MEASURING SYSTEM AND METHOD FOR MEASURING A MEASUREMENT VARIABLE OF A FLOWING FLUID

Abstract

A measuring system includes: a lumen forming a flow path and a flow obstruction arranged in the flow path for effecting a disturbance in a flowing fluid; a sensor arrangement adapted to produce a first sensor signal and a second sensor signal; and transmitter electronics. The transmitter electronics are adapted to receive both the first and second sensor signals and to convert such into first and second sensor signal sampling sequences approximating the first and second sensor signals, respectively, the transmitter electronics further adapted using a digital adaptive filter to ascertain from the first sampling sequence a filter coefficients set and therewith to form a z-transfer function for filtering the second sampling sequence such that the z-transfer function is determined by the filter coefficients set, the signal filter and the second sampling sequence to produce a wanted signal sequence, to produce therefrom digital measured values representing a measurement variable.

Claims

1-33. (canceled)

34. A measuring system for measuring at least one measurement variable, changeable as a function of time, of a fluid flowing along a flow path with a predetermined flow direction, the measuring system comprising: a tube arrangement comprising a lumen defining a first portion of the flow path, a second portion of the flow path disposed in a flow direction downstream of the first portion, and a third portion of the flow path disposed in the flow direction downstream of the second portion and a tube wall surrounding the lumen; a flow obstruction arranged within the tube arrangement in the second portion of the flow path, the flow obstruction configured to effect a disturbance in the flowing fluid, the disturbance dependent on the at least one measurement variable and/or serving as a measurable effect dependent on the at least one measurement variable; a first sensor arrangement configured to generate a first sensor signal having a first frequency spectrum influenced by the fluid flowing within the first portion; a second sensor arrangement configured to generate a second sensor signal having a second frequency spectrum influenced by the fluid flowing within the third portion, the second frequency spectrum deviating from the first frequency spectrum and/or including at least one wanted component, the at least one wanted component including a spectral signal component influenced by the at least one measurement variable as regards at least one signal parameter; and a transmitter electronics including a microprocessor and configured to: receive the first sensor signal and convert such into a first sensor signal sampling sequence approximating the first sensor signal, the first sensor signal sampling sequence including a first sequence of digital sampled values, defined by S.sub.D1[m]=S.sub.D1[t.sub.m.Math.f.sub.s1], using a first sampling rate, defined by f.sub.s1=1/(t.sub.m+1-t.sub.m)=1/T.sub.s1, from the first sensor signal at different sampling points in time, given by t.sub.n=n.Math.T.sub.s1; receive the second sensor signal and convert such into a second sensor signal sampling sequence approximating the second sensor signal, the second sensor signal sampling sequence including a second sequence of digital sampled values, defined by S.sub.D2[n]=S.sub.D2[t.sub.n.Math.f.sub.s2] using a second sampling rate, defined by f.sub.s2=1/(t.sub.n+1-t.sub.n)=1/T.sub.s2, from the second sensor signal at different sampling points in time, given by t.sub.n=n.Math.T.sub.s2, such that the second sensor signal sampling sequence approximates at least one wanted spectral signal component of the second sensor signal influenced by the at least one measurement variable; using a digital adaptive filter, ascertain from the first sensor signal sampling sequence a wanted signal filter coefficients set including a set of N filter coefficients; using the wanted signal filter coefficients set, generate a first z-transfer function of a wanted signal filter, defined as: $G_{FIR}^{*} (z) = Z (g [n]) = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. z^{- k} = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. e^{- j ω T_{s 2},}$ wherein w.sub.k are the filter coefficients, the wanted signal filter being a digital filter adapted to filter the second sensor signal sampling sequence such that the first z-transfer function of the wanted signal filter is determined by the wanted signal filter coefficients set; generate a wanted signal sequence, using the wanted signal filter and the second sensor signal sampling sequence, the wanted signal sequence being a sequence of digital function values defined by: ${\hat{S}}_{D 2} [n] = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. S_{D 2} [n - k],$ to generate from the wanted signal sequence a measured values sequence, being a sequence of digital measured values representing the at least one measurement variable and following one after the other in time.

35. The measuring system of claim 34, wherein the transmitter electronics is configured to determine the filter coefficients of the wanted signal filter coefficients set using a least mean squares algorithm and/or a recursive least squares algorithm.

36. The measuring system of claim 34, wherein the transmitter electronics includes a memory configured to store at least the filter coefficients of the wanted signal filter coefficients set.

37. The measuring system of claim 34, wherein the transmitter electronics is configured to repeatedly calculate a transversal filter coefficients set of M filter coefficients determining a second z-transfer function, defined by: $G_{LPE}^{*} (z) = Z (g [m]) = {.Math.}_{k = 1}^{M} w 1_{k} .Math. z^{- k} or$ $G_{L P E}^{*} (z) = Z (g [m]) = {.Math.}_{k = 1}^{M} w 1_{k} .Math. z^{- k} = {.Math.}_{k = 1}^{M} w 1_{k} .Math. e^{- j ω T_{s 1}},$ of a transversal filter of the digital adaptive filter.

38. The measuring system of claim 37, wherein the transmitter electronics is configured to ascertain the wanted signal filter coefficients set for the wanted signal filter from the transversal filter coefficients set of the transversal filter.

39. The measuring system of claim 34, wherein the digital adaptive filter is configured to generate from the first sensor signal sampling sequence an estimated signal sequence, being a sequence of digital function values, defined by: ${\hat{S}}_{D 1} [m] = \overset{M}{\underset{k = 1}{.Math.}} w 1_{k} .Math. S_{D 1} [m - k],$ calculated from the first sensor signal sampling sequence using a digital transversal filter such that the estimated signal sequence is at least at times equal to or at least approximately equal to the sensor signal sampling sequence or has a minimum of least squares residuals from the sensor signal sampling sequence under a best linear unbiased prediction.

40. The measuring system of claim 34, wherein the transmitter electronics is configured to ascertain a frequency of the wanted component based on the wanted signal sequence.

41. The measuring system of claim 34, wherein the transmitter electronics is configured to determine a flow velocity and/or a volume flow rate of the fluid based on a frequency of the wanted component obtained from the wanted signal sequence.

42. The measuring system of claim 34, wherein the second portion, or the flow obstruction formed therewith, is adapted to increase a flow velocity of the fluid flowing passed and/or through and/or to lessen a static pressure prevailing in the fluid flowing passed and/or through and/or to effect a pressure difference dependent on a volume flow rate along a measuring path formed by the first, second and third portions.

43. The measuring system of claim 34, wherein the second portion, or the flow obstruction formed therewith, is adapted to induce vortices in the fluid such that a Kármán vortex street is formed in the fluid flowing downstream of the flow obstruction.

44. The measuring system of claim 34, wherein the flow obstruction is formed by a diaphragm.

45. The measuring system of claim 34, wherein the flow obstruction is formed by a prismatic bluff body.

46. The measuring system of claim 34, wherein the flow obstruction is formed by a nozzle.

47. The measuring system of claim 34, wherein: the first sensor arrangement includes a pressure sensor disposed at the first portion; and/or the second sensor arrangement includes a pressure sensor disposed at least partially at the third portion; and/or the first sensor arrangement includes a microphone disposed at the first portion; and/or the second sensor arrangement includes a microphone disposed at least partially at the third portion; and/or the second sensor arrangement includes a sensor paddle protruding into the third portion; and/or the first sensor arrangement includes two ultrasonic transducers, both disposed at the first portion; and/or the second sensor arrangement includes two ultrasonic transducers, both disposed at least partially at the third portion; and/or the transmitter electronics is electrically connected both with the first sensor arrangement and the second sensor arrangement; and/or the second portion includes a prismatic bluff body; and/or the second portion includes a diaphragm; and/or at least the second portion includes a vibronic measuring transducer; and/or a smallest distance between the first and third portions amounts to greater than a three times a smallest caliber of the tube arrangement; and/or a smallest distance between the first and third portions amounts to less than ten times a greatest caliber of the tube arrangement.

48. A method for measuring at least one measurement variable, changeable as a function of time, of a fluid flowing along a flow path with a predetermined flow direction, the method comprising: providing the flow path, which includes a first portion, a second portion disposed in the flow direction downstream of the first portion, and a third portion disposed in the flow direction downstream of the second portion, wherein within the second portion a flow obstruction is configured to effect a disturbance in the flowing fluid dependent on the at least one measurement variable and/or a measurable effect dependent on the at least one measurement variable; enabling the fluid to flow along the flow path such that volume portions of the fluid flow from the first portion to the second portion and then to the third portion, wherein the flow obstruction of the second portion effects the disturbance; generating a first sensor signal having a first frequency spectrum influenced by the fluid flowing within the first portion; converting the first sensor signal into a first sensor signal sampling sequence of digital sampled values approximating the first sensor signal obtained from the first sensor signal at different, time-equidistant sampling points in time at a constant sampling rate; generating a second sensor signal having a second frequency spectrum influenced by the fluid flowing within the second portion and/or within the third portion, wherein the second frequency spectrum deviating from the first frequency spectrum and/or includes at least one wanted spectral signal component influenced by the at least one measurement variable or the disturbance with respect to at least one signal parameter; converting the second sensor signal into a second sensor signal sampling sequence of digital sampled values approximating the second sensor signal obtained from the second sensor signal at different, time-equidistant sampling points in time at a constant sampling rate, wherein the second sensor signal sampling sequence approximates at least one wanted spectral signal component of the second sensor signal influenced by the at least one measurement variable; using the first sensor signal sampling sequence and a digital adaptive filter to determine from the first sensor signal sampling sequence at least one wanted signal filter coefficients set, including at least five filter coefficients and/or filter coefficients at least partially differing from one another; using the wanted signal filter coefficients set to define a first z-transfer function of a wanted signal filter, the first z-transfer function defined as: $G_{FIR}^{*} (z) = Z (g [n]) = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. z^{- k} = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. e^{- j ω T_{s 2},}$ wherein the wanted signal filter is a digital filter configured to filter the second sensor signal sampling sequence such that the first z-transfer function of the wanted signal filter is determined by the wanted signal filter coefficients set, wherein N is the number of filter coefficients, w.sub.k, and T.sub.se is the sampling period of the second sensor signal; using the second sensor signal sampling sequence and the wanted signal filter to generate a wanted signal sequence, wherein the wanted signal sequence is a sequence of digital function values calculated from the second sensor signal sampling sequence using the wanted signal filter, the wanted signal sequence; and generating a measured values sequence from the wanted signal sequence, wherein the measured values sequence is a sequence of digital measured values representing the at least one measurement variable and following one after the other in time.

49. The method of claim 48, wherein: the filter coefficients of the wanted signal filter coefficients set are determined using an least mean squares algorithm and/or a recursive least squares algorithm; and/or at least two of the filter coefficients of the wanted signal filter coefficients set differ from one another; and/or the wanted signal filter coefficients set, or the wanted signal filter defined therewith, includes five or more filter coefficients; and/or the sampling rate of the first sensor signal sampling sequence and the sampling rate of the second sensor signal sampling sequence are the same.

50. The method of claim 48, further comprising recurringly and/or cyclically replacing a wanted signal filter coefficients set previously determined from the first sensor signal sampling sequence and used to determine the first z-transfer function of the wanted signal filter with a subsequent wanted signal filter coefficients set.

51. The method of claim 50, wherein the replacing of the wanted signal filter coefficients set previously determined with the subsequent wanted signal filter coefficients set is repeated cyclically at an exchange rate such that the exchange rate is lower than the sampling rate of the first sensor signal sampling sequence and/or is lower than the sampling rate of the second sensor signal sampling sequence.

52. The method of claim 48, wherein the digital adaptive filter comprises a digital transversal filter having a second z-transfer function defined as: $G_{LPE}^{*} (z) = Z (g [m]) = {.Math.}_{k = 1}^{M} w 1_{k} .Math. z^{- k} or$ $G_{L P E}^{*} (z) = Z (g [m]) = {.Math.}_{k = 1}^{M} w 1_{k} .Math. z^{- k} = {.Math.}_{k = 1}^{M} w 1_{k} .Math. e^{- j ω T_{s 1}},$ wherein M is the number of transversal filter coefficients, w1.sub.k.

53. The method of claim 52, further comprising determining the wanted signal filter coefficients set for the wanted signal filter from the transversal filter coefficients set of the transversal filter such that the wanted signal filter coefficients set includes the filter coefficients of the transversal filter coefficients set.

54. The method of claim 52, further comprising generating an estimated signal sequence using the transversal filter and the first sensor signal sampling sequence, wherein the estimated signal sequence is a sequence of calculated digital function values from the first sensor signal sampling sequence using the digital transversal filter.

55. The method of claim 54, further comprising: determining the transversal filter coefficients set from filter coefficients defining the second z-transfer function of the digital transversal filter such that the estimated signal sequence of the first sensor signal sampling sequence approximates or predicts the first sensor signal sampling sequence such that the estimated signal sequence has a minimum of least squares residuals from the first sensor signal sampling sequence; and/or determining the wanted signal filter coefficients set for the wanted signal filter from the transversal filter coefficients set of the transversal filter when the estimated signal sequence for a predetermined sample, or time, interval equals or at least approximately equals the first sensor signal sampling sequence such that the estimated signal sequence has a minimum of least squares residuals from the first sensor signal sampling sequence.

56. The method of claim 54, further comprising generating an estimate error sequence in which a deviation between a sampling value of the first sensor signal sampling sequence and a function value of digital function values representing the estimated signal sequence.

57. The method of claim 56, further comprising generating the estimate error sequence from the first sensor signal sampling sequence such that the digital function values calculated from the first sensor signal sampling sequence correspond to the estimate error sequence using an estimate error function determined by the second z-transfer function of the digital transversal filter using the transversal filter coefficients set.

58. The method of claim 52, wherein: the wanted signal filter coefficients set includes all M filter coefficients of the transversal filter coefficients set such that each filter coefficient of the transversal filter coefficients set is adopted as a filter coefficient of the wanted signal filter coefficients set and/or that; and/or the wanted signal filter coefficients set, or the wanted signal filter defined therewith, includes a non-zero filter coefficient and/or a predetermined filter coefficient which the transversal filter coefficients set, or the transversal filter defined therewith, does not include, and/or wherein the transversal filter coefficients set, or the transversal filter defined therewith, includes five or more filter coefficients; and/or wherein the filter coefficients of the transversal filter coefficients set are determined using a least mean squares algorithm and/or using a recursive least squares algorithm.

59. The method of claim 48, wherein the second sensor signal includes at least one wanted spectral signal component influenced by the at least one measurement variable as regards at least one signal parameter, including one of an amplitude, a frequency and a phase angle.

60. The method of claim 59, wherein the second sensor signal sampling sequence includes, or approximates, the at least one wanted component.

61. The method of claim 60, wherein the wanted signal sequence includes, or approximates, at least the wanted component.

62. The method of claim 48, further comprising: generating the first sensor signal using a first sensor arrangement disposed at least partially at the first portion and/or at least partially within the first portion; and generating the second sensor signal using a second sensor arrangement disposed at least partially at the third portion and/or at least partially within the third portion.

63. The method of claim 48, wherein effecting the disturbance in the fluid flowing through the second portion comprises: increasing a flow velocity of the fluid flowing within the second portion; and/or lessening a static pressure prevailing in the fluid flowing within the second portion; and/or providing a pressure gradient dependent on a volume flow within the fluid flowing along the flow path; and/or inducing vortices in the fluid flowing within the second portion as to form a Kámán vortex street in the fluid flowing downstream of the flow obstruction.

64. The method of claim 48, wherein: the first sensor arrangement includes a pressure sensor positioned at the first portion; and/or the second sensor arrangement includes a pressure sensor positioned at the second and/or third portion; and/or the second sensor arrangement includes a sensor paddle protruding into the third portion; and/or the first sensor arrangement includes at least one ultrasonic transducer disposed at the first portion; and/or the second sensor arrangement includes at least one ultrasonic transducer disposed at the second and/or third portion; and/or the second portion includes a bluff body; and/or the second portion includes a diaphragm; and/or the second portion includes a tube arrangement of a vibronic measuring transducer, comprising two or more tubes and/or a line branching and/or a line junction.

65. The method of claim 48, wherein the method is performed using a measuring system adapted to perform the method, the measuring system comprising: a tube arrangement comprising a lumen defining the first portion of the flow path, the second portion of the flow path disposed in a flow direction downstream of the first portion, and the third portion of the flow path disposed in the flow direction downstream of the second portion and a tube wall surrounding the lumen; the flow obstruction arranged within the tube arrangement in the second portion of the flow path, the flow obstruction configured to effect a disturbance in the flowing fluid, the disturbance dependent on the at least one measurement variable and/or serving as a measurable effect dependent on the at least one measurement variable; a first sensor arrangement configured to generate a first sensor signal having a first frequency spectrum influenced by the fluid flowing within the first portion; a second sensor arrangement configured to generate a second sensor signal having a second frequency spectrum influenced by the fluid flowing within the third portion, the second frequency spectrum deviating from the first frequency spectrum and/or including at least one wanted component, the at least one wanted component including a spectral signal component influenced by the at least one measurement variable as regards at least one signal parameter; and a transmitter electronics including a microprocessor and configured to: receive the first sensor signal and convert such into a first sensor signal sampling sequence approximating the first sensor signal, the first sensor signal sampling sequence including a first sequence of digital sampled values, defined by S.sub.D1[m]=S.sub.D1[t.sub.m.Math.f.sub.s1], using a first sampling rate, defined by f.sub.s1=1/(t.sub.m+1-t.sub.m)=1/T.sub.s1, from the first sensor signal at different sampling points in time, given by t.sub.n=n.Math.T.sub.s1; receive the second sensor signal and convert such into a second sensor signal sampling sequence approximating the second sensor signal, the second sensor signal sampling sequence including a second sequence of digital sampled values, defined by S.sub.D2[n]=S.sub.D2[t.sub.n.Math.f.sub.s2] using a second sampling rate, defined by f.sub.s2=1/(t.sub.n+1-t.sub.n)=1/T.sub.s2, from the second sensor signal at different sampling points in time, given by t.sub.n=n.Math.T.sub.s2, such that the second sensor signal sampling sequence approximates at least one wanted spectral signal component of the second sensor signal influenced by the at least one measurement variable; using a digital adaptive filter, ascertain from the first sensor signal sampling sequence a wanted signal filter coefficients set including a set of N filter coefficients; using the wanted signal filter coefficients set, generate a first z-transfer function of a wanted signal filter, defined as: $G_{FIR}^{*} (z) = Z (g [n]) = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. z^{- k} = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. e^{- j ω T_{s 2},}$ wherein w.sub.k are the filter coefficients, the wanted signal filter being a digital filter adapted to filter the second sensor signal sampling sequence such that the first z-transfer function of the wanted signal filter is determined by the wanted signal filter coefficients set; generate a wanted signal sequence, using the wanted signal filter and the second sensor signal sampling sequence, the wanted signal sequence being a sequence of digital function values defined by: ${\hat{S}}_{D 2} [n] = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. S_{D 2} [n - k],$ to generate from the wanted signal sequence a measured values sequence, being a sequence of digital measured values representing the at least one measurement variable and following one after the other in time.

66. The method of claim 65, wherein the method is performed for setup and/or commissioning of the measuring system.

Description

[0076] THE FIGURES OF THE DRAWING SHOW AS FOLLOWS

[0077] FIGS. 1, 2, 3 examples of embodiments of measuring systems of the invention;

[0078] FIG. 4 schematically, measuring- and evaluating methods especially executable by means of measuring systems according to FIGS. 1, 2, 3;

[0079] FIG. 5a, 5b in different, partially sectioned views, a first variant of a tube arrangement suitable for forming a measuring system of the invention;

[0080] FIG. 6a, 6b in different, partially sectioned, views, a second variant of a tube arrangement suitable for forming a measuring system of the invention;

[0081] FIG. 7a, 7b in different, partially sectioned, views, a third variant of a tube arrangement suitable for forming a measuring system of the invention;

[0082] FIG. 8 a fourth variant of a tube arrangement suitable for forming a measuring system of the invention; and

[0083] FIG. 9a, 9b schematically, a flow diagram of a method of the invention, or an embodiment thereof.

[0084] Shown schematically in FIGS. 1, 2, 3, 4, 5a, 5b, 6a, 6b 7a, 7b and 8 are examples of embodiments of measuring systems for measuring at least one measurement variable x, in given cases, also a measurement variable x changeable as a function of time, especially a pressure, a pressure difference, a temperature, a density, a flow parameter such as, e.g., a flow velocity and/or a volume flow rate, of a fluid FL flowing along a flow path with a predetermined flow direction, or a corresponding method (FIG. 4). The flow path can be embodied, for example, by means of a pipeline, or by means of a component of a filling plant, a tank farm, a chemical plant and/or a plant, in which a product is made from a raw or starting material by the application of chemical, physical or biological procedures, a heat supply network, a circulatory system of a turbine or, for example, also a component of a natural- or biogas plant or a gas supply network. Accordingly, the fluid FL can be, for example, an oil, an aqueous liquid, a vapor or, for example, also a condensate drained from a vapor line, or, for example, also hydrogen, nitrogen, oxygen or helium, methane, carbon dioxide, air, phosgene, or, in given cases, also compressed natural- or biogas.

[0085] The measuring system of the invention comprises at least one tube arrangement 100 (for example, one insertable into the course of the above mentioned pipeline, or embodied as a component of the same) having a lumen 100*, by means of which, as well as also shown in FIGS. 1, 2, 3, 4, 5a, 5b, 6a, 6b, 7a, 7b and 8, there is formed a first portion 100-1 of the above described flow path, a second portion 100-2 of the flow path located in the flow direction downstream of the first portion 100-1, as well as a third portion 100-3 of the flow path located in the flow direction downstream of the second portion 100-2. Additionally, the tube arrangement 100 includes a tube wall 110 surrounding the lumen 100*, for example, a metal and/or monolithic tube wall 110, as well as a flow obstruction 120 (for example, a flow obstruction 120 fixedly connected to an inside of the tube wall facing the lumen 100* and/or a monolithic flow obstruction 120) arranged within the tube arrangement in the second portion 100-2 of the flow path for effecting a (measuring system internal) disturbance d in the flowing fluid; this, especially, also in such a manner that the disturbance d depends on the at least one measurement variable x (d=f{x}), or can be helpful as a measurable effect dependent on the at least one measurement variable. Tube arrangement 100 can have a single tube or a plurality of tubes guiding the fluid in parallel and/or serially connected. Tube wall 110 and the flow obstruction 120 can, for example, be of the same material, for example, in given cases, a stainless steel or a nickel-based alloy. Alternatively or supplementally, tube wall 110 and flow obstruction 120 can, for example, also be components of one and the same, for example, cast or sintered, monolithic, formed piece. In this way, the tube wall can in advantageous manner be free of joints, which are most often complicated to produce and/or test, or free of undesired or disturbing welded seams on the inside of the tube wall.

[0086] In an additional embodiment of the invention, the portion 100-2, and the therein embodied flow obstruction 120, are adapted to increase a flow velocity of the fluid flowing through and/or past and/or to lessen a static pressure reigning within the fluid and/or to provide along a measuring path formed by means of the portions 100-1, 100-2, 100-3 a pressure difference dependent on a volume flow and/or pressure fluctuations dependent on flow velocity. For example, the portion 100-2, or the flow obstruction 120 formed therewith, can also be adapted to induce vortices in the fluid flowing past, in such a manner that a Kármán vortex street is formed in the fluid flowing downstream of the flow obstruction 120. The flow obstruction 120 can, as well as also shown schematically in FIGS. 5a, 5b, 6a, 6b, 7a, 7b and 8, accordingly, among other things, also be formed by means of a diaphragm (FIG. 6a, 6b), for example, a standard diaphragm, by means of a, for example, supercritical, nozzle, by means of a cone (FIG. 7a, 7b) and/or, for example, a prismatically formed, bluff body (FIG. 5a, 5b). In another embodiment of the invention, at least the portion 100-2 is formed by means of a vibronic measuring transducer comprising, for example, two or more tubes and/or a line branching and/or a line junction. The measuring transducer can, for example, however, also be a component of a Coriolis-mass flow-measuring device, or a vibronic density-measuring device (FIG. 8). In an additional embodiment of the invention, the portions are, furthermore, so embodied and arranged that, not least of all in order to be able properly to form the above-mentioned disturbance d for the measuring, a smallest distance between the portion 100-1 and the portion 100-3 amounts to greater than 3-times a smallest caliber of the tube arrangement and/or that, for example, in order to be able to form the measuring system as compactly as possible, a smallest distance between the portion 100-1 and the portion 100-3 amounts to less than 10-times a greatest caliber of the tube arrangement.

[0087] As shown schematically in FIGS. 1, 2, 3, 4, 5a, 5b, 6a, 6b, 7a, 7b and 8, in each case, or evident from a combination of the figures, the measuring system of the invention comprises, furthermore, an inlet side, first sensor arrangement 210, which is adapted to produce at least one, for example, electrical or optical, first sensor signal s1, which has a first frequency spectrum influenced by the fluid flowing within the portion 100-1, as well as an outlet side, second sensor arrangement 220 (for example, a sensor arrangement 220 of the same type- or construction as sensor arrangement 210), which is adapted to produce at least one, for example, electrical or optical or sensor signal s1 equal type, second sensor signal s2, which has a second frequency spectrum influenced by the fluid flowing within the portion 100-3, especially deviating from the above described, first frequency spectrum of the sensor signal s1; this, especially, in such a manner that the sensor signal s2, or its frequency spectrum, contains at least one wanted component s.sub.W—for example, a wanted component s.sub.W not contained in the sensor signal s1-, namely a spectral signal component influenced by the at least one measurement variable x, or the above described disturbance d, as regards at least one signal parameter, for example, an amplitude, a frequency or a phase angle,. Each of the sensor signals s1, s2 can have, for example, an electrical (alternating-)voltage corresponding to the measurement variable x and/or an electrical (alternating-)electrical current corresponding to the measurement variable x. In the above-described case, in which the induced disturbance d is a Kármán vortex street, for example, such a spectral signal component of the sensor signal can serve as wanted component s.sub.W, whose signal frequency corresponds to an instantaneous shedding rate of Karman vortex street forming vortices from the flow obstruction 120 embodied by means of the bluff body.

[0088] As shown schematically in FIGS. 1, 2, 3, 4, 5a, 5b, 6a, 6b, 7a, 7b and 8, the sensor arrangement 210 can be arranged at least partially directly at the portion 100-1 and/or at least partially within the portion 100-1 and/or the sensor arrangement 220 can be arranged at least partially directly at the portion 100-3 and/or at least partially within the portion 100-3. The sensor arrangement 210 can be formed, for example, by means of a conventional, first, physical to electrical-transducer element, in given cases, also only positioned at the portion 100-1, and the sensor arrangement 220 can be formed, for example, by means of a conventional, second, physical to electrical-transducer element, in given cases, only positioned at the portion 100-3. Serving as physical to electrical-transducer element for the sensor arrangement 210, and/or for the sensor arrangement 220, can be, in each case, for example, a capacitive pressure sensor, in given cases, a capacitive and/or inductive microphone, for example, also a dynamic microphone, a piezo microphone and even a high frequency capacitor microphone, and/or a pair of ultrasonic transducers positioned diametrally opposite one another on the tube arrangement. At least for the above-referenced case, in which the flow obstruction 120 is formed by means of a prismatic bluff body, and/or a Karman-type vortex street is formed by means of the flow obstruction 120 in the flowing fluid, for example, also a sensor paddle protruding into the portion 100-3 can serve as physical to electrical-transducer element for the sensor arrangement 220.

[0089] As, among others, evident from FIGS. 1, 2, 3, 4, the measuring system comprises, furthermore, a transmitter electronics 20-, for example, a transmitter electronics 20 contained in an industrial grade, robust, in given cases, also pressure-, or explosion resistant, and/or at least against water spray externally sealed, protective housing 200 and/or formed, for example, by means of at least one microprocessor (μC). Transmitter electronics 20 is electrically connected to the sensor arrangements 210, 220, or communicates at least with the sensor arrangements 210, 220 during operation of the measuring system. The at least two sensors signals s1, s2 can, such as schematically shown in FIGS. 1 and 3, or directly evident from their combination, be fed to the transmitter electronics 20, for example, by means of corresponding connection wires. The above-mentioned protective housing 200 can, for example, be made of a metal, for instance, a stainless steel or aluminum, and/or be produced by means of a casting method, such as e.g. an investment casting- or a pressure casting method (HPDC); it can, however, for example, also be formed by means of a plastic cast part produced in an injection molding method. The measuring system can, as well as also shown in FIGS. 1 and 3, be embodied, for example, also as a prefabricated (for example, by the manufacturer) measuring system in compact construction, consequently also as a self-contained, compact-measuring device, in such a manner that the protective housing 200 together with the transmitter electronics 20 arranged therein is positioned directly on the tube arrangement, in given cases, also quite near to the sensor arrangements 210, 220, and is connected—for example, by means of a neck shaped connection nozzle 300—rigidly, in given cases, also releasably, with the tube arrangement. In accordance therewith, used as measuring system, for example, insertable into the course of the pipeline, consequently ultimately forming a section of the pipeline, can be a prefabricated vortex flow measuring device or, for example, also a prefabricated pressure difference flow measuring device. The measuring system can, thus, at least as regards its mechanical construction, for example, also correspond to those of the above mentioned JP-A 0682281, US-A 2017/0328750, US-A 2011/0247423, US-A 2007/0084298, WO-A 95/08758, WO-A 00/34744, WO-A 2008/061551, WO-A 2009/158605, WO-A 2013/180843, WO-A 2018/016984 or the German patent applications DE102017012067.6, and DE102017012066.8. Alternatively, the protective housing 200 can, for example, however, also be remote from the tube arrangement and be connected by means of corresponding cables with the tube arrangement and the accompanying sensor arrangements.

[0090] The transmitter electronics 20 is adapted, furthermore, to receive each of the sensor signals s1, s2 and to process them, for example, to generate the measured values X.sub.M, in given cases, also in real time and/or in the form of fieldbus transferable digital values, namely, digital values in each case encapsulated in a corresponding fieldbus-telegram and representing the at least one measurement variable x. The measured values X.sub.M generated by means of the transmitter electronics 20 can, for example, be displayed on-site and/or be transmitted—per wire, e.g. DIN IEC 60381-1 conforming, via connected fieldbus and/or wirelessly per radio, e.g. IEEE 802.15.1 or IEEE 802.15.4 conforming—to an electronic data processing system, for instance, a programmable logic controller (PLC) and/or a process control station. For displaying measuring system internally produced measured values and/or, in given cases, measuring system internally generated system status messages, such as, for instance, a failure message or an alarm, on-site, the measuring system can have, for example, a display- and interaction element HMI, such as, for instance, an LCD-, OFED- or TFT display placed in the protective housing 200 behind a window pane correspondingly provided therein, together with a corresponding input keypad and/or a touch screen communicating with the transmitter electronics 20. In given cases, the display- and interaction element HMI can also be portable and even be embodied—such as shown in FIG. 3—as a component of the transmitter electronics 20. In advantageous manner, the, for example, also remotely parameterable, transmitter electronics 20 can, furthermore, be so designed that during operation of the measuring system it can exchange, via a data transmission system, for example, a fieldbus system and/or wirelessly per radio, measuring—and/or other operating data, such as, for instance, current parameter measured values of the flowing fluid, measuring system specific system diagnostic values and/or setting values serving for control of the measuring system, with a superordinated electronic data processing system, for example, a programmable logic controller (PLC), a personal computer and/or a work station. Furthermore, the transmitter electronics 20 can be so designed that it can be supplied from an external energy supply, for example, also via the aforementioned fieldbus system. Alternatively or supplementally, however, also a chemical energy storer can be used for energy supply of the measuring system, for instance, in the form of a single-use battery-, or a rechargeable battery-pack placed within the protective housing 200 or within a separate supply module appropriately docked on the protective housing 200. Particularly for the mentioned case, in which the measuring system is provided for coupling to a fieldbus- or other communication means, the, for example, also (re-)programmable on-site and/or via communication apparatus, transmitter electronics 20 can, furthermore, have a communication interface COM embodied for data communication according to one of the relevant industry standards. The communication interface COM can be adapted e.g. to transfer measuring- and/or operating data, consequently measured values representing the at least one measurement variable, to the above-mentioned programmable logic controller or to a superordinated process control system and/or to receive settings data for the measuring system. Moreover, the transmitter electronics 20 can, for example, have an internal power supply circuit PSC, which is fed during operation via the aforementioned fieldbus system from an external energy supply provided in the aforementioned data processing system. In such case, the transmitter electronics 20 can, furthermore, e.g. be so embodied that it is electrically connectable by means of a two-wire connection 2L, for example, configured as a 4-20 mA electrical current loop, with the external electronic data processing system and via that be supplied with electrical energy as well as being able to transmit measured values to the data processing system; the measuring system can, however, for example, also be embodied as a so-called four-conductor measuring device, in the case of which the internal power supply circuit PSC of the transmitter electronics 20 is connected by means of a first pair of lines with an external energy supply and the above-mentioned internal communication circuit COM of the transmitter electronics 20 is connected by means of a second pair of lines with an external data processing circuit or an external data sending system.

[0091] For processing the at least two sensors signals s1, s2, or for generating the measured values X.sub.M from the sensor signals s1, s2, the transmitter electronics 20 can, such as also shown schematically in FIG. 3, have, furthermore, a measuring- and evaluating-circuit μC—for example, one formed by means of one or more microprocessors and/or by means of one or more digital signal processors (DSP) and/or by means of one or more programmable logic chips (FPGA) and/or by means of one or more customer specific programmed logic chips (ASIC) and/or installed as a microcomputer. Each of the sensor signals s1, s2 can, accordingly, firstly be conditioned in the transmitter electronics 20 for further evaluation, for example, by means of a signal input stage A/D provided in the measuring- and evaluating circuit μC and equally as well forming, in each case, an interface to the sensor arrangement 210, and to the sensor arrangement 220, namely suitably preamplified and—not least of all for the purpose of a corresponding band limiting for ensuring the Nyquist sampling theorem—thereafter be filtered. The measuring- and evaluating circuit μC can, additionally, have, as well as also shown schematically in FIG. 3, at least one non-volatile memory EEPROM, for example, serving for storing of control- and operating programs, and/or setting values determining functions of the measuring- and evaluating circuit μC, and/or volatile memory RAM, for example, serving for the temporary storing of sampled values generated by means of the signal input stage A/D and/or integrated in the, in given cases, provided, at least one microprocessor. Additionally, for example, also program-code for evaluation programs for the measuring- and evaluating circuit μC serving for generating measured values can stored be persistently in the non-volatile data memory EEPROM and, upon the starting of the transmitter electronics 20, be loaded into the volatile data memory RAM. Equally, measured values generated during operation by means of the transmitter electronics 20, or its measuring- and evaluating circuit μC, can be loaded in one of the volatile memory RAM and/or the non-volatile-memory EEPROM and kept, at least temporarily, for later further processing.

[0092] As shown in FIGS. 3 and 4, the transmitter electronics 20 of the measuring system of the invention is, furthermore, also adapted to convert both the, in given cases, firstly, conditioned sensor signal s1 into a first sensor signal sampling sequence s.sub.D1 approximating the sensor signal s1, namely a first sensor signal sampling sequence s.sub.D1 in the form of a sequence of digital sampled values S.sub.D1[m]=S.sub.D1[t.sub.m.Math.f.sub.s1] won with a sampling rate f.sub.s1=1/(t.sub.m+1-t.sub.m)=1/T.sub.s1 from the sensor signal s1 at different sampling points in time t.sub.m=m.Math.T.sub.s1, as well as also to convert the, in given cases, firstly, conditioned sensor signal s2 into a second sensor signal sampling sequence s.sub.D2 approximating the sensor signal s2, namely a second sensor signal sampling sequence s.sub.D2 in the form of a sequence of digital sampled values S.sub.D2[n]=S.sub.D2[t.sub.n.Math.f.sub.s2] won with a sampling rate f.sub.s2=1/(t.sub.n+1-t.sub.n)=1/T.sub.s2 from the sensor signal s2 at different sampling points in time t.sub.n=n.Math.T.sub.s2; this, especially, in such a manner that the second sensor signal sampling sequence s.sub.D2 approximates at least the above-mentioned at least one wanted component s.sub.W, or that at least an instantaneous frequency and/or at least one instantaneous amplitude and/or at least one instantaneous phase angle of the wanted component s.sub.W can be ascertained based on the sensor signal sampling sequence s.sub.D2. The above indicated sampling rates f.sub.s1, f.sub.s2 are kept constant for at least one given time interval, in such a manner that the sampling points in time t.sub.m, t.sub.n are equidistantly spaced in time from one another, at least during the time interval. Each of the sampling rates f.sub.s1, f.sub.s2 is, furthermore, selected sufficiently high, that at least a frequency interval enclosing the possible signal frequencies of the variable wanted component s.sub.W during operation is contained re-constructably in each of the sensor signal sampling sequences s.sub.D1, s.sub.D2. The sampling rates f.sub.s1, f.sub.s2 can be selected, for example, sufficiently high that they amount to greater than twice a highest signal frequency of the wanted components s.sub.W of the sensor signal s2. Alternatively, or in supplementation, the sampling rate f.sub.s1 can, furthermore, also be so set that it equals sampling rate f.sub.s2. For forming the sampling sequences s.sub.D1, s.sub.D2, the required clock signals, i.e. clock signals defining the sampling rates f.sub.s1, f.sub.s2 can be provided, for example, by means of a clock signal generator and corresponding, in given cases, also adjustable, frequency dividers provided in the measuring- and evaluating circuit μC. The sensor signal sampling sequences s.sub.D1, s.sub.D2 are then further evaluated by means of the measuring- and evaluating circuit μC, in such a manner that, based on the sensor signal sampling sequences s.sub.D1, s.sub.D2, the at least one measured value is ascertained, or a corresponding measured values sequence x.sub.M is produced, namely a sequence of digital measured values X.sub.M following one after another in time, consequently digital measured values X.sub.M representing the at least one measurement variable and following one after the other in time; this, for example, in such a manner that, based on the frequency of the wanted component s.sub.W, a flow velocity and/or a volume flow rate of the fluid FL flowing along the flow path is ascertained, for instance, for the above described case, in which by means of the flow obstruction 120 a Kármán vortex street is produced in the fluid FL flowing downstream thereof and that, correspondingly, the frequency of the wanted component s.sub.W corresponds to a shedding rate of vortices shed on the flow obstruction 120, and thus to pressure fluctuations associated therewith. Alternatively or supplementally, based on the sensor signal sampling sequences s.sub.D1, s.sub.D2, for example, also the above-mentioned pressure difference between the portion 100-1 and the portion 100-3 can be ascertained, and, based on that, the flow velocity and/or a volume flow rate of the fluid FL can be calculated.

[0093] As already mentioned, at times, even upstream of the portion 100-1, consequently even before reaching the sensor arrangement 210, e.g. outside of the measuring system, the flowing fluid FL can experience an external disturbance, which changes as a function of time, or is not directly predictable, in such a manner that the external disturbance influences both the sensor signal s1, e.g. its frequency spectrum, as well as also—together with the above described (internal) disturbance d—the sensor signal s2, e.g. its frequency spectrum. As a result, the sensor signal s2 can have besides the wanted component also numerous other signal components, which have, for example, only a small frequency distance from the wanted component and/or a significantly greater amplitude. Such disturbances can be caused e.g. by pump or valve induced pressure pulsations in the flowing fluid or, however, for example, also by vibrations of the pipeline.

[0094] In order nevertheless to be able to filter to collect the wanted component s.sub.W contained in the sensor signal s.sub.2 as rapidly as possible, equally as well, as precisely as possible, from the sensor signal s.sub.2, FIG. 4 shows implemented in the transmitter electronics 20, for example, in its measuring- and evaluating circuit μC, a digital adaptive filter LPE, namely a digital filter serving for the (digital) filtering of the sensor signal sampling sequence s.sub.D1. A digital adaptive filter is, as is known, a special signal processing filter, which has the property of being able to change its z-transfer function automatically during operation, namely controlled by an internally executed control algorithm, in such a manner that a sampling sequence applied on the input is processed by means of a transversal filter adaptable as regards its pass-through region, or a center frequency characterizing it, for example, a filter having a finite impulse response (finite impulse response filter), and in the case of which the pass-through region, or the transfer function, of the transversal filter is changed by numerical recalculation of the filter coefficients until an output sequence generated by means of the transversal filter agrees at least approximately, or sufficiently exactly, with a desired target sequence.

[0095] The transmitter electronics 20 of the measuring system is, accordingly, further adapted by means of of the above described digital adaptive filter LPE to ascertain from the sensor signal sampling sequence s.sub.D1, firstly, a wanted signal filter coefficients set W, namely a set of N filter coefficients w.sub.k having, for example, a plurality N of not less than five (N≥5) filter coefficients w.sub.k, and, such as shown schematically in FIGS. 4, and 9a, thereafter by means of the wanted signal filter coefficients set W to form a transfer function, e.g. a z-transfer function G.sub.FIR* (z), of a wanted signal filter FIR-N, namely a digital filter serving for the (digital) filtering of the sensor signal sampling sequence s.sub.D2, in such a manner that the above-mentioned z-transfer function G.sub.FIR* (z) of the wanted signal filter FIR-N, thus a pass-through region, or a center frequency of the wanted signal filter FIR-N, is determined by the wanted signal filter coefficients set W. The filter coefficients w.sub.k of the wanted signal filter coefficients set W can, in such case, be so selected that at least two-, for example, a plurality or all—of the filter coefficients w.sub.k of the wanted signal filter coefficients set W differ from one another, for example, have different magnitudes and/or different sign. The wanted signal filter FIR-N can be, for example, a digital filter with finite impulse response.

[0096] Furthermore, the transmitter electronics 20 is, additionally, also adapted by means of the wanted signal filter FIR-N as well as by means of the sensor signal sampling sequence s.sub.D2 to produce a wanted signal sequence ŝ.sub.D2, namely a sequence of digital function values

[00001] ${\hat{S}}_{D 2} [n] = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. S_{D 2} [n - k]$

calculated by means of the wanted signal filter FIR from the sensor signal sampling sequence s.sub.D2; this according to an additional embodiment at least at times in such a manner that, as well as also indicated in FIG. 9a, the wanted signal sequence ŝ.sub.D2 contains, or approximates, at least the wanted component (ŝ.sub.D2=ŝ.sub.D2 {S.sub.N}). Furthermore, the transmitter electronics 20 is, additionally, also adapted to produce from the above described, wanted signal sequence ŝ.sub.D2 the sequence of digital measured values X.sub.M serving as measured values sequence x.sub.M, for example, based on the wanted signal sequence ŝ.sub.D2 recurringly to ascertain the above-mentioned frequency of the wanted component s.sub.W, for instance, in order based on the so won frequency of the wanted component, such as already mentioned, to calculate current flow velocity and/or volume flow rate of the flowing fluid FL. Alternatively or supplementally, the transmitter electronics 20, or its measuring- and evaluating circuit μC can, furthermore, for example, also be adapted, based on a signal frequency recurringly ascertained from the wanted signal sequence ŝ.sub.D2 for the wanted component s.sub.W recurringly to calculate a flow velocity and/or a volume flow rate of the flowing fluid FL or, for example, from the above described wanted signal sequence ŝ.sub.D2 and the sensor signal sampling sequence s.sub.D1 recurringly to calculate a pressure difference and/or a volume flow rate of the flowing fluid FL. Additionally, the measuring- and evaluating circuit μC, or the transmitter electronics 20 formed therewith, can also be adapted, for ascertaining the measured value X.sub.M, or the production of the measured values sequence x.sub.M, firstly, yet again to filter, or still further to smooth, the wanted signal sequence ŝ.sub.D2, for example, by means of an additional digital signal filter FIR-N* following the wanted signal filter FIR-N, or integrated therein. The signal filter FIR-N* can, for example, be a FIR-filter configured as a low-, high- and/or bandpass filter, in given cases, also with a pass-through region adapted and/or updatable for the wanted component, or with a center frequency adapted and/or updatable for the wanted component.

[0097] The z-transfer function G.sub.FIR* (z) formed by means of the wanted signal filter coefficients set W for the wanted signal filter FIR-N correspondingly to be applied to the sensor signal sampling sequence s.sub.D2 generated with the sampling rate T.sub.s2 can generally be formulated, for example, in the following way:

[00002] $\begin{matrix} G_{FIR}^{*} (z) = Z (g [n]) = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. z^{- k} = {.Math.}_{k = 0}^{N - 1} w_{k} .Math. e^{- j ω T_{s 2}} . & (1) \end{matrix}$

[0098] The wanted signal filter coefficients set W, or the wanted signal filter FIR-N formed therewith, can, such as already indicated, contain five or more (N≥5) for example, even greater than 10 (N>10), filter coefficients w.sub.k. For the above described case, in which the transmitter electronics 20, or its measuring- and evaluating circuit μC, has an, especially non-volatile-, memory EEPROM, the filter coefficients w.sub.k of the wanted signal filter coefficients set W can additionally, for example, also be stored, for example, persistently, in the memory EEPROM. Moreover, the measuring- and evaluating circuit μC, or the transmitter electronics 20 formed therewith, can, for instance, for the purpose of increasing the computing speed, have a first signal-, or microprocessor serving for ascertaining the wanted signal filter coefficients set W, consequently serving for executing the adaptive filter LPE, as well as a second signal-, or microprocessor serving for processing the sensor signal sampling sequence s.sub.D2 to form the wanted signal sequence ŝ.sub.D2, consequently serving for executing the wanted signal filter FIR-N.

[0099] In an additional embodiment, it is, furthermore, provided, thus the transmitter electronics 20 is, furthermore, adapted, at times, for example, also recurringly and/or cyclically with a predeterminable, or predetermined exchange rate, to replace with the wanted signal filter coefficients set W the wanted signal filter coefficients set W*, firstly, determining the above-mentioned z-transfer function G.sub.FIR * (z) of the wanted signal filter FIR-N, —and, for example, likewise earlier ascertained from the sensor signal sampling sequence s.sub.D1 and/or differing from the wanted signal filter coefficients set W; this, for example, also in such a manner that the transmitter electronics 20 regularly completely recalculates the wanted signal filter coefficients set W and thereafter automatically replaces the current, equally as well, to be replaced, wanted signal filter coefficients set W*with the new wanted signal filter coefficients set W, regularly according to the above mentioned exchange rate, or, for example, only when required, for instance, because the current wanted signal filter coefficients W* and the new wanted signal filter coefficients set W differ from one another by more than a predetermined measure of tolerance. The replacing of the wanted signal filter coefficients set W* firstly determining the z-transfer function G.sub.FIR* (z) of the wanted signal filter FIR-N by the wanted signal filter coefficients set W with the exchange rate can be cyclically repeated, for example, in such a manner that the exchange rate is lower than the sampling rate f.sub.s1 of the sensor signal sampling sequence s.sub.D1 and/or is lower than the sampling rate f.sub.s2 of the sensor signal sampling sequence s.sub.D2.

[0100] In an additional embodiment of the invention, the digital adaptive filter LPE is ready-made, or the transmitter electronics is 20 adapted, to generate from the sensor signal sampling sequence s.sub.D1, firstly, an estimated signal sequence ŝ.sub.D1, namely a sequence of digital function values Ŝ.sub.D1[m] calculated from the sensor signal sampling sequence s.sub.D1 by means of the adaptive filter LPE; this especially with the goal, or in such a manner, that the estimated signal sequence ŝ.sub.D1, at least at times, equals or at least approximately equals the sensor signal sampling sequence s.sub.D1, or has a minimum of least squares residuals (BLUP—Best Linear Unbiased Prediction) from the sensor signal sampling sequence s.sub.D1. For such purpose, the transmitter electronics 20 can, furthermore, also be adapted to ascertain the filter coefficients w.sub.k of the wanted signal filter coefficients set W by means of an LMS algorithm (Least Mean Squares algorithm) and/or by means of an RMS algorithm (recursive least squares algorithm).

[0101] In an additional embodiment, it is, accordingly, furthermore, provided that the above-mentioned digital adaptive filter LPE, as well as also indicated in FIG. 9b, comprises a transversal filter FIR-A—here to be applied correspondingly to the sensor signal sampling sequence s.sub.D1—namely a transversal filter FIR-A in the form of a digital filter having a z-transfer function G.sub.LPE* (z) determined by a transversal filter coefficients set W1, namely a set of M filter coefficients w1.sub.k[n]. The transversal filter FIR-A can be, for example, a digital filter with finite impulse response (FIR filter). Accordingly, the z-transfer function G.sub.FIR* (z) of the transversal filter FIR-A formed by means of the transversal filter coefficients set W1 can generally, i.e. applied to the sensor signal sampling sequence s.sub.D1 generated with the sampling rate T.sub.s1, be formulated, for example, in the following way:

[00003] $\begin{matrix} G_{LPE}^{*} (z) = Z (g [m]) = {.Math.}_{k = 1}^{M} w 1_{k} .Math. z^{- k} = {.Math.}_{k = 1}^{M} w 1_{k} .Math. e^{- j ω T_{s 1}} . & (2) \end{matrix}$

[0102] For the above described case, in which the transmitter electronics 20, or its measuring- and evaluating circuit μC, has an, especially non-volatile-, memory EEPROM, the filter coefficients w1.sub.k of the transversal filter coefficients set W1 can, additionally, for example, also be stored, for example, persistently, in the memory EEPROM, in given cases, also together with the filter coefficients w.sub.k of the wanted signal filter coefficients set W. The transmitter electronics 20, or its measuring- and evaluating circuit μC, can, additionally, furthermore, be provided, or adapted, recurringly to change the transfer function, e.g. the z-transfer function of transversal filter FIR-A, consequently a pass-through region, or a center frequency of the transversal filter FIR-A characterizing it, by numerical recalculation the M filter coefficients w1.sub.k[n], in such a manner that the above-mentioned estimated signal sequence ŝ.sub.D1 is provided on the output of the transversal filter and that the estimated signal sequence ŝ.sub.D1, as a result, at least approximately, or sufficiently exactly agrees with the sensor signal sampling sequence s.sub.D1—here serving as target sequence to be achieved. Accordingly, in an additional embodiment of the invention, it is provided, e.g. the transmitter electronics is 20 adapted, by means of the transversal filter FIR-A as well as the sensor signal sampling sequence s.sub.D1 to produce the estimated signal sequence ŝ.sub.D1 as a sequence of digital function values ŝ.sub.D1[m] calculated by means of the digital transversal filter FIR-A from the sensor signal sampling sequence s.sub.D1; this in agreement with the above described z-transfer function G.sub.LPE* (z) of the transversal filter FIR-A (Eq. 2) , for example, according to the formula:

[00004] $\begin{matrix} {\hat{S}}_{D 1} [m] = \underset{k = 1}{\overset{M}{.Math.}} w 1_{k} .Math. S_{D 1} [m - k] . & (3) \end{matrix}$

[0103] The ascertaining of the filter coefficients w1.sub.k of the transversal filter coefficients set W1 can, such as already indicated, occur, for example, in such a manner, e.g. with the goal, that the estimated signal sequence ŝ.sub.D1 approximates or predicts the sensor signal sampling sequence s.sub.D1 as well as possible, or, especially, as a result, equals or at least approximately equals the sensor signal sampling sequence s.sub.D1, or has a minimum of least squares residuals (BLUP—Best Linear Unbiased Prediction) from the sensor signal sampling sequence s.sub.D1. For such purpose, according to an additional embodiment of the invention, by means of the transmitter electronics 20, or the therein implemented digital adaptive filter LPE, as well as also schematically shown in FIG. 9b, an estimate error sequence err.sub.D, namely a sequence of digital function values Err.sub.D[m]=f(S.sub.D1[m], Ŝ.sub.D1[m]), is ascertained, of which each shows—at the respective sampling point in time t.sub.m, or instantaneously—a deviation between a particular sampling value S.sub.D1[m] of the sensor signal sampling sequence s.sub.D1 and a function value Ŝ.sub.D1[m] of the estimated signal sequence ŝ.sub.D1 approximating the sampling value S.sub.D1[m]; this, for example, in such a manner that, recurringly, in each case, a digital function value Err.sub.D[m]=S.sub.D1[m]-Ŝ.sub.D1[m] is formed, which shows a corresponding difference between the sampling value S.sub.D1[m] of the sensor signal sampling sequence s.sub.D1 and the, in each case, associated function value Ŝ.sub.D1[m] of the estimated signal sequence ŝ.sub.D1. Based on the above described z-transfer function G.sub.PE* (z) of the digital transversal filter FIR-A, an estimate error function E * (z) correspondingly serving for production of the estimate error sequence err.sub.D from the sensor signal sampling sequence s.sub.D1 can be formed, for example, according to the following formula:

[00005] $\begin{matrix} E * (z) = 1 - G_{L P E}^{*} (z) = 1 - \underset{k = 1}{\overset{M}{.Math.}} w 1_{k} .Math. z^{- k} & (4) \end{matrix}$

[0104] and the digital function values Err.sub.D [m] of the estimate error sequence err.sub.D calculated from the sensor signal sampling sequence s.sub.D1 can correspond to the function:

[00006] $\begin{matrix} {Err}_{D} [m] = S_{D 1} [m] - {.Math.}_{k = 1}^{M} w 1_{k} .Math. S_{D 1} [m - k] & (5) \end{matrix}$

[0105] As already mentioned, the filter coefficients w1.sub.k of the transversal filter coefficients set W1, or of the estimate error function E * (z) formed therewith, can be ascertained, furthermore, for example, in each case, by means of an LMS- and/or RMS algorithm executed in the transmitter electronics 20, or its measuring- and evaluating circuit μC, for example, in such a manner that the function values Err.sub.D [m] are at least approximately zero. The wanted signal filter coefficients set W for the wanted signal filter FIR-N can, such as already indicated, and shown in FIGS. 9a and 9b, thereafter be ascertained from the transversal filter coefficients set W1 of the transversal filter FIR-A, for example, by just using them directly, in case the estimated signal sequence ŝ.sub.D1 at least for a predetermined sample-, or time, interval -, for example, of greater than M, or M.Math.T.sub.s1—equals or at least approximately equals the sensor signal sampling sequence s.sub.D1, or has a minimum of least squares residuals (BLUP—Best Linear Unbiased Prediction) from the sensor signal sampling sequence s.sub.D1, or in case the estimate error function E * (z) is approximately zero for a correspondingly long time. In an additional embodiment of the invention, it is accordingly provided that the wanted signal filter coefficients set W contains all M filter coefficients w1.sub.k of the transversal filter coefficients set W1; this, especially, also in such a manner that each filter coefficient w.sub.1k of the transversal filter coefficients set W1 is incorporated as filter coefficient w.sub.k of the wanted signal filter coefficients set W (w.sub.1k.fwdarw.w.sub.k), or that, for each filter coefficient w.sub.1k of the transversal filter coefficients set W1, w.sub.1k=W.sub.k. Accordingly, the transversal filter coefficients set W1 equally as the wanted signal filter coefficients set W, and the transversal filter FIR-A equally as the wanted signal filter FIR-N, can contain five or more, for example, also greater than 10 (M>10), filter coefficients w1.sub.k. Particularly for the above-described case, in which based on the wanted signal sequence ŝ.sub.D2 the above-mentioned frequency of the wanted component s.sub.W is recurringly ascertained, according to an additional embodiment of the invention, it is, additionally, provided that the wanted signal filter coefficients set W, or the wanted signal filter FIR-N formed therewith, contains, at least at times, at least one filter coefficient w1.sub.0 different from zero, for example, a negative and/or predetermined filter coefficient w1.sub.0, which the transversal filter coefficients set W1, and the transversal filter FIR-A formed therewith, do not contain. The filter coefficient w1.sub.0 can, for example, amount to −1 (w1.sub.0=−1), so that, thus, as a result, the wanted signal sequence ŝ.sub.D2 is formed for practical purposes by subtracting a sensor signal estimated sequence (or a corresponding synthesized sensor signal sampling sequence) for the sensor signal s1 suitably synchronized with the sampling point in time t.sub.n from the sensor signal sampling sequence s.sub.D2. Alternatively or supplementally, wanted signal filter coefficients set W and transversal filter coefficients set W1, or the signal filters (FIR-N, FIR-A) formed therewith can, at least at times, be equal, for example, in order based on both the wanted signal sequence ŝ.sub.D2 as well as also the sensor signal sampling sequence s.sub.D1 and/or the estimated signal sequence ŝ.sub.D1, to ascertain the above-mentioned, volume flow dependent, pressure difference between the fluid flowing in the portion 100-1 and the fluid flowing in the portion 100-3.

MEASURING SYSTEM AND METHOD FOR MEASURING A MEASUREMENT VARIABLE OF A FLOWING FLUID

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