Systems and methods for controlling flow rate using differential pressure measurements

1. A system for controlling a mass or volumetric flow rate through a device, the system comprising:

a flow control device operable to modulate a flow rate of a fluid through a tested device;

a device testing system configured to operate the flow control device over a range of fluid flow conditions to achieve a plurality of different flow rates through the tested device;

one or more pressure sensors configured to measure a plurality of pressure differentials across the tested device, each of the measured pressure differentials corresponding to one of the plurality of different flow rates through the tested device;

a flow rate sensor configured to measure the plurality of different flow rates through the tested device, each of the measured flow rates corresponding to one of the measured pressure differentials;

a device clusterer configured to organize a plurality of devices into clusters based on one or more device characteristics associated with the devices and configured to generate a clustered set of test data comprising (1) the measured pressure differentials and corresponding flow rates for the tested device and (2) measured pressure differentials and corresponding flow rates for one or more other devices organized into a same cluster as the tested device;

a regression model trainer configured to generate regression coefficients (a and b) for a flow rate model using all the measured pressure differentials and corresponding flow rates in the clustered set of test data, wherein the flow rate model estimates a flow rate ({circumflex over (F)}) as a function of a pressure differential (ΔP) and the regression coefficients (a and b), the flow rate model comprising {circumflex over (F)}=aΔP b ;

a flow rate estimator configured to use the flow rate model to estimate a flow rate through an untested device as a function of a new measured pressure differential across the untested device; and

a controller configured to use the estimated flow rate to generate a control signal for a controllable device and operate the controllable device using the control signal, the control signal causing the controllable device to adjust the flow rate through the untested device.

2. The system of claim 1 , wherein the tested device is a first heat exchanger and the untested device is a second heat exchanger that has one or more device characteristics in common with the first heat exchanger.

3. The system of claim 2 , wherein the one or more device characteristics comprise at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type.

4. The system of claim 1 , wherein the flow rate estimator is a component of the untested device and the estimated flow rate is a flow rate through the untested device.

5. The system of claim 1 , wherein the flow rate estimator is a component of a controller for the tested or untested device.

6. The system of claim 1 , wherein the device clusterer is configured to select the untested device from a plurality of devices organized into a same cluster as the tested device.

7. The system of claim 1 , further comprising an uncertainty calculator configured to:

determine an uncertainty of one or more of the regression coefficients in the flow rate model;

generate a set of uncertainty model parameters based on the determined uncertainties; and

use the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate.

8. A method for controlling a mass or volumetric flow rate through a tested device, the method comprising:

operating a flow control device to modulate a flow rate of a fluid through a tested device over a range of fluid flow conditions to achieve a plurality of different flow rates through the tested device;

measuring pressure differentials across the tested device and corresponding flow rates through the tested device at a plurality of different pressure differentials and flow rates;

organizing a plurality of devices comprising the tested device and one or more other devices into clusters based on one or more device characteristics associated with the plurality of devices, wherein the one or more device characteristics comprise at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type;

generating a clustered set of test data comprising (1) the measured pressure differentials and corresponding flow rates for the tested device and (2) measured pressure differentials and corresponding flow rates for one or more of the other devices organized into a same cluster as the tested device;

generating regression coefficients (a and b) for a flow rate model using all the measured pressure differentials and corresponding flow rates in the clustered set of test data, wherein the flow rate model estimates a flow rate ({circumflex over (F)}) as a function of a pressure differential (ΔP) and the regression coefficients (a and b), the flow rate model comprising {circumflex over (F)}=aΔP b ;

measuring a new pressure differential across the tested device;

estimating a new flow rate through the tested device using the new pressure differential as an input to the flow rate model;

generating a control signal for a controllable device using the new flow rate; and

operating the controllable device using the control signal, the control signal causing the controllable device to adjust the flow rate through the tested device.

9. The method of claim 8 , further comprising:

determining an uncertainty of one or more trained parameters in the flow rate model;

generating a set of uncertainty model parameters based on the determined uncertainties; and

using the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate.

10. A method for controlling a mass or volumetric flow rate through a device, the method comprising:

operating a flow control device to modulate a flow rate of a fluid through a first device over a range of fluid flow conditions to achieve a plurality of different flow rates through the first device;

measuring pressure differentials across the first device and corresponding flow rates through the first device at a plurality of different pressure differentials and flow rates;

organizing a plurality of devices comprising the first device and one or more other devices into clusters based on one or more device characteristics associated with the plurality of devices;

generating a clustered set of test data comprising (1) the measured pressure differentials and corresponding flow rates for the first device and (2) measured pressure differentials and corresponding flow rates for one or more other devices organized into a same cluster as the first device;

training a flow rate model using all the measured pressure differentials and corresponding flow rates in the clustered set of test data, wherein the flow rate model estimates a flow rate as a function of a pressure differential;

measuring a pressure differential across a second device that has one or more device characteristics in common with the first device;

estimating a flow rate through the second device using the measured pressure differential across the second device as an input to the flow rate model;

generating a control signal for a controllable device using the estimated flow rate; and

operating the controllable device using the control signal, the control signal causing the controllable device to adjust the flow rate through the tested device.

11. The method of claim 10 , wherein the first device is a first heat exchanger and the second device is a second heat exchanger that has one or more device characteristics in common with the first heat exchanger;

wherein the one or more device characteristics comprise at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type.

12. The method of claim 10 , further comprising:

determining an uncertainty of one or more trained parameters in the flow rate model;

generating a set of uncertainty model parameters based on the determined uncertainties; and

using the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate.