TEMPORAL DELAY DETERMINATION FOR CALIBRATION OF DISTRIBUTED SENSORS IN A MASS TRANSPORT NETWORK
A method and system of calibrating uncalibrated sensors among sensors distributed along a pipeline network include designating a set of the sensors as upstream sensors based on their geopositions, and designating remaining ones of the sensors other than the set of the sensors as downstream sensors. The method also includes determining a temporal delay associated with each of the sensors. Calibrating the uncalibrated sensors is based on the corresponding temporal delay and on calibrated sensors among the sensors.
1 . A computer-implemented method of calibrating uncalibrated sensors among sensors distributed along a pipeline network, the method comprising:
designating a set of the sensors as upstream sensors based on their geopositions;
designating remaining ones of the sensors other than the set of the sensors as downstream sensors;
determining, using a processor, a temporal delay associated with each of the sensors; and
calibrating, using the processor, the uncalibrated sensors based on the corresponding temporal delay and on calibrated sensors among the sensors.
2 . The computer-implemented method according to claim 1 , further comprising obtaining a time-varying signal from each of the sensors.
3 . The computer-implemented method according to claim 2 , wherein the determining the temporal delay includes isolating a subset of the time-varying signal associated with each of the sensors such that a duration of every subset is the same and a start time and an end time of every subset is determined for each of the sensors.
4 . The computer-implemented method according to claim 2 , wherein the determining the temporal delay includes solving an equation representing mass conservation law that is given by:
|Σ iεU Σ t strt +Δt i t end +Δt i Q i ( t )−Σ iεD Σ t strt +Δt i t end +Δt i Q i ( t )| norm , where
U refers to the upstream sensors, D refers to the downstream sensors, tstrt and tend are start and end times, respectively, that are fixed for all the sensors, Δt is the temporal delay associated with each of the sensors, and Q(t) is iso-thermal mass flow rate obtained from the time-varying signal of each of the sensors.
5 . The computer-implemented method according to claim 4 , wherein the determining the temporal delay includes determining the Δt for each of the sensors that makes a result of the equation less than a threshold value.
6 . The computer-implemented method according to claim 4 , further comprising determining the iso-thermal mass flow rate for each of the sensors as:
Q i ( t )= p i ( t ) q i ( t ), where
p(t)=1 and q(t) is flow rate indicated by the time-varying signal based on the pipeline network transporting water, and determining the iso-thermal mass flow rate for each of the sensors as:
Q i ( t )= p i ( t )( p upstream −p i ( t )), where
p(t)=is pressure indicated by the time-varying signal based on the pipeline network transporting natural gas, and p upstream is an upstream pressure value determined based on monitoring the sensors.
7 . The computer-implemented method according to claim 6 , wherein the calibrating the uncalibrated sensors includes obtaining measured values of pressure {circumflex over (p)} and flow rate {circumflex over (q)} from the time-varying signal from each of the sensors and determining coefficients α, β, a, and b for each of the uncalibrated sensors that minimize the equation, given that:
q i =α i {circumflex over (q)} i +β i , and
p i =a i {circumflex over (p)} i +b i .
8 . A system to calibrate uncalibrated sensors among sensors distributed along a pipeline network, the system comprising:
a memory device configured to store geopositions of each of the sensors; and
a processor configured to designate a set of the sensors as upstream sensors based on their geopositions, designate remaining ones of the sensors other than the set of the sensors as downstream sensors, determine a temporal delay associated with each of the sensors, and calibrate the uncalibrated sensors based on the corresponding temporal delay and on calibrated sensors among the sensors.
9 . The system according to claim 8 , further comprising an interface configured to receive a time-varying signal from each of the sensors.
10 . The system according to claim 9 , wherein the processor determines the temporal delay by isolating a subset of the time-varying signal associated with each of the sensors such that a duration of every subset is the same and a start time and an end time of every subset is determined for each of the sensors.
11 . The system according to claim 9 , wherein the processor determines the temporal delay by solving an equation representing mass conservation law that is given by:
|Σ iεU Σ t strt +Δt i t end +Δt i Q i ( t )−Σ iεD Σ t strt +Δt i t end +Δt i Q i ( t )| norm , where
U refers to the upstream sensors, D refers to the downstream sensors, tstrt and tend are start and end times, respectively, that are fixed for all the sensors, Δt is the temporal delay associated with each of the sensors, and Q(t) is iso-thermal mass flow rate obtained from the time-varying signal of each of the sensors.
12 . The system according to claim 11 , wherein the processor determines the temporal delay by determining the Δt for each of the sensors that makes a result of the equation less than a threshold value.
13 . The system according to claim 11 , wherein the iso-thermal mass flow rate for each of the sensors is given by:
Q i ( t )= p i ( t ) q i ( t ), where
p(t)=1 and q(t) is flow rate indicated by the time-varying signal based on the pipeline network transporting water, and the iso-thermal mass flow rate for each of the sensors is given by:
Q i ( t )= p i ( t )( p upstream −p i ( t )), where
p(t)=is pressure indicated by the time-varying signal based on the pipeline network transporting natural gas, and p upstream is an upstream pressure value determined based on monitoring the sensors.
14 . The system according to claim 13 , wherein the processor calibrates the uncalibrated sensors by obtaining measured values of pressure {circumflex over (p)} and flow rate {circumflex over (q)} from the time-varying signal from each of the sensors and determining coefficients α, β, a, and b for each of the uncalibrated sensors that minimize the equation, given that:
q i =α i {circumflex over (q)} i +β i , and
p i =α i {circumflex over (p)} i +b i .
15 . A computer program product for calibrating uncalibrated sensors among sensors distributed along a pipeline network, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to perform a method comprising:
designating a set of the sensors as upstream sensors based on their geopositions;
designating remaining ones of the sensors other than the set of the sensors as downstream sensors;
determining a temporal delay associated with each of the sensors; and
calibrating the uncalibrated sensors based on the corresponding temporal delay and on calibrated sensors among the sensors.
16 . The computer program product according to claim 15 , further comprising obtaining a time-varying signal from each of the sensors.
17 . The computer program product according to claim 16 , wherein the determining the temporal delay includes isolating a subset of the time-varying signal associated with each of the sensors such that a duration of every subset is the same and a start time and an end time of every subset is determined for each of the sensors.
18 . The computer program product according to claim 16 , wherein the determining the temporal delay includes solving an equation representing mass conservation law that is given by:
|Σ iεU Σ t strt +Δt i t end +Δt i Q i ( t )−Σ iεD Σ t strt +Δt i t end +Δt i Q i ( t )| norm , where
U refers to the upstream sensors, D refers to the downstream sensors, tstrt and tend are start and end times, respectively, that are fixed for all the sensors, Δt is the temporal delay associated with each of the sensors, and Q(t) is iso-thermal mass flow rate obtained from the time-varying signal of each of the sensors, and determining the Δt for each of the sensors that makes a result of the equation less than a threshold value.
19 . The computer program product according to claim 18 , further comprising determining the iso-thermal mass flow rate for each of the sensors as:
Q i ( t )= p i ( t ) q i ( t ), where
p(t)=1 and q(t) is flow rate indicated by the time-varying signal based on the pipeline network transporting water, and determining the iso-thermal mass flow rate for each of the sensors as:
Q i ( t )= p i ( t )( p upstream −p i ( t )), where
p(t)=is pressure indicated by the time-varying signal based on the pipeline network transporting natural gas, and p upstream is an upstream pressure value determined based on monitoring the sensors.
20 . The computer program product according to claim 19 , wherein the calibrating the uncalibrated sensors includes obtaining measured values of pressure {circumflex over (p)} and flow rate {circumflex over (q)} from the time-varying signal from each of the sensors and determining coefficients α, β, a, and b for each of the uncalibrated sensors that minimize the equation, given that:
q i =α i {circumflex over (q)} i +β i , and
p i =a i {circumflex over (p)} i +b i .