Method of calibrating and linearizing the output of fluid measuring instruments
First Claim
1. A method of calibrating and linearizing the output of an instrument that includes a particular transducer having an output that is a non-linear function of a concentration of a component of interest in a fluid, comprising:
- (a) producing a first equation which is characteristic of the output of a typical transducer of the type to be used in the instrument as a function of the concentration of the component of interest,(b) producing a second equation which gives the concentration of the component of interest as a function of the output of said typical transducer,(c) applying a first fluid having a known non-zero concentration of the component of interest to the particular transducer to be used in the instrument and measuring the actual output thereof,(d) substituting a value corresponding to said known concentration into the first equation and evaluating the first equation to determine the estimated output of said typical transducer,(e) using said actual and estimated outputs to determine the relative sensitivity of the particular transducer,(f) applying a second fluid having a known nonzero concentration of the component of interest to the particular transducer and measuring the actual output thereof,(g) correcting the measured output of step (f) for said relative sensitivity and using the result and the second equation to produce the linearized concentration value corresponding to the concentration of said second fluid,(h) applying a sample fluid having an unknown concentration of the component of interest to the particular transducer and measuring the actual output thereof,(i) correcting the measured output of step (h) for said relative sensitivity and using the result and the second equation to produce the linearized concentration value corresponding to the concentration of said sample fluid, and(j) referencing the concentration value of step (i) to that of step (g) and displaying the result as the concentration of the component of interest in the sample fluid.
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Accused Products
Abstract
A method for calibrating and linearizing the output of an instrument that includes a transducer having an output that is a nonlinear function of a property of interest of a fluid. The results of measurements performed on a plurality of transducers of the type to be used in the instrument are used to produce first and second equations which give the direct and inverse responses of a typical transducer. The results of further measurements on the particular transducer to be used in the instrument are used with the first equation to define how the second equation may be used to give accurate results with the particular transducer. The instrument is then calibrated and the results used with the second equation to produce an accurate linearized value for display as the output of the instrument.
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Citations
22 Claims
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1. A method of calibrating and linearizing the output of an instrument that includes a particular transducer having an output that is a non-linear function of a concentration of a component of interest in a fluid, comprising:
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(a) producing a first equation which is characteristic of the output of a typical transducer of the type to be used in the instrument as a function of the concentration of the component of interest, (b) producing a second equation which gives the concentration of the component of interest as a function of the output of said typical transducer, (c) applying a first fluid having a known non-zero concentration of the component of interest to the particular transducer to be used in the instrument and measuring the actual output thereof, (d) substituting a value corresponding to said known concentration into the first equation and evaluating the first equation to determine the estimated output of said typical transducer, (e) using said actual and estimated outputs to determine the relative sensitivity of the particular transducer, (f) applying a second fluid having a known nonzero concentration of the component of interest to the particular transducer and measuring the actual output thereof, (g) correcting the measured output of step (f) for said relative sensitivity and using the result and the second equation to produce the linearized concentration value corresponding to the concentration of said second fluid, (h) applying a sample fluid having an unknown concentration of the component of interest to the particular transducer and measuring the actual output thereof, (i) correcting the measured output of step (h) for said relative sensitivity and using the result and the second equation to produce the linearized concentration value corresponding to the concentration of said sample fluid, and (j) referencing the concentration value of step (i) to that of step (g) and displaying the result as the concentration of the component of interest in the sample fluid. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method of calibrating and linearizing the output of an instrument that includes a particular transducer having an output that is a non-linear function of the concentration of a gas of interest, comprising:
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(a) producing a first polynomial equation which is characteristic of the output of a typical transducer of the type to be used in the measurement as a function of the concentration of the gas of interest, (b) producing a second polynomial equation which gives the concentation of the gas of interest as a function of the output of said typical transducer, (c) applying a gas having substantially none of the gas of interest to the particular transducer to be used in the instrument, measuring the resulting output thereof, and storing that output for use as a zero correction value, (d) applying a first gas having a first known nonzero concentration of the gas of interest to the particular transducer and measuring the actual output thereof, (e) substituting a value corresponding to said first concentration into said first equation and evaluating the first equation to determine the estimated output of the typical transducer, (f) subtracting the zero correction value from the actual output of the particular transducer to produce a zerocorrected actual output, (g) using said estimated output and the zerocorrected actual output to determine the relative sensitivity of the actual transducer, (h) applying a second gas having a second known non-zero concentration of the gas of interest to the particular transducer and measuring the actual output thereof, (i) correcting the measured output of step (h) for the zero correction value and said relative sensitivity, and using the result and the second equation to produce the linearized concentration value corresponding to said second concentration, (j) applying a sample gas having an unknown concentration of the gas of interest to the particular transducer and measuring the actual output thereof, (k) correcting the measured output of step (j) for the zero correction value and said relative sensitivity, and using the result and the second equation to produce the linearized concentration value corresponding to said unknown concentration, and (l) producing an output signal that is indicative of the ratio of said linearized concentration values and said second concentration. - View Dependent Claims (10, 11, 12, 13)
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14. A method of calibrating and linearizing the output of an instrument that includes a particular transducer having an output V that is a non-linear function of the magnitude C of a property of interest of a fluid, comprising:
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(a) performing a series of measurements on each of a plurality of transducers of the type to be used in the instrument, (b) selecting a first equation V=f1 (C) of a type that is suitable for use in representing the response of a typical one of said transducers, where f1 is a first function having at least one unknown coefficient, (c) selecting a second equation C=f2 (V) of a type that is suitable for use in representing the inverse response of the typical one of said transducers, where f2 is a second function having at least one unknown coefficient, (d) determining the values of the unknown coefficients of the first function to adapt said first equation to represent the response of the typical transducer, (e) determining the values of the unknown coefficients of the second function to adapt said second equation to represent the inverse response of the typical transducer, (f) applying to the particular transducer a fluid having substantially a zero magnitude of the property of interest and measuring the output Vo thereof, (g) applying to the particular transducer a first fluid having a first known magnitude Cs1 of the property of interest and measuring the actual output Vsa thereof, (h) substituting Cs1 into the first equation and evaluating the first equation to determine the estimated output Vse of said particular transducer, (i) determining the ratio K of Vse to Vsa -Vo, (j) applying to the particular transducer a second fluid having a second known magnitude Cs2 of the property of interest and measuring the actual output Vc thereof, (k) using the second equation to determine the value of Cc, which corresponds to V=K (Vc -Vo), (l) applying to the particular transducer a fluid having an unknown magnitude of the property of interest and measuring the actual output Vu thereof, (m) using the second equation to determine the value Cu which corresponds to V=K (Vu -Vo) and (n) producing as an output a signal indicative of the value Cout, where Cout =Cu (Cs2 /Cc). - View Dependent Claims (15, 16, 17, 18)
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19. A method of calibrating and linearizing the output of an instrument that includes a particular transducer having an output V that is a non-linear function of the magnitude C of a property of interest of a fluid, comprising:
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(a) performing a series of measurements on each of a plurality of transducers of the type to be used in the instrument, (b) selecting a first equation V=f1 (C) of a type that is suitable for use in representing the response of a typical one of said transducers, where f1 is a first function having at least one term with an unknown coefficient, (c) selecting a second equation C=f2 (V) of a type that is suitable for use in representing the inverse response of the typical one of said transducers, where f2 is a second function having at least one term with an unknown coefficient, (d) determining the values of the unknown coefficients of the first function to adapt said first equation to represent the response of the typical transducer, (e) determining the values of the unknown coefficients of the second function to adapt said second equation to represent the inverse response of the typical transducer, (f) applying a fluid for which C is substantially equal to zero to the particular transducer and measuring and storing the resulting output Vo thereof, (g) applying to the particular transducer a first fluid having a first known magnitude Cs1 of the property of interest and measuring the actual output Vsa thereof, (h) substituting Cs1 into the first equation and evaluating the first equation to determine the estimated output Vse of said typical transducer, (i) determining the ratio K=Vse /(Vsa -Vo), (j) evaluating the second equation for Cmax =f2 (KVmax) where Vmax is the maximum output of the typical transducer, (k) determining the ratio
space="preserve" listing-type="equation">K'"'"'=0.95 (V.sub.cap)/C.sub.maxwhere Vcap is the maximum V value which can be handled by the instrument, (l) reformulating the second equation as
space="preserve" listing-type="equation">C=K'"'"'f.sub.2 (K[V-V.sub.o ]),(m) applying to said particular transducer a second fluid having a second known magnitude Cs2 of the property of interest and measuring the output Vc thereof, (n) using the reformulated second equation to determine the linearized value Cc which corresponds to V=Vc, (o) applying to the particular transducer a sample fluid having an unknown magnitude of the property of interest and measuring the output Vu thereof, (p) using the reformulated second equation to determine the value Cu which corresponds to V=Vu, and (q) producing as an output a signal indicative of the value Cout where Cout =Cu (Cs2 /Cc). - View Dependent Claims (20, 21, 22)
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Specification