PREDICTION METHOD FOR MONITORING PERFORMANCE OF POWER PLANT INSTRUMENTS

• US 20100274745A1
• Filed: 10/06/2009
• Published: 10/28/2010
• Est. Priority Date: 04/22/2009
• Status: Active Grant

• Current Assignee: Korea Electric Power Corporation (Government of South Korea)
• Original Assignee: Korea Electric Power Corporation (Government of South Korea)
• Inventors: Seo, In Yong, Lee, Jae Yong, Park, Moon Ghu, Shin, Ho Cheol
• Granted Patent: US 8,781,979 B2
• Time in Patent Office: Days
• US Class Current: 706/12
• CPC Class Codes: G06F 18/2411 based on the proximity to a decision surface, e.g. support vector machines
• CPC Class Codes: G06N 20/00 Machine learning
• CPC Class Codes: G06N 20/10 using kernel methods, e.g. support vector machines [SVM]

Abstract

Disclosed is a prediction method for monitoring performance of power plant instruments. The prediction method extracts a principal component of an instrument signal, obtains an optimized constant of a SVR model through a response surface methodology using data for optimization, and trains a model using training data. Therefore, compared to an existing Kernel regression method, accuracy for calculating a prediction value can be improved.

Claims

1. A prediction method for monitoring performance of power plant instruments comprising:

displaying entire data in a matrix;

normalizing the entire data into a data set;

trisecting the normalized data set into three data sets, wherein the three data sets comprising a training data set, a optimization data set, and a test data set;

extracting a principal component of each of the normalized training data set, the optimization data set, and the test data set;

calculating an optimal constant of a Support Vector Regression (SVR) model to optimize prediction value errors of data for optimization using a response surface method;

generating the Support Vector Regression (SVR) training model using the optimal constant;

obtaining a Kernel function matrix using the normalized test data set as an input and predicting an output value of the support vector regression model; and

de-normalizing the output value into an original range to obtain a predicted value of a variable.

2. The prediction method of claim 1, wherein the displaying entire data in a matrix is represented by the following equation:

3. The prediction method of claim 1, wherein the normalizing the entire data is performed through the following Equation:

4. The prediction method of claim 1, wherein the trisecting the normalized data set is performed through the following equation, having an n×

m dimension;

Z_ts=[Z_3i+1,1 Z_3i+1,2 . . . Z_3i+1,m]

Z_tr=[Z_3i+2,1 Z_3i+2,2 . . . Z_3i+2,m]

Z_op=[Z_3i+3,1 Z_3i+3,2 . . . Z_3i+3,m] 

 

<

Equation 9>

where i=0, 1, 2, n−

1, the normalized data set being referred to as Z, the data set for training being referred to as Z_tr, the data set for optimization being referred to as Z_op, and the data set for test being referred to as Z_ts.

5. The prediction method of claim 1, wherein extracting a principal component of each of the normalized training data set, the optimization data set, and the test data set, dispersion of the principal component that is an eigenvalue of a covariance matrix is arranged according to its size, and principal components P_tr, Z_op, and P_ts with respect to Z_tr, Z_op, and Z_ts are selected until a cumulative sum reaches greater than 99.5%, starting with the principal component of the largest percentage dispersion value, to extract principal components of each of the normalized data sets Z_tr, Z_op, and Z_ts.

6. The prediction method of claim 5, wherein a matrix obtained by subtracting an average value of each variable from each of the data sets Z_tr, Z_op, and Z_ts, is called a matrix A and is represented by the following equation:

A=Z_tr−

Z_tr

7. The prediction method of claim 6, wherein an eigenvalue λ

of A^TA and a singular value S of A are obtained through the following equations;

8. The prediction method of claim 7, wherein an eigenvector of AA^T that is an n×

n matrix is obtained, and then a unitary matrix U is obtained, and an eigenvalue A is obtained through the following Equation A and then is substituted into the following Equation B to obtain an eigenvector e₁, e₂, . . . , e_m of n×

1 with respect to each eigenvalue λ

;

|AA^T−

λ

I|=0 

 

Equation A

(AA^T−

λ

I)X=0 

 

Equation B

9. The prediction method of claim 8, wherein the dispersion of each principal component is obtained through the following Equation:

10. The prediction method of claim 9, wherein the percentage is obtained by dividing dispersion of each principal component by the sum of dispersions of entire principal components through the following equations:

11. The prediction method of claim 10, wherein the p number of the principal components up to preferred percentage dispersion (for example, 99.98%) is selected by performing a cumulative calculation starting with the largest percentage dispersion % σ

_p.

12. The prediction method of claim 11 wherein the principal component is extracted through the following equation.

Ptr=[S₁e₁ S₂e₂ . . . S_pe_p]

13. The prediction method of claim 12, wherein compressing input variables x₁, x₂, . . . , x_m of an m-dimension into the principal components θ

₁, θ

₂, . . . , θ

_m of a p-dimension is performed through the following equations;

14. The prediction method of claim 13, wherein an Optimum Regression Line (ORL) obtained as the Support Vector Regression (SVR) with respect to a k^th output is represented by the following Equation:

f_k(θ

)=w_K^Tθ

+b_k

where k is 1, 2, . . . , m.

15. The prediction method of claim 14, wherein, when an ε

-insensitive Loss Function with respect to a k^th output variable y^(k) is defined by the following equation, and an optimization equation for obtaining an ORL with respect to y^(k) is represented by the following equation;

16. The prediction method of claim 15, wherein the optimization problem is represented as a dual problem by the following equation:

17. The prediction method of claim 16, wherein Lagrange multipliers λ

_k,1 and λ

_ki* are substituted into the following equation to determine an ORL with respect to a k^th output variable of Auto Associative Support Vector Regression (AASVR);

18. The prediction method of claim 17, wherein, when the result of nonlinearly mapping from primal data into a space of high-dimension is called a vector Φ

(•

), an optimal nonlinear regression line of the following equation is obtained using a Kernel function defined as an inner product of Φ

(•

), that is the result of the nonlinear mapping;

19. The prediction method of claim 18, wherein a bias term is calculated using θ

_r and θ

_s, which is an arbitrary support vector, through the following equation;

20. A prediction method for monitoring performance of power plant instruments comprising:

displaying entire data in a matrix;

normalizing the entire data into a data set;

extracting a principal component of the normalized data set;

calculating an optimal constant of a Support Vector Regression (SVR) model to optimize prediction value errors of data for optimization using a response surface method;

generating the Support Vector Regression (SVR) model using the optimal constant;

obtaining a Kernel function matrix using the normalized data set as an input and predicting an output value of the support vector regression model; and

de-normalizing the output value into an original range to obtain a predicted value of a variable.