (K), damping parameter (C) and mass parameter (M) are determined according to the equations M=1/2jRω _d , K=(ω _n ) ² M and C=2ζω _n M .

In another embodiment of the method, the pole-residue frequency response function comprises a second order pole-residue frequency response function.

In another embodiment of the method, the pole-residue frequency response function comprises a second-order pole-residue frequency response function comprising

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; jC\&omega;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; .</span>$

确定刚度参数(K)，依据M＝K/(ω_n)²确定质量参数(M)，以及依据

确定阻尼参数(C)。In another embodiment of the method, the pole-residue frequency response function comprises a second-order pole-residue frequency response function comprising and based on

Determine the stiffness parameter (K), determine the quality parameter (M) according to M=K/(ω _n ) ² , and determine the quality parameter (M) according to

Determine the damping parameter (C).

In another embodiment of the method, the method further comprises detecting a stiffness change (ΔK) if the second stiffness characteristic (K ₂ ) differs from the stiffness parameter (K) by more than a predetermined stiffness tolerance.

In another embodiment of the method, the method further comprises quantifying the stiffness change (ΔK) from the comparison of K and _K2 .

Description of drawings

Like reference numerals denote like elements throughout the drawings.

Figure 1 shows a flow meter including a meter assembly and meter electronics;

Figure 2 shows meter electronics in accordance with an embodiment of the invention;

3 is a flowchart of a method for determining a stiffness parameter (K) of a flowmeter according to an embodiment of the present invention;

4 is a flowchart of a method for determining the change in stiffness (ΔK) of a flow meter in accordance with an embodiment of the present invention

Figure 5 shows meter electronics according to another embodiment of the invention;

6 is a flowchart of a method for determining a stiffness parameter (K) of a flowmeter according to an embodiment of the present invention;

Fig. 7 shows the implementation of solving poles (λ) and residues (R) according to an embodiment of the present invention;

Figure 8 is a block diagram illustrating calculation of M, C and K system parameters according to an embodiment of the present invention;

FIG. 9 shows an overall FRF-based stiffness estimation system according to an embodiment of the present invention;

10 is a flowchart of a method for determining a stiffness parameter (K) of a flowmeter according to an embodiment of the present invention;

FIG. 11 shows an embodiment of solving equation (29) for M, C and K of the second-order pole-residue response according to an embodiment of the present invention;

Fig. 12 shows an overall FRF-based stiffness estimation system according to an embodiment of the present invention.

Detailed ways

1-12 and the following description describe specific examples to teach those skilled in the art how to make and use the best mode of the invention. In order to teach the principles of the invention, some conventional aspects have been simplified and omitted. Variations from these examples may be appreciated by those skilled in the art 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 in order to form multiple variations of the invention. As a result, the invention is not limited to the specific examples described below, but only by the claims and their equivalents.

FIG. 1 shows a Coriolis flow meter 5 including a meter assembly 10 and meter electronics 20 . Meter assembly 10 responds to the mass flow and density of process material. Via leads 100, meter electronics 20 is connected to meter assembly 10 to provide density, mass flow and temperature information via path 26, as well as other information not relevant to the present invention. A Coriolis flowmeter configuration is described, however it will be apparent to those skilled in the art that the 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' with flanged 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 towards each other at flow tube assembly blocks 120 and 120'. Flow tubes 130 and 130' are bent at two symmetrical locations along their length and are substantially parallel throughout their entire length. Tie rods 140 and 140' serve to define axes W and W' about which each flow tube oscillates.

Side legs 131, 131' and 134, 134' of flow tubes 130 and 130' are fixedly attached to flow tube assembly blocks 120 and 120', which in turn are fixedly attached to manifolds 150 and 150'. This provides a continuous closed material path through Coriolis meter assembly 10 .

When flanges 103 and 103' having holes 102, 102' are connected, via inlet port 104 and outlet port 104', a production line (not shown) carrying the processed material to be measured passes through the Orifice 101 , where material enters end 104 of the flow meter, is directed through manifold 150 to flow tube assembly block 120 having surface 121 . Inside manifold 150, material is divided and routed through flow tubes 130 and 130'. Based on the current flow tubes 130 and 130', the process material is recombined in a separate flow in the manifold 150' and thereafter routed to be connected to the production line (not shown) through the flange 103' having the bolt holes 102' ) outlet port 104'.

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 diagonal tie rods 140 and 140'. Since the Young's modulus of the flow tube changes with temperature, and this change affects flow and density calculations, a resistance temperature detector (RTD) 190 is fitted to the flow tube 130' to continuously measure the temperature of the flow tube. The temperature of the flow tube and thus the voltage developed across the RTD for a given current passing therethrough is governed by the temperature of the material passing through the flow tube. The temperature dependent voltage exhibited across the RTD is used in a known manner by meter electronics 20 to compensate for changes in the modulus of elasticity of flow tubes 130 and 130' due to any change in flow tube temperature. The RTD is connected to meter electronics 20 by leads 195 .

The two flow tubes 130 and 130' are driven by a driver 180 in opposite directions about their respective bending axes W-W and W'-W' and in a first out-of-phase bending mode called flowmeter. The drive mechanism 180 may comprise any of a number of known arrangements, such as a magnet fitted to the flow tube 130', and an opposing coil fitted to the flow tube 130, through which an alternating current is passed in order to vibrate the two flow tubes. A suitable drive signal is applied to drive mechanism 180 by meter electronics 20 via lead 185 .

Meter electronics 20 receives the RTD temperature signal on lead 195 and the left and right speed signals are presented on leads 165L and 165R, respectively. Meter electronics 20 generates drive signals appearing on leads 185 to drive element 180 and vibrating tubes 130 and 130'. Meter electronics 20 process left and right speed signals and RTD signals to calculate mass flow and density through meter assembly 10 . This information, together with other information, is supplied to the utilization device 29 via the meter electronics 20 on the path 26 .

FIG. 2 shows meter electronics 20 according to an embodiment of the invention. Meter electronics 20 may include interface 201 and processing system 203 . Meter electronics 20 receives a vibration response 210 , such as from meter assembly 10 . The meter electronics 20 processes the vibrational response 210 to obtain flow characteristics of the flow material flowing through the meter assembly 10 . Furthermore, in the meter electronics 20 according to the invention, the vibration response 210 is also processed to determine the stiffness parameter (K) of the meter assembly 10 . Additionally, meter electronics 20 may process two or more of these vibrational responses over time to detect changes in stiffness (ΔK) in meter assembly 10 . Stiffness determinations can be made under flowing or non-flowing conditions. A no-flow determination may offer the advantage of a reduced noise level in the resulting vibrational response.

As previously discussed, the Flow Calibration Factor (FCF) reflects material properties and cross-sectional properties of the flow tube. The mass flow rate of the flow material flowing through the flowmeter is determined by multiplying the measured time delay (or phase difference/frequency) by the FCF. The FCF may relate to the stiffness characteristics of the instrument assembly. If the stiffness characteristics of the meter assembly change, the FCF also changes. Changes in the stiffness of the flow meter will therefore affect the accuracy of the flow measurement produced by the flow meter.

The present invention is interesting because it allows the meter electronics 20 to perform stiffness determinations in the field without performing actual flow calibration tests. It allows stiffness determination without calibration of test benches or other specific equipment or specific fluids. This is desirable because performing flow calibration in the field is expensive, difficult and time consuming. However, better and easier calibration checks are desirable because the stiffness of the meter assembly 10 can change over time. Such changes may be due to factors such as corrosion of the flow tubes, erosion of the flow tubes, and damage to the meter assembly 10 .

The present invention can be expressed using a mathematical model. Open-loop, a second-order drive model can represent the vibration response of the flowmeter, including:

$\mathrm{<span\; class="notranslate">\; m</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

是流管位移的速度，并且x是加速度。这通常被称作MCK模型。该公式可被重新设置成以下形式：where f is the force applied to the system, M is the mass of the system, C is the damping property, and K is the stiffness property of the system. The term K includes K=M(ω ₀ ) ² and the term C includes C=M2ζω ₀ , where ζ includes the delay characteristic, and ω ₀ =2πf ₀ , where f ₀ is the natural/resonance of the meter assembly 10 in Hz frequency. Furthermore, x is the physical displacement distance of the vibration,

is the velocity of flow tube displacement, and x is the acceleration. This is often referred to as the MCK model. The formula can be reformulated as follows:

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HSA00000109999600071.png,HSA00000109999600091.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Equation (2) can be further processed into a transfer function form. In transfer function form, using force-up displacement terms, including:

$\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HSA00000109999600071.png,HSA00000109999600091.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Well-known magnetic equations can be used to simplify Equation (3). Two applicable equations are:

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; PO</span>}}<span\; class="notranslate">\; *</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

as well as

f = BL _DR *I (5)

对于每一拾取传感器，通常已知或测量拾取灵敏度因数BL_PO。通过方程(5)的驱动器180产生的力(f)等于驱动器灵敏度因数BL_DR乘以被供给至驱动器180的驱动电流(I)。通常已知或测量驱动器180的驱动器灵敏度因数BL_DR。因数BL_PO和BL_DR都是温度的函数，并且可被温度测量校正。The sensor voltage VEMF of equation (4) (at the pickup sensor 170L or 170R) is equal to the pickup sensitivity factor BL _PO multiplied by the pickup speed of motion

For each pickup sensor, the pickup sensitivity factor BL _PO is typically known or measured. The force (f) generated by the driver 180 by equation (5) is equal to the driver sensitivity factor BL _DR multiplied by the drive current (I) supplied to the driver 180 . The driver sensitivity factor BL _DR of driver 180 is typically known or measured. The factors BL _PO and BL _DR are both functions of temperature and can be corrected by temperature measurements.

By substituting magnetic equations (4) and (5) into the transfer function of equation (3), the result is:

$\frac{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; PO</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HSA00000109999600071.png,HSA00000109999600091.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

If the meter assembly 10 is driven open loop at resonance, that is, at the resonance/natural frequency ω ₀ (where ω ₀ =2πf ₀ ), then equation (6) can be rewritten as:

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; PO</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

By substituting the stiffness, equation (7) is simplified to:

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}_{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; PO</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;K</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Here, the stiffness parameter (K) can be separated to obtain:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; PO</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; BL</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&zeta;V</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

As a result, the stiffness parameter (K) can be determined by measuring/quantifying the damping characteristic (ζ) as well as the driving voltage (V) and driving current (I). The response voltage (V) from the pickup can be determined from the vibration response and the drive current (I). The step of determining the stiffness parameter (K) is discussed in more detail below in connection with FIG. 3 .

In use, the stiffness parameter (K) can be tracked over time. For example, statistical techniques can be used to determine any changes (ie, the stiffness parameter (K)) over time. A statistical change in the stiffness parameter (K) may indicate that the FCT has changed for a particular flow meter.

The present invention provides a stiffness parameter (K) that does not rely on stored or recalled calibration density values. This is in contrast to the prior art where a known flow material is used for factory calibration operations in order to obtain a density standard that can be used for all future calibration operations. The present invention provides a stiffness parameter (K) obtained solely from the vibration response of the flowmeter. The present invention provides a stiffness detection/calibration method that does not require a factory calibration step.

Interface 201 receives vibration response 210 from one of velocity sensors 170L and 170R via lead 100 of FIG. 1 . Interface 201 may perform any necessary or desired signal conditioning, such as formatting, amplification, buffering, etc. in any manner. Alternatively, some or all of the signal conditioning may be performed in the processing system 203 . Additionally, interface 201 may allow communication between meter electronics 20 and external devices. The interface 201 is capable of any of electrical, optical or wireless communication.

In one embodiment interface 201 is coupled to a digitizer (not shown), wherein the sensor signals comprise analog sensor signals. The digitizer samples and digitizes the analog vibration response and generates 210 a digital vibration response.

Processing system 203 manages the operation of meter electronics 20 and processes flow measurements from meter assembly 10 . The processing system 203 executes one or more processing programs and thereby processes the flow measurements to generate one or more flow characteristics.

Processing system 203 may include a general purpose computer, a microprocessor system, logic circuits, or some other general purpose or custom processing device. Processing system 203 may be distributed among multiple processing devices. Processing system 203 may include any manner of integral or self-contained electronic storage medium, such as storage system 204 .

Storage system 204 may store flow meter parameters and data, software programs, constants and variables. In one embodiment, storage system 204 includes programs executed by processing system 203 , such as stiffness program 230 to determine a stiffness parameter (K) of flow meter 5 .

In one embodiment the stiffness program 230 may arrange the processing system 203 to receive a vibration response from the flow meter comprising a response to vibration of the flow meter at the fundamental resonant frequency, determine the frequency of the vibration response (ω ₀ ), determine Response voltage (V) and drive current (I) of the vibration response, measure the attenuation characteristic (ζ) of the flowmeter, and from frequency (ω ₀ ), response voltage (V), drive current (I) and attenuation characteristic (ζ) Determine the stiffness parameter (K) (see Figure 3 and related discussion).

In one embodiment the stiffness program 230 may arrange the processing system 203 to receive the vibration response, determine the frequency, determine the response voltage (V) and drive current (I), measure the damping characteristic (ζ) and determine the stiffness parameter (K). In this embodiment the stiffness routine 230 further arranges for the processing system 203 to receive a vibratory response from the flow meter at a _second time t, repeat the determining and measuring steps for the second vibratory response, thereby producing a second stiffness characteristic ( _K2 ) , compare the second stiffness characteristic (K ₂ ) with the stiffness parameter (K), and if the difference between the second stiffness characteristic (K ₂ ) and the stiffness parameter (K) is greater than the tolerance 224, detect the stiffness change (ΔK) (see Figure 4 and related discussions).

In one embodiment, storage system 204 stores variables used to operate flow meter 5 . Storage system 204 in one embodiment stores variables, such as vibration response 210, which may be received from speed/pickoff sensors 170L and 170R, for example.

In one embodiment, storage system 204 stores constants, coefficients and operating variables. For example, the storage system 204 may store the determined stiffness characteristic 220 and the second stiffness characteristic 221 generated at a subsequent point in time. The storage system 204 can store operating values, such as the frequency 212 of the vibration response 210 , the voltage 213 of the vibration response 210 , and the driving current 214 of the vibration response 210 . The storage system 204 may further store the vibration target 226 and the measured damping characteristic 215 of the flow meter 5 . Additionally, storage system 204 may store constants, thresholds or ranges, such as tolerance 224 . Additionally, storage system 204 may store data accumulated over time periods, such as stiffness changes 228 .

FIG. 3 is a flowchart 300 of a method for determining a stiffness parameter (K) of a flow meter in accordance with an embodiment of the present invention. In step 301, a vibration response is received from a flow meter. This vibrational response is the flowmeter's response to vibrations at the fundamental resonant frequency. The vibration can be continuous or intermittent. The flow material may flow through meter assembly 10, or may be steady.

In step 302, the frequency of the vibratory response is determined. The frequency ω ₀ can be determined from the vibrational response by any method, procedure or hardware.

In step 303, the vibration response voltage (V or V _EMF ), and the drive current (I) are determined. This voltage and drive current can be obtained from an unprocessed or tuned vibration response.

In step 304, the damping characteristic of the flow meter is measured. The damping characteristic is measured by allowing the vibration response of the flowmeter to decay down to the vibration target while the damping characteristic is measured. This attenuation can be performed in several ways. The drive signal amplitude can be reduced, the driver 180 can actually perform braking of the meter assembly 10 (in a suitable flow meter), or the driver 180 can be simply boosted in power until the target is reached. In one embodiment, the vibration target includes a reduced level in drive set point. For example, if the drive setpoint is currently at 3.4mV/Hz, then for damping measurements, the drive setpoint can be reduced to a lower value, such as 2.5mV/Hz. In this manner, meter electronics 20 may allow meter assembly 10 to simply coast until the vibration response substantially matches the new drive target.

In step 305, a stiffness parameter (K) is determined from frequency, voltage, drive current and damping characteristic (ζ). The stiffness parameter (K) can be determined according to equation (9) above. In addition to determining and tracking stiffness (K), the method also determines and tracks damping parameters (C) and mass parameters (M).

The method 300 can be performed iteratively, periodically, or randomly. The method may be performed at predetermined landmarks, such as at predetermined hours of operation, when flow material changes, and the like.

FIG. 4 is a flowchart 400 of a method for determining a change in stiffness (ΔK) of a flow meter in accordance with an embodiment of the present invention. In step 401, a vibration response is received from a flow meter, as previously discussed.

In step 402, the frequency of the vibrational response is determined, as previously discussed.

In step 403, the voltage and drive current for the vibratory response are determined, as previously discussed.

In step 404, the decay characteristic (ζ) of the flow meter is measured, as previously discussed.

In step 405, the stiffness parameter (K) is determined from the frequency, voltage, drive current and damping characteristic (ζ), as previously discussed.

In step 406, a second vibration response is received at a second time _t2 . A second vibration response results from the vibration of meter assembly 10 at time _t2 .

In step 407, a second stiffness characteristic _K2 is generated from the second vibrational response. For example, the second stiffness characteristic K ₂ can be generated using steps 401 to 405 .

In step 408, the second stiffness characteristic _K2 is compared with the stiffness parameter (K). This comparison includes a comparison of the stiffness characteristics obtained at different times in order to detect stiffness changes (ΔK).

In step 409, any stiffness change (ΔK) between _K2 and K is determined. This stiffness change determination may employ any manner of statistical or mathematical methods for determining significant changes in stiffness. This change in stiffness (ΔK) can be stored for future use and/or transmitted to a remote location. Furthermore, this change in stiffness (ΔK) can trigger an alarm condition in the meter electronics 20 . The stiffness change (ΔK) in one embodiment is first compared to a tolerance 224 . An error condition is determined if the stiffness change (ΔK) exceeds the tolerance 224 . In addition to determining and tracking stiffness (K), the method also determines and tracks damping parameters (C) and mass parameters (M).

The method 400 can be performed iteratively, periodically, or randomly. The method may be performed at predetermined landmarks, such as at predetermined hours of operation, when flow material changes, and the like.

FIG. 5 shows meter electronics 20 according to another embodiment of the invention. The meter electronics 20 in this embodiment may include an interface 201 , a processing system 203 and a storage system 204 as previously discussed. Meter electronics 20 receives three or more vibration responses 505 , such as from meter assembly 10 . The meter electronics 20 processes the three or more vibrational responses 505 to obtain flow characteristics of the flow material flowing through the meter assembly 10 . Additionally, the three or more vibration responses 505 may also be processed to determine a stiffness parameter (K) of the meter assembly 10 . Meter electronics 20 may further determine a damping parameter (C) and a mass parameter (M) from the three or more vibration responses 505 . These meter assembly parameters may be used to detect changes to the meter assembly 10, as previously discussed.

Storage system 204 may store processing programs, such as stiffness program 506 . Storage system 204 may store received data, such as vibration responses 505 . Storage system 204 may store pre-programmed or user-entered values such as stiffness tolerance 516 , damping tolerance 517 , and mass tolerance 518 . Storage system 204 may store working values such as pole (λ) 508 and residue (R) 509 . Storage system 204 may store determined final values, such as stiffness (K) 510 , damping (C) 511 and mass (M) 512 . The storage system 204 may store comparative values generated and manipulated over time periods, such as second stiffness ( _K2 ) 521, second mass ( _M2 ) 522, stiffness change (ΔK) 530, damping change (ΔC) 531, and Mass change (ΔM) 532 . Stiffness change (ΔK) 530 may include a change in the stiffness parameter (K) of meter assembly 10 as measured over time. Stiffness change (ΔK) 530 may be used to detect and determine physical changes of meter assembly 10 over time, such as corrosion and erosion effects. Additionally, the mass parameter (M) 512 of the meter assembly 10 can be measured and tracked over time and stored in mass change (ΔM) 532, and the damping parameter (C) 511 can be measured over time and stored in damping Change (ΔC) 531. Mass change (ΔM) 532 may indicate the increased presence of flow material in meter assembly 10 and damping change (ΔC) 531 may indicate flow tube changes including material degradation, erosion and corrosion, cracking, and the like.

In operation, meter electronics 20 receives three or more vibration responses 505 and processes vibration responses 505 using stiffness program 506 . In one embodiment, the three or more vibrational responses 505 include five vibrational responses 505, as will be discussed below. Meter electronics 20 determines poles (λ) 508 and residues (R) 509 from vibration response 505 . Poles (λ) 508 and residues (R) 509 may include first-order poles and residues, or may include second-order poles and residues. Meter electronics 20 determines stiffness parameter (K) 510 , damping parameter (C) 511 and mass parameter (M) 512 from poles (λ) 508 and residue (R) 509 . Meter electronics 20 may further determine a second stiffness (K ₂ ) 520 , may determine a stiffness change (ΔK) 530 , from the stiffness parameter (K) 510 and the second stiffness (K ₂ ) 520 may determine a stiffness change (ΔK) 530 , And the stiffness change (ΔK) 530 and the stiffness tolerance 516 may be compared. If the stiffness change (ΔK) 530 exceeds the stiffness tolerance 516 , the meter electronics 20 may initiate any manner of error logging and/or error handling routines. Likewise, the meter electronics 20 can further track the damping and mass parameters over time, and can determine and record the second damping (C ₂ ) 521 and the second mass (M ₂ ), and the resulting damping change (ΔC) 531 and mass change (ΔM) 532. Damping change (ΔC) 531 and mass change (ΔM) 532 may likewise be compared to damping tolerance 517 and mass tolerance 518 .

The invention can be described using a mathematical model. Open-loop, a second-order drive model can represent the vibration response of the flowmeter, including:

$\mathrm{<span\; class="notranslate">\; m</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

是加速度。这通常被称作MCK模型。该公式可被重新布置成下面的形式：where f is the force applied to the system, M is the mass parameter of the system, C is the damping parameter, and K is the stiffness parameter. Term K includes K=M(ω ₀ ) 2 and term C includes C=M2ζω ₀ , where ω ₀ =2πf ₀ , and f ₀ is the resonant frequency of meter assembly 10 in Hz. The term ζ includes the attenuation characteristic measure obtained from the vibration response, as discussed previously. Furthermore, x is the physical displacement distance of the vibration, is the velocity of flow tube displacement, and

is the acceleration. This is often referred to as the MCK model. This formula can be rearranged as follows:

$<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="ms"\; filenames="HSA00000109999600071.png,HSA00000109999600091.png"\; state="\{\{state\}\}">ms</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cs</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ms</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Equation (11) can be further processed into a transfer function form while ignoring the initial conditions. turn out:

Further processing can transform Equation (12) into a first-order pole-residual frequency response function form, including:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\frac{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

where λ is the pole, R is the residue, term (j) includes the square root of -1, and ω is the circular excitation frequency (in radians per second).

The system parameters include the natural/resonant frequency (ω _n ) defined by the pole, the damped natural frequency (ω _d ) and the damping characteristic (ζ).

ω _n =|λ| (14)

ω _d =imag(λ) (15)

$\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The stiffness parameters (K), damping parameters (C) and mass parameters (M) of the system can be obtained from the poles and residuals.

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; J</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

C=2ζω _n M (19)

Therefore, the stiffness parameter (K), damping parameter (C) and mass parameter (M) can be calculated from good estimates of the poles (λ) and residuals (R).

The poles and residues can be estimated from the measured frequency response function. The poles (λ) and residues (R) can be estimated using some form of direct or iterative computation.

The response near the driving frequency is dominated by the first term of equation (13), with the complex conjugate terms contributing only a small, approximately constant "remainder" of the response. As a result, equation (13) can be simplified to:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

项)依据速度除以力。因此，方程(20)可被变换成下面的形式：In equation (20), the H(ω) term is the measured frequency response function (FRF) obtained from the three or more vibration responses. In this derivation, H consists of the displacement output divided by the force input. However, in the typical case of voice coil pickup in a Coriolis flowmeter, the measured FRF (i.e.

item) is based on velocity divided by force. Therefore, equation (20) can be transformed into the following form:

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;R</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$

Equation (21) can be further rearranged into a form that is easily solved for the poles (λ) and residues (R).

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; j\&omega;</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j\&omega;R</span>}$

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>\frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}$

$\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}\end{array}\right]\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; R</span>}\\ \mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right\}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

确定极点(λ)和残数(R)。项H，R和λ是复数。Equation (22) forms an over-determined system of equations. Equation (22) can be solved computationally so that from the velocity/force FRF

Determine the poles (λ) and residues (R). The terms H, R and λ are complex numbers.

In one embodiment, the forcing frequency ω is 5-tone. In this embodiment 5 tones include the driving frequency and 2 tones above the driving frequency and 2 tones below the driving frequency. These tones can be separated by 0.5-2Hz from the fundamental frequency. However, the forced frequency ω may include more tones or fewer tones, such as 1 tone above and below the driving frequency. However, there is a good compromise between the accuracy of the 5-tone impact results and the processing time required to obtain this result.

It should be noted that in the preferred FRF measurement, two FRFs are measured for a specific drive frequency and vibration response. One FRF measurement is taken from driver to right pick-off (RPO) and one FRF measurement is taken from driver to left pick-off (LPO). This method is called Single Input, Multiple Output (SIMO). Among the distinguishing new features of the present invention, SIMO techniques are used to better estimate the poles (λ) and residues (R). Previously, two FRFs were used to give two separate pole (λ) and residual (R) estimates. Recognizing that both FRFs share a common pole (λ), but separate residuals ( _RL ) and ( _RR ), the two measurements can be advantageously combined for a more robust pole and residual determination.

$\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; LPO</span>}}}{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \frac{{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; RPO</span>}}}{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}\end{array}\right]\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}\\ \mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right\}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; three</span>}<span\; class="notranslate">\; )</span>$

Equation (23) can be solved in any number of ways. In one embodiment, the equations are solved by recursive least squares. In another embodiment, the equations are solved by pseudo-inverse techniques. In another embodiment, since all measurements are available at the same time, standard Q-R decomposition techniques can be used. This Q-R decomposition technique is discussed in Modern Control Theory (William Brogan, copyright 1991, Prentice Hall, pp. 222-224, 168-172).

In use, the stiffness parameter (K) as well as the damping parameter (C) and mass parameter (M) can be tracked over time. For example, statistical techniques can be used to determine any change in the stiffness parameter (K) over time (ie, stiffness change (ΔK)). A statistical change in the stiffness parameter (K) may indicate that the FCF for a particular flow meter has changed.

The present invention provides a stiffness parameter (K) that does not rely on storing or retrieving calibrated density values. This is in contrast to the prior art where known flow material is utilized in factory calibration operations in order to obtain a density standard that can be used for all future calibration operations. The present invention provides a way to derive the stiffness parameter (K) from only the vibration response of the flowmeter. The present invention provides a stiffness detection/calibration method that does not require a factory calibration step.

FIG. 6 is a flowchart 600 of a method for determining a stiffness parameter (K) of a flow meter in accordance with an embodiment of the present invention. In step 601, three or more vibration responses are accepted. The three or more vibratory responses may be received from the flow meter. The three or more vibration responses may include a fundamental fundamental frequency response and two or more non-fundamental frequency responses. In one embodiment, one tone above the fundamental frequency response is received and one tone below the fundamental frequency response is received. In another embodiment, two or more tones are received above the fundamental frequency response and two or more tones are received below the fundamental frequency response.

In one embodiment, the tones are spaced substantially equally above and below the fundamental frequency response. Alternatively, the tones are not equally spaced.

In step 602, a first order pole-residue frequency response is generated from the three or more vibrational responses. The first order pole-residue frequency response has the form given in equation (23).

In step 603, a quality parameter (M) is determined from the first order pole-residue frequency response. The quality parameter (M) is determined by determining the first-order poles (λ) and first-order residues (R) of the vibration response. Then, the natural frequency ω _n , the damping natural frequency ω _d , and the damping characteristic (ζ) are determined from the first-order pole (λ) and the first-order residue (R). Subsequently, the damped natural frequency ω _d , the residual (R) and the imaginary term (j) are plugged into equation (17) to obtain the mass parameter (M).

In step 604, a stiffness parameter (K) is determined from the solution of equation (18). The solution is plugged into equation (18) using the natural frequency ω _n and the mass parameter (M) determined from step 603 to obtain the stiffness parameter (K).

In step 605, a damping parameter (C) is determined from the solution of equation (19). The solution takes the decay characteristic (ζ), the natural frequency ω _n , and a determined mass parameter (M).

Figure 7 shows an implementation of a pole (λ) and residue (R) solution according to an embodiment of the invention. This embodiment follows equation (23). The FRF input is on the left side of the figure. These FRF inputs are in this embodiment the five frequencies (four test signal frequencies and the driving frequency) at which the FRF coefficients are calculated. The FRF_L and FRF_R inputs are the drive pickup complex FRF coefficients calculated at those frequencies, corresponding to and These FRF coefficients enter the B input of the QR solver block 701 . On an item-by-item basis, dividing by jω from the FRF coefficients forms the A matrix for the QR solver block 701, and the A matrix includes columns of 1 and 0 so as to comply with equation (23). This matrix is reformulated into the appropriate [10×3] complex dimension and enters the A input of the QR solver block 701 . The x-vector output of the QR solver block 701 includes the left and right residues _RL and _RR and the pole λ. These outputs are passed from the QR block 701 for processing to generate system parameters.

FIG. 8 is a block diagram illustrating calculation of M, C and K system parameters according to an embodiment of the present invention. This embodiment determines the M, C and K system parameters from the pole and residual estimates for each of equations (14-16) and equations (17-19). These residuals are purely imaginary to the true standard mode model. However, there will often be some real part due to noise in the measurement data and due to model fitting numerical precision issues. Therefore, the absolute value of the residue is used, which has a similar effect of dividing j per equation (17). The mass and stiffness are calculated using the poles and residues of each equation (17-18). It should be noted that there is a "left" and a "right" mass and stiffness, that is, the mass stiffness calculated from the FRF of the LPO/driver and RPO/driver. Due to the asymmetry of the coils and magnets and the structure itself, from right to left, the mass and stiffness estimates can be different. The differential change or differential ratio represents a non-uniform change in mass or stiffness and can be used to give additional diagnostic information about changes in FCF or integrity of flow.

Two other outputs from system parameter calculations are the damping coefficient, Z(zeta) or ζ, and the natural frequency ω _n . This embodiment gives a more certain or better estimated set of global parameters.

Estimation of ω _n yields a good quality check for closed-loop drive systems. If the drive is actually operating at resonance, then the drive frequency will agree to within a few millihertz for natural frequency estimation. If the difference is greater than a few millihertz, a warning flag can be set indicating that the drive system is not working properly or that the current stiffness estimate is suspect.

FIG. 9 shows an overall FRF-based stiffness estimation system according to an embodiment of the present invention. There are seven different inputs to the stiffness estimation subsystem, represented by the pentagons as signal sources (five on the upper left and two on the far right). The "RawDrive" and "RawPOs" inputs are raw readings for pickup voltage and drive current. These signals are down-sampled to 2 kHz, eg by decimation, and then fed into the FRF coefficient estimation subsystem. The "CmdmA" input is the commanded current taken from the output of the corresponding digital drive system. The "StiffnessEnable" estimate is a logic input that allows the digital drive system to take control when the FCF calibration algorithm is active. The "freq" input is the drive frequency, as estimated by the digital drive system. It is an input to the test signal generator subsystem and the stiffness calculation subsystem.

The FRF Stiffness Calculation block 902 outputs system parameter estimates M and KLeft and Right and ζ and FreqEst. These are the main diagnostic outputs used in FCF calibration. The figure also shows the frequency difference alarm block 903 and the frequency difference error block 904 which implement the drive quality check discussed above by comparing the drive frequency to the estimated natural frequency.

Measuring FRF usually requires current measurements, requiring additional analog-to-digital (A/D) converters. However, this embodiment avoids the need for an additional A/D converter using calibrated command currents. The CL input selection block 906 and the CL output correction block 907 execute the calibration algorithm. This calibration step utilizes the "Test Signal FRF" block 901 in order to calculate the frequency response function of the actual (RawDrive) current versus the commanded current (CmdmA) at one state of the control logic. During the FCF check logic state process, the FRF between the raw POs and the command current is calculated and corrected by the raw data of the command current FRF coefficients to give the FRFs for further processing.

The FRF stiffness estimation algorithm outputs a "test signal" output to the left of the center of the graph in the figure. The test signal output includes stimuli at four test frequencies that are added to the drive command immediately prior to the output. These test signals are added to the digital drive signals when FCF verification is enabled.

The logic is such that when FCF parity is off, the digital drive signal just passes through a switch or other device, in this case, through an interpolation filter, from its base rate (typically 4kHz) to the appropriate output The digital drive signal is upsampled at a high rate (typically 8kHz). When FCF verification is enabled, a test signal upsampled from 2 to 4 kHz is added to the digital drive signal. The drive signal is then constructed from the closed-loop drive frequency signal and 4 test tones, which are then all passed through an upsampling filter.

The FCF calibration procedure is expected to be transparent to the drive system. In one embodiment, the test signal is removed from the pickup in order to ensure good frequency and amplitude estimation for the closed loop drive. This is done with a bank of notch filters tuned to the precise frequency of the test signal.

In another embodiment, the pole-residue method may employ a second-order pole-residue frequency response function to achieve better results. The second-order pole-residue method provides a more realistic fit to the real numbers than the first-order pole-residue method. The tradeoff is greater numerical complexity and increased processing time.

The MCK embodiment of stiffness estimation starts with a simple second-order system model, as shown in equation (24) below. Due to the pickup of the flowmeter measured velocity, not position, the equation is differentiated and then estimated at a specific frequency ω.

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Mrs.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cs</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}}$

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{{\mathrm{<span\; class="notranslate">\; Mrs.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cs</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}}$

$\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; jC\&omega;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$

Since the goal is to solve for M, C and K from measurements of drive current (or force) and pick-up voltage (or velocity), it is convenient to rewrite equation (24) so as to separate the unknowns. This yields equation (25).

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; jC\&omega;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 25</span>}<span\; class="notranslate">\; )</span>$

At this point, the equation can be separated into real and imaginary parts.

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \}</span>$

$\mathrm{<span\; class="notranslate">\; C\&omega;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Im</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 26</span>}<span\; class="notranslate">\; )</span>$

方程(26)可被重新写成：expand

Equation (26) can be rewritten as:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; C\&omega;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;\; Re</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 27</span>}<span\; class="notranslate">\; )</span>$

因此可以建立：The second equation is now simple, algebraic arithmetic. To further simplify the first part of the equation, the measured resonant drive frequency is used. because

Therefore it is possible to build:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 28</span>}<span\; class="notranslate">\; )</span>$

As long as ω≠ω _n . Returning M from this solution for K, three solutions for M, C and K are given in equation (29).

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Re</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 29</span>}<span\; class="notranslate">\; )</span>$

It should be pointed out that given the resonant frequency ω _n , the driver picks up FRF at a specific frequency ω ₁ is sufficient to solve the equations and determine the parameters M, C and K. This is particularly useful; when the FRF is obtained at multiple frequencies, the least squares fit to the data is simply the average of the individual estimates for each coefficient. This is a simpler way of doing good than the pseudo-inverse that would typically have to be performed. It should be noted, however, that the restriction of ω≠ _ωn precludes the use of resonantly driven FRFs in the solution for K or M. This is not particularly surprising since the height of the peak at resonance is determined only by damping. But one potential disadvantage of this approach is that the parameters estimated from the left and right pick data must not depend on each other. This is in contrast to the pole-residue approach, where some advantage is gained by restricting left and right picks to estimate the same pole regardless of their difference in magnitude.

FIG. 10 is a flowchart 1000 of a method for determining a stiffness parameter (K) of a flow meter in accordance with an embodiment of the present invention. In step 1001, three or more vibration responses are received, as previously discussed.

In step 1002, a second order pole-residue frequency response is generated from the three or more vibrational responses. The second order pole-residue frequency response has the form given in equation (24).

的虚数部分)，以及FRF的振幅(也就是

的绝对值)。In step 1003, a stiffness parameter (K) is determined from the solution of equation (29). The solution takes the natural frequency ω _n , one or more frequency tones ω, the imaginary part of the FRF (that is,

the imaginary part of ), and the amplitude of the FRF (that is,

absolute value).

In step 1004, a quality parameter (M) is determined from the second order pole-residue frequency response. The mass parameter (M) is determined from the solution of equation (29), and is obtained using the stiffness parameter (K) and the natural frequency ω _n .

的实数部分)，以及FRF的振幅(也就是

的绝对值)获得该阻尼参数(C)。In step 1005, a damping parameter (C) is determined from the second order pole-residue frequency response. The damping parameter (C) is determined from the solution of equation (29), and using the one or more frequency tones ω, the real part of the FRF (i.e.

the real part of ), and the amplitude of the FRF (that is,

absolute value) to obtain the damping parameter (C).

或Hdot)。通过选择器块丢弃(discard)驱动频率FRF，因为它不能用于如在前描述的M和K求解中。K求解被计算为：Figure 11 shows an embodiment of solving equation (29) for M, C and K of the second order pole-residue response according to an embodiment of the present invention. Inputs appear as oval input ports at the left of the figure. These are the measured drive frequency ω_drive, which is used in equation (29) as _ωn , the five frequencies at which the FRF coefficients are calculated (the four test signal frequencies and the drive frequency, denoted by ω_test), and at The drivers computed at those frequencies pick up complex FRF coefficients (

or Hdot). The driving frequency FRF is discarded by the selector block because it cannot be used in the M and K solves as previously described. K-solve is calculated as:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;\; Im</span>}<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 30</span>}<span\; class="notranslate">\; )</span>$

It is an equivalent form of the solution method given in equation (29). The solution for C is of the same form as the derived solution in equation (29), and M is computed directly from the solution for K. Note that an averaging operation is applied to each coefficient estimate. This mean result in the solve method is a least squares fit to the input data. Finally, given M, C and K estimates, the decay characteristic (ζ or Z) is calculated as:

$\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 31</span>}<span\; class="notranslate">\; )</span>$

The damping characteristic (ζ) is considered to be a more useful parameter than the damping parameter C. Thus, mass M, stiffness K and damping properties (ζ) are the outputs of the measurements.

Fig. 12 shows an overall FRF-based stiffness estimation system according to an embodiment of the present invention. There are six different inputs to the system, represented by the pentagons as signal sources (three on the upper left and three on the lower right). The "RawDrive" and "RawPOs" inputs are raw readings from pickup and drive currents. These are down-sampled to 2 kHz by a Decimator block 1201 and then fed into the FRF coefficient estimation subsystem. The "DriveDemod" inputs are the sine and cosine signals at the drive frequency obtained from the digital drive system. These signals are combined with a sinusoid generated at the test frequency and fed into the FRF coefficient estimation subsystem as a basis for demodulation. The "StiffnessEnable" estimate is a logic input that allows the digital drive system to control when the stiffness estimation algorithm is active. The "freq" input is the drive frequency, as estimated by the digital drive system. It is an input to the test signal generation block 1204 and the stiffness calculation block 1206 . The "Temp" input is the temperature reading from the flow meter that is input into the temperature correction block 1207 . The FRF stiffness estimation algorithm outputs system parameter estimates, as well as a "test signal" output at the far left of the diagram. The test signal output includes stimuli at the four test frequencies that are added to the drive command.

These inputs and outputs form the bulk of the interface to the digital drive. The test signal is added to the drive command immediately before output to the driver device. In order to make this FCF verification procedure transparent to the drive system, the test signal must be removed from the pickup. In one embodiment this can be done with a bank of notch filters tuned to the precise frequency of the test signal.

The test signal FRF block 1208 of FIG. 11 performs demodulation. The pickup and drive signals are demodulated at each of the five input frequencies (the four generated test signal frequencies and the drive frequency). After complex demodulation using the sine and cosine basis, the real and imaginary parts of each signal are decimated down to lower frequencies and low-pass filtered to 0.4Hz. These signals must be uncontaminated in this region, since any spectral components in 0.4Hz of the test signal will not be suppressed and will show up at the output. The complex coefficients for the pickup and drive currents at each frequency are then used to estimate the FRF at that frequency. The power spectrum is averaged over multiple samples and a lower rate FRF estimate is output.

Meter electronics and methods according to the present invention may be employed in accordance with either embodiment, thereby providing several advantages, if desired. The present invention provides a stiffness parameter (K) that basically relates to flow tube stiffness of the flowmeter. The present invention provides a stiffness parameter (K) that does not rely on stored or recalled calibration values for generation. The present invention provides a stiffness parameter (K) obtained solely from the vibration response of the flowmeter. Likewise, the invention provides mass parameters (M) and damping parameters (C) from the vibrational response.

The present invention provides a stiffness detection/calibration method that does not require a factory calibration step. The present invention can perform the stiffness/FCF calibration method in the field. The present invention can perform the stiffness/FCF calibration method at any time. The present invention can implement a stiffness/FCF calibration method that does not require calibration test loops and/or known flow materials. The present invention can implement a stiffness/FCF calibration method that determines the change in stiffness of the flow meter over time.

Claims (41)

1. the instrument electronic device (20) that is used for flowmeter (5), this instrument electronic device (20) comprises that for the interface (201) that receives from three or more vibratory responses of flowmeter (5) wherein these three or more vibratory responses comprise basic fundamental frequency response and two or more non-fundamental frequency response; And the disposal system (203) of communicating by letter with interface (201), wherein this instrument electronic device (20) further comprises:

Disposal system (203) is arranged to receive these three or more the vibratory responses from interface (201), produce single orders or higher order pole-residue frequency response function more from these three or more vibratory responses, and from this single order or more higher order pole-residue frequency response function determine at least stiffness parameters K.

2. the instrument electronic device of claim 1 (20), wherein disposal system (203) further be arranged to from this single order or more higher order pole-residue frequency response function determine damping parameter C.

3. the instrument electronic device of claim 1 (20), wherein disposal system (203) further be arranged to from this single order or more higher order pole-residue frequency response function determine mass parameter M.

4. the instrument electronic device of claim 1 (20), wherein disposal system (203) further be arranged to from this single order or more higher order pole-residue frequency response function calculate limit λ, left residue R _LWith right residue R _R

5. the instrument electronic device of claim 1 (20), wherein these three or more vibratory responses comprise at least one tone that is higher than fundamental frequency response and are lower than at least one tone of fundamental frequency response.

6. the instrument electronic device of claim 1 (20), wherein these three or more vibratory responses comprise at least two tones that are higher than fundamental frequency response and at least two tones that are lower than fundamental frequency response.

7. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function.

8. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

Wherein the R item comprises residue, and the λ item comprises that limit and ω item comprise circular excitation frequency.

9. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

And wherein according to equation M=1/2jR ω _d, K=(ω _n) ²M and C=2 ζ ω _nM determines stiffness parameters K, damping parameter C and mass parameter M, and wherein the M item comprises mass parameter, the ζ item comprises attenuation characteristic, ω _nItem comprises natural frequency and ω _dItem comprises damped natural frequency.

10. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function.

11. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises

Wherein the M item comprises mass parameter, and the C item comprises damping parameter, and the K item comprises stiffness parameters, and the ω item comprises circular excitation frequency.

12. the instrument electronic device of claim 1 (20), wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises

And foundation wherein $K=\left({\left({\mathrm{\&omega;}}_n\right)}^2\mathrm{\&omega;Im}\right[\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\left]\right)/({\left({\mathrm{\&omega;}}_n\right)}^2-{\mathrm{\&omega;}}^2){\left|\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\right|}^2)$ Determine stiffness parameters K, according to M=K/ (ω _n) ²Determine mass parameter M, and foundation

Determine damping parameter C, wherein the ω item comprises circular excitation frequency.

13. a method that is used for the stiffness parameters K of definite flowmeter, the method comprises:

Receive three or more vibratory responses, wherein these three or more vibratory responses comprise basic fundamental frequency response and two or more non-fundamental frequency response;

Produce single orders or higher order pole-residue frequency response function more from these three or more vibratory responses; And

From this single order or more higher order pole-residue frequency response function determine at least stiffness parameters K.

14. the method for claim 13, further comprise from this single order or more higher order pole-residue frequency response function determine damping parameter C.

15. the method for claim 13, further comprise from this single order or more higher order pole-residue frequency response function determine mass parameter M.

16. the method for claim 13, further comprise from this single order or more higher order pole-residue frequency response function calculate limit λ, left residue R _LWith right residue R _R

17. the method for claim 13, wherein these three or more vibratory responses comprise at least one tone that is higher than fundamental frequency response and at least one tone that is lower than fundamental frequency response.

18. the method for claim 13, wherein these three or more vibratory responses comprise at least two tones that are higher than fundamental frequency response and at least two tones that are lower than fundamental frequency response.

19. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function.

20. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

Wherein the R item comprises residue, and the λ item comprises that limit and ω item comprise circular excitation frequency.

21. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

And wherein according to equation M=1/2jR ω _d, K=(ω _n) ²M and C=2 ζ ω _nM determines stiffness parameters K, damping parameter C and mass parameter M, and wherein the M item comprises mass parameter, the ζ item comprises attenuation characteristic, ω _nItem comprises natural frequency and ω _dItem comprises damped natural frequency.

22. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function.

23. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises

Wherein the M item comprises mass parameter, and the C item comprises damping parameter, and the K item comprises stiffness parameters, and the ω item comprises circular excitation frequency.

24. the method for claim 13, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises $\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)=\frac{\stackrel{\&CenterDot;}{X}\left(\mathrm{\&omega;}\right)}{F\left(\mathrm{\&omega;}\right)}=\frac{\mathrm{j\&omega;}}{-M{\mathrm{\&omega;}}^2+\mathrm{jC\&omega;}+K},$ And foundation wherein $K=({\left({\mathrm{\&omega;}}_n\right)}^2\mathrm{\&omega;}$ $\mathrm{Im}\left[\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\right])/({\left({\mathrm{\&omega;}}_n\right)}^2-{\mathrm{\&omega;}}^n){\left|\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\right|}^2)$ Determine stiffness parameters K, according to M=K/ (ω _n) ²Determine mass parameter M, and foundation

Determine damping parameter C, wherein the ω item comprises circular excitation frequency.

25. the method for claim 13 further comprises:

At the second time t ₂The place receives second group of three or more vibratory response from flowmeter;

Produce the second stiffness characteristics K from these second group of three or more vibratory response ₂

Compare the second stiffness characteristics K ₂With stiffness parameters K; And

If the second stiffness characteristics K ₂Different from predetermined tolerance from stiffness parameters K are then detected stiffness variation Δ K.

26. the method for claim 25 further comprises if the second stiffness characteristics K ₂Different from the predetermined stiffness tolerance from stiffness parameters K are then detected stiffness variation Δ K.

27. the method for claim 25 further comprises from stiffness parameters K and the second stiffness characteristics K ₂relatively quantize stiffness variation Δ K.

28. a method that is used for the stiffness variation Δ K of definite flowmeter, the method comprises:

Receive three or more vibratory responses, wherein these three or more vibratory responses comprise basic fundamental frequency response and two or more non-fundamental frequency response;

Produce single orders or higher order pole-residue frequency response function more from these three or more vibratory responses;

From this single order or more higher order pole-residue frequency response function determine at least stiffness parameters K;

At the second time t ₂The place receives second group of three or more vibratory response from flowmeter;

Produce the second stiffness characteristics K from these second group of three or more vibratory response ₂

Compare the second stiffness characteristics K ₂With stiffness parameters K; And

If the second stiffness characteristics K ₂Different from predetermined tolerance from stiffness parameters K are then detected stiffness variation Δ K.

29. the method for claim 28 further comprises if the second stiffness characteristics K ₂Different from the predetermined stiffness tolerance from stiffness parameters K are then detected stiffness variation Δ K.

30. the method for claim 28 further comprises from stiffness parameters K and the second stiffness characteristics K ₂relatively quantize stiffness variation Δ K.

31. the method for claim 28, wherein said determine to comprise from this single order or more higher order pole-residue frequency response function further determine damping parameter C.

32. the method for claim 28, wherein said determine to comprise from this single order or more higher order pole-residue frequency response function further determine mass parameter M.

33. the method for claim 28, wherein said determine further to comprise from this single order or more higher order pole-residue frequency response function calculate limit λ, left residue R _LWith right residue R _R

34. the method for claim 28, wherein these three or more vibratory responses comprise at least one tone that is higher than fundamental frequency response and at least one tone that is lower than fundamental frequency response.

35. the method for claim 28, wherein these three or more vibratory responses comprise at least two tones that are higher than fundamental frequency response and at least two tones that are lower than fundamental frequency response.

36. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function.

37. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

Wherein the R item comprises residue, and the λ item comprises that limit and ω item comprise circular excitation frequency.

38. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise first order pole-residue frequency response function, this first order pole-residue frequency response function comprises

And wherein according to equation M=1/2jR ω _d, K=(ω _n) ²M and C=2 ζ ω _nM determines stiffness parameters K, damping parameter C and mass parameter M, and wherein the M item comprises mass parameter, the ζ item comprises attenuation characteristic, ω _nItem comprises natural frequency and ω _dItem comprises damped natural frequency.

39. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function.

40. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises

Wherein the M item comprises mass parameter, and the C item comprises damping parameter, and the K item comprises stiffness parameters, and the ω item comprises circular excitation frequency.

41. the method for claim 28, wherein this single order or more higher order pole-residue frequency response function comprise second order limit-residue frequency response function, this second order limit-residue frequency response function comprises $\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)=\frac{\stackrel{\&CenterDot;}{X}\left(\mathrm{\&omega;}\right)}{F\left(\mathrm{\&omega;}\right)}=\frac{\mathrm{j\&omega;}}{-M{\mathrm{\&omega;}}^2+\mathrm{jC\&omega;}+K},$ And foundation wherein $K=\left({\left({\mathrm{\&omega;}}_n\right)}^2\mathrm{\&omega;Im}\right[\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\left]\right)/({\left({\mathrm{\&omega;}}_n\right)}^2-{\mathrm{\&omega;}}^2){\left|\stackrel{\&CenterDot;}{H}\left(\mathrm{\&omega;}\right)\right|}^2)$ Determine stiffness parameters K, according to M=K/ (ω _n) ²Determine mass parameter M, and foundation

Determine damping parameter C, wherein the ω item comprises circular excitation frequency.

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