HK1037719B - Parameter sensors and method for vibrating conduit utilizing normal modal decompositi - Google Patents

Description

Parameter sensor and method for oscillating conduit using natural mode decomposition

The present invention relates to process parameter sensors, methods of operation, and computer program products, and in particular, to oscillating duct parameter sensors, methods of operation, and computer program products.

Coriolis effect mass flowmeters are commonly used to measure mass flow and other information of a material flowing through a conduit. Example coriolis flowmeters are disclosed in U.S. patent No. 4109524, 29/8/1978, 4491025, 1/1985, and Re31450, 11/2/1982, to smith et al. These flow meters typically include one or more conduits having a straight or curved configuration. Each conduit may be viewed as having a set of oscillatory wave modes including, for example, simple bending, twisting, radial, and coupled wave modes. In a typical mass flow measurement application, as a material flows through the conduits, each conduit is driven to oscillate in a resonant manner in one of its natural wave modes. The mass and stiffness characteristics of the conduit, in combination with the characteristics of the substance flowing in the conduit, affect the oscillatory wave modes of the oscillating substance-filled system.

A typical component of a coriolis flow meter is the drive or trigger system. The drive system is operable to apply a periodic physical force to the conduit to oscillate the conduit. The drive system generally includes at least one actuator mounted to a conduit of the flow meter. The actuator may comprise one of a number of well known electromechanical devices such as a voice coil device having a magnet mounted to a first conduit and a coil mounted to a second conduit in opposed relationship to the magnet. A driver typically provides a periodic, e.g., sinusoidal or square wave, drive signal to the start coil. The periodic drive signal causes the actuator to drive the two conduits in an opposite periodic pattern.

When there is an effective "zero" flow through the driven meter conduit, points along the conduit will oscillate at approximately the same phase or "zero flow" phase with respect to the driver depending on the wave mode of the driven vibration. As material begins to flow from the inlet of the meter out of the outlet of the meter via the conduit, coriolis forces resulting from the material flow cause a phase shift between spatially spaced points along the conduit, with the phase at the inlet side of the conduit generally lagging behind the actuator and the phase at the outlet side of the conduit generally leading the actuator. The phase shift produced between the two locations of the conduit is approximately proportional to the mass flow rate of the substance through the conduit.

Unfortunately, the non-linearity and asymmetry of the flowmeter structure and the vibrations introduced into the flowmeter structure by external sources such as pumps can compromise the accuracy of the measurement results obtained using conventional phase shift or time delay methods. This can be reduced, for example, by using a balanced mechanical structure that reduces the effects of external vibrations and frequency domain filtering to remove frequency components associated with unwanted vibrations. However, mechanical structural methods are limited by geometric considerations, and frequency domain filtering methods are inefficient at removing unwanted vibrational energy that occurs at or near the relevant resonant frequency, such as at the drive frequency used to trigger the conduit.

In view of the foregoing, it is an object of the present invention to provide a vibrating conduit parameter sensor, method of operation and computer program product that accurately estimate process parameters in a sensor conduit having structural non-linearities and asymmetries in the presence of external vibrations.

The above and other objects, features and advantages are realized in a vibrating conduit parameter sensor, method of operation and computer program product in which a motion signal representing motion of a vibrating conduit is processed to decompose the conduit motion into real natural modal components from which a process parameter, such as mass flow, can be estimated. In one embodiment of the invention, a wave mode filter is applied to the motion signal to form an output that best represents a component of the motion of the conduit associated with one or more real eigen-wave modes, such as a wave mode that is preferably associated with Coriolis forces associated with matter within the conduit. Estimates of process parameters, such as mass flow, are then generated from the outputs using, for example, conventional phase difference techniques. In another embodiment of the invention, real normal modal motion is estimated from the plurality of motion signals, and a process parameter is estimated from a subset of the estimated real normal modal motion, for example, from motion in a real normal mode that is preferably associated with coriolis forces.

Since the motion of the catheter is decomposed into real normal modal components, a more accurate estimate of the process parameter can be obtained. For example, a wave mode filter may pass components of conduit motion corresponding to real natural wave modes that are closely related to Coriolis forces while reducing components of conduit motion related to external noise sources. Thus, the filtered output is less likely to be corrupted by noise and vibration and is therefore best suited for generating accurate estimates of process parameters such as mass flow. Similarly, the estimated real natural modal motion of a selected wave mode associated with coriolis forces can be used to generate an accurate estimate of a process parameter while ignoring modal motion originating from other sources.

Specifically, in accordance with the present invention, a process parameter sensor for determining a process parameter includes: a conduit configured to contain a substance; and a plurality of motion receptors operable to generate a plurality of motion signals indicative of motion at a plurality of locations of the conduit. A real normal modal decomposer is responsive to the plurality of motion receptors and is operable to process the plurality of motion signals to decompose motion represented by the plurality of motion signals into real normal modal components. A process parameter estimator is responsive to the real normal mode decomposer and is operable to estimate a process parameter based on one of the real normal mode components.

In one embodiment of the invention, the real normal mode decomposer comprises a wave mode filter operable to generate an output from the plurality of motion signals that is best representative of a component of motion associated with a real normal mode of the conduit, such as a real normal mode associated best with coriolis forces. The process parameter estimator is responsive to the wave mode filter and is operable to estimate a process parameter based on the output.

In another embodiment of the invention, the real normal modal resolver comprises a real normal modal motion estimator operable to estimate the real normal modal motion from the received plurality of motion signals. The process parameter estimator is operable to estimate a process parameter based on the estimated real natural modal motion, e.g., based on estimated motion of a set of real natural wave modes that are closely related to coriolis forces. The real natural modal motion estimator may comprise means for estimating motion in a first actual natural wave mode and means for estimating motion in a second actual natural wave mode, the second actual natural wave mode preferably being related to coriolis forces. The process parameter estimator may include means for normalizing the estimated motion in the second real eigen-mode relative to the estimated motion in the first real eigen-mode to generate a normalized estimate of the motion in the second real eigen-mode. Means may be provided for estimating the process parameter from a normative estimate of motion in the second real, natural-wave mode.

In accordance with a method aspect of the present invention, a plurality of motion signals are received that are indicative of motion at a plurality of locations of a vibrating conduit containing a substance. The received plurality of motion signals are processed to decompose the motion into a plurality of real normal modal components. A process parameter is estimated based on one of the real normal modal components.

In accordance with a method aspect of the present invention, the motion signal may be processed to generate an output that best represents the motion component associated with the real natural wave mode of the vibrating conduit. A wave mode filter may be applied to the plurality of motion signals and the process parameters estimated from the filtered outputs. For example, first and second filtered signals may be generated that are representative of motion at respective first and second locations of the catheter. The process parameter may be estimated by determining a phase difference between the first filtered signal and the second filtered signal and estimating the mass flow based on the determined phase difference.

In accordance with another method aspect of the present invention, real normal modal motion, i.e., motion in a multiple single degree of freedom (SDOF) system, can be estimated from a plurality of received motion signals. The process parameters may be estimated from the estimated real normal modal motion. For example, motion in respective first and second real eigen-modes can be estimated, with the second real eigen-mode being optimally related to coriolis forces. The process parameter may be estimated by normalizing the estimated motion in the second real eigen-wave mode relative to the estimated motion in the first real eigen-wave mode to generate a normalized estimate of the motion in the second real eigen-wave mode. The process parameter may be estimated based on a normative estimate of motion in the second real eigen-wave mode.

In accordance with other method aspects of the present invention, a plurality of real eigen-wave modes are triggered within a conduit, a plurality of motion signals representing motion in response to the triggering are received, the plurality of motion signals are processed to decompose the conduit motion into a plurality of real eigen-modal components from which process parameters may be estimated. The above-described trigger applied to the catheter may be a broadband trigger, such as a series of substantially consecutive triggers of different frequencies or a trigger formed by converting energy from a substance in the catheter by, for example, Fluid Structure Interaction (FSI).

The computer program product for estimating a process parameter of the present invention includes first computer readable program code means for processing a plurality of signals representing motion of a material-containing conduit to decompose the motion into a plurality of real normal modal components. Second computer readable program code means estimates a process parameter based on a real normal modal component of the plurality of real normal modal components. In a first embodiment, the first computer readable program code means comprises computer readable program code means for processing the plurality of motion signals to generate an output that best represents the motion component associated with the real natural wave mode of the vibrating conduit. The second computer readable program code means comprises computer readable program code means for estimating a process parameter based on the output. In another embodiment, the computer readable program code means comprises computer readable program code means for estimating real normal modal motion from the plurality of motion signals. The second computer readable program code means includes computer readable program code means for estimating a process parameter related to the substance based on the estimated real normal modal motion. Thus, improved process parameter estimates may be provided.

FIG. 1 illustrates an exemplary process parameter sensor catheter configuration;

FIG. 2 illustrates one embodiment of a process parameter sensor of the present invention;

FIG. 3 illustrates another embodiment of a process parameter sensor of the present invention;

FIG. 4 shows an exemplary embodiment of a wave mode filter of the present invention;

FIG. 5 illustrates an exemplary embodiment of a process parameter estimator of the present invention;

FIGS. 6 and 7 illustrate exemplary operations in accordance with aspects of wave mode filtering of the present invention;

8-12 illustrate the number of modes of a process parameter sensor conduit configuration;

FIG. 13 depicts another embodiment of a process parameter sensor of the present invention;

FIG. 14 illustrates an exemplary real normal modal motion estimator of the present invention

Example (c);

FIG. 15 illustrates an exemplary embodiment of a process parameter estimator of the present invention;

FIGS. 16 and 17 illustrate exemplary operations for estimating process parameters from estimated real natural modal motion, in accordance with aspects of the present invention;

fig. 18A and 18B show real natural modes triggered with broadband triggering from Fluid Structure Interaction (FSI).

The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. Those of ordinary skill in the art should appreciate that the present invention can be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the scope of the invention to those of ordinary skill in the art. In the drawings, like reference numerals refer to like parts throughout.

The following description refers, in large part, to coriolis flow meters in which, for materials such as fluid flowing through a vibrating conduit, process parameters, such as mass flow rate, of a material processing system are estimated. However, those skilled in the art will recognize that the present invention is also applicable to vibrating conduit process parameter sensors other than in-line sensors. For example, the present invention may be applied to a sampling vibrating conduit densitometer that includes a conduit configured to contain a sample of a substance drawn from a substance processing system.

In the embodiments described herein, a motion signal representing motion of a sensor catheter is processed to decompose the catheter motion into real normal modal components. The decomposition of the real normal modal scores can be performed in a number of ways. For example, a wave-mode filter may be used to pass components of the sensor conduit motion that are associated with a set of predetermined real eigenmodes while reducing components of the conduit motion that are associated with other real eigenmodes that are not supposed to be. Although the modal response corresponding to the catheter motion need not be explicitly determined, the wave-mode filtering "decomposes" the catheter motion into corresponding components associated with corresponding real eigen-modes.

Additionally, real natural modal motion, i.e., motion in a coordinate system in a multiple single degree of freedom (SDOF) system, can be unambiguously estimated from the motion signal and used to generate process parameter estimates. For example, wave mode filtering may be achieved with a two-step approach that includes using a modal transformation to transform motion of the conduit into corresponding real natural modal motion and applying a selected inverse modal transformation to the actual natural modal motion to generate a filtered output that best represents components of the conduit motion that are associated with one or more predetermined real natural wave modes. The filtered output may be processed to estimate process parameters using, for example, conventional phase difference techniques.

In accordance with another aspect of the invention, process parameters may be determined directly from the estimated real normal modal motion. For example, the real normal modal motion of a real normal wave mode that is closely related to coriolis force is normalized with respect to the real normal modal motion of another wave mode to generate a scaling factor. The scaling factor may be used to estimate mass flow.

Modal behavior of vibrating conduit

The behavior of a vibrating structure, such as a sensor conduit, is described below in terms of one or more natural wave modes having an associated natural vibration frequency. The wave modes and associated natural frequencies can be described mathematically by eigenvectors and associated eigenvalues that are unique in relative quantity rather than absolute quantity and orthogonal to the mass and stiffness of the structure. The set of linearly independent vectors described above can be used in the transformation to decompose equations that describe the motion of the structure. In particular, the response of the structure to a trigger may be represented as a superposition of proportional wave modes, the proportion representing the contribution of each wave mode to the motion of the structure. Depending on the trigger, some modes may contribute more than others. Certain wave modes are undesirable because they provide energy at the resonant frequency of the predetermined wave mode, thereby falsifying measurements taken at the resonant frequency of the predetermined wave mode, such as phase difference measurements taken at the drive frequency.

Conventional flow meters typically use structural and temporal filtering to reduce the effects of unwanted wave modes. Common structural filtration techniques include: using mechanical features such as support bars designed to cancel bending wave modes in and out of phase, actuators are used that are arranged such that they are less likely to trigger a non-corresponding wave mode, and susceptors are used that are arranged such that they are less sensitive to a non-corresponding wave mode. Structural filtering techniques are very effective at reducing the energy of unwanted wave modes, but are limited by geometric and structural limitations.

Temporal filtering techniques can generally vary the signal of a receptor according to time domain or frequency domain parameters. For example, a typical coriolis flow meter includes frequency domain filters designed to remove frequency components that are significantly correlated with undesired wave modes. However, non-resonant energy from a non-due wave mode can have a significant effect on energy generation at the predetermined wave mode resonant frequency. Since frequency domain filters are generally ineffective at distinguishing the contributions of multiple modes at a given frequency, determining the contribution of the undesired mode at a frequency is a significant source of error in the process parameter measurements.

It can be assumed that a sensor conduit with negligible attenuation and zero flow has a purely real natural or natural vibrational wave mode, i.e. in each wave mode, each point of the structure can simultaneously reach a maximum displacement. However, practical conduits with non-negligible attenuation and material flowing therethrough generally have a complex response to triggering, i.e., points on the structure generally do not simultaneously reach maximum amplitude. The motion of the catheter structure described above can be described as complex wave modes with real and imaginary components or with both magnitude and phase components. Coriolis forces exerted by the flowing material introduce this complexity into the motion of the sensor conduit.

Even complex, the motion of the catheter structure can be described as a superposition of proportional natural or "eigen" wave modes, because the real and imaginary parts of the complex wave modes are by definition linearly independent. To represent complex motions, complex proportionality coefficients are used in combining the real eigenmodes of the above components. A particular real eigen-mode may be closely related to the imaginary component of the complex mode and significantly less related to the real component of the complex mode. Thus, these particular real natural wave modes may be more closely related to the Coriolis force associated with the material in the sensor conduit, such that the particular real natural wave modes can provide information that is used to generate accurate estimates of parameters associated with the material.

As an illustrative example, a dual-elbow 3-inch coriolis flowmeter was analyzed. A theoretical model of the conduit structure of such a flowmeter is shown in fig. 1. Conventional velocity receptors 105A, 105B, 105C oriented to measure velocity in direction z are located at left, drive, and right positions on catheter assembly 10, respectively. A respective accelerometer 105D, 105E is disposed on a respective one of the conduits 103A, 103B at a location near the right susceptor and is oriented to measure lateral acceleration in direction x. The outputs of the accelerometers 105D, 105E are combined to generate lateral absolute velocity information.

A response vector x may be formed from the motion receptors 105A-E_response}：

Wherein the diagonal lateral response is a response at 45 degrees to the x and y axes. Real natural mode 'filter' matrix [ phi ]]I.e. such that the physical motion vector x_responseA real normal mode transformation matrix associated with a real normal mode motion vector η may be defined as:

{x_response}＝[Φ]{η} (2)

the real normal mode transformation matrix [ phi ] may be determined using a variety of techniques. For example, trial and error or inverse techniques may be used as described in U.S. patent application 08/890785, assigned to the assignee of the present application, filed on 11/7/1997 and U.S. patent application entitled "general modal space drive control for vibrating catheter process parameter sensors", filed on 25/2/1998, both of which are incorporated herein by reference in their entirety as if their text existed in the present document.

For the exemplary catheter structure 10 of fig. 1, a real normal modal transformation matrix can be determined experimentally:

the columns of the real number eigenmode transformation matrix [ phi ] represent, from left to right, a first out-of-phase bending wave mode, an in-phase transverse wave mode, an out-of-phase twisted wave mode, and a second out-of-phase bending wave mode, respectively.

Available mode transformation matrix [ phi ]]Will moveVector { x_responseThe physical motion represented by is decomposed into real normal modal components. For example, in the case of the modal motion vector { η }, the modal transformation matrix [ Φ ] can be obtained by multiplying both sides of equation (2) in advance by the modal transformation matrix [ Φ ]]To solve equation (2) explicitly:

{η}＝[Φ]^-1{x_response} (4)

wherein, in terms of the exemplary structure of FIG. 1

As described in detail herein, the real natural modal motions may be directly usedη) to estimate process parameters associated with one or more real eigen-wave modes of the conduit structure, such as the coriolis force-related wave mode. In addition, a mode transformation matrix [ phi ] can be used]To determine a wave-mode filter which can be applied to the physical motion x_responseTo generate a filtered physical domain response that optimally includes physical motion { x } associated with one or more modes of the conduit_responseThe component of (c). Such filtered responses may be used to estimate process parameters.

FIG. 2 illustrates an exemplary embodiment of the vibrating conduit parameter sensor 5 of the present invention. The sensor 5 comprises a catheter assembly 10. The duct assembly 10 includes an inlet flange 101, an outlet flange 101', a manifold 102, and first and second ducts 103A, 104A. The support bars 106, 106' connect the conduits 103A, 103B. An actuator 104 is connected to the conduits 103A, 103B, the actuator 104 being operable to vibrate the conduits 103A, 103B in response to the driver 20. The plurality of motion receptors 105A-E are operable to generate a plurality of motion signals indicative of motion at a plurality of locations of the catheter 103A, 103B, i.e., to generate signals indicative of displacement, velocity, or acceleration of the catheter 103A, 103B. Motion receptors 105A-E may include a plurality of devices such as coil receptors, optical or ultrasonic motion sensors, accelerometers, inertial rate sensors, and other devices. Lead 100 is connected to actuator 104 and motion receptors 105A-E.

When catheter assembly 10 is inserted into a material handling system. Material flowing in the material handling system will enter the conduit assembly 10 through the inlet flange 101. The material then flows through manifold 102 where it is introduced into conduits 103A, 103B. After exiting the conduits 103A, 103B, the material will flow back into the manifold 102 and exit the meter assembly 10 through the outlet flange 101'. The material, when flowing through the conduits 103A, 103B, induces coriolis forces that cause the conduits 103A, 103B to perturb.

Actuator 104 may drive conduits 103A, 103B in opposite directions about respective bending axes W-W and W '-W' resulting in what is commonly referred to as a first out-of-phase bending mode in conduit assembly 10. Actuator 104 may comprise any of a variety of well-known devices, such as a linear actuator comprising a magnet mounted to first conduit 103A and an opposing coil mounted to second conduit 103B. An alternating current caused by the driver 20 by a drive signal provided by the drive wire 110 passes through the coil to generate a mechanical force that vibrates the conduits 103A, 103B. The trigger provided by actuator 104 is substantially coherent, e.g., limited to a narrow frequency range or broadband, as described in detail below.

Although the parameter sensor 5 shown in FIG. 2 is shown as including an integral actuator 104, one of ordinary skill in the art will recognize that other techniques may be used to vibrate the conduits 103A, 103B of the present invention. For example, a power source such as a pump or compressor may be used to create a broad band trigger on the exterior of conduit assembly 10 and to transmit such trigger to conduit assembly 10, for example, via one of flanges 101, 101'. Similarly, as described in detail below, broadband triggering may also be created by transferring energy from the substance in the conduits 103A, 103B with a Fluid Structure Interaction (FSI) mechanism.

A real normal modal resolver 30 is responsive to the motion sensors 105A-E and is operable to resolve the motion of the conduits 103A, 103B represented by the signal on the wire 111 into a plurality of real normal modal components 35. The process parameter estimator 40 is responsive to the real normal mode decomposer 30 and operates to generate an estimate 45 of the process parameter from the plurality of real normal mode components 35. As described herein, the real normal modal decomposer 30 decomposes the catheter motion in a variety of ways, such as wave-mode filtering the catheter motion or estimating the real normal modal motion corresponding to the catheter motion.

Wave mode filtration

In accordance with one aspect of the invention, a "wave mode filter" may be used with the motion signal to generate a filtered version of the output indicative of catheter motion, wherein components of catheter motion associated with undesired wave modes are reduced. The wave mode filter represents a product of a real normal modal transformation that maps conduit motion to motion in a multiple single degree of freedom (SDOF) system, i.e., real normal modal motion, and a selected inverse real normal modal transformation that maps a selected portion of the real normal modal motion, i.e., motion in a set of predetermined real normal wave modes, back to the physical domain.

Using a selected inverse real eigenmode transformation matrix [ phi ]]Converting real normal modal motion vector { η } into a filtered motion vector { x }_filteredIn which components associated with unwanted real eigenmodes can be eliminated:

{x_filtered}＝[Φ^*]{η} (6)

with the exemplary structure of FIG. 1, the matrix [ Φ ] may be transformed according to the real eigenmodes]Transformation of matrix phi by replacing real number eigenmodes]Wherein elements associated with the non-real solid-state wave mode with zero are used to construct a selected inverse real-mode eigenmode transformation matrix [ phi ]^*]：

By transforming the matrix [ phi ] with the real number with zero as shown in equations (6) and (7)]Corresponding selected inverse real number eigenmode transformation matrix [ phi ]^*]To replace the natural mode transformation matrix [ phi ]]The elements associated with the non-real solid-state wave mode with zero can eliminate the motion vector { x } of the conduit corresponding to the non-real natural mode_responseThe component of (c). However, it will be appreciated by those skilled in the art that a selected inverse real eigenmode transformation matrix [ phi ] may be used^*]The non-zero value of the above element table to eliminate said component.

Combining equations (4) and (6):

{x_filtered}＝[Φ^*][Φ]^-1{x_response}＝[ψ]{x_response}

(8)

wherein the wave mode filter matrix [ ψ ] is given by:

[ψ]＝[Φ^*][Φ]^-1 (9)

wave mode filter matrix psi]For catheter motion vector { x_responseIs processed so that the filtered output motion vector x_filteredOptimally representing the catheter motion vector x_responseThe components of the wave associated with one or more predetermined modes. Wave mode filter matrix psi]Can also be generated by:

[ψ]＝[Φ][A][Φ]^-1

where [ a ] is a matrix whose elements other than the diagonal are zero, and the diagonal element corresponding to a predetermined wave mode is set to 1, for example,

for filtered output { x_filteredProcessing to generate accurate estimates of process parameters such as mass flow. For example, the filtered output { x ] may be measured according to conventional phase or time difference Coriolis measurement techniques_filteredAnd (6) processing. In the case of the exemplary system shown in FIG. 1, this is done by: such as by determining the phase difference between components of the filtered output corresponding to the right and left susceptors 105A, 105C using zero crossings such as described in U.S. patent RE31450 to Smith, U.S. patent 4879911 to Zolock, and U.S. patent 5231884 to Zolock, or similar phase or time difference techniques using a Digital Signal Processor (DSP) or similar digital computing device. Thus, the information provided by the additional susceptors 105B, 105D, 105E may be used to filter out components of the catheter motion that are associated with, for example, unwanted transverse wave modes.

The number of positions on the sensor catheter represented by the motion signal may be intentionally chosen to exceed the number of real normal modal components into which the catheter motion is decomposed. In this case, the real normal mode transformation matrix and the selected inverse real normal mode transformation matrix have more rows than columns. Therefore, the general inverse of the real eigenmode transformation matrix is used in the calculation of the wave-mode filter matrix of equation (9). In this way, the motion signal provides an overdetermined source of information to decompose the catheter motion into a given number of real eigen-wave modes. Thus, process parameters estimated from such over-determined information may be spatially integrated to provide potentially more accurate estimates. The above-described spatial integration is described in U.S. patent application entitled "improved vibrating conduit parameter sensor and method of operation with spatial integration", assigned to the assignee of the present application and filed concurrently herewith.

Fig. 3 shows an exemplary parameter sensor 5 that implements the wave mode filtering of the present invention. Real normal mode decomposer 30 includes a wave mode filter 330 responsive to motion receptors 105A-E. Wave mode filter 30 may decompose the motion of conduits 103A, 103B represented by the motion signals generated by susceptors 105A-E into a plurality of real eigenmode components by generating a filtered output 35, filtered output 35 optimally representing one or more components of the motion of conduits 103A, 103B associated with one or more of a plurality of real eigenmode modes, such as real eigenmode associated with coriolis forces exerted by matter contained in conduits 103A, 103B.

Fig. 4 illustrates an exemplary embodiment of the wave mode filter 330 and the process parameter estimator 40. A sampler 432, such as a sample and hold or similar circuit, provides means for receiving the motion signal 431 of the motion receptor, sampling the motion signal 431 and generating samples 433 therefrom for later conversion by an analog-to-digital converter (a/D)434 into digital signal values 435. The detailed operation of sampler 433 and a/D434 may be performed by a variety of circuits known to those of ordinary skill in the art and need not be described in further detail herein. One of ordinary skill in the art will recognize that motion signal 431 may be processed in a variety of ways. For example, antialiasing filtering, post-sampling filtering, and similar signal processing may be used. It will also be appreciated that in general the receiving and converting means shown in figure 3 may be implemented in dedicated hardware, firmware or software running on dedicated or general purpose data processing means or a combination thereof. For example, sampling and analog-to-digital conversion functions may be included within susceptors 105A-E.

The wave mode filter 330 portion may be included within a computer 50, such as a microprocessor, microcontroller, Digital Signal Processor (DSP), or similar device. The computer 50 may, for example, comprise a pipelined DSP specifically adapted for linear algebraic calculations, such as the TMS320C4X series of DSPs sold by Texas instruments. With the computer 50 configured with suitable program code, e.g., software and/or firmware, and data stored, e.g., in a storage medium 60 such as Random Access Memory (RAM), electrically erasable programmable read-only memory (EEPROM), magnetic disk, or the like, the computer 50 may provide means 436 for generating motion vectors 437 representing sensor catheter motion from the digital values 435. The wave mode filter 330 includes means 438 for multiplying the motion vector 437 by a wave mode filter matrix to generate a filtered motion vector 35 that best represents the component of the catheter motion vector that is associated with one or more predetermined wave modes.

The process parameter estimator 40 may also be implemented in the computer 50. The process parameter estimator 40 may calculate an estimate 45 of the process parameter, such as an estimated mass flow rate, from the filtered motion vector 35, such as by being implemented as software or firmware running on the computer 50. For example, as shown in FIG. 5, the process parameter estimator 40 may include means 542 for determining a phase difference between components of the filtered output 35 and means 544 for estimating a mass flow rate based on the determined phase difference.

FIG. 6 illustrates operations 600 for estimating process parameters in accordance with the wave mode filtering aspect of the present invention. A plurality of motion signals may be received that represent motion at a plurality of locations of a vibrating conduit containing a substance from a substance processing system (block 610). The received signals are processed to decompose the motion of the conduit into motion in a plurality of real eigen-wave modes by generating an output that best represents a component of the conduit motion that is associated with the real eigen-wave modes that are best associated with Coriolis forces applied by matter passing through the conduit (block 620). Process parameters are estimated based on the outputs (block 630).

FIG. 7 illustrates operations 700 for estimating process parameters in accordance with another wave-mode filtering aspect of the present invention. The motion signal is received (block 710) and processed to generate a motion vector representing the motion of the sensor catheter (block 720). The motion vector is multiplied by the selected inverse real eigenmode transformation matrix to generate a filtered motion vector that best represents the components of the motion vector that are associated with one or more real eigenmode modes (block 730). Process parameters are estimated from the filtered motion vectors (block 740).

It will be recognized that blocks and combinations of blocks shown in fig. 6 and 7 can be implemented by program instructions and/or data executing on a computer or data processor, such as the computer shown in fig. 4. As used herein, computer readable program code includes, but is not limited to, content such as operating system commands (e.g., object code), high-level language instructions, etc., and data that may be read, accessed or otherwise used in conjunction with the above-described program instructions.

The program code may be loaded into a computer or similar data processing device, including, but not limited to, a microprocessor, microcontroller, Digital Signal Processor (DSP), or the like. The combination of the program code and the computer may provide an apparatus operable to perform the functions specified in the flowchart block or blocks. Similarly, the program code may be loaded into a computer or data processing apparatus, and the program code and computer may provide means for implementing the functions specified in the block in the flowchart.

The program code may also be stored in a computer readable storage medium such as a magnetic disk or tape, bubble memory, programmable memory such as electrically erasable programmable read-only memory (EEPROM), or the like. The stored program code may cause a computer accessing the storage medium to function, and thus, the program code stored in the storage medium constitutes an article of manufacture including program code means for implementing the function specified in the flowchart block or blocks. The program code may also be loaded onto a computer to perform a series of operational steps to thereby execute a process, and thus, the program code may provide steps for implementing the functions specified in the flowchart block or blocks in conjunction with the computer. Accordingly, blocks of the flowchart support apparatus operable to perform the specified functions, combinations of means for performing the specified functions, combinations of steps for performing the specified functions and computer readable program code means embodied in a computer readable storage medium for performing the specified functions.

It will also be recognized that, in general, each block of the flowchart, and combinations of blocks in the flowchart, can be implemented by special purpose hardware, software or firmware executed on a general purpose computer, or combinations thereof. For example, the functions of the blocks of the flow diagrams may be implemented in an Application Specific Integrated Circuit (ASIC), a programmable gate array or similar special purpose device, or by program instructions and data loaded into and executed by a microprocessor, microcontroller, DSP or other general purpose computing device.

Estimating process parameters from estimated modal motion

In accordance with another aspect of the invention, a process parameter, such as mass flow, may be estimated directly from an estimate of estimated real natural modal motion, i.e., motion from a sensor conduit type that includes a multiple single degree of freedom (SDOF) system. As described above, the complex mode can be represented as a superposition of real eigenmodes scaled by a complex scaling factor:

{Φ_complex}＝[Φ]{α} (10)

wherein, { Φ_complexIs the complex wave mode vector. [ phi ] of]Is for the complex wave mode vector { phi_complexThe matrix of real eigen-mode vectors is constructed, { α } is a vector of normal complex proportionality coefficients.

In a coriolis flowmeter, the motion of a sensor conduit is complex using coriolis accelerations associated with fluid flowing in the sensor conduit. Thus, the proportionality coefficient for the imaginary part of the complex flow wave mode is proportional to the flow velocity and can be provided for determiningInformation on the constant flow rate. However, the number of { α } would be affected by the absolute number of real normal modal motions, which as noted above may be arbitrary. FIGS. 8 and 10 show the real component (Re [ alpha 1 ]) of the proportionality coefficient alpha 1])_m1、(Re[α1])_m2With the real component l corresponding to the first out-of-phase bending wave mode at the respective first and second absolute modal numbers m1, m2, fig. 9 and 11 show the imaginary component of the proportionality coefficient α 2 (lm α 2) for the 3-inch dual tube coriolis flowmeter shown in fig. 1])_m1、(lm[α2])_m2The imaginary component corresponds to a first output phase twist wave mode over a range of mass flow rates at mode numbers m1, m 2. As can be seen in FIGS. 8 and 10, the real component (Re [ α 1 ]) for the first scaling factor α 1])_m1、(Re[α1])_m2Generally independent of flow rate, while FIGS. 9 and 11 show the imaginary component (lm [ α 2 ]) of the second scaling factor α 2])_m1、(lm[α2])_m2Is related to the flow rate in a substantially linear manner. However, the real number component (Re [ α 1 ]) of the first scale factor α 1])_m1、(Re[α1])_m2And an imaginary component (lm [ α 2 ]) of the second scaling factor α 2])_m1、(lm[α2])_m2Are related to the absolute modal number.

One aspect of the present invention stems from the fact that: since the relative number of real eigenmodes representing complex motions is constant (assuming no structural changes), the imaginary component lm [ α 2 ] of α 2 can be reduced by making the imaginary component lm [ α 2 ] constant]Real number component Re [ alpha 1 ] to alpha 1]Normalized, a flow measurement based on the distortion mode scaling factor α 2 insensitive to the number of absolute modes can be performed. As shown in FIG. 12, the imaginary component (lm [ α 2 ]) of FIG. 9 is used])_m2Relative real component of the curve (Re [ alpha ] 1)])_m2The normalization results in the formation of an imaginary component (lm [ alpha 2 ]) for normalization])_{m2，normalized}Substantially identical to the curve for the imaginary component (lm [ α 2 ]])_m1The curves of (a) are the same, thus illustrating that the normalized imaginary component of α 2 is generally insensitive to the absolute number of wave modes.

For the exemplary 3-inch Coriolis sensor described above, the pass-throughBy determining the normalized imaginary component of the first out-of-phase twist mode scaling factor and dividing by the known flow rate, the flow rate calibration factor K can be determined for the known flow rate_cal：

To determine the unknown mass flow rate, rate_knownDetermining a normalized imaginary component of the first out-of-phase distortion mode scaling factor corresponding to the unknown flow rate and multiplying the component by a calibration factor K_cal：

Shifting the term to equation (10):

{α}＝[Φ]^-1{Φ_complex} (13)

the form of equation (13) is similar to that of equation (4). By analogy, the catheter motion vector corresponds to a single-mode complex motion vector, and the scale coefficient vector corresponds to a real normal mode motion vector. Thus, by determining the ratio of the modal responses estimated for the conduit twist and bending wave modes, the mass flow rate for an exemplary 3-inch coriolis sensor can be estimated.

The above techniques may be generalized. Higher order estimates may be achieved, for example, by using a combination of scaling factors for the Coriolis force-related modes that are normalized with respect to one or more scaling factors associated with such modes, which are associated with the triggering of the sensor conduit. For the exemplary bent-tube 3-inch coriolis meter, the coefficients associated with the higher-order twist and bending wave modes, respectively, are used.

The above techniques may also be applied to different catheter configurations. The bending and twisting wave modes described with respect to the exemplary 3-inch dual tube coriolis sensor may be generally divided into symmetrical and asymmetrical wave modes, respectively. In general, by defining a plane of symmetry perpendicular to the flow axis of the sensor conduit, a symmetric wave mode can mean a wave mode in which motion on a first face of the plane of symmetry can be reflected by motion on a second face of the plane of symmetry. For example, the bending wave modes of the U-shaped Coriolis sensor conduit of FIG. 1 are symmetrical with respect to the y-z plane shown. An asymmetric wave mode then denotes a wave mode in which a motion on a first face of the plane of symmetry represents a reflection and a phase rotation of the motion on a second face of the plane of symmetry. For example, the twisted wave mode of the U-shaped sensor conduit of FIG. 1 is asymmetric with respect to the y-z plane of FIG. 1. Straight tube software has similar symmetric and asymmetric wave modes. The invention may therefore also be extended to parameter sensors using one or more straight tubes, and, more generally, sensors using a variety of catheter configurations.

As above with respect to wave mode filtering, the number of locations on the sensor catheter may be selected to exceed the number of real normal modal motion estimation aspects. This means that the real number eigenmode transformation matrix [ 2 ]Φ]With more rows than columns. To estimate the real natural modal motion [ eta ]]Using a real number eigenmode transformation matrix [ phi ]]General inverse of (1) ([ phi ]]⁺Namely:

{η}＝[Φ]+{x_response} (14)

thus, by spatially integrating the final estimate of real natural mode motion, the motion signal can provide an over-determined source of information to map catheter motion { x }_responseDecomposed into real normal modal motion eta.

Fig. 13 shows an exemplary parameter sensor 5 for process parameter estimation directly from real normal modal motion. The real normal mode decomposer 30 includes a real normal mode motion estimator 1130 responsive to motion signals generated by the plurality of motion receptors 105A-E. The real normal modal motion estimator 1130 resolves the motion of the conduits 103A, 103B represented by the aforementioned motion by producing an estimate of the real normal modal motion 35. The process parameter estimator 40 generates estimated process parameters 45 based on the estimated real natural modal motions 35.

Fig. 14 shows an exemplary embodiment of the real normal modal motion estimator 1330. The real normal modal motion estimator 1330 may be included in a computer 50, such as a microprocessor, microcontroller, Digital Signal Processor (DSP), or similar device. For example, the computer 50 may comprise a pipelined DSP specifically adapted for linear algebraic calculations, such as one of the DSPs in the TMS320C4X series sold by Texas instruments. The computer 50 is configured with suitable program code, e.g., software and/or firmware, and data, e.g., stored in a storage medium 60 such as Random Access Memory (RAM), Electrically Erasable Programmable Read Only Memory (EEPROM), magnetic disk, or the like, and the computer 50 may provide means 1438 for multiplying the motion vectors 437 by a modal transformation matrix to generate the estimated real natural modal motion vectors 35. The process parameter estimator 40 may also be implemented within the computer 50. By way of example and implementation as software or firmware running on the computer 50, the process parameter estimator 40 may calculate an estimate 45 of a process parameter, such as a mass flow rate, based on the estimated real normal modal motion vectors 35.

As shown in fig. 15, the real normal modal motion estimator 1330 may include means 1532 for generating an estimate 1533 of motion in the first real normal mode and means 1534 for generating an estimate 1535 of motion in the second real normal mode. For example, with a dual U-tube flow meter such as that shown in FIG. 1, the first and second wave modes may correspond to the first out-of-phase bending wave mode and the first out-of-phase twisting wave mode, respectively, described above. The process parameter estimator 40 may include means 1542 for normalizing the second real normal modal motion 1535 with respect to the first real normal modal motion 1533 to generate a normalized estimate 1543 of motion in the second real normal mode. The means for estimating 1544 may be responsive to the normalizing means 1542 for generating the estimated process parameter 45 based on the normalized estimate 1543. As shown, the estimated modal responses 1533, 1535 may be fed back to the driver 28 for selectively triggering one or more selected real natural wave modes, as described in the aforementioned patent application "general modal space drive control for vibrating conduit process parameter sensors".

FIG. 16 illustrates operations 1600 for estimating process parameters in accordance with an aspect of the subject invention. A plurality of motion signals representative of motion of the sensor conduit is received (block 1610). The motion signal is processed to decompose the catheter motion into a plurality of real eigen-wave modes by estimating motion in the plurality of real eigen-wave modes (block 1620). Process parameters are estimated based on the estimated real normal modal motion (block 1630).

FIG. 17 illustrates operations 1700 for estimating process parameters in accordance with another aspect of the invention. A plurality of motion signals representative of motion of the sensor catheter are received (block 1710) and a motion vector is generated therefrom (block 1720). The motion vectors are multiplied by a modal transformation matrix to generate a real normal modal motion vector that represents real normal modal motion corresponding to the catheter motion (block 1730). The component of the real normal modal motion vector corresponding to the first mode, e.g., the mode associated with the coriolis force applied by the material in the sensor conduit, is normalized against the component of the real normal modal motion vector corresponding to the second mode, e.g., the mode substantially not associated with the coriolis force, such as the drive mode (block 1740). A process parameter, such as mass flow, is estimated based on the normalized component of the estimated wave mode response (block 1750).

It will be recognized that blocks and combinations of blocks shown in fig. 16 and 17 can be implemented by program instructions and/or data executing on a computer or data processor, such as the computer shown in fig. 14. As used herein, computer readable program code includes, but is not limited to, content such as operating system commands (e.g., object code), high-level language instructions, etc., and data that may be read, accessed or otherwise used in conjunction with the above-described program instructions.

The program code may be loaded into a computer or similar data processing device, including, but not limited to, a microprocessor, microcontroller, Digital Signal Processor (DSP), or the like. The combination of the program code and the computer may provide an apparatus operable to perform the functions specified in the flowchart block or blocks. Similarly, the program code may be loaded into a computer or data processing apparatus, and the program code and computer may provide means for implementing the functions specified in the flowchart block or blocks.

The program code may also be stored in a computer readable storage medium such as a magnetic disk or tape, bubble memory, programmable memory such as electrically erasable programmable read-only memory (EEPROM), or the like. The stored program code may cause a computer accessing the storage medium to function, and thus, the program code stored in the storage medium constitutes an article of manufacture including program code means for implementing the function specified in the flowchart block or blocks. The program code may also be loaded onto a computer to perform a series of operational steps to thereby implement a process, and thus, the program code may provide steps for implementing the functions specified in the flowchart block or blocks in conjunction with the computer. Accordingly, blocks of the flowchart support apparatus operable to perform the specified functions, combinations of means for performing the specified functions, combinations of steps for performing the specified functions and computer readable program code means embodied in a computer readable storage medium for performing the specified functions.

It will also be recognized that, in general, each block of the flowchart, and combinations of blocks in the flowchart, can be implemented by special purpose hardware, software or firmware executed on a general purpose computer, or combinations thereof. For example, the functions of the blocks of the flow diagrams may be implemented in an Application Specific Integrated Circuit (ASIC), a programmable gate array or similar special purpose device, or by program instructions and data loaded into and executed by a microprocessor, microcontroller, DSP or other general purpose computing device.

Broadband triggering

The real eigenmode decomposition of the present invention may use wideband triggering. In fact, wideband triggering is desirable because triggering a predetermined and unwarranted real eigenmode provides more complete information to identify a predetermined real modal response and generate accurate parameter estimates therefrom. The broadband trigger may include, but is not limited to, a random or frequency sweep trigger. The frequency sweep trigger may be provided by one or more actuators operatively associated with the sensor conduit, for example by causing a series of substantially consecutive triggers to act on the sensor conduit at different frequencies. The random scan trigger may be applied to the catheter by one or more actuators using, for example, a broadband actuator drive signal or a pulse of predetermined duration. Broadband triggering may also be provided by random environmental forces acting on the sensor conduit, for example by converting energy from a substance contained in the sensor conduit, such as Fluid Structure Interaction (FSI), or by vibrations otherwise imparted to the conduit structure from a pump, compressor, or similar device.

The efficacy of broadband triggering with external triggering such as that provided by FSI has been studied with dual tube CFM300 coriolis flowmeters produced by Micro Motion, Inc operating in a passive manner, i.e., without triggering from the starter. Fig. 18A and 18B show the amplitude at frequencies corresponding to the real natural wave modes of the sensor at 200 pounds per minute and 600 pounds per minute mass flow rates, respectively. As can be seen from these figures, the amplitudes at the frequencies corresponding to the first and second out-of-phase torsional wave modes 1801A, 1801B, 1802A, 1802B are a function of mass flow, thus illustrating that an external broadband trigger may provide information for real natural modal decomposition of conduit motion to determine process parameters such as mass flow in accordance with real natural modal decomposition techniques such as those detailed above.

The ability to use broadband triggering provided by an external vibration source, such as an FSI, allows for the construction of a "passive" vibrating conduit sensor, i.e., a sensor that does not include an actuator. Such passive sensors are particularly advantageous in energy-limited applications or in applications where driving energy is a safety concern, such as in explosive or flammable environments.

Conclusion

As described herein, an estimate of a process parameter may be generated with a real eigenmodal decomposition of the sensor catheter's response to a trigger. The catheter response is decomposed into real eigenmode components, such as motion in a plurality of real eigenmodes or components of the catheter motion associated with such real eigenmodes. The real normal modal components are then used to generate estimates of process parameters such as mass flow, density, viscosity, etc.

Because the conduit response is decomposed into real natural components, effects from sources such as pump vibrations and fluid disturbances may be filtered out by ignoring, eliminating, reducing, or otherwise filtering out real natural modal components that are not associated with coriolis forces. In this way, parameter estimates may be obtained that may be more accurate than estimates obtained using conventional techniques.

Furthermore, because the sensor of the present invention can distinguish between wave modes, no single mode or near single mode triggering is required. In fact, the sensor catheter may be triggered with only environmental triggers. Thus, it is possible to construct "passive" parameter sensors, i.e. sensors comprising only motion sensors but no actuators, which are of particular advantage in explosive environments or in applications where energy consumption is an important consideration.

The real eigenmode decomposition of the present invention can be used to improve the efficiency of typical parameter sensors. For example, a typical curved tube coriolis flowmeter may be improved by providing additional motion receptors that generate motion signals that can be processed with a wave-mode filter to provide a modally filtered signal for use in typical phase difference coriolis measurements. Conventional flowmeters can also be updated, for example, by replacing conventional coriolis measurement electronics with DSP-based sensor electronics that can implement a real natural modal motion estimator and a process parameter estimator that can directly calculate mass flow or other process parameters based on the estimated real natural response. In addition to conventional straight and curved tube sensors, the modal decomposition used in the present invention is also optimal in sensors with unusual, e.g., asymmetric or unbalanced, conduit geometries.

One of ordinary skill in the art will recognize that the techniques of the present invention may be combined with other techniques to form improved process parameter techniques. For example, spatial filtering provided by the real natural modal decomposition techniques described herein may be combined with frequency domain filtering to achieve spatio-temporal filtering. Since the present invention is suitable for linear algebraic calculations, spatial integration may be provided along with the present invention by generating a motion signal that can provide information for a number of positions that exceed the number of real eigenmodal components into which catheter motion is decomposed. Thus, an over-determined source of information may be provided to decompose the catheter motion into a given number of real natural modes, as described in the above-identified U.S. patent application "improved vibrating catheter parameter sensor and method of operation using spatial integration".

The figures and description of the invention disclose embodiments of the invention. Although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation. Those of ordinary skill in the art may make, use or sell other embodiments that achieve, verbatim or content equivalent, within the scope of the appended claims.

Claims (46)

1. A device (5) for estimating a process parameter (45) of a substance flowing through a conduit (103A-103B) vibrated by a driver (104), wherein said process parameter is estimated from a plurality of motion signals indicative of motion of said conduit, said motion signals being generated by a plurality of motion receptors (105A-105D) fixed to said conduit, the device (5) characterized by:

a real natural modal decomposer (30) receiving said plurality of motion signals from a plurality of motion receptors (105A-105D) associated with the conduits (103A-103B) and processing said plurality of motion signals to decompose motion represented by said plurality of motion signals into a plurality of real natural modal components (35); and

a process parameter estimator (40) responsive to the generation of said plurality of real normal modal components (35) and estimating a process parameter (45) from one of said plurality of real normal modal components (35).

2. The apparatus (5) of claim 1, wherein the real normal mode decomposer (30) comprises a wave mode filter (330) operable to generate an output from the plurality of motion signals that best represents a motion component associated with a real normal mode of the conduit (103A-103B); and

the process parameter estimator (40) is responsive to the output generated by the wave mode filter and estimates a process parameter based on the output.

3. The apparatus (5) of claim 2, wherein the wave mode filter (330) operates to optimally pass components of conduit motion associated with real eigen-modes.

4. The apparatus (5) of claim 2, wherein the wave-mode filter (330) represents a product of a real normal modal transformation mapping motion in a physical domain to motion in a plurality of single degree of freedom (SDOF) systems and a selected inverse real normal modal transformation mapping motion in a predetermined set of the plurality of single degree of freedom systems to motion in the physical domain.

5. The apparatus of claim 2, wherein the wave mode filter (330) is operative to generate an output preferentially representing a component of conduit motion associated with a real eigen-wave mode that is optimally associated with a coriolis force associated with the material in the conduit.

6. The apparatus (5) of claim 2, wherein said process parameter estimator (40) comprises a mass flow estimator (544).

7. An apparatus (5) as claimed in claim 2, characterized in that the apparatus further comprises means (436) for processing the received motion signals to generate motion vectors (437), and in that the wave-mode filter comprises means (438) for multiplying the motion vectors by a wave-mode filter matrix to generate a filtered motion vector.

8. The apparatus (5) of claim 2, characterized in that:

the wave mode filter (330) operating to represent a first filtered signal representative of motion at a first location of the conduit (103A-103B) and a second filtered signal representative of motion at a second location of the conduit (103A-103B); and

the process parameter estimator (40) comprises:

means (542) for determining a phase difference between the first filtered signal and the second filtered signal; and

means (544) responsive to the determination of the phase difference for estimating the mass flow rate based on the determined phase difference.

9. The apparatus (5) of claim 1, characterized in that:

said real normal modal decomposer (30) comprises a real normal modal motion estimator (1330) operable to estimate real normal modal motion from the received plurality of motion signals; and

the process parameter estimator (40) is operable to estimate the process parameter (35) based on the estimated real normal modal motion.

10. The apparatus (5) of claim 9, wherein the real normal modal motion estimator (1330) is operable to apply a real normal modal transformation to the received plurality of motion signals to generate the estimate of real normal modal motion.

11. The apparatus (5) of claim 9, wherein:

the real normal modal motion estimator (1330) comprises:

means (436) for generating a motion vector; and

means (1438) for multiplying the motion vector with a real normal modal transformation to generate a real normal modal motion vector; and

the process parameter estimator (40) comprises means for estimating process parameters (35) based on the real normal modal motion vectors.

12. The apparatus (5) of claim 9, wherein:

said real eigenmode motion estimator (1330) operable to estimate motion in a plurality of real eigenmode modes; and

the process parameter estimator (40) is operable to estimate process parameters based on estimated motion for a subset of the plurality of real natural wave modes.

13. The apparatus (5) of claim 12, wherein:

the real normal modal motion estimator (1330) comprises:

means (1532) for estimating motion in a first real natural wave mode; and

means (1534) for estimating motion in a second real eigen-wave mode that is optimally related to coriolis forces; and

the process parameter estimator (40) comprises:

means (1542) for normalizing the estimated motion in the second real eigenmode relative to the estimated motion in the first real eigenmode to produce a normalized estimate of the motion in the second real eigenmode; and

means (1544) for estimating a process parameter based on the normalized estimate of motion in the second real normal mode.

14. An apparatus (5) according to claim 13, characterized in that said means (1542) for normalizing comprises means for normalizing the imaginary component of the motion in the second estimated real eigenmode with respect to the real component of the motion in the first estimated real eigenmode.

15. The apparatus (5) of claim 14, wherein said means (1544) for estimating motion in a first real eigen-wave mode comprises means for estimating motion in a real eigen-wave mode that is optimally related to a trigger applied to said catheter.

16. The apparatus (5) of claim 13, wherein the process parameter estimator (40) includes means for estimating the process parameter based on a normalized estimate of motion in the second real normal mode, a known mass flow rate, and a predetermined normalized estimate of motion in the second real normal mode with the known mass flow rate.

17. An apparatus (5) as claimed in claim 16, characterized in that the process parameter estimator (40) comprises means for estimating the mass flow.

18. The apparatus (5) of claim 13, wherein:

the means (1532) for estimating motion in a first real eigen-wave mode comprises means for estimating motion in a symmetric-wave mode;

said means (1534) for estimating motion in a second real eigen-wave mode comprises means for estimating motion in an asymmetric-wave mode;

said means (1542) for normalizing comprises means for determining a ratio of an imaginary component of the estimated motion in said asymmetric mode to a real component of the estimated motion in said symmetric mode; and

the means (1544) for estimating a process parameter based on a normalized estimate of motion in a second real normal mode includes means for estimating a process parameter based on the determined ratio.

19. An apparatus (5) as claimed in claim 18, characterized in that the means (1544) for determining the process parameter on the basis of the above-determined ratio comprise means for estimating the process parameter on the basis of the determined ratio, a known mass flow and a predetermined ratio corresponding to the known mass flow.

20. An apparatus (5) as claimed in claim 19, characterized in that the means for estimating the process parameter on the basis of the aforementioned determined ratio comprise means for estimating the mass flow.

21. The apparatus of claim 1 wherein said plurality of motion signals represent an over-determined information source for decomposing motion of said catheter into said plurality of real normal modal components.

22. A method (600) of estimating a process parameter (45) of a substance flowing through a conduit vibrated by a driver affixed to the conduit from a plurality of motion signals generated by a plurality of motion receptors affixed to the conduit, the method characterized by the steps of:

receiving (620) the plurality of motion signals from a plurality of motion receptors (105A-105E) associated with a vibrating conduit (103A-103B) comprising a substance, the signals representing motion at a plurality of locations of the vibrating conduit;

processing (630) the received plurality of motion signals to decompose the motion into a plurality of real normal modal components;

a process parameter is estimated (640) from one of the plurality of real normal modal components.

23. The method (600) of claim 22,

the processing step (630) comprises the steps of: processing the motion signal to generate an output that best represents a component of motion associated with a real natural wave mode of the vibrating conduit; and

said step (640) for estimating comprises the steps of: process parameters are estimated from the outputs.

24. The method (600) of claim 23, wherein said processing step (630) comprises the steps of: a wave mode filter (330) is applied to the plurality of motion signals.

25. The method (600) of claim 24, wherein the wave-mode filter (330) represents a product of a real normal modal transformation mapping motion in a physical domain to motion in a multiple single degree of freedom (SDOF) system and a selected inverse real normal modal transformation mapping motion in a selected set of the multiple single degree of freedom systems to motion in the physical domain.

26. The method of claim 24, wherein said processing step (620) comprises the steps of: an output is generated that best represents the component of the motion of the conduit that is associated with the real natural wave mode, which is then best associated with the coriolis force.

27. The method (600) of claim 24, wherein said estimating step (630) includes the step of estimating a mass flow.

28. The method (600) of claim 24, wherein said processing step (610) comprises the steps of:

processing (720) the received plurality of motion signals to generate motion vectors; and

the motion vector is multiplied 730 by a wave-mode filter matrix to generate a filtered motion vector.

29. The method of claim 24, wherein:

the processing step (620) comprises the steps of: generating a first filtered signal representative of motion at a first location of the conduit and a second filtered signal representative of motion at a second location of the conduit; and

the estimating step (630) comprises the steps of:

determining a phase difference between the first filtered signal and a second filtered signal; and

the mass flow is estimated from the determined phase difference.

30. The method (600) of claim 23, wherein:

the processing step (620) comprises the step (1620) of: estimating real normal modal motion from the received plurality of motion signals; and

the step of estimating process parameters (630) comprises the step of (1630): process parameters associated with the aforementioned species are estimated from the estimated real natural modal motion.

31. The method (600) of claim 30, wherein said step of estimating real normal modal motion (1620) comprises the steps of: a real normal modal transformation is applied to the received plurality of motion signals to generate an estimate of the real normal modal motion.

32. The method (600) of claim 31, wherein:

the step of estimating real normal modal motion (1620) comprises the steps of:

generating (1720) a motion vector from the plurality of motion signals; and

multiplying (1730) the motion vector by a real normal modal transformation matrix to generate a real normal modal motion vector; and

the step of estimating a process parameter (1630) includes the step of (1750): process parameters are estimated from the real normal modal motion vectors.

33. The method (600) of claim 30, wherein:

the step of estimating real normal modal motion (1620) comprises: estimating real normal modal motion for a plurality of real normal modes; and

the step of estimating process parameters (1630) includes: estimating a process parameter based on the estimated real normal modal motion of a subset of the plurality of real normal modes.

34. The method (600) of claim 33, wherein:

the step of estimating real normal modal motion (1620) comprises the steps of:

estimating motion in a first real natural wave mode; and

estimating motion in a second real normal mode that is optimally related to coriolis forces; and

the step of estimating process parameters (1630) includes the steps of:

normalizing (1740) the estimated motion in the second real eigen-mode relative to the estimated motion in the first real eigen-mode to generate a normalized estimate of the motion in the second real eigen-mode; and

a process parameter is estimated (1750) from the normalized estimate of motion in the second real normal mode.

35. The method (600) of claim 34, wherein said step of normalizing (1740) comprises the steps of: normalizing the imaginary component of the motion in the second real eigenmode relative to the real component of the motion in the first real eigenmode.

36. The method (600) of claim 34,

said step of receiving a plurality of motion signals (610) comprises the steps of: receiving the plurality of motion signals and simultaneously causing a trigger to act on the catheter;

said step (630) for estimating the motion in the first real natural wave mode comprises the steps of: motion is estimated in a real natural wave mode that is optimally related to the trigger applied to the catheter.

37. A method according to claim 34, characterized in that said step of estimating process parameters (630) comprises the step of (1750): the process parameter is estimated based on the normalized estimate of motion in the second real normal mode, the known mass flow rate, and the predetermined normalized estimate of motion in the second real normal mode with the known mass flow rate.

38. The method of claim 37 wherein said step of estimating a process parameter comprises the step of estimating a mass flow rate.

39. The method (600) of claim 34, wherein:

said step of estimating motion in a first real eigen-mode comprises the step of estimating motion in a symmetric mode;

said step of estimating motion in a second real eigen-mode comprises the step of estimating motion in an asymmetric wave mode;

the step of normalizing (1740) comprises the steps of: determining a ratio of an imaginary component of the estimated motion in the asymmetric wave mode to a real component of the estimated motion in the symmetric wave mode; and

said step (1750) of estimating a process parameter from a normalized estimate of motion in a second real eigen-wave mode comprises the steps of: the process parameter is estimated based on the ratio determined above.

40. The method (600) of claim 39, wherein the step of estimating process parameters (630) comprises the steps of: a process parameter is estimated based on the determined ratio, a known mass flow rate, and a predetermined ratio corresponding to the known mass flow rate.

41. A method (600) as claimed in claim 40 wherein said step (630) for estimating process parameters from said determined ratio comprises the step of estimating mass flow.

42. The method (600) of claim 22, wherein the number of said positions exceeds the real normal modal component of the decomposition, whereby said plurality of motion signals represent an overdetermined source of information for decomposing the motion of said catheter into said plurality of real normal modal components.

43. The method (600) of claim 22, wherein said receiving step (610) is preceded by the step of: triggering a plurality of real natural wave modes in the aforementioned catheter, and wherein the receiving step comprises the steps of: a plurality of motion signals representing motion are received in response to the triggers.

44. The method of claim 43, wherein said triggering step comprises the steps of: a broadband trigger is applied to the catheter.

45. The method of claim 43, wherein said triggering step comprises the steps of: a series of substantially coherent triggers having different frequencies are provided.

46. The method of claim 43, wherein said triggering step comprises the steps of: energy from the material in the aforementioned conduit is converted to trigger a plurality of real eigen-wave modes.