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US 2014/0174946 A1Published application
System and method for estimating impedance in electrochemical impedance spectroscopy
AssigneesKing Abdulaziz City for Science and Technology, King Fahd University of Petroleum and Minerals
InventorsAHMED MOHAMED YAMANI, SAEED OMAR SAEED ALJABRI
Life of this patent
Estimating the term…
Abstract
The method for estimating impedance in electrochemical impedance spectroscopy is an iterative method, combining high order statistic (HOS) deconvolution and adaptive filtering (AF) to estimate impedance in electrochemical impedance spectroscopy for such applications as measuring the degree of electrolytic corrosion in a coated metal pipe, for example.
Claims3
A method for estimating impedance in electrochemical impedance spectroscopy, comprising the steps of:
- (a) establishing an initial estimate of resistance of an electrolytic solution RS0, an initial estimate of impedance z0, an initial estimate of voltage v0, an initial estimate of capacitance of a coating of a piece of coated metal Cc0, an initial estimate of a polarization resistance of an interface between the electrolytic solution and the piece of coated metal Rpo0, an initial estimate of a charge transfer resistance at the interface between the electrolytic solution and the piece of coated metal Rct0, and an initial estimate of double-layer capacitance at the interface between the electrolytic solution and the piece of coated metal Cdl0;
- (b) setting an integer i equal to zero;
- (c) calculating an i-th estimate of the resistance of the electrolytic solution RSi as
- RS
- i
- =
- RS
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- RS
- i
- -
- 1
- ,
- where μ is a pre-set step size, vt is an i-th estimate of voltage, I is an i-th estimate of current, and zi is an i-th estimate of impedance;
- (d) setting vi-1 equal to a measured voltage across the coating and calculating an i-th estimate of the capacitance of the coating Cci as
- Cc
- i
- =
- Cc
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δCc
- i
- -
- 1
- ;
- (e) setting Ii-1 equal to a current measured at the interface between the electrolytic solution and the piece of coated metal and calculating an i-th estimate of the polarization resistance of the interface between the electrolytic solution and the piece of coated metal Rpoi as
- Rpo
- i
- =
- Rpo
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rpo
- i
- -
- 1
- ;
- (f) setting vi-1 equal to a voltage across a corroded portion at the interface between the electrolytic solution and the piece of coated metal and calculating an i-th estimate of the double-layer capacitance at the interface Cdli as
- Cdl
- i
- =
- Cdl
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Cdl
- i
- -
- 1
- ;
- (g) calculating an i-th estimate of the charge transfer resistance at the interface Rcti as
- Rct
- i
- =
- Rct
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rct
- i
- -
- 1
- ;
- (h) calculating an i-th estimate of a weight vector wi as
- w
- i
- =
- q
- jCc
- i
-
- Rpo
- i
-
- [
- (
- δ
-
-
- z
- δ
-
-
- Rpo
- i
- )
- -
- 2
- -
- 1
- ]
- ;
- (i) calculating the i-th estimate of the impedance as
- z
- i
- =
- RS
- i
- +
- Rct
- i
- 1
- +
- j
-
-
- w
- i
-
- Rct
- i
-
- Cdl
- i
- ;
- and
- (j) if |zi−zi-1| is greater than a pre-set threshold, then setting i=i+1 and returning to step (c);
- otherwise, saving zi in non-transitory computer readable memory and displaying zi.
287 more elements
A system for estimating impedance in electrochemical impedance spectroscopy, comprising:
- a processor;
- computer readable memory coupled to the processor;
- a user interface coupled to the processor;
- a display coupled to the processor;
- software stored in the memory and executable by the processor, the software having:
- means for calculating an i-th estimate of the resistance of the electrolytic solution RSi as
- RS
- i
- =
- RS
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- RS
- i
- -
- 1
- ,
- where μ is a pre-set step size, vi is an i-th estimate of voltage, I is an i-th estimate of current, and zi is an i-th estimate of impedance;
- means for setting vi-1 equal to a measured voltage across the coating and calculating an i-th estimate of the capacitance of the coating Cci as
- Cc
- i
- =
- Cc
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Cc
- i
- -
- 1
- ;
- means for setting Ii-1 equal to a current measured at the interface between the electrolytic solution and the piece of coated metal and calculating an i-th estimate of the polarization resistance of the interface between the electrolytic solution and the piece of coated metal Rpoi as
- Rpo
- i
- =
- Rpo
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rpo
- i
- -
- 1
- ;
- means for setting vi-1 equal to a voltage across a corroded portion at the interface between the electrolytic solution and the piece of coated metal and calculating an i-th estimate of the double-layer capacitance at the interface Cdli as
- Cdl
- i
- =
- Cdl
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Cdl
- i
- -
- 1
- ;
- means for calculating an i-th estimate of the charge transfer resistance at the interface Rcti as
- Rct
- i
- =
- Rct
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rct
- i
- -
- 1
- ;
- means for calculating an i-th estimate of a weight vector wi as
- w
- i
- =
- q
- jCc
- i
-
- Rpo
- i
-
- [
- (
- δ
-
-
- z
- δ
-
-
- Rpo
- i
- )
- -
- 2
- -
- 1
- ]
- ;
- and
- means for calculating the i-th estimate of the impedance as
- z
- i
- =
- RS
- i
- +
- Rct
- i
- 1
- +
- j
-
-
- w
- i
-
- Rct
- i
-
- Cdl
- i
- .
291 more elements
A computer software product that includes a non-transitory storage medium readable by a processor, the non-transitory storage medium having stored thereon a set of instructions for performing estimation of impedance in electrochemical impedance spectroscopy, the instructions comprising:
- (a) a first set of instructions which, when loaded into main memory and executed by the processor, causes the processor to establish an initial estimate of resistance of an electrolytic solution RS0, an initial estimate of impedance z0, an initial estimate of voltage v0, an initial estimate of capacitance of a coating of a piece of coated metal Cc0, an initial estimate of a polarization resistance of an interface between the electrolytic solution and the piece of coated metal Rpo0, an initial estimate of a charge transfer resistance at the interface between the electrolytic solution and the piece of coated metal Rct0, and an initial estimate of double-layer capacitance at the interface between the electrolytic solution and the piece of coated metal Cdl0;
- (b) a second set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set an integer i equal to zero;
- (c) a third set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate an i-th estimate of the resistance of the electrolytic solution RSi as
- RS
- i
- =
- RS
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- RS
- i
- -
- 1
- ,
- where μ is a pre-set step size, vi is an i-th estimate of voltage, I is an i-th estimate of current, and zi is an i-th estimate of impedance;
- (d) a fourth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set vi-1 equal to a measured voltage across the coating and calculate an i-th estimate of the capacitance of the coating Cci as
- Cc
- i
- =
- Cc
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Cc
- i
- -
- 1
- ;
- (e) a fifth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set Ii-1 equal to a current measured at the interface between the electrolytic solution and the piece of coated metal and calculate an i-th estimate of the polarization resistance of the interface between the electrolytic solution and the piece of coated metal Rpoi as
- Rpo
- i
- =
- Rpo
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rpo
- i
- -
- 1
- ;
- (f) a sixth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set vi-1 equal to a voltage across a corroded portion at the interface between the electrolytic solution and the piece of coated metal and calculate an i-th estimate of the double-layer capacitance at the interface Cdli as
- Cdl
- i
- =
- Cdl
- i
- -
- 1
- +
- μ
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Cdl
- i
- -
- 1
- ;
- (g) a seventh set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate an i-th estimate of the charge transfer resistance at the interface Rcti as
- Rct
- i
- =
- Rct
- i
- -
- 1
- +
- μ
-
-
- (
- v
- i
- -
- 1
- -
- I
- i
- -
- 1
-
- z
- i
- -
- 1
- )
-
- I
- i
- ·
- δ
-
-
- z
- i
- -
- 1
- *
- δ
-
-
- Rct
- i
- -
- 1
- ;
- (h) an eighth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate an i-th estimate of a weight vector wi as
- w
- i
- =
- q
- j
-
-
- Cc
- i
-
- Rpo
- i
-
- [
- (
- δ
-
-
- z
- δ
-
-
- Rpo
- i
- )
- -
- 2
- -
- 1
- ]
- ;
- (i) a ninth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate the i-th estimate of the impedance as
- z
- i
- =
- RS
- i
- +
- Rct
- i
- 1
- +
- j
-
-
- w
- i
-
- Rct
- i
-
- Cdl
- i
- ;
- and
- (j) a tenth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set i=i+1 and return to the third set of instructions if |zi−zi-1| is greater than a pre-set threshold, otherwise saving zi in the non-transitory storage medium and displaying zi.
293 more elements
Dependencies are inferred from the claim text.