MXPA01001061A - Vibrating conduit and methods for generating compensated mass flow estimates - Google Patents

Abstract

A process parameter associated with a material contained in a conduit is estimated by estimating a real normal modal residual flexibility component associated with a real normal mode of motion of the conduit. A plurality of motion signals representing motion of the conduit is received. A residual-flexibility-compensated estimate of mass flow is generated from the received plurality of motion signals and the estimated real normal modal residual flexibility component. Related apparatus and computer program products are also described.

Description

VIBRANT DUCT AND METHOD FOR GENERATING COMPENSATED TFTSKD FLOW ESTIMATIVE VALUES BACKGROUND OF THE INVENTION The present invention is concerned with parameter detectors, operating methods and computer program products and more particularly, with vibratory duct parameter detectors, methods of operation and products of computer program.

PROBLEM APPROACH Coriolis effect mass flow meters are commonly used to measure mass flow and other information as to materials that flow through a conduit. Exemplary flow meters are described in U.S. Patent Nos. 4,109,524 of August 29, 1978, 4,491,025 of January 1, 1985 and Re. 31,450 of February 11, 1982, all issued to E. Smith et al. These flow meters commonly include one or more conduits that have a straight or curved configuration. It can be seen that each conduit has a set of vibration modes which include, for example, single, torsional, radial and coupled bending modes. In a typical mass flow measurement application, each conduit is driven to oscillate in resonance in one of its natural modes as the material flows through the conduit. The vibration modes Ref: 125977 of the vibrating system, full of material, are affected by the combined characteristics of mass and rigidity of the conduits and the characteristics of the material that flows inside the conduits. A typical component of a flow meter Coriolis is the drive system or excitation system. The drive system operates to apply a periodic physical force to the duct that causes the duct to oscillate. The drive system commonly includes at least one actuator mounted to the conduit (s) of the flow meter. The actuator may comprise one of the many well-known electromechanical devices, such as a voice coil device having a magnet mounted to a first conduit and a coil of wire mounted to a second conduit, in an opposite relationship to the magnet. An actuator commonly applies a periodic wave drive signal, for example, sinusoidal or square to the coil of the actuator. The periodic actuation signal causes the actuator to drive the two conduits in an opposite periodic configuration. When there is an effectively "zero" flow through a conduit of the flow meter, the points along the conduit tend to oscillate with approximately the same phase or a "zero flow" phase with respect to the controller, depending on the mode of the vibration driven.

As the material begins to flow from the inlet of the flow meter, through the flow conduit and outward through an outlet of the flow meter, the Coriolis forces arising from the material flow tend to induce phase shifts between the spatially spaced points along the conduit, with the phase on the inlet side of the conduit being generally delayed from the actuator and the phase on the outlet side of the conduit which is generally advanced to the actuator. The induced phase shift between the two sites in the conduit is approximately proportional to the mass flow rate through the conduit. Unfortunately, the accuracy of the measurements obtained using conventional phase shift or delay methods can be compromised by the non-linearities and asymmetries in the flow meter structure, as well as by the vibration induced to the structure of the flow meter by sources external such as pumps. These effects can be reduced, for example, by using balanced mechanical designs that reduce the external effects of vibration and by using frequency domain filtering to eliminate frequency components associated with undesirable vibrations. Nevertheless, mechanical design procedures may be restricted by geometric considerations and frequency domain filtering may not be effective to eliminate the undesirable vibrational energy that occurs at or near resonant frequencies of interest such as the drive frequency used to excite the conduit. One type of error commonly found in mass flow measurement applications is the "zero offset". As mentioned above, mass flow rate measurements commonly involve determining a phase or time difference between the motion signals produced by transducers in the structure of the detector conduit. The zero offset represents a polarization or displacement in this measurement of phase or time differences, such that a zero mass flow rate does not produce a zero phase difference or time difference. To reduce zero displacement error, conventional mass flow measurement techniques commonly measure the displacement of zero as a phase or time difference between the motion signals measured under a zero controlled mass flow condition. The phase difference or time measurements carried out under other flow conditions are then compensated according to the phase difference or zero flow time measured to produce more accurate results.

However, these techniques have potential disadvantages. Changes in process temperatures or detector mounting conditions can cause the zero shift to fall over time and lead to error measurements. To compensate for this drop, it may be necessary to periodically re-measure the zero offset. This may be inconvenient, since conventional zero offset compensation techniques may require that the flow be stopped to generate an updated zero offset measurement.

BRIEF DESCRIPTION OF THE INVENTION In light of the foregoing, it is an object of the present invention to provide mass flow detectors and methods for determining mass flow that are less sensitive to changes in process and assembly conditions. These and other objects, features and advantages are provided according to the present invention by methods, apparatus and computer program products in which the "residual flexibility", that is, residual movement attributable to the contributions of the displaced resonance of the Real normal modes, is determined by solving the movement of a vibratory duct of a mass flow detector in real normal modal components. A component of normal modal residual flexibility associated with at least one actual normal mode of movement of the conduit is estimated and used to generate an estimated value of residual flexibility compensated for mass flow. In accordance with one aspect of the present invention, the actual normal modal residual flexibility component is estimated using signals representing the movement of the conduit to a substantially zero mass flow condition. In accordance with an aspect of "dynamic zeroing", two actual normal modal residual flexibility components are determined, which include a "normal dynamic" residual normal modal flexibility component measured at zero flow and a modal residual flexibility component. real "dynamic" normal that is measurable under non-zero mass flow conditions. The two components of real normal modal residual flexibility are combined to provide an estimate value of the residual flexibility that is used to generate an estimated value of residual flexibility compensated for mass flow. Because the real dynamic normal residual residual flexibility component can be estimated as the material flows through the detector, the estimated value of the residual flexibility can be updated to compensate for changes in the structural dynamics of the detector without requiring the shutdown of the detector. equipment . According to another aspect of the present invention, a function is identified that describes the movement of the vibrating duct in a real normal mode as a function of the frequency. Then, the identified function is used to estimate a residual real normal modal component associated with the actual normal mode by adjusting movement measurements of the actual conduit, for example, movement at nonzero mass flow rates to the identified function. For example, a plurality of movement values of the detector conduit in an actual normal mode can be measured at a plurality of selected frequencies and these values used to determine a mode scaling for the actual normal mode, such that duct in the real normal mode at a displaced resonant frequency, for example, a detector excitation frequency, can be estimated. Then, this measurement of the residual motion can be used to generate an estimated value of residual flexibility compensated for the mass flow through the detector. The present invention arises from the discovery that residual flexibility in a mass flow detector can be attributed to shifted resonance contributions of various vibrational modes of the detector structure.

Using real normal modal decomposition techniques, the present invention can accurately measure the movement of the duct associated with the actual normal modal movement of displaced resonance and thereby provide an accurate measurement of residual flexibility for use in generating more accurate flow measurements. mass In accordance with aspects of the present invention, the estimated value of the movement of the displaced resonance conduit can be effected without requiring zero mass flow in the detector conduit. In particular, according to the present invention, a process parameter associated with a material contained in a conduit is estimated by estimating an actual normal modal residual flexibility component associated with a real normal mode of conduit movement. A plurality of movement signals are received which represent the movement of the conduit. An estimate value of residual flexibility compensated is generated from the plurality of received motion signals and the estimated actual normal modal residual flexibility component. According to one aspect of the present invention, the conduit is excited at an excitation frequency. An actual normal modal residual flexibility component associated with the actual normal mode at the excitation frequency is estimated. A plurality of movement signals representing the movement of the conduit in response to the excitation are received and the movement of the conduit at the excitation frequency is determined from the received plurality of movement signals. An estimate value of residual flexibility compensated for mass flow is generated from the movement determined at the excitation frequency and the estimated component of actual normal modal residual flexibility. According to another aspect, a first plurality of movement signals representing the movement of the conduit under a substantially zero mass flow condition is received and processed to resolve the movement of the conduit under substantially zero mass flow condition to a plurality of components Real normal manners. A real normal modal residual flexibility component is estimated from the resolved plurality of real normal modal components. A second plurality of motion signals representing the movement of the conduit is received and an estimated value of residual flexibility compensated for the mass flow is generated from the second received plurality of motion signals and the estimated component of actual normal modal residual flexibility. The estimation of residual flexibility and mass flow can be carried out in a physical coordinate domain or a modal coordinate domain. The first plurality of motion signals can be filtered in step to produce a filtered representation in step mode of the movement of the conduit under substantially zero mass flow condition and an estimate value of the residual physical motion associated with a real normal mode can be generated from the representation filtered in step mode of the movement conduit. Alternatively, the first plurality of motion signals may be processed to estimate the estimated normal residual normal modal movement under the substantially zero mass flow condition. In accordance with a related "dynamic zeroing" aspect of the present invention, a first component of actual normal modal residual flexibility associated with a first real normal mode of movement of the conduit under the substantially zero mass flow condition is estimated. A second component of real normal modal residual flexibility associated with a second normal real mode of duct movement under a non-zero mass flow condition is estimated. An estimated value of compensated residual flexibility is generated from the second received plurality of motion signals, the first estimated normal normal residual residual flexibility component and the second estimated normal normal residual residual flexibility component. The first real normal mode is preferably more highly correlated with the material flow in the conduit than the second real normal mode. According to yet another aspect of the present invention, an operative function for describing the movement of the conduit in a real normal mode as a function of the frequency is identified. A first value representing the movement of the vibrating duct at a selected frequency is determined. An actual normal modal residual resiliency component associated with the actual normal mode is estimated by adjusting the first value with the identified function. A plurality of motion signals representing the movement of the conduit is received and an estimated value of residual flexibility compensated for the mass flow is generated from the second plurality of motion signals received and the estimated actual normal modal residual flexibility component. In a modal coordinate domain modality, a real normal modal residual flexibility component is estimated by determining an escalation transformation concerning the first value to the identified function and estimating a real normal modal residual flexibility component associated with the actual normal mode of the identified function and the determined escalation transformation. An estimated value of compensated residual mass flow flexibility is generated from the actual normal modal residual resilience component estimated in a mode coordinate domain. In a mode sfiltering mode, the residual physical motion associated with a real normal mode is estimated from the frequency response function. An estimated value of residual flexibility compensated for the mass flow is generated by way filtration of a plurality of received motion signals to produce a filtered representation in the mode passage of the movement conduit as the material flows through it and generate an estimated value of residual flexibility compensated for the mass flow from the representation filtered in smode and the estimated residual physical movement. Computer program apparatus and products are also described to generate an estimate value of the mass flow of compensated residual flexibility for the material in a vibrating duct.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 illustrates an exemplary structure of the detector conduit.

Figures 2-4 illustrate the actual normal mode frequency responses of the exemplary conduit structure of Figure 1. Figures 5-6 illustrate one embodiment of a vibratory duct parameter detector according to the present invention. Figures 7-11 are flow chart illustrations and schematic diagrams illustrating operations for generating an estimate value of residual flexibility compensated for mass flow in accordance with aspects of the present invention. Figures 12A-B illustrate frequency responses of modes of an exemplary detector conduit structure. Figures 13-16 are flow chart illustrations and schematic diagrams illustrating operations for generating residual estimate values of mass flow compensated flexibility in accordance with aspects of the present invention.

DETAILED DESCRIPTION OF THE MODALITIES The present invention will now be more fully described hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. Those skilled in the art will appreciate that the invention can be implemented in many different forms and should not be construed as limited to the embodiments summarized herein; rather, these embodiments are provided in such a way that this disclosure is complete and complete and will bring the full scope of the invention to those skilled in the art. In the drawings, like reference numbers refer to like elements from beginning to end. In the embodiments described herein, the motion signals representing the movement of a detector conduit are processed to resolve the movement of the conduit in a plurality of real normal modal components. The actual normal modal decomposition can be implemented in a variety of ways. For example, a mode pass filter may be used to pass motion components of the detector conduit that are associated with a desired actual normal setting. Although the modal responses corresponding to the movement of the conduit do not need to be explicitly determined, the step filtering mode "resolves" notwithstanding the movement of the conduit in respective components associated with the respective actual normal modes. Alternatively, the actual normal modal movement, that is, movement in the coordinate system of a plurality of systems of a single degree of freedom (SDOF), can be estimated explicitly from the movement signals and used to generate estimated values of process parameters.

I. General view A. Modal behavior of a detector conduit The behavior of a vibrating structure such as a Coriolis flow meter conduit can be described in terms of one or more normal natural or real modes having associated natural vibration frequencies. These real normal modes and the associated natural frequencies can be described mathematically in terms of associated eigenvectors and eigenvalues, the eigenvectors are unique in relative magnitude but not absolute magnitude and orthogonal with respect to the mass and rigidity of the structure. The linearly independent set of vectors can be used as a transformation to decouple equations that describe the movement of the structure. In particular, the response of the structure to an excitation can be represented as a superposition of scaled modes, the scaling represents the contribution of each mode to the movement of the structure. Depending on the excitement, some modes may contribute more than others. Some modes may be undesirable because they do not contribute energy to the resonant frequency in a desired way and can therefore corrupt the measurements taken at the resonant frequency as desired, such as measurements of phase difference taken at the excitation frequency. It can be assumed that a detector conduit structure with negligible damping and zero flow has purely real natural or normal vibration modes, that is, in each mode, each point of the structure reaches a maximum displacement simultaneously. However, a real conduit having non-negligible damping and a material flowing therethrough has a response to the generally complex excitation, that is, points of the structure in general do not arrive simultaneously at the maximum amplitude. The movement of the conduit structure can be described as a complex mode having real and imaginary components or alternatively magnitude and phase components. The Coriolis forces imparted to the flowing material introduce complexity to the movement of the detector conduit. Even if the complex movement of the structure of a conduit can be described as a superposition of natural or "normal" scaled modes. To represent complex motion, complex scaling coefficients are used in the combination of the real constituent modes. The particular real normal modes can be closely correlated with the imaginary component of the complex mode that is significantly less correlated with the real component of the complex mode. Thus, these particular real normal modes can be closely correlated with the Coriolis forces associated with the material in the detector conduit and thus provide information to generate an exact estimate value of a parameter, eg, mass flow, associated with the material. As an illustrative example, a flow tube of Coriolis of 7.6 cm (3 inches) of curved double tube was analyzed experimentally. A conceptual model of the conduit structure of this meter is illustrated in Figure 1. The conventional transducers 105A, 105B, 105C, oriented to measure the velocity in a z-direction, were positioned in respective left, right and drive sites in the set 10 of the conduit. Respective accelerometers 105D, 105E were placed in respective conduits 103A, 103B, near the site of the right transducer and were oriented to measure lateral acceleration along a direction x. The outputs of accelerometers 105D, 105E were integrated to produce lateral absolute velocity information.

A response vector. { xres uesta} was built from the outputs of the motion transducers 105A-E: right response, Z drive response, Z '*, response} , = left answer, Z. (D lateral biased response, XZ lateral response, X where the skewed lateral response is a response along a 45 degree direction with respect to the x and z axes A real normal modal matrix [F], this is a matrix of normal normal modal transformation concerning the physical motion vector { xEespuesta) (in physical coordinates) to a real normal modal motion vector. { n} (in "modal" coordinates), it can be identified in such a way that: response l = [F]. { n} (2) The actual normal modal transformation matrix [F] can be identified using a variety of techniques. For example, trial and error or inverse techniques can be used. For the exemplary conduit structure 10 of Figure 1, a real normal modal transformation matrix [F] was determined experimentally; "2.497 0.014 - 0.079 - 5.067 5.063 6.344 0.038 - 0.84 - 3.248 - 4.403 Kg - s2 [F] = 2.552 - 0.063 - 0.072 5.217 5.188 (3) cm 0.801 0.356 0.564 1.384 1.637 0.052 0.732 - 1.519 0.084 0.0983 From left to right, the columns of the real normal modal transformation matrix [F] correspond to a first mode of bending out of phase, a lateral mode in phase, a lateral mode out of phase, a mode of torsion out of phase and a second mode of bending out of phase respectively, for the conduit structure 10. The modal transformation matrix [F] can be used to solve the physical movement represented by the motion vector. {Xresuestal in real normal modal components For example, the equation ( 2) can be explicitly solved for the modal movement vector {.?.} By premultiplying both sides of equation (2) by the reciprocal of the modal transformation matrix [F]: {?.} = [F]. {Xrespuesta.}. (4) in gift of, for the ej ejlar structure of figure 1, "0.0024 0.021 1 0.0138 0.0057 - 0.0027" -0.0031 0.00008 - 0.0847 0.2727 0.1053 Kg - s2 [FJ- = -0.0014 0.00008 - 0.0388 0.1317 - 0.0674 (5) cm -0.1771 0 0.0167 0.0018 0.0008 0.0165 -0.0104 0.0094 0.0004 0.0008 The actual normal modal movement. { ? } it can be used directly to estimate a process parameter associated with one or more of the normal modes for the structure of the conduit, for example, modes associated with the Coriolis force. Alternatively, the modal transformation matrix [F] can be used to identify a "mode pass filter" that can be applied to physical movement. { xresPuesta} to produce a filtered physical domain response that preferably includes physical movement components. { ^ answer) associated with one or more conduit modes. This filtered response can be used to estimate a process parameter. A normal inverse selective normal transformation matrix [F] can be used to translate a real normal modal movement vector. { ? } to a filtered motion vector. { Xfütrado} in which the components associated with the undesirable real normal modes are attenuated:. { Xfiltered} = [F 'l (?) (6) For the exemplary structure of Fig. 1, a normal inverted normal modal transformation matrix selective [F] was constructed from the real normal modal transformation matrix [F] by replacing those elements of the real normal modal transformation matrix [F] associated with the real undesirable normal modes with zeros: As shown in equations (6) and (7), the components of the movement vector of the conduit. { Xrespuestal corresponding to undesirable real normal modes can be attenuated by using a normal inverse normal modal transformation matrix [F] that corresponds to the real normal modal transformation matrix [F] with zeros that replace those elements of the modal transformation matrix real normal [F] associated with the actual undesirable normal modes. Those skilled in the art will appreciate, however, that the attenuation of these components could be obtained using nonzero values for these elements of the normal inverse selective normal transformation matrix [F]. Combining the equations (4) and (6): Í Xfiltrada} = [F '] [F] _1. { answer } = [?] { answer } (8) where the mode filter filter [?] Is given by: [?] = [F '] [F] "1 (9) The mode filter filter [?] Processes the vector of movement of the conduit. {Xrespuesta.}. in such a way that the vector of filtered exit movement. {Xfütrada.}., preferably represents components of the movement vector of the conduit. More desired modes The mode filter filter [?] can also be generated by: [?] = [F] [A] [F] -i (10) where [A] is a "diagonal" matrix whose elements displaced from the diagonal are zeros, with selected diagonal elements corresponding to the desired modes adjusted to one, for example: The filtered output. { Xfütraa } it can be processed to generate exact estimated values of process parameters such as mass flow. For example, the filtered output. { Xfiítrada} it can be processed according to conventional phase difference or phase difference Coriolis measurement techniques, as described in the aforementioned patent application "Vibrating Conduit Parameter Sensors, Methods and Computer Program Products Utilizing Real Normal Modal Decomposition". For the exemplary system illustrated in Figure 1, this can be effected by determining a phase difference or time difference between components of the filtered output. { Xfutrada } corresponding to the right and left transducers 105A, 105B using for example zero crossing techniques or similar phase or time difference techniques such as those described in US patent RE31,450, issued to Smith, US patent 4,879,911 issued to Zolock and US Patent 5,231,884 issued to Zolock or similar phase or time difference techniques implemented in a digital domain using a digital signal processor (DSP) or other computing device.

B. Residual flexibility and zero displacement A Coriolis flow meter is commonly excited or "driven" to cause a fluid or other material in the meter conduit to suffer a Coriolis acceleration. This excitation is commonly imparted at the resonant frequency or near the resonant frequency of a vibrational mode of the structure of the detector conduit, for example at the resonant frequency in a so-called "drive" or "excitation" mode. It is often assumed that a periodic excitation applied to the resonant frequency of one mode of the detector conduit produces a unimodal response, that is, a response limited to that drive or excitation mode. However, in reality, excitation commonly produces movement in additional real normal modes beyond the drive or excitation mode. As described above, the shifted resonance response of the real normal modes other than the drive mode can contribute to residual flexibility at the frequency of the drive mode and thus measurement phenomena such as zero shift in phase difference measurements or time carried out at the excitation frequency.

For the 7.6 cm (three inch) Coriolis flow meter analyzed experimentally, nine modes that have resonances between 0 and 40 Hz were identified. Figure 2 illustrates the total physical response 210 of the detector's left transducer and the frequency responses of the first nine modes of the structure. As illustrated, there are many modes that have a non-zero response to the excitation frequency? D. The displaced resonances of these modes contribute to the residual flexibility at the excitation frequency? D. Of particular interest is the first off-phase torsion mode 220 having a resonance frequency at about 325 Hz. For the experimentally analyzed detector, this mode represents one of a family of "flow modes" that are highly correlated with acceleration of Coriolis material inside the detector conduit. For the illustrated responses of Figure 2, this torsion mode contributes to the greater residual flexibility at the excitation frequency? D. Figure 3 illustrates phase responses corresponding to the magnitude responses of Figure 2. Residual flexibility can affect the phase of the response and can thus introduce polarization or zero shift in the phase difference or time measurements used to estimate the flow mass As illustrated in Figure 4, which shows the phase responses of Figure 3 amplified close to the excitation frequency Δd, the difference 430 between the phase 410 of the signal of the left movement transducer and the phase 420 of the signal of the right-hand transducer exhibits zero-flow polarization, which illustrates the potential effects of shifted resonance contributions from modes other than the drive mode in phase difference measurements.

II. Determination of residual flexibility by real normal modal decomposition Analytically, the displaced resonance contributions of the real normal modes other than the drive mode at zero flow can be determined by identifying a portion of the response of the conduit at the excitation frequency that is attributable to these contributions of displaced resonance, that is, by estimating a "real normal modal residual flexibility component" of duct movement that contributes to residual flexibility. Then, the estimated normal normal residual residual flexibility component can be used to generate an estimated value of residual flexibility compensated for mass flow according to a variety of different techniques.

Figure 5 illustrates an exemplary embodiment of a vibration duct parameter detector 5 according to the present invention. The detector 5 includes a conduit assembly or assembly 10. The conduit assembly 10 includes an inlet flange 101, an outlet flange 101 ', a manifold 102 and first and second conduits 103A, 103B. The crossbars 106, 106 'are connected to the conduits 103A, 103B. Connected to the conduits 103A, 103B is an actuator 104 which is operative to vibrate the conduits 103A, 103B in response to an actuator 20. The movement transducers 105A, 105B are operative to produce a plurality of movement signals that represent movement. in a plurality of conduit sites 103A, 103B, for example signals representing displacement, velocity or acceleration of conduits 103A, 103B. The motion transducers 105A, 105B may include a variety of devices such as coil-type speed transducers, optical or ultrasonic motion detectors, accelerometers, inertial velocity detectors and the like. The conductors 100 are connected to the actuator 104 and the motion transducers 105A, 105B. When the conduit assembly 10 is inserted into a material processing system, the material flowing in the material processing system enters the conduit assembly 10 through the entrance flange 101. Then the material flows through the manifold 102, where it is directed to ducts 103A, 103B. After leaving the conduits 103A, 103B, the material flows back to the manifold 102 and exits the meter assembly 10 through the flange or outlet flange 101 '. As the material flows through the conduits 103A, 103B it gives rise to Coriolis forces that disturb the conduits 103A, 103B. The conduits 103A, 103B may be driven by the actuator 104 in opposite directions around their respective bending axes W- and W -VI 'inducing what is commonly referred to as a first bending mode out of phase in the assembly or conduit assembly 10. The actuator 104 may comprise any of the many well-known devices, such as a linear actuator including a magnet mounted to the first conduit 103A and an opposite spool mounted to the second conduit 103B. An alternating current induced by a drive signal provided by an actuator 10 via a drive conductor 110 passes through the coil, generating mechanical force that vibrates the conduits 103A, 103B. The excitation provided by the actuator 104 may be substantially coherent, eg, confined to a narrow frequency range or may be wideband.

Although it is shown that the parameter detector 5 illustrated in Figure 5 includes an integral actuator 104, those skilled in the art will appreciate that the vibration of the conduits 103A, 103B according to the present invention can be obtained by other techniques. For example, wide-band excitation external to the conduit assembly 10 can be generated by such sources as pumps or compressors and transported to the conduit assembly 10 for example, via one of the flanges or flanges 101, 101 '. Similarly, wide-band excitation can be generated by transferring energy from a material in conduits 103A, 103B through, for example, a fluid-structure interaction mechanism (FSI). The parameter detector 5 includes an estimator 30 of the actual normal modal residual resiliency component that is configured to receive motion signals from the motion transducers 105A, 105B on the conductors 111 and operative to estimate a component 35 of actual normal modal residual flexibility of movement of the conduits 103A-B. A mass flow estimator of compensated residual flexibility is sensitive to the estimator 30 of the actual normal modal residual resiliency component, configured to receive motion signals from the motion transducers 105A, 105B and operative to generate an estimate value 45 of compensated residual flexibility. of the mass flow from the motion signals and the component 35 of estimated actual normal modal residual flexibility. As illustrated in Figure 6, the estimator 30 of the actual normal modal residual resiliency component and the mass flow estimator of compensated residual flexibility can be implemented using a computer 50, eg, a microprocessor, microcontroller, digital signal processor (DSP) or the like. In the illustrated embodiment of Figure 6, both the estimator 30 of the actual normal modal residual resiliency component and the compensated residual flexibility mass flow estimator 40 include circuits 610 that receive motion signals 606, such as a sampling device. 612, for example, a sample and fastener device or similar circuit that samples the motion signals 606 and produces samples 613 therefrom for subsequent conversion to digital signal values 615 by an analog to digital converter (A / D) 614. The operations of the sampling device 612 and / or the D / A 614 can be performed by a variety of circuits known to those skilled in the art and need not be discussed in more detail in this. . Those skilled in the art will appreciate that movement signals 606 can be processed in a variety of ways. For example, anti-alias filtration, post-sampling filtering and processing of similar signals can be applied. It will also be understood that, in general, the reception means 610 illustrated in Figure 6 can be implemented using physical elements, firmware (programs that were written on the computer's electronic circuits or in its ROM memory and can not be modified by the user) or special-purpose programming elements that are executed in special or general-purpose data processing devices or combinations thereof. For example, the functions of sampling and analog-to-digital conversion can be integrated with the transducers 105A, 105B. The computer 50 may, for example, comprise a concurrently running DSP especially suitable for linear algebraic calculations, such as a DSP of the DSP TMS320C4X family sold by Texas Instruments, Inc., configured with appropriate program code, eg, programming elements. and / or firmware and data stored, for example, in a storage medium 60 such as a random access memory (RAM), electrically erasable programmable read-only memory (EEPROM), magnetic disk or the like, the computer 50 provides means 620 for calculating an estimated value of the residual normal normal component 35 of the digital values 615, also as a means 630 for calculating a value 45 estimate of residual flexibility compensated for mass flow from the digital values 615. It will be appreciated that other computing devices, such as microcontrollers, microprocessors, field programmable gate arrays (FPGA) and the like can be used similarly. Figure 7 illustrates operations 700 for estimating a process parameter from motion signals that represent movement of a conduit containing a material. A component of actual normal modal residual flexibility associated with a real normal mode of movement of the conduit is estimated (block 710). A plurality of motion signals is received which represents the movement of the detector conduit as the material flows through it (block 720). An estimated value of residual flexibility compensated for the mass flow is then generated from the received plurality of motion signals and the estimated actual normal modal residual flexibility component (block 730). The estimated value of the real normal modal residual flexibility component and the estimated mass flow estimate of compensated residual flexibility can be generated in a variety of ways. In accordance with one aspect of the present invention, the actual normal modal residual flexibility component is estimated from motion signals that represent the movement of the conduit under a substantially zero mass flow condition. In accordance with an aspect of "dynamic zero adjustment", a first component of normal normal residual residual flexibility associated with a real normal mode related to the flow is estimated from movement signals representing the movement of the conduit under a condition of substantially zero mass flow, a second component of real normal modal residual flexibility is estimated from motion signals that represent the movement of the conduit under a non-zero mass flow condition and an estimated value of compensated residual flexibility of mass flow is generated at Starting from the first and second components of estimated normal residual modal flexibility. The second component of real normal modal residual flexibility can be updated by measurements under non-zero flow conditions, allowing residual estimated values of exact compensated flexibility to be generated without requiring the paralysis of the mass flow for the recalibration of the detector. According to another aspect of the present invention, a real normal modal residual flexibility component can be estimated without requiring measurements under a condition without flow. A frequency response function or "delta function" for a mode other than the drive mode, for example a function describing the frequency response of a torsion mode related to the flow, is identified using, for example, pole. Measurements of the actual frequency response for this mode are made at frequencies different from the excitation frequency, preferably at frequencies close to the mode resonant frequency. The measured values are then adjusted to the identified frequency response function to estimate the scaling of the mode. The scaling of the estimated mode is then used to generate an estimated value of the residual flexibility contribution in this way at the excitation frequency. Because mode scaling can be determined from conduit information under non-zero flow conditions, flow retention is not required for detector calibration. The discussion herein provides various techniques for generating estimated values of a real normal modal residual flexibility component and generating an estimated value of residual flexibility compensated for mass flow therefrom. This discussion is carried out with reference to the flow chart illustrations and schematic diagrams of Figures 5-16. It will be understood that, in general, blocks or combinations of blocks can be implemented in the flow diagram illustrations and schematic diagrams of Figures 5-16 using program codes that can be read by computer, for example, program instructions and / or data that they are put into operation in a computer or data processor, such as computer 50 illustrated in figure 6. As used herein, the program code that can be read by computer may include, but is not limited to such items such as operating system commands (eg, object code), high-level language instructions and the like, as well as data that can be read, accessed or otherwise used in conjunction with such program instructions. The program code may be loaded into a similar computer or data processing apparatus or computer in which, but not limited to, a microprocessor, a microcontroller, a digital signal processor (DSP) or the like are included. The combination of the program code and computer can provide an apparatus that is operative to implement a function or functions specified in a block or blocks of the flow chart illustrations or schematic diagrams. Similarly, the program code may be loaded into a computer or computer or data processing device in such a way that the program code and computer provide means to carry out the function or functions specified in a block or blocks. The program code may also be stored in a storage medium that can be read by computer or computer such as a magnetic disk or tape, a bubble memory, a programmable memory device such as an electrically erasable programmable read only memory (EEPROM). ) or the like. The code of the stored program can instruct a computer that has access to the storage means to operate in such a way that the program code stored in the storage medium forms a manufacturing article that includes program code means to implement the function or functions specified in a flow diagram or block or blocks of diagram diagram. The program code can also be loaded into a computer to cause a series of operational steps to be executed, implementing a process such that the program code, in conjunction with the computer, provides steps to implement the functions specified in the program. a flow chart or block or blocks of schematic diagrams. Thus, the blocks of the flowchart illustrations and schematic diagrams support operating apparatuses to carry out the specified functions, combinations of means for carrying out the specified functions, combinations of steps carrying out the specified functions and means of code. of programs that can be read by computer, implemented in a storage medium that can be read by computer, to execute the specified functions. It will also be understood that in general each block of the flowchart illustrations and schematic diagrams and combinations of blocks in the flow chart illustrations and schematic diagrams can be implemented by physical elements, programming elements or special purpose firmware running in a general-purpose computer or combinations thereof. For example, the functions of the blocks of flowchart illustrations and schematic diagrams can be implemented by means of an application-specific integrated circuit (ASIC), programmable gate arrangement or similar special purpose device or by program and data instructions loaded onto and executed by a microprocessor, microcontroller, DSP or other general purpose computing device. Those skilled in the art will also appreciate that although reference is made to digital implementation using a microprocessor, DSP microcontroller or other computing device, the functions of the illustrations and schematic diagrams of flow chart can also be implemented using analogous calculation or processing elements, such as analog filters, analog arithmetic components and the like.

A. Estimation of an actual normal modal residual flexibility component using drive mode filtration According to a first aspect of the present invention, the residual movement of the conduit under a substantially zero mass flow condition with modes other than the drive mode to a frequency of interest, for example, the excitation frequency of the detector, is determined by filtering that portion of the duct movement attributable to the "actuation" or "excitation" mode. Then the actual normal modal residual flexibility component is used to generate an estimated value of residual flexibility compensated for the mass flow at unknown mass flow rates. The filtering of the driving mode can be carried out in a modal coordinate domain or by way filtering in a physical coordinate domain. According to a first technique, an estimated mass flow estimate of residual flexibility compensated using modal domain calculations is generated. The residual normal normal movement under a substantially zero mass flow condition in at least one mode other than the drive mode is estimated. Then the motion signals representing the movement of the detector conduit under a subsequent unknown mass flow condition are then processed to estimate the actual normal modal movement of the conduit under the condition of unknown mass flow. Then the residual normal normal modal movement to the substantially zero mass flow condition is subtracted from the estimated normal normal modal movement to the unknown mass flow condition to generate an estimated value of residual flexibility compensated for the movement of the actual normal modal conduit to the condition of Unknown mass flow. Then the estimated value of residual flexibility compensated for the movement of the conduit can be used to generate an estimated value of residual flexibility compensated for the mass flow using modal mass flow estimation techniques. With reference to figure 8, the actual normal movement. { ? } No flow under a substantially zero mass flow condition can be estimated from a physical coordinate domain representation. { x} No flow of the conduit movement under the substantially zero mass flow condition when using a modal filter [F] -1. . { ? } without flow = [F] _1. { X } ] without flow (12) where. { ? } No flow represents the modal response under the substantially zero mass flow condition y. { x} No flow represents a physical quantity such as displacement, velocity or the like under the substantially zero mass flow condition represented for example by a movement signal received from a motion transducer operatively associated with the detector conduit structure. A component of real normal modal residual flexibility. { ? res? duai} no flow d the modal response of zero flow. { ? } No flow at the excitation frequency associated with modes other than the driving mode can be used to generate an estimated value of residual flexibility compensated for the mass flow under an unknown mass flow condition by estimating the actual normal modal movement. { ? } flow under the unknown mass flow condition from a physical domain representation. { x} Fuction of the movement of the duct under the unknown mass flow condition and subtract the actual normal modal residual flexibility component. { ? res? duai} without flow to generate an estimated value of compensated residual flexibility. { ? } fiujo, compensated for the movement of the conduit under the condition of unknown mass flow:. { ? } flow, compensated = i? } flow ~. { ? residual} no flow (13) The estimated value of residual flexibility compensated. { ? } fiow, co-testing of the actual normal modal motion under the condition of non-zero mass flow can then be used to generate an estimated value of residual flexibility compensated for the mass flow 45 using for example a mass flow estimator 810 that is operative to estimate the flow mass directly from the actual normal modal movement in modal domain coordinates as described in the patent application mentioned above "Vibrating Conduit Parameter Sensors", Methods and Computer Program Products Utilizing Real Normal Modal Decomposition. "Figure 9 illustrates operations 900 to generate an estimate value of the mass flow of residual flexibility compensated using modal domain calculations A plurality of motion signals representing the movement of the low conduit a substantially zero mass flow condition is received (block 910) The residual real normal modal movement under the substantially zero mass flow condition is estimated from the received motion signals (block 920). the movement of the conduit under an unknown mass flow condition are received (block 930). The actual normal modal movement under the unknown mass flow condition is estimated from the received motion signals (block 940). Then an estimated value of residual flexibility compensated for mass flow is generated from the estimated normal residual normal modal movement and the estimated normal normal modal movement under the unknown mass flow condition (block 950). According to an alternative technique, an estimated value of the mass flow of compensated residual flexibility is generated using step filtration techniques in a physical coordinate domain. The movement . { x} of a detector conduit can be observed as the sum of physical movements. { Xaccionamiento} attributable to the drive mode and the residual physical movement. { residuai} attributed to other modes. t ^} =. { Xaccionamiento} ' { residual / (14) Reshaping equation (14) ("residual) = { X.}. _ { Xctioning; (14) A general form of a matrix [?] of step filter mode, using a reverse procedure is: [?] = [F] [A] [F] "1 (16) where [A] is a diagonal matrix designed to pass selected modes as described above, [F] is a matrix of form so with the columns corresponding to the mode forms and the rows to the physical response sites and [F] "1 is the generalized reciprocal of the modal matrix.

The physical movement portion of the conduit attributable to the drive mode can be described as:. { X drive L = L i J drive. { / (1 ') where [?] Drive is a mode pass filter configured to pass only the driving or driving mode. By replacing equations (16) and (17) in equation (15) and factoring we have:. { Xresidual = (11 J - L * j drive). { X.}. (lo) With reference to figure 10, an estimated value of compensated residual flexibility. { x} Flue, compensated for physical movement under an unknown flow condition can be estimated from a physical response. { x} nUjo under the condition of unknown flow and a physical response. { xJsm flow under a substantially zero mass flow condition by: i X i flow, compensated =. { X / flow - (L -L J _ L * driveJ) i X} without flow (19) Thus, the residual flexibility compensation process involves calculating a residual flexibility vector at a substantially zero flow and subtracting this vector from the physical response. { x} I run to an unknown flow. The residual flexibility response compensated. { x} Flue, compensated, -that is, the response with residual phase flexibility differences eliminated, can then be used to generate an estimate value of the mass flow using eg a conventional mass estimator 1010 using phase measurement techniques. . Figure 11 illustrates exemplary operations for 1100 to generate an estimate value of the mass flow of residual flexibility compensated according to this technique based on modal filtration. Movement signals representing movement of the conduit under a substantially zero mass flow condition are received (block 1110). The received signals are filtered by step in a manner as described above to estimate the residual physical motion under the substantially zero mass flow condition (block 1120). Then the motion signals representing the movement of the conduit under an unknown mass flow condition are received (block 1130). Physical movement under the condition of unknown mass flow is determined (block 1140) and an estimated value of the mass flow of compensated residual flexibility is generated from the estimated physical movement under the condition of unknown mass flow and the estimated residual physical movement (block 1150).

B. Dynamic Zero Adjustment In accordance with another aspect of the present invention, two actual normal modal residual flexibility components are estimated and used to generate an estimate value of the mass flow of compensated residual flexibility. A first component of real normal modal residual flexibility is estimated from motion signals that represent motion under a substantially zero mass flow condition, as described above. A second component of normal "dynamic" real residual modal flexibility is estimated under non-zero mass flow conditions and can thus be periodically re-estimated as the detector is used to update the zero-offset calibration of the detector without requiring stopping the flow. The first and second components of real normal modal residual flexibility are used to generate an estimated value of residual flexibility compensated for mass flow. This aspect of the present invention arises from the discovery that the actual normal modes of a detector conduit can be classified either as "more correlated with the flow" or "less correlated with the flow". The modes most correlated with the flow are modes that have a response that is responsive to flow through the detector conduit, while modes less correlated with the flow are, as might be expected, significantly less sensitive to the flow velocity. Modes less correlated with the flow could include, for example, the lateral mode of the experimentally analyzed detector described above. The modes most correlated with the flow contribute to residual flexibility substantially at zero flow. In many cases, it is reasonable to assume that the residual flexibility associated with the modes most correlated with the flow is relatively non-variable over time, which means that zero deviation is probably not caused by changes in flow modes. However, modes less correlated with the flow may be relatively insensitive to the flow velocity, but sensitive to changes in boundary conditions. Changes in boundary conditions can result in a short or long-term deviation from zero as these modes change. For example, changes in boundary conditions can shift the frequency laterally for the exemplary detector described above, resulting in a change in this contribution so as to residual flexibility or zero displacement. By way of illustration, using experimental data for the 7.6 cm (three inch) detector described above, the modal matrix (or "mode") [F] for the detector can be reduced to 3 columns, corresponding to a mode of drive (out-of-phase bending) at 125 Hz, a lateral mode in phase at 132 Hz and an out-of-phase torque mode: the rows of the modal matrix [F] correspond to the right drive and left transducer sites and the rear biased and lateral accelerometers as described above. The modal matrix [F], scale factors of mode Qr and poles? R for N normal modes r, can be used to determine the frequency response function matrix [H] The response vector. { x} can be calculated from the frequency response function [H] and the drive force. { F.}. remembering that: { x} = [H] { F.}. (21) The modal responses for the three modes can be extracted with the modal filter constructed from the form matrix [F] using, for example, an inverse method. Figures 12A-B show the magnitude and phase respectively, for a physical response x and modal responses? Fiexion,? Torsion-iaterai / as a function of the frequency for the exemplary system. The time delay caused by the residual flexibility of a physical response can be calculated by calculating the phase angle between the motion signals produced by the right and left transducers and by dividing by the excitation frequency Δd to determine a time difference ? t. For the data in the figures 12A-B: Z () -Z (x3) A r '? T = -i- ^ - = 146 nanoseconds.

Two different mode step filters can be defined, which include a first pass filter so as to pass the bending and lateral modes to produce a physical response vector. { x} D? and a second pass filter so as to pass the bending and twisting mode to produce a physical response vector. { x} t > t. where . { xb? (? d)} ,. { xbt (? d) } Y . { ? (? d)} are the physical response vector of the combined bending and lateral mode, the physical response vector of the combined bending and torsion mode and the modal response vector respectively, all evaluated at the excitation frequency? d. Calculating the contribution zero displacement of each of the filtered components of step of mode. { XM (? D)} ,. { Xt (?) } at zero flow for the detector analyzed experimentally:? tb? = ^ / i-U xbi?) = l nanoseconds and?, = Z (xb?) - Z (xbll) _ l35? Tbt nanoseconds,?. that is, the response of lateral mode is associated with 11 nanoseconds displacement of zero and the response of the torsion mode is associated with 135 nanoseconds zero displacement. The response of the torsion mode correlated with the flow is generally confused with the flow, so that it can be difficult to determine the displacement of zero due to this mode under flowing conditions. However, the torsion mode correlated with the flow is generally decoupled from the boundary conditions and can be considered non-variable over time. It can be assumed that the lateral mode component less correlated with the flow is insensitive to the flow velocity, but can vary considerably with boundary conditions. For example, if the resonant frequency of the lateral mode decreases by 4 Hz due to changes in boundary conditions, the individual modal contributions to the zero shift become:? Tbi = (* «?) - (*« 3), 23 nanoSecond and 135 nanoseconds, The displacement of the total zero using the contribution of this frequency of lateral mode is thus of 158 nanoseconds, a change attributable to the change in the resonant frequency of the lateral mode. The displacement of the zero? Tbt associated with the response of the torsion mode does not change to 135 nanoseconds, since the displacement of the frequency in a lateral mode does not affect the torsion mode. From these observations, it becomes clear that changes can be tracked in a less correlated way with the flow to verify changes in boundary conditions. Changes in the mode least correlated with the flow can be verified under non-zero flow conditions, thus allowing the compensation in terms of residual flexibility to be updated dynamically without requiring a flow retention. Figure 13 illustrates exemplary operations 1300 to generate residual estimate values of compensated mass flow flexibility according to a dynamic zero-fit technique. A first component of real normal modal residual flexibility associated with a real normal mode more correlated with the flow, for example, the torque mode of the detector described above is estimated for a substantially zero mass flow condition (block 1310). A second component of actual normal modal residual flexibility associated with a less correlated mode with the flow, for example the detector side mode described above, is then estimated under a non-zero mass flow condition (block 1320). The movement signals representing the movement of the conduit are then received (block 1330) and an estimated value of compensated residual flexibility of the mass flow is estimated therefrom using the first and second components of real normal modal residual flexibility (block 1340) . Subsequently, the second real normal modal residual flexibility component is updated (block 1320), additional motion signals are received (block 1330) and a new estimated value of compensated residual flexibility of the mass flow is generated from the motion signals received. using the second updated actual normal modal residual flexibility component (block 1340). It will be understood that the estimation processes indicated in Figure 13 can be carried out either in the modal or physical domain, using the techniques and apparatus described above with reference to Figures 5-11. The modal response of a particular real normal mode, for example, the lateral mode described above, can also be calculated from an estimated pole value for the desired mode using a predetermined frequency response function for the mode instead of the measurement of the movement of the real conduit. For example, instead of measuring the modal response for the lateral mode, an estimated value of the lateral mode modal response could be calculated using equations (20) and (21) for a known force. { F.}. when adjusting r = 2. 2. Estimation of the actual normal residual motion when estimating scaling of the mode shape According to another aspect of the present invention, the residual flexibility associated with a real normal mode at a given frequency, for example, an excitation frequency at which carry out measurements of phase difference or time, it is estimated from the movement measured in the real normal mode at frequencies different from the given frequency. For example, the actual normal modal movement can be measured at frequencies close to the excitation frequency and the measured movement used to interpolate the residual flexibility at the excitation frequency. According to the present invention, several linear, polynomial or other interpolation techniques can be used to generate an estimated value of the actual normal modal movement at the excitation frequency from the actual normal modal movement measured at frequencies other than the excitation frequency. . In accordance with one aspect of the present invention, a least squares technique is used to adjust the measured data representing motion in a real normal mode to an assumed frequency response or "delta" function using measurements at frequencies at which the response is measured more easily. A frequency response or "delta" function? R for a single degree of freedom for a r mode of interest generally takes the form: where? r is the eigenvalue of the mode r,? r represents the movement in the mode r, Nr is the modal excitation in the mode r, kr is a scalar that scales the modal response? r and * indicates a complex conjugate. An eigenvalue can be assumed or estimated from the measurements. For example, an eigenvalue can be estimated using a variety of well-known pole estimation techniques, such as those described in "Modal Testing: Theory and Practice," by DJEwin, published by John Wiley and Sons, Inc. ( 1984). An eigenvalue is a complex number that has a real part that represents the damping of the mode r and the imaginary part that represents the muted natural frequency Omr of the r mode. A damping mode may be difficult to measure, but for a typical Coriolis mass flow meter, it can be assumed that the damping is low. Assuming negligible damping: As described above, the response of the flow-correlated modes such as the torsion mode of the exemplary detector of Figure 1 is generally confused with the flow, which can make it difficult to measure the residual flexibility associated with such a manner near the excitation frequency under a non-zero flow condition. However, be it. { ? r} which represents a vector of delta functions corresponding to real normal modes highly related to the flow, a least squares technique can be used to calculate an "escalation matrix" [k] that is related to the movement measured in the modes correlated with the flow at the frequencies removed from the excitation frequency to the vector. { ? r} of delta functions. Then, the scaling matrix [k] can be used to generate an exact estimate value of the residual flexibility at the excitation frequency that is attributable to the modes correlated with the flow by applying the scaling transformation [k] to the vector . { ? } of delta functions. In particular, the structure of the conduit is excited to one or more selected frequencies under a non-zero flow condition. Although the selected frequencies can be chosen arbitrarily, the further away from the excitation (drive) frequency d, in general the less the modal response of the modes correlated with the flow is distorted by the mass flow through the conduit. Preferably, the selected frequencies used to estimate a mode r are chosen close to the resonant frequency cOmr of mode r. A physical force { F.}. , known, for example, either by direct measurement or by inference of a parameter such as a drive current, is applied at a selected frequency? s. The physical force. { F.}. it can be transformed to a modal excitation. { N.}. through: . { N.}. = [F] T. { F.}. (24; A physical response { x} by force . { F.}. it can be transformed into a modal response. { ? } through: . { ? } = [FJUx} (25) For a modal response matrix A®, flow for modes r obtained at a plurality of selected frequencies [? S], it is assumed that: where [? (? r,? s)] represents a matrix generated when evaluating the vector. { ? r} delta functions for the modes r to the plurality of selected frequencies? s. Solving equation (26) for the scaling matrix: where t indicates a pseudoinverse. So, the modal response? ? ) if flow to a Nr l0 frequency? Low zero flow, that is, the movement associated with the modes correlated with the flow at the frequency?, can be estimated (in modal domain coordinates) by: - ?, (? r,?.) r. { ? r (? "?)} . (28) flow Normally, it is desired to estimate the residual flexibility associated with the modes correlated with the flow at an excitation frequency? D, which can be obtained by estimating the fit? =? d in equation (28). As described above, the residual flexibility for a mode correlated with the flow, that is, the torsion mode, is determined. However, it will be appreciated that the techniques described above are also applicable to modes less correlated with the flow. For example, the residual flexibility associated with a lateral mode negligibly correlated with the flow, such as that described by the exemplary detector of Figure 1, could similarly be estimated from a delta function describing the frequency response of the lateral mode. An estimate value of the actual normal modal movement of residual flexibility compensated at a given frequency, that is, actual normal modal movement compensated for residual flexibility associated with undesirable modes can be produced by measuring the actual normal modal movement. { ? } flow to the given frequency and subtracting the actual normal modal movement. { ? r} No flow associated with unwanted modes. Assuming a constant modal excitation. { N.}. , the normal normal modal movement of residual flexibility compensated for? } flow, compensated is given by: \ T [flow, compensated = i? / flow -. { ^ Go / no flow, compensated (- - 'Then, the normal normal compensated modal movement can be used to generate an estimated value of • residual flexibility compensated for the mass flow at the unknown flow velocity, in a manner similar to that described above.

However, in some applications, it may be more convenient to determine the residual flexibility in physical coordinates. The transformation of the domain of modal coordinates to the domain of physical coordinates, an estimated value of residual flexibility compensated in the physical domain is given by:. { X (?) } flow, compensated = [F]. { ? (?) } flow, compensated (30) To compensate for a residual flexibility associated with a mode correlated with the flow, for example:. { (?) } nuJO, MmptnM_o where [AacCi? nam? ento] and [Amodo_fiUjo] are diagonal matrices designed to pass the driving modes and correlated with the flow respectively. Rearranging equation (31) in terms of pass-mode filters [? Acclimatization] and [? odo_f iu3o] for the drive modes and correlated with the flow, respectively: i * (?)} = [?, M]. { ? - (?) Jp "j0 + .4 n.?-_. { * (?), ln? lj0 (32) [? m ^ _nuj.] [? - (? í)] [? r (? r,?,)] < . { ? r (? "?)} . Figure 14 illustrates exemplary operations 1400 to generate an estimate value of residual flexibility compensated for mass flow. A function is identified that describes the movement of the detector conduit in an actual normal mode as a function of the frequency (block 1410). A value representing the movement of the conduit at a selected frequency, for example a frequency close to the resonant frequency of the actual normal mode is determined (block 1420). For example, motion signals representing the movement of the detector conduit under a non-zero flow condition could be received and movement in the actual normal mode could be determined from them at a plurality of selected frequencies near the frequency resonant of normal mode real. An actual normal modal residual flexibility component associated with the actual normal mode is then estimated (blog 1430) using for example the least squares techniques described above. A plurality of motion signals representing the movement of the conduit at an unknown mass flow rate is then received (block 1440) and an estimated value of compensated residual flexibility of the mass flow is generated from the received motion signals and the component of estimated actual normal modal residual flexibility (block 1450). Figure 15 illustrates operations 1500 for estimating the residual normal normal modal movement for use in generating an estimated residual flexibility value compensated for mass flow in a modal coordinate domain. A delta function that describes movement in a real normal mode is identified (block 1510). Movement signals representing the movement of the conduit are received (block 1520). The received motion signals are processed to generate a first plurality of values representing the movement of the conduit at a plurality of selected frequencies (block 1530). For example, the first plurality of values can describe the movement in a mode correlated with the flow to a plurality of selected frequencies near the mode resonant frequency. The identified delta function is evaluated at the plurality of selected frequencies to generate a second plurality of values (block 1540). Then a scaling transformation mode is determined from the first and second plurality of values, for example using equation (27) (block 1550). The residual normal normal modal movement at a frequency of interest, for example, the excitation frequency, can then be determined from the scaling transformation and the delta function (block 1560) and used to generate an estimated value of compensated residual flexibility (block 1570) using for example, the techniques described with respect to figure 9. Figure 16 illustrates exemplary operations 1600 to generate an estimate value of residual flexibility compensated for mass flow in a physical coordinate domain. A delta function that describes the movement in a real normal mode, for example a mode correlated with the flow or other mode, is identified (block 1610). Movement signals representing the movement of the conduit are received, for example, movement signals representing the movement of the conduit under a non-zero mass flow condition (block 1620). The received motion signals are processed to generate a first plurality of values representing the movement of the conduit at a plurality of selected frequencies (block 1630). The identified delta function is evaluated at the plurality of selected frequencies to generate a second plurality of values (block 1640). The delta function is evaluated at the frequency of interest, for example, the excitation frequency (block 1650) and a mode pass filter is applied to a product of the first plurality of values, the second plurality of values and the value of the delta function at the frequency of interest to generate an estimated value of the residual physical movement at the frequency of interest (block 1660), along the lines of equation (32). The estimated residual physical movement can then be used to generate an estimated value of residual flexibility compensated for mass flow (block 1670) using for example the techniques described with respect to figure 11.

III. Conclusion In accordance with the present invention, the "residual flexibility", that is, the residual motion attributable to resonant contributions displaced in normal ways, is determined by the decomposition of the movement of a vibrating duct from a mass flow detector into modal components real normals. An actual normal modal residual flexibility component associated with at least one actual normal mode of the pipeline movement is estimated and used to generate an estimated value of residual flexibility compensated for mass flow. The actual normal modal residual flexibility component can be estimated from signals representing movement of the conduit to a substantially zero mass flow condition. The estimation can be carried out in a modal coordinate domain or by using mode step filtering in a physical coordinate domain. The actual normal modal residual flexibility component may comprise a first component estimated from motion signals that represent movement of the detector conduit under a substantially zero mass flow condition and a second "dynamic" component that may be generated from signals of movement representing movement of the conduit under non-zero mass flow conditions. The second component can be updated dynamically under non-zero flow conditions. According to another aspect of the present invention, a function describing the movement of the vibrating duct in a real normal mode as a function of frequency, for example, a frequency response or "delta" function is identified. The function is used to estimate a residual real normal modal component associated with the actual normal mode by adjusting measurements of the actual movement of the conduit to the function, for example, by measuring plurality of detector movement values in a real normal mode to a plurality of selected frequencies and using least squares techniques to determine a scaling mode for the actual normal mode. The mode scaling can be used to generate an estimated value of a real normal modal residual flexibility component. The actual normal modal decomposition used according to the present invention can provide more accurate estimated values of residual flexibility. The most accurate estimate of residual flexibility can lead, for example, to an improved compensation for zero displacement in mass flow measurements of phase difference or time. In addition, according to aspects of the present invention, estimates of residual flexibility can be made without requiring zero mass flow in the detector conduit. The drawings and specification of the present application describe embodiments of the invention. Although specific terms are used, they are used in a generic and descriptive sense only and not for purposes of limitation. It is expected that persons skilled in the art can and will effect, use or sell alternative modalities that are within the scope of the following claims either literally or under the doctrine of equivalents. It is noted that, in relation to this date, the best method known to the applicant to carry out the aforementioned invention, is that which is clear from the present description of the invention.

Claims (22)

1. CLAIMS Having described the invention as above, the content of the following claims is claimed as property: 1.
2. A method for estimating a process parameter for a material flowing through a vibrating duct in an apparatus that measures process parameters, the method is characterized in that it comprises the steps of: estimating an actual normal modal residual flexibility component associated with a real normal mode movement of the conduit; receiving a plurality of movement signals representing movement of the conduit at different points along the conduit and generating an estimate value of residual flexibility compensated for by the process parameter from the plurality of motion signals and the residual flexibility component normal real.
3. The method according to claim 1, characterized in that the actual normal modal residual flexibility component is estimated from a real modal movement under a substantially zero flow condition and a real normal modal movement under an unknown mass flow condition under a substantially zero flow condition and a real normal modal condition under an unknown mass flow condition, the step of estimating the actual normal modal residual flexibility component comprises the steps of: receiving a first plurality of motion signals that represent movement of the duct under a substantially zero mass flow condition; estimating the residual normal normal modal movement under substantially zero flow condition from the first plurality of motion signals; receiving a second plurality of motion signals representing movement of the conduit under an unknown mass flow condition and estimating "the residual normal normal modal movement under the unknown mass flow condition from the second plurality of motion signals. method according to claim 2, characterized in that the step of estimating the process parameter includes the steps of: generating the estimated residual flexibility value compensated for the process parameter from the normal residual normal modal movement under the substantially zero flow condition and the residual normal normal modal movement under the condition of unknown mass flow
4. 4. The method according to claim 1, characterized in that the step of estimating the actual normal modal residual flexibility component comprises the step of: receiving a first plurality of movement signs that represent movement from the conduit to a substantially zero mass flow condition; filtering in step the first plurality of motion signals to estimate the residual physical motion under substantially zero mass flow condition; receiving a second plurality of motion signals representing the movement of the conduit to an unknown mass flow condition and estimating the physical movement to the unknown mass flow condition.
5. 5. The method of compliance with the claim 4, characterized in that the step of estimating the process parameter comprises the step of: generating the estimated value of residual flexibility compensated for the process parameter from the estimated physical movement under the condition of unknown mass flow and the residual physical movement.
6. The method according to claim 1, characterized in that the step of estimating the actual normal modal residual flexibility component comprises the steps of: estimating a first component of normal normal modal residual flexibility associated with the actual normal mode correlated with the flow under a substantially zero mass flow condition and estimating a second component of actual normal modal residual flexibility associated with a mode less correlated with the flow to an unknown mass flow condition.
7. 7. The method according to claim 6, characterized in that the step of estimating the process parameter comprises the step of: generating an estimate value of residual compensated flexibility of the process parameter from the received plurality of motion signals, the first component of actual normal modal residual flexibility and the second component of real normal modal residual flexibility.
8. The method according to claim 1, characterized in that the step of estimating the actual normal modal residual flexibility component comprises the steps of: identifying a function describing the movement of the conduit in a normal mode as a function of the frequency; determine a value representing the movement of the conduit at a selected frequency and estimate the actual normal residual flexibility component when adjusting the value to the function.
9. The method according to claim 1, characterized in that the step of estimating the actual normal modal residual flexibility component comprises the step of: identifying a function describing the movement of the conduit in a real normal mode as a function of the frequency.
10. 10. The method of compliance with the claim 9, characterized in that the step of estimating the process parameter comprises the step of: generating a first plurality of values representing the actual modal movement at a plurality of selected frequencies; evaluating the function at the plurality of selected frequencies near a resonant frequency of the mode to generate a second plurality of values; determining a scale scaling transformation from the first plurality of values and the second plurality of values; estimate the residual normal normal modal movement at a drive frequency from the mode scaling transformation and the function and generate the residual flexibility process parameter compensated from the residual normal normal motion estimated at the drive frequency.
11. The method according to claim 9, characterized in that the step of estimating the process parameter comprises the step of: generating a first matrix representing the physical movement of the conduit at a plurality of selected frequencies; evaluating the function at the plurality of selected frequencies near a resonant frequency of the mode for generating a second matrix; evaluate the second matrix at the drive frequency; apply a mode pass filter to a product of the first matrix and the second matrix and evaluate the function to generate an estimate value of the residual physical movement at the drive frequency and generate the estimated value of the process parameter from Estimated value of residual physical movement at the drive frequency.
12. 12. An apparatus having a conduit, an actuator that vibrates the conduit as the material flows through the conduit and detectors that measure the movement of the conduit in at least two different locations and generate signals representative of the movement, where the apparatus produces an estimate value of a process parameter of the material, the apparatus is characterized in that it includes: an estimator of the actual normal modal residual flexibility component that receives signals from the detectors and estimates an actual normal modal residual component associated with a normal mode real conduit; a mass flow estimator of compensated residual flexibility that is sensitive to an estimate of the actual normal modal residual component and that generates a process parameter of residual flexibility compensated from the signals and the actual normal modal component.
13. The apparatus according to claim 12, characterized in that the estimator of the actual normal modal residual resilience component comprises: means for receiving a first plurality of movement signals representing the movement of the conduit under a substantially zero mass flow condition and means for estimating the residual normal normal modal movement under a substantially zero mass flow condition from the first plurality of motion signals; means for "receiving a second plurality of motion signals representing the movement of the conduit under an unknown mass flow condition and means for estimating the residual normal normal modal movement under the unknown mass flow condition from the second plurality of
14. 14. The apparatus according to claim 13, characterized in that the mass flow estimator of compensated residual flexibility comprises: means for generating the estimated value of residual flexibility compensated for by the process parameter from the normal residual normal motion under the substantially zero mass flow condition and the residual normal normal modal movement under the condition of unknown mass flow
15. 15. The apparatus according to claim 12, characterized in that the estimator of the actual normal modal residual flexibility component comprises: means for receiving a first plurality of motion signals representing the movement of the conduit to a substantially zero mass flow condition; means for the filtering of step of the first plurality of motion signals to estimate the residual physical movement under the substantially zero mass flow condition; means for receiving a second plurality of motion signals representing the movement of the conduit to an unknown mass flow condition and means for estimating physical movement to the unknown mass flow condition.
16. 16. The apparatus according to claim 15, characterized in that the mass flow estimator of compensated residual flexibility comprises: means for generating the estimated value of compensated residual flexibility of the process parameter from the estimated physical movement under the condition of mass flow unknown and the residual physical movement.
17. 17. The apparatus in accordance with the claim 12, characterized in that the estimator of the actual normal modal residual flexibility component comprises: means for estimating a first component of real normal modal residual flexibility associated with the actual normal mode correlated with the flow under a substantially zero mass flow condition and means for estimating a second component of actual normal modal residual flexibility associated with a mode less correlated with the flow to an unknown mass flow condition.
18. 18. The apparatus according to claim 17, characterized in that the mass flow estimator of compensated residual flexibility comprises: means for generating the estimated residual flexibility value compensated for the process parameter from the received plurality of motion signals, the first component of real normal modal residual flexibility and the second component of real normal modal residual flexibility.
19. 19. The apparatus in accordance with the claim 12, characterized in that the estimator of the actual normal modal residual resilience component comprises: means for identifying a function that describes the movement of the conduit in a real normal mode as a function of the frequency; means for determining a value representing the movement of the conduit at a selected frequency and means for estimating the actual normal residual flexibility component when adjusting such value to the function.
20. 20. The apparatus in accordance with the claim 19, characterized in that the estimator of the actual normal modal residual resilience component comprises: means for identifying a function that describes the movement of the conduit in a real normal mode as a function of the frequency.
21. 21. The apparatus according to claim 20, characterized in that the mass flow estimator of compensated residual flexibility comprises: means for generating a first plurality of values representing a real modal movement at a plurality of selected frequencies: means for evaluating the function to the plurality of selected frequencies near a resonant mode frequency to generate a second plurality of values; means for determining a scale scaling transformation from the first plurality of values and the second plurality of values; means for estimating the residual normal normal modal movement at a drive frequency from the scaling transformation of the mode and such function and means for generating the residual flexibility process parameter compensated from the residual normal normal motion estimated at the frequency drive .
22. 22. The apparatus in accordance with the claim 20, characterized in that the mass flow estimator of compensated residual flexibility comprises: means for generating a first matrix representing the physical movement of the conduit at a plurality of selected frequencies; means for evaluating the function at the plurality of selected frequencies near a resonant frequency so as to generate a second matrix; means for evaluating the second matrix at the drive frequency; means for applying a mode pass filter to a product of the first matrix and the second matrix and evaluating the function for generating an estimate value of the residual physical movement at the drive frequency and means for generating the estimated value of the parameter process from the estimated value of the residual physical movement to the drive frequency.