Physics-constrained sensor assignment optimization method for thermal hydraulic systems

1. A method for determining an optimal sensor set, the method comprising:

identifying, by one or more processors, a set of possible faults of a thermal hydraulic system and a set of diagnostic objectives associated with the set of possible faults;

obtaining, by the one or more processors, a plurality of descriptions of a respective plurality of sensor sets, wherein obtaining the plurality of descriptions includes:

receiving a piping and instrumentation diagram (P&ID) of the thermal hydraulic system,

extracting, from the P&ID, a first description of a first sensor set of the plurality of sensor sets, and

generating, based on the first description, a second description of a second sensor set of the plurality of sensor sets,

wherein each description of the plurality of descriptions includes types of sensors of a respective sensor set of the plurality of sensor sets and locations of the sensors of the respective sensor set, and each description is different from other descriptions of the plurality of descriptions;

for each particular sensor set of the plurality of sensor sets:

determining, by the one or more processors, based on a particular description of the plurality of descriptions that corresponds to the particular sensor set, a diagnostic capability of the particular sensor set corresponding to a measure of how many diagnostic objectives of the set of diagnostic objectives are met by the particular sensor set; and

calculating, by the one or more processors, a score of the particular sensor set based on the particular description and the diagnostic capability, wherein a score of a sensor set is increased by a monetary cost of the sensor set and decreased by the sensor set meeting a diagnostic objective of the set of diagnostic objectives;

identifying, by the one or more processors, the optimal sensor set that has a lowest score of the plurality of sensor sets; and

displaying, by the one or more processors, an indication of the optimal sensor set.

2. The method of claim 1 , wherein at least one diagnostic objective of the set of diagnostic objectives includes diagnosing a fault of the set of possible faults.

3. The method of claim 1 , wherein at least one diagnostic objective of the set of diagnostic objectives includes uniquely diagnosing a fault of the set of possible faults.

4. The method of claim 1 , wherein at least one diagnostic objective of the set of diagnostic objectives includes diagnosing a fault of the set of possible faults within a threshold distance.

5. The method of claim 1 , wherein the monetary cost of the sensor set includes an installation cost of installing the sensor set.

6. The method of claim 1 , wherein the monetary cost of the sensor set includes a maintenance cost of maintaining the sensor set.

7. The method of claim 1 , further comprising:

receiving, at the one or more processors, a system description of the thermal hydraulic system, the system description indicating:

for each component of a plurality of components of the thermal hydraulic system, a type of the component and the location of the component in the thermal hydraulic system; and

connections between the plurality of components;

wherein determining the diagnostic capability of the particular sensor set includes:

constructing, based on physical conservation laws, the system description, and the particular description of the particular sensor set, a plurality of physics-based models corresponding to the plurality of components;

generating residual expressions using analytical redundancy relations of the plurality of physics-based models; and

determining the diagnostic capability of the particular sensor set based on the residual expressions.

8. The method of claim 7 , wherein constructing the plurality of physics-based models includes retrieving, based on the system description and the particular description of the particular sensor set, the plurality of physics-based models from a database including a plurality of generic-physics based models.

9. The method of claim 7 , wherein:

each residual expression can evaluate to a zero residual or a non-zero residual;

each fault of the set of possible faults corresponds to a combination of zero residuals and non-zero residuals; and

determining the diagnostic capability of the particular sensor set based on the residual expressions includes:

determining, for possible combinations of zero residuals of the residual expressions and non-zero residuals of the residual expressions, whether a corresponding fault of the set of possible faults can be diagnosed.

10. The method of claim 9 , wherein determining, for possible combination of zero residuals and non-zero residuals, whether the corresponding fault of the set of possible faults can be diagnosed includes determining whether a fault of the set of possible faults can be diagnosed within a predetermined probability threshold.

11. The method of claim 7 , wherein receiving the system description includes receiving the P&ID of the thermal hydraulic system.

12. The method of claim 1 , further comprising:

determining, by the one or more processors, available sensor locations of the thermal hydraulic system, wherein:

generating the second description includes generating the second description based on the available sensor locations.

13. The method of claim 1 , wherein generating the second description includes generating the second description using a genetic algorithm.

14. The method of claim 1 , wherein displaying the indication of the optimal sensor set includes displaying at least one of a description of the optimal sensor set or a score of the optimal sensor set.

15. A computer system for determining an optimal sensor set, the computer system comprising:

one or more processors; and

a non-transitory computer-readable medium storing thereon instructions that, when executed by the one or more processors, cause the computer system to:

identify a set of possible faults of a thermal hydraulic system and a set of diagnostic objectives associated with the set of possible faults;

obtain a plurality of descriptions of a respective plurality of sensor sets, wherein obtaining the plurality of descriptions includes:

receiving a piping and instrumentation diagram (P&ID) of the thermal hydraulic system,

extracting, from the P&ID, a first description of a first sensor set of the plurality of sensor sets, and

generating, based on the first description, a second description of a second sensor set of the plurality of sensor sets,

wherein each description of the plurality of descriptions includes types of sensors of a respective sensor set of the plurality of sensor sets and locations of the sensors of the respective sensor set, and each description is different from other descriptions of the plurality of descriptions;

for each particular sensor set of the plurality of sensor sets:

determine, based on a particular description of the plurality of descriptions that corresponds to the particular sensor set, a diagnostic capability of the particular sensor set corresponding to a measure of how many diagnostic objectives of the set of diagnostic objectives are met by the particular sensor set; and

calculate a score of the particular sensor set based on the particular description and the diagnostic capability, wherein a score of a sensor set is increased by a monetary cost of the sensor set and decreased by the sensor set meeting a diagnostic objective of the set of diagnostic objectives;

identify the optimal sensor set that has a lowest score of the plurality of sensor sets; and

display an indication of the optimal sensor set.

16. The computer system of claim 15 , wherein the instructions further cause the one or more processors to:

receive a system description of the thermal hydraulic system, the system description indicating:

for each component of a plurality of components of the thermal hydraulic system, a type of the component and the location of the component in the thermal hydraulic system; and

connections between the plurality of components;

wherein the instructions cause the computer system to determine the diagnostic capability of the particular sensor set by:

constructing, based on physical conservation laws, the system description, and the particular description of the particular sensor set, a plurality of physics-based models corresponding to the plurality of components;

generating residual expressions using analytical redundancy relations of the plurality of physics-based models; and

determining the diagnostic capability of the particular sensor set based on the residual expressions.

17. The computer system of claim 16 , wherein the instructions cause the computer system to construct the plurality of physics-based models by:

retrieving, based on the system description and the particular description of the particular sensor set, the plurality of physics-based models from a database including a plurality of generic-physics based models.

18. The computer system of claim 16 , wherein:

each residual expression can evaluate to a zero residual or a non-zero residual;

each fault of the set of possible faults corresponds to a combination of zero residuals and non-zero residuals; and

the instructions cause the computer system to determine the diagnostic capability of the particular sensor set based on the residual expressions by:

determining, for possible combinations of zero residuals of the residual expressions and non-zero residuals of the residual expressions, whether a corresponding fault of the set of possible faults can be diagnosed.

19. The computer system of claim 16 , wherein the instructions cause the computer system to:

receive the system description by receiving the P&ID of the thermal hydraulic system;

and

the instructions further cause the computer system to:

extract, from the P&ID, available sensor locations of the thermal hydraulic system; and

generate the second description further based on the available sensor locations.