Method and apparatus for determining a quality metric of a measurement of a fluid parameter
View Patent ↗An apparatus for measuring a parameter of a fluid passing through a pipe includes a spatial array of at least two sensors disposed at different axial locations along the pipe. Each of the sensors provides a signal indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe. A signal processor constructs at least a portion of a k-ω plot using the signals and detects at least one ridge in the k-ω plot. A slope of the at least one ridge is indicative of the parameter of the fluid. The signal processor determines a quality metric by comparing an accumulated energy (power) of k-ω pairs along the at least one ridge with an accumulated energy (power) of k-ω pairs along at least one ray extending in the k-ω plot. The quality metric is indicative of a quality of the at least one ridge.
1. An apparatus for measuring a parameter of a fluid passing through a pipe, the apparatus comprising:
a spatial array of at least two sensors disposed at different axial locations along the pipe, each of the sensors providing a signal indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe; and
a signal processor configured to:
construct from the signals at least a portion of a k-ω plot, where the k-ω plot is indicative of a dispersion relation for the unsteady pressure within the pipe,
detect at least one ridge in the k-ω plot, a slope of the at least one ridge being indicative of the parameter of the fluid, and
compare an accumulated energy for k-ω pairs along the at least one ridge with an accumulated energy for k-ω pairs along at least one ray extending in the k-ω plot to determine a quality metric indicative of a quality of the at least one ridge.
2. The apparatus of claim 1 , wherein the accumulated energy for k-ω pairs along the at least one ridge is a sum of the powers associated with the k-ω pairs along the at least one ridge.
3. The apparatus of claim 1 , wherein the accumulated energy for k-ω pairs along the at least one ray is a sum of the powers associated with the k-ω pairs along the at least one ray.
4. The apparatus of claim 1 , wherein the accumulated energy for k-ω pairs along the at least one ray is an average accumulated energy for k-ω pairs along a plurality of rays.
5. The apparatus of claim 1 , wherein the at least one ray has a slope indicative of a reference velocity.
6. The apparatus of claim 5 , wherein the slope of the at least one ridge is indicative of a best velocity, and the reference velocity is determined as a function of the best velocity.
7. The apparatus of claim 5 , wherein the slope of the at least one ridge is indicative of a best velocity, and the reference velocity is independent of the best velocity.
8. The apparatus of claim 5 , wherein the signal processor is further configured to:
determine accumulated energies for a plurality of rays in the k-ω plot, the slopes of the plurality of rays indicating a plurality of trial velocities, and
select the reference velocity from the trial velocities by comparing the accumulated energies for the plurality of rays.
9. The apparatus of claim 8 , wherein the slope of the at least one ridge is indicative of a best velocity, and the trial velocities include: a trial velocity determined as a function of the best velocity and a trial velocity independent of the best velocity.
10. The apparatus of claim 8 , wherein the slope of the at least one ridge is indicative of a best velocity, and the signal processor determines the quality metric using:
Q
=
P
BEST
VELOCITY
-
P
REFERNCE
P
BEST
VELOCITY
+
P
REFERNCE
where P best velocity is the accumulated energy for k-ω pairs along the at least one ridge in a linear scale, P reference is the accumulated energy for k-ω pairs along the at least one ray in a linear scale, and Q is the quality metric.
11. The apparatus of claim 1 , wherein the slope of the at least one ridge is indicative of a best velocity, and the signal processor determines the quality metric using:
Q
=
P
BEST
VELOCITY
-
P
REFERNCE
P
BEST
VELOCITY
+
P
REFERNCE
where P best velocity is the accumulated energy for k-ω pairs along the at least one ridge in a linear scale, P reference is the accumulated energy for k-ω pairs along the at least one ray in a linear scale, and Q is the quality metric.
12. The apparatus of claim 1 , wherein the at least one ridge includes a first acoustic ridge in a left plane of the k-ω plot and a second acoustic ridge in the right plane of the k-ω plot, and the accumulated energy for k-ω pairs along the at least one ridge is a sum of the powers associated with the k-ω pairs along the first and second acoustic ridges.
13. The apparatus of claim 1 , wherein the parameter of the fluid includes at least one of: velocity of the fluid and speed of sound of the fluid.
14. The apparatus of claim 1 wherein the at least two pressure sensors are selected from a group consisting of: piezoelectric, piezoresistive, strain gauge, PVDF, optical sensors, ported ac pressure sensors, accelerometers, velocity sensors, and displacement sensors.
15. The apparatus of claim 1 , wherein the at least two pressure sensors are wrapped around at least a portion of the pipe and do not contact the fluid.
16. The apparatus of claim 1 , wherein the signal processor is further configured to
compare the quality metric to a threshold value; and
determine the parameter of the fluid using the slope of the at least one ridge in response to the quality metric reaching the threshold value.
17. A method for determining a quality metric of a measurement of a parameter of a fluid flowing through a pipe, the measurement being made using a spatial array of at least two sensors disposed at different axial locations along the pipe, each of the sensors providing a signal indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe, the method comprising:
constructing from the signals at least a portion of a k-ω plot, where the k-ω plot is indicative of a dispersion relation for the unsteady pressure within the pipe;
detecting at least one ridge in the k-ω plot, a slope of the at least one ridge being indicative of the parameter of the fluid;
comparing an accumulated energy for k-ω pairs along the at least one ridge with an accumulated energy for k-ω pairs along at least one ray extending in the k-ω plot to determine a quality metric indicative of a quality of the at least one ridge.
18. The method of claim 17 , wherein the accumulated energy for k-ω pairs along the at least one ridge is a sum of the powers associated with the k-ω pairs along the at least one ridge.
19. The method of claim 17 , wherein the accumulated energy for k-ω pairs along the at least one ray is a sum of the powers associated with the k-ω pairs along the at least one ray.
20. The method of claim 17 , wherein the accumulated energy for k-ω pairs along the at least one ray is an average accumulated energy for k-ω pairs along a plurality of rays.
21. The method of claim 17 , wherein the at least one ray has a slope indicative of a reference velocity.
22. The method of claim 21 , wherein the slope of the at least one ridge is indicative of a best velocity, and the reference velocity is determined as a function of the best velocity.
23. The method of claim 21 , wherein the slope of the at least one ridge is indicative of a best velocity, and the reference velocity is independent of the best velocity.
24. The method of claim 21 , further comprising:
determining accumulated energies for a plurality of rays in the k-ω plot, the slopes of the plurality of rays indicating a plurality of trial velocities, and
selecting the reference velocity from the trial velocities by comparing the accumulated energies for the plurality of rays.
25. The method of claim 24 , wherein the slope of the at least one ridge is indicative of a best velocity, and the trial velocities include: a trial velocity determined as a function of the best velocity and a trial velocity independent of the best velocity.
26. The method of claim 24 , wherein the slope of the at least one ridge is indicative of a best velocity, and the quality metric is determined using:
Q
=
P
BEST
VELOCITY
-
P
REFERNCE
P
BEST
VELOCITY
+
P
REFERNCE
where P best velocity is the accumulated energy for k-ω pairs along the at least one ridge in a linear scale, P reference is the accumulated energy for k-ω pairs along the at least one ray in a linear scale, and Q is the quality metric.
27. The method of claim 17 , wherein the slope of the at least one ridge is indicative of a best velocity, and the quality metric is determined using:
Q
=
P
BEST
VELOCITY
-
P
REFERNCE
P
BEST
VELOCITY
+
P
REFERNCE
where P best velocity is the accumulated energy for k-ω pairs along the at least one ridge in a linear scale, P reference is the accumulated energy for k-ω pairs along the at least one ray in a linear scale, and Q is the quality metric.
28. The method of claim 17 , wherein the parameter of the fluid includes at least one of: velocity of the fluid and speed of sound of the fluid.
29. The method of claim 17 , wherein the at least one ridge includes a first acoustic ridge in a left plane of the k-ω plot and a second acoustic ridge in the right plane of the k-ω plot, and the method further comprises:
summing the powers associated with the k-ω pairs along the first and second acoustic ridges to determine the accumulated energy for the at least one ridge.
30. The method of claim 17 , further comprising:
comparing the quality metric to a threshold value, and
determining the parameter of the fluid using the slope of the at least one ridge in response to the quality metric reaching the threshold value.
31. A computer storage medium encoded with machine-readable computer program code for measuring a parameter of a fluid passing through a pipe using a spatial array of at least two sensors disposed at different axial locations along the pipe, each of the pressure sensors providing a time-domain signal indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe, the storage medium including instructions for causing a computer to implement a method, when executed by a computer processor comprising:
constructing from the signals at least a portion of a k-ω plot, where the k-ω plot is indicative of a dispersion relation for the unsteady pressure within the pipe,
detecting at least one ridge in the k-ω plot, a slope of the at least one ridge being indicative of the parameter of the fluid,
comparing an accumulated energy for k-ω pairs along the at least one ridge with an accumulated energy for k-ω pairs along at least one ray extending in the k-ω plot to determine a quality metric indicative of a quality of the at least one ridge.
32. The storage medium of claim 31 , wherein the at least one ray has a slope indicative of a reference velocity, and the method further comprises:
determining accumulated energies for a plurality of rays in the k-ω plot, the slopes of the plurality of rays indicating a plurality of trial velocities, and
selecting the reference velocity from the trial velocities by comparing the accumulated energies for the plurality of rays.
33. The storage medium of claim 32 , wherein the slope of the at least one ridge is indicative of a best velocity, and the quality metric is determined using:
Q
=
P
BEST
VELOCITY
-
P
REFERNCE
P
BEST
VELOCITY
+
P
REFERNCE
where P best velocity is the accumulated energy for k-ω pairs along the at least one ridge in a linear scale, P reference is the accumulated energy for k-ω pairs along the at least one ray in a linear scale, and Q is the quality metric.