Non-invasive method for measurement of physical properties of free flowing materials in vessels

Abstract

Methods and apparatus for measuring physical properties of material in a vessel are provided. In one example, the method includes capturing a response to a vibration initiated by a source in mechanical communication with the vessel, generating a vibration response spectrum based on the response, and calculating at least one value of at least one physical property of the material based on at least one pre-established relationship between the at least one physical property and one or more characteristics of the vibration response spectrum.

Claims

1. A method for measuring physical properties of non-gaseous free flowing material in a vessel, the method comprising: receiving data characterizing the vessel and at least one sample of the material in the vessel; initiating a vibration on a wall of the vessel by one of an external source or an internal source in mechanical communication with the vessel; capturing a response to the vibration; generating a vibration response spectrum based on the response; determining a search zone within the vibration response spectrum based on a configuration of the vessel, a type of attachment between the vessel and another object, and the at least one sample of the material in the vessel; determining at least one pre-established relationship between at least one physical property of the material and one or more characteristics of the vibration response spectrum of the search zone; measuring an ambient temperature within a predefined proximity of the vessel; determining a difference between the measured ambient temperature and a set process temperature; computing a correction to the at least one pre-established relationship based on the difference; and calculating at least one value of at least one physical property of the material based on the at least one corrected pre-established relationship.

2. The method of claim 1, wherein initiating the vibration includes at least one of initiating a solid body interaction with the wall, initiating a fluid-dynamic interaction with the wall, initiating a ballistic percussion interaction with the wall, or initiating an electro-dynamic interaction with the wall.

3. The method of claim 1, wherein initiating the vibration includes applying a mechanical load to the outside wall of the vessel, and the mechanical load includes at least one of a single pulse, a pulse train, or a periodic pulse.

4. The method of claim 3, wherein the mechanical load is modulated according to at least one of amplitude modulation, frequency modulation, pulse modulation, pulse-code modulation, or pulse-width modulation.

5. The method of claim 1, wherein capturing the response includes: converting an oscillation into a digital signal; analyzing the digital signal to calculate one of a wall response time, a damping factor, a signal harmonic spectrum, or a variable characterizing a magnitude of the oscillation; and adjusting a gain applied to the response.

6. The method of claim 1, wherein calculating the at least one value includes calculating at least one value of material level in the vessel, material bulk density, kinematic viscosity, or dynamic viscosity of the material.

7. The method of claim 1, wherein calculating the at least one value includes calculating at least one value of at least one physical property of a homogeneous liquid, a heterogeneous liquid, or a loose solid.

8. The method of claim 1, wherein calculating the at least one value includes calculating at least one value of at least one physical property of a moving material or a still material.

9. The method of claim 1, wherein the vessel is one of a silo, a tank, or a pipe.

10. The method of claim 1, wherein calculating the one or more characteristics of the vibration response spectrum of the search zone is a frequency of one of a spectrum harmonic.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) Various aspects of at least one example are discussed below with reference to the accompanying figures, which are not intended to be drawn to scale. The figures are included to provide an illustration and a further understanding of the various aspects and examples, and are incorporated in and constitute a part of this specification, but are not intended as a definition of the limits of the examples disclosed herein. The drawings, together with the remainder of the specification, serve to explain principles and operations of the described and claimed aspects and examples. In the figures, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every figure. In the figures:

(2) FIG. 1 is a time diagram of the pipe vibration response captured by a vibration sensor, such as the Ultimo DVM vibration sensor;

(3) FIG. 2 is a plot of the vibration spectrum of the signal shown in the FIG. 1: 1Spectrum line associated with the pipe's vibration fundamental harmonic; 2Search zone on the frequency domain for the fundamental harmonic frequency tracking;

(4) FIG. 3 is a graph of the family of curves representing the relationship between the material bulk density and the frequency value of the pipe's fundamental harmonic; the pipe is clamped at two sides; the distance between the clamps=50 in.; the pipe OD=3.5 in.; the pipe ID=3.07 in.;

(5) FIG. 4 is a generalized flowchart of the measurement algorithm;

(6) FIG. 5 shows the device's functional block diagram;

(7) FIG. 6 depicts an exploded 3D view of the mechanical design of an embodiment;

(8) FIGS. 7, 8 are the assembly drawings of the mechanical design of an embodiment;

(9) FIG. 9 illustrates a side view of an embodiment;

(10) FIG. 10 illustrates an inertia force-based actuation of the vessel body in an embodiment;

(11) FIG. 11 illustrates actuation via a vibrating member of the vessel's construction;

(12) FIG. 12 illustrates actuation caused by a pipe local resistance to moving content material;

(13) FIG. 13 shows the functional diagram of the device for measuring the mass flow using a combination of the percussion density meter and the volumetric flow meter;

(14) FIG. 14 illustrates positioning of a thermal sensor for monitoring the temperature of the ambient air and calculating the process temperature within the pipe or vessel, thereby providing for the device's invariance to ambient temperature changes and for measuring the content material physical property at a set temperature that differs from the instantaneous process temperature; and

(15) FIG. 15 illustrates positioning of the thermal sensor for the high-accuracy monitoring the process temperature within the pipe or vessel for the purpose of measuring the content material physical property at a set temperature that differs from the instantaneous process temperature.

DETAILED DESCRIPTION

(16) Aspects and examples disclosed herein relate to apparatus and processes for determining physical properties of a material housed within a vessel. For instance, according to one example, an apparatus includes a striker, vibration sensor and controller configured to determine the density belonging to a set of measured physical variables characterizing the vessel content. In some examples, the non-gaseous material is a fluid. In other examples, the non-gaseous material is a solid. According to another example, an apparatus, such as the apparatus described above, executes a method for determining physical properties of a material housed within a vessel. While executing the exemplary method, the apparatus determines the density of a non-gaseous material disposed within the vessel by calculating the instantaneous density values using a pre-established relationship between the density and the measured property or properties of the vibration spectrum of the vessel equipped with the vibration sensor.

(17) It is to be appreciated that examples of the methods and apparatuses discussed herein are not limited in application to the details of construction and the arrangement of components set forth in the following description or illustrated in the accompanying drawings. The methods are capable of implementation in other examples and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. In particular, acts, elements and features discussed in connection with any one or more examples are not intended to be excluded from a similar role in any other examples.

(18) Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. Any references to examples or elements or acts of the systems and methods herein referred to in the singular may also embrace examples including a plurality of these elements, and any references in plural to any example or element or act herein may also embrace examples including only a single element. References in the singular or plural form are not intended to limit the presently disclosed systems or methods, their components, acts, or elements. The use herein of including, comprising, having, containing, involving, and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. References to or may be construed as inclusive so that any terms described using or may indicate any of a single, more than one, and all of the described terms. In addition, in the event of inconsistent usages of terms between this document and documents incorporated herein by reference, the term usage in the incorporated reference is supplementary to that of this document; for irreconcilable inconsistencies, the term usage in this document controls. Moreover, titles or subtitles may be used in the specification for the convenience of a reader, which shall have no influence on the scope of the embodiments disclosed herein.

(19) Measurement Apparatus

(20) Some examples disclosed herein improve upon, operate with, or adapt to devices described in PCT Application No. PCT/US10/44292. According to one example, a device for non-invasively measuring physical properties of a free-flowing non-gaseous material contained in a vessel is provided. The device includes a driver that causes a striker to move toward, and physically impact, a wall of the vessel. The device is arranged to mechanically isolate (after a strike has been applied to the vessel wall) the device's mass and motion (and the mass and motion of the device's internal and external components) from the combined oscillation of the vessel wall and the material contained within the vessel. It is to be appreciated that such mechanical isolation does not include, however, any sensing or coupling components of the device. These components remain in mechanical communication with the vessel wall after the strike has been applied. The isolation will reduce (or eliminate) interference to the oscillation caused by the mass and motion of the device and its components.

(21) FIGS. 6-8 illustrate embodiments including components designed to mechanically isolate a device (other than its sensing and coupling components) from a vessel after the device applies a strike. The device includes a housing 40 mounted on a support plate 50, a body cover 24, and an end cover 20. The mounting plates 68 connect with an object (such as a vessel) wall and have holes for a mounting bracket 66. The mounting bracket 66, guide posts 52 and a top support plate 26 are connected by screws (or any other suitable fastener), and form a guide frame for the housing 40. The housing 40 and the support plate 50 have holes for linear bearings 38, 46, and 48 which allow slide movement of the housing 40 on the guide posts 52.

(22) A striker linear bearing mounted in the center of the housing 40 serves as guide for a striker shaft 58. A first end of the shaft 58 has elastic striker tip 64, and a second end connected with a cross beam 34. The cross beam 34 is connected with cores of a pair of solenoids 36 and with pair of dashpots 44. Rods of the dashpots 44 are connected with the support plate 50. A pair of dashpots 42 is connected by a first end with the top support plate 26 and by a second end with the housing 40. A pair of bumpers 32 serves as a positive stop for the housing 40. A pair of bumpers 30 serves as a positive stop for the cross beam 34, which is connected to the solenoid cores and the striker shaft 58. The body cover 24 has a vent breather 27. A sensor 28 is rigidly connected with the stationary part of the illustrated embodiment. Seals 22 are mounted on the end cover 20 and the support plate 50. Return springs 56 are mounted on the posts 52 and the striker shaft 58. These springs are supported by spring support washers 60 and are adjusted by adjusting collars 59. Bumper washers 62 serve as stops for support plate 50. An electrical conduit 54 may further be attached or in communication with support plate 50.

(23) At the moment of time when the driving voltage pulse energizes the solenoid of the driver, its core begins moving toward the vessel wall that accelerates the striker resulting in making an impact at the vessel wall. During the striker's motion toward the vessel wall, a reactive force of this motion creates a movement of members 40, 20, 24 and 50 in the direction opposite to the striker motion. In this process, Dampers 42, 44 are smoothing mutual oscillations of all moving members of the device. After each strike, recoil springs bring the moving members to their initial positions. A sensor (accelerometer in the one embodiment) that measures the wall oscillation is firmly linked to the vessel wall by posts 5, top support plate 26 and mounting bracket 66. Because immediately after the impact has been applied to the vessel wall, the movable masses of the striker 58 and the housing 40 become involved in a decaying oscillating process of relative motion by sliding over the guiding posts 52, their influence on the vessel wall oscillation is minimized, thereby allowing an undisturbed monitoring of combined oscillation of the vessel wall and the portion of the material attached to the wall inside the vessel.

(24) According to another example illustrated in FIG. 10, a reaction force is directed toward the pipe wall. The reaction force is caused by the inertia force of the moving and then quickly ceasing to move striker. The reaction force is used to initiate oscillation in the vessel body without the striker coming in dynamic contact with the vessel wall.

(25) In another example illustrated in FIGS. 11 and 12, the vessel body is forced to oscillate by a vibrating member of the vessel's construction such as a motor, a pump, a compactor or a local resistance inside the vessel that causes eddy currents within the material. In this example, the device's sensor acquires the vibration of the vessel body despite the device's striker being immobile.

(26) In an application of the device directed to measuring the mass flow rate of the material moving through a pipe, the device is equipped with a volumetric flow measuring unit that measures the mass flow of the pipe content by multiplying the measured material density by the measured volumetric flow. In an example having a vortex-type volumetric flow, the device has an immobile (or removed) striker. This device utilizes pipe body vibration initiated by a source located outside of the device. In particularly, the vibration is initiated by the turbulence generated when the material flow meets resistance from the vortex flow meter shedder member as shown in the functional diagram of FIG. 13.

(27) In another example, as shown in the FIG. 14, the support plate 50 is modified to accommodate a thermal sensor located in high proximity to the outer wall of the support plate thereby allowing for monitoring ambient air temperature variations. As is described further below, the signal from this thermal sensor is used to create a link to the device's output that provides for the high stability of measurement under wide changes of the ambient air temperature.

(28) In another example, the output from the first temperature sensor located within the support plate 50 is connected to the microprocessor. The output of the second temperature sensor located in proximity to the vibration sensing mechanism is also connected to the microprocessor. The second temperature sensor measures temperature around the vibration sensing means electronics. As is described further below, a simultaneous use of two thermal sensors provides for establishing a highly effective thermal stability link within the device. In addition, the output of the first thermal sensor can be used for calculating the value of the process temperature within the pipe or vessel.

(29) In another device, as shown in the FIG. 15, at least one thermal sensor is incorporated into the mounting bracket of the device that is used for the device's attachment to the pipe or vessel. This sensor's output is used for an accurate calculation of the process temperature required in those cases when there is a need in measuring the content material physical property at a set temperature that differs from the instantaneous process temperature.

(30) Measurement Processes

(31) Exemplary methods disclosed herein are based on monitoring the oscillatory motion of the segment of the vessel defined by the mechanical members that affix the vessel to a rigid plain that is substantially immobile relative to the vessel. Such motion may be initiated by the application of a temporal mechanical load directed at the wall. Such motion may be initiated by an external source of vibration such as a working pump, a motor, a compactor and similar objects. In this regard, a zero order approximation mechanical system, the properties of which the method exploits, can be classified as the beam with a uniformly distributed mass and a concentrated mass attached to the beam. In this model or approximation, the mass of the empty pipe segment together with the mass of the material constitute the mass of the pipe filled with the material that is used in the approximate beam model of the vessel. The oscillation of the beam is used to obtain information for determining several physical properties of the material filling the pipe segment including the density of this material, among others. The method of measurement is applicable to, at least, both basic types of non-gaseous free flowing vessel contents that are liquid materials, homogeneous and non-homogeneous; and loose solids including powders and other granulated materials. Due to the nature of the beam model the method provides for the measurement of the bulk density of these materials.

(32) Integrally, one example process 1300 is a sequence of the following acts, as illustrated in FIG. 4. The method's flowchart is comprised of two branches that depict two sub methods. A selection of the sub method depends on the manner in which oscillatory motion is imparted to the vessel. Below, the method will be described in its general form including both sub methods. Process 1300 begins at 1302 by the act of entry of data characterizing the vessel and the material filling the vessel. At 1304, the manner in which oscillatory motion is imparted to the vessel is selected. If striking is selected, then at 1306 the measurement apparatus determines acceptable values of the striking force and the vibration sensor gain. If striking is not selected then at 1308 the measurement apparatus determines the acceptable value of the vibration sensor gain. At 1310, the measurement apparatus initiates vibration at least at a single predetermined position on the outside wall of the vessel filled with non-gaseous free flowing matter to the known level. At 1312, the measurement apparatus captures the wall's oscillatory response to the mechanical load. At 1314, the measurement apparatus generates the vibration response signal spectrum (also called a vibration response spectrum). At 1316, the measurement apparatus selects parameters of the vibration spectrum that will be used to generate the measurement. At 1318, the measurement apparatus calculates the values of the measured variables using pre-determined relationships between the selected properties of the vibration spectrum and the measured variables obtained with regards to the measurement application data inserted at 1302. Process 1300 ends at 1320.

(33) Below, each act of the proposed method is described in detail for an example of the method that utilizes a single source of vibration and a single measured variable. In the following method description, for the sake of clarity, the single measured variable will be the density of the material filling the vessel and the vessel type will be a pipe.

(34) Act 1302:

(35) Entering data characterizing the vessel and the material filling the vessel.

(36) The parameters of the vessel and the filling material that are collectively described by the term Measurement Application Data should be sufficient for mathematically generating the vibration spectrum in the case of a single degree of freedom dynamic system beam with a uniformly distributed mass and a concentrated mass attached to the beam. A list of the Measurement Application Data corresponding to this dynamic system is presented below. 1. Pipe outside diameter (OD) 2. Pipe inside diameter (ID) or wall thickness 3. Pipe length between the pipe supports surrounding the measurement apparatus 4. Material of the pipe 5. Expected filling material's mean value of density 6. Type of the pipe supports, e.g., both ends simply supported or both ends clamped 7. Location of the concentrated mass, e.g., Mid-span or Free end
Act 1306:

(37) Determining an acceptable value of the striking force that should be applied to a vessel wall for the vessel actuation and an acceptable value of the vibration sensor gain.

(38) The process 1306 executes if striking is selected as the manner in which oscillatory motion is imparted to the vessel. According to the physics of the disclosed method of measuring by percussion, the point level, density or viscosity measurement requires that the sensor output signal satisfy certain conditions of a signal representation. This condition may include a dynamic range value, a time-based window of observation value and a signal decaying behavior. An adaptive strike control process is suggested to support the sensor output signal's satisfaction of the conditions of the signal representation regardless of parameters of the measurement application. The process performs a search for the acceptable value of the striking force and the gain of the vibration sensor and includes execution of the following operations: Initializing vibration of the vessel by striking at the wall at a certain beginning value of the striking force and a certain beginning value of the vibration sensor gain Capturing the sensor response Evaluating the sensor output signal against the criteria of the signal representation Adjusting the values of the striking force and the vibration sensor gain using the logic of two nested loops; beginning and ending values of the striking force and the gain are pre-determined by the design of the measurement apparatus Issuing a Failure to obtain acceptable striking force and vibration sensor gain message in the case when the force and the gain do not produce a sensor output signal that satisfies the conditions of the signal representation described above Using the obtained acceptable values of the striking force and the vibration sensor gain in the measurement beyond the process 1306 when the force and the gain produce a sensor output signal that satisfies the conditions of the signal representation described above
Act 1308:

(39) Determining an acceptable value of the vibration sensor gain.

(40) The process 1308 executes if striking is not selected as the manner in which oscillatory motion is imparted to the vessel actuation and passive vibration sensing is selected instead. The process performs a search for the acceptable value of the gain of the vibration sensor and includes execution of the following operations: Capturing the sensor response Evaluating the sensor output signal against the criteria of the signal representation Adjusting the value of the vibration sensor gain using the logic of the loop; beginning and ending values of the vibration sensor gain are pre-determined by the design of the measurement apparatus Issuing a Failure to obtain vibration sensor gain message in the case when the gain does not produce a sensor output signal that satisfies the conditions of the signal representation described above Using the obtained acceptable values of the vibration sensor gain in the measurement beyond the process 1310 when the gain produces a sensor output signal that satisfies the conditions of the signal representation described above
Act 1310:

(41) Initializing vibration at least at a single predetermined position on the outside wall of a vessel filled with some matter to a predetermined level.

(42) The vibration originates in the neighborhood of a mechanical impact with its center located on the outside wall of the vessel. The impact load's time diagram could be of various forms including a single pulse, a trainload of pulses (also called a pulse train), or a continuous periodical load (also called a continuous periodical pulse) as particular examples. Each load-type allows any kind of modulation, for example, Amplitude Modulation, Frequency Modulation, Pulse Modulation, Pulse-Code Modulation, or their combinations. In some examples, the mechanical impact at the wall may originate via an application of any suitable energy source depending on the technical requirements of the particular measurement project. Suitable energy sources may include a solenoid, a spring, a hydraulic and an air pressure-based drives.

(43) Act 1312:

(44) Capturing the wall oscillatory response to the mechanical load.

(45) A mechanical vibration captured by the receiver of the measuring system is quantified and stored in data storage of a computing mechanism executing the method.

(46) Act 1314:

(47) Producing vibration sensor response signal spectrum.

(48) The stored, quantified dataset is an input for a consequent data processing operation performed by a controller that is coupled to the data storage. This data processing operation results in the generation of the signal's harmonic representation through the application of the Fast Fourier Transform Procedure delivering the signal's amplitude spectrum defined on a range of frequencies.

(49) A search zone within vibration spectrum may be defined by calculating values of the fundamental harmonic frequency that are linked to upper and lower boundary values of the measured density within the known density range and with the consequent broadening of the calculated frequency range to account for possible discrepancies between the theoretical parameters of the single degree of freedom mechanical model and the parameters of the actual measurement application, e.g., pipe stiffness.

(50) Act 1316:

(51) Designating certain properties of the vibration spectrum as estimating variables of the measuring system and obtaining instantaneous values of these estimating variables.

(52) The particular properties of the vibration spectrum used as the estimating variables depend on which physical variable is targeted for measurement. For example, for measuring the density of the filling material, the frequency of the fundamental harmonic of the vibration spectrum should be used.

(53) This is so because a single degree of freedom mechanical dynamic system is characterized by the following relationship between the fundamental harmonic frequency and the parameters of the mechanical dynamic system:

(54) $\begin{array}{cc}f\frac{1}{2}\sqrt{\frac{k}{M}}& \left(1\right)\end{array}$
Where k denotes stiffness; M denotes oscillating mass. Assuming that there is no any additional mass attached to the wall, the expression for the total mass of the pipe segment between the supports can be described as follows.
M=M.sub.p+M.sub.c(2)
In the formula (2) M.sub.p represents the mass of the empty pipe segment; M.sub.c represents the mass of the filling material in the pipe. For a given empty pipe, the mass of the empty pipe is a constant value (attrition not being considered). However, the mass of the pipe content changes in time. For any pipe segment of the length (L) supported according a pipe support standard (e.g., the ASTM standard), the stiffness of the segment is not affected by changes in the environment including the changes of the ambient temperature, which can be a main measurement disturbing factor. Thus it is true that the density of the filling material is proportional to the square value of the period (T) of the fundamental harmonic, .sub.cT.sup.2. In the case of the single degree of freedom system model, this relationship is described by the formula:

(55) ${}_c=\frac{k{T}^2-4{}^2{M}_p}{4{}^2{V}_c}$
Where V.sub.c denotes the volume occupied by the filling material in the pipe segment of the length L.

(56) A similar approach can be taken toward more complex systems including the case of the beam with uniformly distributed mass and a concentrated mass of the measuring device attached to the pipe. Depending on the selected measured variable, the relationship between the properties of the vibration spectrum and the measured variable may have different view and different representation, e.g., a formula or a lookup table. Higher harmonics of the vibration spectrum may participate in these relationships too.

(57) Act 1318:

(58) Calculating values of the measured variables using pre-determined relationships between the selected properties of the vibration spectrum and the measured variables obtained with regards to the measurement application data entered at 1302.

(59) Continuing the pipe segment example, a conversion of the estimating variable f into the measured variable .sub.c can be performed using the following formulas.

(60) $\begin{array}{cc}{}_c=\frac{{}^4\mathrm{EIg}}{{}^3{L}^4{d}^2{f}^2}-\frac{4{\mathrm{cgM}}_s}{{\mathrm{Ld}}^2}-\frac{\left(D^2-d^2\right)}{d^2}I=q\left(D^4-d^4\right)M_s=\frac{1}{g}{W}_s& \left(3\right)\end{array}$
Where DPipe OD;

(61) dPipe ID;

(62) Density of the pipe wall material

(63) EYoung Modulus of the pipe wall material

(64) IMoment of Inertia of the pipe cross sectional area

(65) gGravity constant

(66) W.sub.sWeight of the vibration sensor used for producing the vibration spectrum

(67) M.sub.sMass of the vibration sensor

(68) B, cMeasurement application-dependent parameters

(69) qMeasurement units conversion factor

(70) It is to be appreciated that another important feature of the examples disclosed herein is that using an adequate mathematical model of the dynamic system Vessel with Filling MaterialActuator allows control of the accuracy of measurement by managing the amount of the measurement application data required for the measuring device setup. In the filling material density measurement example described below, the method is modified by the inclusion of acts for controlling the accuracy of the measuring device during the device's installation and setup. In this example the process continues beyond the act 1318.

(71) Act 1320:

(72) Obtaining at least two different values of the measured variable from two different material samples via a standard measuring device or a standard method. The two values of the measured variable must differ sufficiently to allow an effective improvement of the accuracy of the method. In the particular case of the material density measurement flowing through a 3 in. size pipe of the length 60 in., the difference between the material samples measurement should be greater or equal to 5%.
Act 1322:

(73) Calculating corrected values of the parameters B and c in the formula using the following expressions.

(74) $\begin{array}{cc}B=L\sqrt[4]{\frac{{}^3{d}^2{f}_1^2{f}_2^2\left({}_{c2}-{}_{c1}\right)}{\mathrm{EIg}\left(f_1^2-f_2^2\right)}}c=L\frac{f_2^2\left[d^2{}_{c2}+\left(D^2-d^2\right)\right]-f_1^2\left[d^2{}_{c1}+\left(D^2-d^2\right)\right]}{4{\mathrm{gM}}_s\left(f_1^2-f_2^2\right)}{f}_j{f}_j\left(t,t^{*}\right){}_{\mathrm{cj}}{}_{\mathrm{cj}}\left(t,t^{*}\right)j=1,2& \left(4\right)\end{array}$
Where f.sub.jf.sub.j(t, t*), j=1, 2 denotes the measuring device-generated frequency of the fundamental harmonic obtained at the moment of time t=t*. .sub.cj.sub.cj(t,t*), j=1, 2 denotes the density of the material sample obtained at the same moment of time t=t*.
Act 1324:

(75) Substituting values of the parameters B and c in the formula (3) with their values calculated using the formula (4).

(76) Act 1326:

(77) Calculating corrected values of the filling material density using the formula (3).

(78) Act 1328:

(79) Obtaining at least one value of the measured variable from a material sample via a standard measuring device or a standard method. The material sample measurement could be a single measurement or a statistically processed measurement (e.g., averaged by a number of measurements on the same material sample).
Act 1328:

(80) Calculating the measured variable's offset value as follows.
=.sub.c*(t=t*).sub.c.sup.0(f,t=t*)(5) Where .sub.c*(t=t*) denotes the material sample density measurement by the standard device or the standard method; the measurement time-stamped at t=t*; .sub.c.sup.0(f,t=t*) denotes the measurement of the filling material density produced by the measuring instrument of the method disclosed herein using the formula (3) and time-stamped at t=t*.
Act 1330:

(81) Calculating the corrected value of the measured variable using the following formula.
.sub.c=.sub.c.sup.0+(6)
The theory behind the formula (6) is that the density described by the formula (3) is represented by a family of almost parallel curves thereby making the correction (6) useful. The process 1300 of this example of the method ends at 1332.

(82) Depending on the measurement application's specification, certain acts can be skipped in the example of the method described above. For example, in the case where trend analysis is required, the acts 1320-1332 from the second method example may be skipped and the outcome of the measuring device will be governed by the acts 1302-1320 of the first example of the measurement method. In the case when the accuracy of the measuring device should be sufficient for a typical process control application, the acts 1320-1326 may be skipped in the second example of the measurement method. The entire method of the second example should be used for obtaining the best accuracy of measurement.

(83) In another example, to further enhance the long term stability of the measurement method, the method includes computation of a correction to the measured variable values to account for noise caused due the susceptibility to thermal energy of electronic parts of a vibration sensor. In this example, the correction is computed as a function of a link between the temperature inside the vibration sensor and the measured variable. In another example, the method includes computation of another correction to the measured variable values to account for noise caused due the susceptibility to thermal energy of mechanical parts of the vibration sensor. In this example, the correction is computed as a function of a link between the ambient temperature and the measured variable. The utilization of the links depends on the environmental conditions such that each of the links could be used solely and independently or both links could be used simultaneously and in some interrelationship.

(84) In another example of the method, the ambient temperature data obtained within a predefined proximity of the vessel's outer surface could be used for implementing the process temperature compensation function when certain properties should be measured at a set process temperature regardless of the temperature value existing on the moment of measurement. When executed, this temperature compensation function converts a value of physical property measured at a recorded temperature to a value (i.e., a compensated value) that the physical property would be measured to have at the set process temperature. This function is important in various chemical engineering measurement applications.

(85) The various temperature-based corrections and compensations described herein are additional acts executed within some examples of the earlier described measurement process 1300 that modify the generated output readings in accordance with the acts of the process 1300.

(86) Process 1300 depicts one particular sequence of acts in a particular example. The acts included in process 1300 may be performed by, or using, one or more computer systems specially configured as discussed herein. Some acts are optional and, as such, may be omitted in accord with one or more examples. Additionally, the order of acts can be altered, or other acts can be added, without departing from the scope of the systems and methods discussed herein. In addition, as discussed above, in at least one example, the acts are performed on a particular, specially configured machine, namely a measurement device configured according to the examples disclosed herein.

(87) Having thus described several aspects of at least one embodiment, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the scope of the embodiments discussed herein. Accordingly, the foregoing description and drawings are by way of example only.