Method and system for nonlinear state estimation

• US 7,386,426 B1
• Filed: 04/28/2000
• Issued: 06/10/2008
• Est. Priority Date: 04/30/1999
• Status: Expired due to Term

• Current Assignee: SmartSignal Corporation (Emerson Electric Company)
• Original Assignee: SmartSignal Corporation (Emerson Electric Company)
• Inventors: Black, Christopher L., Hines, J. Wesley
• Primary Examiner(s): Shah; Kamini
• Assistant Examiner(s): DAY, HERNG DER
• Application Number:
  US09/561,238
• Time in Patent Office: 2,965 Days
• Field of Search: 703/2, 703/3, 703/4, 703/6, 702/104, 702/179, 702/181, 702/189
• US Class Current: 703/2
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 30/02 Marketing; Price estimation or determination; Fundraising

Abstract

An NSET method and apparatus for modeling and monitoring the status of a system is disclosed. The NSET employs a nonlinear similarity operator in place of linear matrix multiplication, to estimate a set of sensor data based on learned reference data, responsive to receiving a set of actual sensor data. Regularization is used in the generation of the estimate. The estimated data values and the actual sensor data are differenced to produce residuals, which are statistically tested with a SPRT to detect anomalies. Cluster centers may be used to represent learned reference data. The detection of anomalies can be used advantageously for sensor calibration verification.

Claims

1. An apparatus for monitoring an instrumented system, comprising:

a memory for storing a set of reference observations (A) of said system;

at least one processor for executing operational instructions;

operational instructions for obtaining an input observation (y) of data values representative of the state of the system;

operational instructions for generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation technique based on said input observation (y) and on said reference observations (A) by applying a nonlinear similarity operator in substitution for linear matrix multiplication in the formation of a prototype matrix (A^T⊕

A) from said reference observations; and

operational instructions for comparing said estimate to a corresponding data value of said input observation and determining a condition of said instrumented system,

wherein said nonlinear similarity operator is chosen from the set consisting of the following terms and the following terms added to one and inverted;

Bernoulli difference;

Relative entropy;

Euclidean norm;

City block distance;

Linear correlation coefficient;

Common mean linear correlation coefficient;

Root mean power error; and

Scaled mean power error.

2. An apparatus according to claim 1, wherein said nonlinear state estimation technique is regularized by performing ridge regression.

3. An apparatus according to claim 1, wherein said nonlinear state estimation technique is regularized by performing truncated singular value decomposition.

4. An apparatus according to claim 1, wherein operational instructions for comparing include instructions for determining the difference between said estimate and said corresponding data value to form a residual value.

5. An apparatus according to claim 1, further comprising operational instructions for clustering a set of historic data observations of said system to produce said set of reference observations for storage in said memory.

6. An apparatus according to claim 5, in which said operational instructions for clustering are disposed to cluster said set of historic data observations and add to said set of reference observations at least one historic data observation closest to a cluster center.

7. An apparatus according to claim 1, wherein said nonlinear similarity operator is the Euclidean Norm added to one and inverted.

8. An apparatus according to claim 1, wherein said nonlinear similarity operator is the Root Mean Power Error added to one and inverted.

9. An apparatus for monitoring an instrumented system, comprising:

a memory for storing a set of reference observations (A) of said system;

at least one processor for executing operational instructions;

operational instructions for obtaining an input observation (y) of data values representative of the state of the system;

operational instructions for generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation technique based on said input observation (y) and on said reference observations (A) by applying a nonlinear similarity operator in substitution for linear matrix multiplication in forming the product (A^T⊕

y) of said input observation and said reference observations; and

operational instructions for comparing said estimate to a corresponding data value of said input observation and determining a condition of said instrumented system,

wherein said nonlinear similarity operator is chosen from the set consisting of the following terms and the following terms added to one and inverted;

Bernoulli difference;

Relative entropy;

Euclidean norm;

City block distance;

Linear correlation coefficient;

Common mean linear correlation coefficient;

Root mean power error; and

Scaled mean power error.

10. An apparatus according to claim 9, wherein said nonlinear similarity operator is the Euclidean Norm added to one and inverted.

11. An apparatus according to claim 9, wherein said nonlinear similarity operator is the Root Mean Power Error added to one and inverted.

12. An apparatus for monitoring an instrumented system, comprising:

a memory for storing a set of reference observations (A) of said system;

at least one processor for executing operational instructions;

operational instructions for obtaining an input observation (y) of data values representative of the state of the system;

operational instructions for generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation technique based on said input observation (y) and on said reference observations (A) by applying a nonlinear similarity operator in substitution for linear matrix multiplication in forming the product (A^T⊕

y) of said input observation and said reference observations;

operational instructions for comparing said estimate to a corresponding data value of said input observation and determining a condition of said instrumented system; and

operational instructions for matching at least one condition of at least one data value of said input observation with corresponding data of said reference observations in order to select a subset of said reference observations to populate a prototype matrix based on which said estimate is generated.

13. A method for monitoring an instrumented system, comprising:

providing a set (A) of reference observations of said system;

obtaining an input observation (y) of data values representative of the state of the system;

generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation based on said input observation (y) and on said reference observations (A) by applying a nonlinear similarity operator in substitution for linear matrix multiplication in the formation of a prototype matrix (A^T⊕

A) from said reference observations;

comparing said estimate to a corresponding data value of said input observation; and

determining a condition of said instrumented system based on said comparing step,

wherein said nonlinear similarity operator is chosen from the set consisting of the following terms and the following terms added to one and inverted;

Bernoulli difference;

Relative entropy;

Euclidean norm;

City block distance;

Linear correlation coefficient;

Common mean linear correlation coefficient;

Root mean power error; and

Scaled mean power error.

14. A method according to claim 13, wherein said regularized nonlinear state estimation is regularized by performing ridge regression.

15. A method according to claim 13, wherein said regularized nonlinear state estimation is regularized by performing truncated singular value decomposition.

16. A method according to claim 13, wherein said step of comparing includes determining the difference between said estimate and said corresponding data value to form a residual value.

17. A method according to claim 16, wherein said step for comparing further includes performing a sequential probability ratio test on a sequence of said residuals corresponding to a sequence of input observations.

18. A method according to claim 13, further comprising the step of clustering a set of historic data observations of said system to provide said set of reference observations.

19. A method according to claim 18, in which said clustering step includes clustering said set of historic data observations and adding to said set of reference observations at least one historic data observation closest to a cluster center.

20. A method for monitoring an instrumented system, comprising:

providing a set (A) of reference observations of said system;

obtaining an input observation (y) of data values representative of the state of the system;

generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation based on said input observation (y) and on said reference observations (A) by applying a nonlinear similarity operator in substitution for linear matrix multiplication in forming the product (A^T⊕

y) of said input observation and said reference observations;

comparing said estimate to a corresponding data value of said input observation; and

determining a condition of said instrumented system based on said comparing step,

wherein said nonlinear similarity operator is chosen from the set consisting of the following terms and the following terms added to one and inverted;

Bernoulli difference;

Relative entropy;

Euclidean norm;

City block distance;

Linear correlation coefficient;

Common mean linear correlation coefficient;

Root mean power error; and

Scaled mean power error.

21. A method for monitoring an instrumented system, comprising:

providing a set (A) of reference observations of said system;

obtaining an input observation (y) of data values representative of the state of the system;

generating an estimate (y-prime) of at least one data value of said instrumented system using a regularized nonlinear state estimation based on said input observation (y) and on said reference observations (A);

comparing said estimate to a corresponding data value of said input observation;

determining a condition of said instrumented system based on said comparing step; and

matching at least one condition of at least one data value of said input observation with corresponding data of said reference observations in order to select a subset of said reference observations to populate a prototype matrix based on which said estimate is generated.

22. An apparatus for monitoring an instrumented system, comprising:

a memory for storing a set of reference observations of said system;

at least one processor for executing operational instructions;

operational instructions for obtaining an input observation of data values representative of the state of the system;

operational instructions for matching at least one condition of at least one data value of said input observation with corresponding data of said reference observations in order to select a subset of said reference observations;

operational instructions for applying a nonlinear similarity operator to said subset of said reference observations to form a prototype matrix (A^T⊕

A) from said subset of said reference observations;

operational instructions for applying a nonlinear similarity operator in forming the product (A^T⊕

y) of said input observation and said subset of said reference observations;

operational instructions for computing weights from said prototype matrix and said product;

operational instructions for generating an estimate of at least one data value of said instrumented system by combining said subset of said reference observations according to said weights; and

operational instructions for comparing said estimate to a corresponding data value of said input observation and determining a condition of said instrumented system.

23. An apparatus according to claim 22, wherein at least one of said nonlinear similarity operators is a scalar valued function of said reference observations, added to one and inverted.

24. An apparatus for monitoring an instrumented system, comprising:

a memory for storing a set of reference observations of said system;

at least one processor for executing operational instructions;

operational instructions for obtaining an input observation of data values representative of the state of the system;

operational instructions for applying a nonlinear similarity operator to said reference observations to form a prototype matrix (A^T⊕

A) from said reference observations;

operational instructions for applying a nonlinear similarity operator in forming the product (A^T⊕

y) of said input observation and said reference observations;

operational instructions for computing weights from said prototype matrix and said product;

operational instructions for generating an estimate of at least one data value of said instrumented system by combining said reference observations according to said weights;

operational instructions for comparing said estimate to a corresponding data value of said input observation and determining a condition of said instrumented system;

wherein at least one of said nonlinear similarity operators is a scalar valued function of vectors, added to one and inverted.

25. An apparatus according to claim 24, wherein said scalar valued function of vectors is selected from:

Bernoulli difference;

Relative entropy;

Euclidean norm;

City block distance;

Linear correlation coefficient;

Common mean linear correlation coefficient;

Root mean power error;

Scaled mean power error; and

Matrix Multiplication.

26. An apparatus according to claim 25, wherein said scalar valued function of vectors is city block distance.

27. An apparatus according to claim 25, wherein said scalar valued function of vectors is root mean square error.

28. An apparatus according to claim 25, wherein said scalar valued function of vectors is Euclidean distance.