WO2012050262A1 - Method and system for monitoring the performance of plant instruments using ffvr and glrt - Google Patents

Abstract

The present invention relates to a method for monitoring the performance of plant instruments using FSVR and GLRT, comprising: a first step of representing the entire data set (X) as a matrix and classifying the data set into three data subsets for training (Xtr), optimization (Xopt), and testing (Xts); a second step of normalizing all of the data represented as a matrix in the first step; a third step of classifying the normalized data set (Z) into three data subsets for training (Ztr), optimization (Zopt), and testing (Zts); a fourth step of extracting main components from the data subsets (Z) for training (Ztr), optimization (Zopt), and testing (Zts); a fifth step of dividing the data sets and main components into data groups by a desired number; a sixth step of calculating optimal coefficients (ε1,C1,σ1) and (ε2,C2,σ2) of each FSVR model; a seventh step of calculating a fuzzy membership grade (μ1,μ2); an eighth step of calculating output prediction values (Zts1_hat and Zts2_hat); a ninth step of calculating a prediction value for all of the data (Zts_hat); a tenth step of classifying prediction values for the testing data; an eleventh step of calculating prediction values for the sensors in an original scale; and a twelfth step of determining the drift of the sensors.

Description

Method and system for monitoring the performance of power plant instrument using FSL and GRT

The present invention relates to a technology required to monitor the performance of the safety monitoring instrument of a nuclear power plant at all times while the power plant is operating. In particular, the clustering of data, FCM clustering, principal component extraction and FSVR (Fuzzy Support Vector Regression) The method is used to model the system for various cases, and then the three parameters of the regression equation are optimized using response surface methodology, modeled the power plant system, and then used to monitor the instrument signals. In addition to improving the accuracy of predictive calculations compared to kernel regression, FFSy (Fuzzy Support Vector Regression) and GLRT (GLVR) are used to monitor the occurrence of abnormalities including instrument drift using the Generalized Likelihood Ratio Test (GLRT). To monitor the performance of power plant instrumentation using Generalized Likelihood Ratio Test .

In general, all power generation facilities are installed in a number of measuring instruments for the purpose of improving operability and securing safety, and acquire signals in real time and use them in power plant monitoring and protection systems. In particular, the safety channel-related measurement channels of nuclear power plants adopt the concept of multiple instruments to ensure the accuracy and reliability of the measurement signals, and perform inspection and calibration every nuclear cycle (about 18 months) in the operating technical manual. Nuclear power plants around the world are developing technology to extend inspection and calibration cycles by developing condition-based monitoring (CBM) methodologies for instrument calibration that is performed unnecessarily.

1 is a block diagram of a measuring instrument performance monitoring system. As shown in FIG. 1, when the measurement signal is input to the predictive model 1, the predictive model 1 outputs a predicted value of the model with respect to the input measurement value, which is called an auto-associative model. . Subsequently, the comparison module 2 compares the measured value with the predicted value and inputs the difference into the judgment logic 3 and continuously monitors the drift and the failure of the measuring instrument.

Argonne National Laboratory developed the Multivariate State Estimation Technique (MSET) and obtained US patents, which SmartSignal Corporation and Expert Microsystems could use for commercial use. It was commercialized to be. Expert Microsystems Inc., Palo Verde, Limerick 1 & 2, TMI, V.C. In the Summer, Sequoyah 1 and Salem 1 units, products using MSET are installed on-site to monitor the measuring channel online. SmartSignal Corporation has since been unable to use patents on MSET and has developed instrument performance monitoring technology based on kernel regression.

The most commonly used is Knelnel Regression to calculate the instrument's predictions. This method selects other instrument signals that have a high linear correlation with the instrument signal to be predicted as shown in Equation 1, and calculates the regression coefficient so that the sum of the error squares of the predicted and measured values is minimized.

Equation 1

Linear regression analysis can predict independent variables for unknown dependent variables when the regression coefficients are determined by known and independent variables. In the conventional linear regression method, when the dependent variables are linearly related to each other, a problem of multiple collinearity occurs, and a large error occurs in the independent variable for the small noise included in the dependent variable.

Kernel regression does not use parameters such as regression coefficients or weights to optimize the correlation between inputs and outputs, like conventional linear regression or neural networks. It is a non-parametric regression method that calculates the weight of the kernel from the Euclidean distance of the training data set in the memory vector and applies it to the memory vector. Nonparametric regression methods, such as kernel regression, have robust advantages over models and signal noise where input / output relationships are nonlinear. The following is the calculation procedure of the existing kernel regression method.

Step 1: Display training data in the form of a matrix.

Equation 2

Here, X is the training data matrix stored in the memory vector, n is the number of training data, m is the number of the measuring instrument.

Step 2: Sum the Euclidean distance of the training data for the first instrument signal set.

Expression 3

Here, x is training data, q is test data (or Query data), trn is the number of training data, j is the number of the measuring instrument.

Step 3: Using the kernel function, find the weights for each training dataset and a given test dataset.

Equation 4

Here, the Gaussian kernel is used as the weighting function and is defined as follows.

Step 4: The test data estimate is obtained by multiplying each training data by the weight and dividing the sum of the weights.

Equation 5

Step 5: Repeat the process from Step 2 to Step 4 to get predictions for the entire test data.

The above-mentioned auto-associative kernel regression (AAKR) method has the advantages of being nonlinear and robust to signal noise.However, the selected measurement data is stored as a memory vector and the training of the training data set in the memory vector for the measurement signal set Since the kernel weight is calculated from the dian distance and applied to the memory vector to obtain the prediction value of the instrument, the variance of the output prediction value increases, which is less accurate than the linear regression method.

The present invention has been invented in view of the above, and the optimization of parameters (kernel bandwidth σ, loss function ε, penalty C) of FSVR model regression using normalization, fuzzy clustering, extraction of principal components, response surface analysis, and In addition, the FSVR model implementation and output value prediction, the denormalization method of the prediction value, and the failure determination by GLRT are used to model the power plant system and then monitor the signal signal prediction and abnormality of the instrument. The purpose of this study is to provide the performance monitoring method of power plant instrumentation using Fuzzy Support Vector Regression (FSVR) and Generalized Likelihood Ratio Test (GLRT), which can improve the accuracy of prediction calculation and detect early failure.

According to the present invention, by monitoring the performance of the measuring instrument used in the nuclear power plant safety monitoring channel online while operating, the malfunction of the measuring instrument can be monitored in real time to improve the reliability of the measuring instrument, and the instrument calibration cycle of the nuclear power plant is Increase the fuel replacement cycle from 18 months to a maximum of 8 years to reduce calibration costs and radiation exposure of calibration workers in the radiation zone, and to prevent unnecessary downtime by reducing the number of unnecessary calibrations, and to prevent plant outages. By shortening the power consumption, it is possible to increase the utilization rate of the power plant.

Also, fuzzy clustering, principal component analysis, response surface analysis, and FSVR regression modeling can be used to improve the accuracy of prediction calculations compared to conventional kernel regression, and GLRT can be used to detect an early failure of the instrument. Will be.

That is, the prediction method for power plant instrument performance monitoring using Principal Component Analysis (FSVR), Fuzzy Support Vector Regression (FSVR), and GLRT method includes normalization of plant data, extraction of principal components, data clustering, and response surface analysis. The conventional kernel regression method used by optimizing the parameters of the FSVR model regression equation (kernel bandwidth σ, loss function ε, penalty C), implementing the power plant system model using the FSVR, and de-normalizing the output predictions Compared with this, the accuracy of the prediction calculation can be improved. In addition, even in the case of a very small shift drift that cannot be detected by an ordinary alarm system, it is possible to accurately identify a failure early by using the GLRT technique proposed by the present invention to determine the failure of the instrument. .

1 is a block diagram of a performance monitoring system of a general power plant instrument

2 is a schematic configuration diagram of a performance monitoring system of a power plant instrument according to an embodiment of the present invention.

3 is a flowchart of a power plant instrument performance monitoring method using principal component analysis, fuzzy support vector regression (FSVR) and GLRT method according to the present invention.

4 is a general conceptual diagram of an optimal regression line by an SVR.

5 is a diagram illustrating a measurement example of the fuzzy membership size for each cluster.

6 is a diagram for explaining an example of a reaction surface for clusters 1 and 2;

7 is a diagram showing an experimental point in the central composition plan when there are three model parameters.

FIG. 8 is a diagram illustrating a method of extracting an optimal point from a response surface for cluster 2. FIG.

9 is a diagram illustrating an example of a residual when a steady state residual and a shift of δ = 0.01 occur.

10 is a diagram illustrating an example of calculating a value of MSE (GT _i ) according to a window size.

Fig. 11 is a diagram showing an example of failure determination for the case of a normal state and an abnormal state of a measuring instrument.

12 is a graph showing nuclear reactor core output data for accuracy testing.

13 is a graph showing the nuclear power plant pressurizer water level data for accuracy test.

14 is a graph illustrating steam flow rate data of a steam generator for a nuclear power plant for accuracy test.

15 is a graph showing the nuclear power plant steam generator narrow level data for accuracy test.

16 is a graph showing nuclear power plant steam generator pressure data for accuracy test.

FIG. 17 is a graph showing wide-range water level data for a nuclear power plant steam generator for accuracy test.

18 is a graph showing the main water supply flow rate of the nuclear power plant steam generator for the accuracy test.

19 is a graph showing nuclear power plant turbine output data for accuracy test.

20 is a graph illustrating primary flow rate flow rate data for a nuclear power plant for accuracy test.

21 is a graph showing the residual heat removal flow rate data of nuclear power plants for accuracy test.

22 is a graph showing the temperature of the reactor coolant temperature of the nuclear power plant for the accuracy test.

Power plant instrument performance monitoring system using the FSVR and GLRT according to the present invention for achieving the above object,

an input unit 11 receiving time-series field signals for the m field sensors and sending them to the clustering unit 12;

A clustering unit 12 dividing an input signal for the time series field signal received from the input unit 11 into N desired data clusters using a fuzzy clustering method;

A PCA unit 13 for extracting a main component for each data cluster divided into N data clusters received from the clustering unit 12;

An FSVR unit 14 for calculating fuzzy membership grade for each data cluster, training a model, obtaining optimal parameters of the model using response surface analysis, and performing signal prediction on test data;

A comparison operation unit 15 for comparing a signal predicted by the FSVR unit 14 with an input signal to obtain a difference;

After the optimization of the window size and the setting of the management limit line, the GLRT unit 16 for calculating the statistic of the GLRT using the output of the comparison operation unit to determine the drift of the sensor is characterized in that it is configured.

Power plant instrument performance monitoring method using the FSVR and GLRT according to the present invention,

A first step of displaying the entire data set (X) in the form of a matrix and subdividing it into training (Xtr), optimization (Xopt), and test (Xts);

A second step of normalizing the entire data displayed in matrix form in the first step;

A third step of dividing the data set Z normalized in the second step into training (Ztr), optimization (Zopt), and test (Zts);

A fourth step of extracting a principal component of each data set (Ztr) for training (Ztr), optimization (Zopt), and test (Zts) normalized and divided in the third step;

A fifth step of dividing the data set and the principal components into as many data clusters as desired using Fuzzy C-Means (FCM) clustering;

Each FSVR model of reacting with a surface analysis method, the optimization of each data cluster of data (Zopt) for (Z _opt1, Z _opt2) minimizes the prediction error of the optimization data (Zopt) for optimal constant

And

Obtaining a sixth step;

Fuzzy membership grade according to step 6-1 above for each cluster of training data Ztr

Calculating a seventh step;

After training the FSVR model using the training data for each cluster, the principal component vector of the training data, the optimal parameters obtained in the sixth step, and the fuzzy membership grade obtained in the seventh step, An eighth step of obtaining output prediction values Zts1_hat and Zts2_hat by inputting each cluster principal component vector Pts1 and Pts2 of the test data Zts;

A ninth step of connecting prediction values Zts1_hat and Zts2_hat for each cluster to obtain prediction values Zts_hat for the entire data;

Estimates for Experimental Data

Classifying the data in chronological order using the original time index;

The normalized test data obtained in step 10 is normalized to the original range by denormalizing the predicted value of each sensor of the original scale.

Eleventh step of obtaining according to equation 45 and;

And a twelfth step of calculating a residual for the predicted value and determining a drift of the sensor using the GLRT.

Further, in the present invention, the matrix in the first step is

It is characterized by being represented by.

In addition, the present invention, in the second step the normalization,

Where i = 1,2 ... 3n

It is characterized by consisting of.

In the present invention, the normalized entire data set (Z) is

It is characterized by being represented by.

In addition, the present invention, the normalized training (Ztr), optimization (Zopt), experimental (Zts) data set is a formula,

Where i = 0,1,2… n-1

It is characterized by being divided by.

In addition, the present invention, in the fourth step, the variance of the main components in order of magnitude, starting from the main component having the largest percentage variance value until the cumulative sum is 99.5% or more (Ztr), for optimization ( Zopt), the main component (Ptr, Pop, Pts) of each data set of the test (Zts) is selected to extract the main component.

In addition, the present invention, the main component extraction,

In each data set of training (Ztr), optimization (Zopt), and testing (Zts), the mean value of each variable is subtracted.

Step 4-1 represented by;

expression

Depending on the

Eigenvalue of

Finding the equation

Sort in descending order according to the formula

Step 4-2 to obtain a singular value s of A according to;

Eigenvalue from

And obtain the eigenvalue

Expression

Assigning to each eigenvalue

Eigenvector of n × 1 for

By finding n × n matrix

A fourth to third step of obtaining an eigenvector;

expression

4-4 to obtain the dispersion of each main component according to;

expression

And expression

4-5 to obtain a percentage by dividing the variance of each main component by the sum of the variances of all the main components in accordance with;

Percent variance

Steps 4-6 of performing the cumulative calculation from this largest one to selecting p principal components up to a desired percentage variance (eg, 99.98%);

Formulated the main ingredient

4-7 to calculate and extract according to;

And a fourth to eighth step of extracting the main components by the fourth to the fourth to the seventh to the Zopt and Zts data sets.

In addition, the present invention is characterized in that the desired percentage dispersion in the above 4-6 step is 99.98%.

In addition, in the fifth step, the training data (Ztr) is divided into two groups Ztr1 and Ztr2 by using a Fuzzy C-Means (FCM) clustering method. Step 5-1 of dividing Ptr into the same number of clusters Ptr1 and Ptr2;

Repeating step 5-1 for the optimization data (Zopt) and the test data (Zts), and dividing them into normalized data clusters (Zopt1, Zopt2, Zts1, Zts2) and principal component clusters (Popt1, Popt2, Pts1, Pts2), respectively. It is characterized by consisting of the 5-2 step.

In addition, the present invention, the FCM (Fuzzy C-Means) clustering method,

Set of input signals

Cluster Count for

Determine fuzzy coefficient m (= 2), and belong to

Initiating step 1;

Obtaining a center vector vi ^(r) and membership u _ik for each cluster;

Calculating a distance between each cluster center and data to generate a new belonging matrix U ^{(r + 1)} which minimizes the objective function Q;

If the end condition is satisfied, the process ends. If the end condition is not satisfied, r = r + 1 is set. Then, the process proceeds to the step 2, and the steps 2 to 3 are repeated.

In addition, the present invention, the step 1,

expression

(Where, i is the cluster number, k is the number of the pattern, r is the number of iterations, N is the number of sample data of each sensor, u _ik is pointer data X _k being the membership size belonging to the group i)

Characterized in that performed by.

In addition, the present invention, the above step 2,

expression

Characterized in that performed by.

In addition, the present invention, the objective function (Q) in the step 3,

expression

It is characterized by represented by.

In addition, the present invention, the termination condition in the step 4 is

It is characterized by represented by.

In addition, the present invention, the optimum constant of each FSVR model

And

The sixth step of obtaining

The potential (P ₁ ) of each data pointer is calculated using the Euclidean distance between each data pointer of the first cluster of training data (Ztr1) and all other input data, and the fuzzy membership grade is used. )

6-1 step of calculating the;

Step 6-2 selecting the first test point ( v ₁ , v ₂ , v ₃ ) of the test point for the cluster 1;

The first signal of Ztr1 (Ztr1-1) for the selected test point,

And step 6-3, after inputting Ptr1, training the FSVR model to obtain svi (support vector index), w ₁ (weight of SV) and b ₁ (bias);

Step 6-4 by using a Popt svi 1 and to obtain a radial basis function (radial basis function) (Kopt1) ;

6-5 to obtain a prediction value for the first instrument signal of the optimization data Zopt1;

After repeating steps 6-3 to 6-5 with respect to the other instrument signals of Ztr1, the prediction matrix output is performed.

Step 6-6 to obtain;

Residual of measured and predicted values of optimization data (Zopt1)

Calculating a root mean square (RMS) for each of the sixth and sixth steps of storing the root mean square (RMS);

Steps 6-8 for repeating steps 6-2 to 6.7 for other test points and storing RMS values for the residuals;

Steps 6-9 of calculating an average value MSE (Equation 38) of the RMS value of the residual value obtained by using the optimization data Zopt1 with respect to the total number of input signals and calculating a natural log value with respect to the average value;

Optimal Constants of FSVR Model Using Minimized ln {MSE} for Cluster 1 Using Response Surface Methodology

Step 6-10 to obtain and;

Repeat steps 6-1 to 6-10 for cluster 2, and use the FSVR model constant for cluster 2 according to equation 35.

Step 6-11 to obtain; characterized in that made up.

In the present invention, the potential P ₁ of each data pointer is represented by an equation:

(here,

= Number of data in a cluster,

: Radius of first cluster (Ztr1)

It is characterized by.

In addition, in the present invention, steps 6-4 of obtaining a radial basis function Kopt1 are given by

(here,

: Principal component vector of Zopt1,

: Principal component vector with index of svi in Ptr1)

 It is characterized by obtaining by.

In addition, the present invention, the above 6-5 step to obtain the prediction value for the first instrument signal of the optimization data Zopt1,

(here,

: Beta vector with index of svi among beta vector)

It is characterized by obtaining by.

In addition, the present invention, the prediction matrix output

The sixth to sixth steps of

It is characterized by obtained by.

In addition, the present invention, in the sixth to eighth step of the central synthesis plan (CCD) to the test three times (test points 15, 16, 17), but the 15th test using the entire Zopt, 16th The test is characterized in that 1/2 of Zopt and 17th test are performed on the other half of Zopt.

In addition, the present invention, the average value (MSE) in the above step 6-9,

It is characterized by calculating by.

The present invention also provides an optimal constant for the FSVR model for cluster 2.

The sixth to sixth steps to find the equation,

It is characterized by obtaining by.

In addition, the present invention, the optimum constant of the FSVR model,

= (2.0, 0.0005, 10)

= (1.1404, 0.0005, 5.247).

In addition, the present invention, the method for obtaining the optimum constant of the FSVR model using the response surface analysis method in the sixth step,

Sigma (σ), epsilon (ε), and C, respectively, are the FSVR model parameters.

Step 6-10-1;

6-10-2 to determine a search range for each;

The upper and lower bounds of the search range

Wow

6-10-3, which standardizes the model parameters.

Standardized Model Parameters Using Central Synthesis Plan

A step 6-10-4 of setting an evaluation point of the model performance in response to the search range of;

6-10-5 steps of estimating the magnitude of the experimental error and defining the coordinate α of the axial point by the equation α = [number of factor test points] ^1/4 ;

By central composition plan

Model parameters according to the experimental point of

After determining the value of, follow the central synthesis plan (

Test points of) and by the central synthesis plan

Step 6-10-6 of performing an FSVR modeling experiment using the experimental point value of n) as a model parameter;

By central composition plan

6-10-7 obtaining the beta vector and the bias constant of the FSVR model using Ztr, Ptr and fuzzy membership μ at the experimental points of

To estimate the accuracy of each model, the data set Pop is input into m AAFSVRs to normalize the predictions of the optimization data.

6-10-8 calculating the MSE, which is the accuracy of the output model, from Equation 38;

Model Parameter

Steps 6-10-9 of estimating a response surface equation between the log and the log (MSE);

Minimize log (MSE) using estimated response surface

Optimum condition of

6-10-10 to obtain;

Optimal condition

It is characterized by consisting of; 6-10-11 step to convert to the original unit.

In addition, the present invention, the search range for the cluster 1 in the step 6-10-2

: 0.2 to 2.0,

: 0.0005 to 0.05,

: 0.1 to 10.0, and the search range for cluster 2 is

0.3 to 1.9;

: 0.0001 to 0.0009,

It is characterized by setting to 0.1-10.

In addition, the present invention, the standardization of the model parameters in the above 6-10-3 step,

It is characterized by consisting of.

In addition, the present invention, the MSE that is the accuracy of the output model in the step 6-10-8,

(here,

Pop out of the sensor

of

The second input data,

Is an estimate by model)

It is characterized by calculating by.

In the present invention, the reaction surface is a formula

( e means random error)

By taking a quadratic model,

The estimated response surface is

It is characterized by represented by.

In addition, the present invention, in the step 6-10-10

The optimal condition of

It is characterized in that obtained through the partial differential.

In addition, in the present invention, the optimum conditions for the reaction surface obtained for cluster # 1

= (0,0.04525,0) and the optimal conditions for the response surface obtained for cluster # 2

= (1.1364, -0.0005,5.2487).

In addition, the present invention, the optimum conditions in the above step 6-10-11

Is converted into the original unit,

It is characterized by consisting of.

In addition, the present invention, the optimal parameters for cluster # 1

,

,

The estimated log (MSE) under this condition is -5.3249,

Each of the best parameters for cluster # 2

,

,

It is characterized in that the log (MSE) predicted under this condition is -5.4170.

In addition, the eighth step of obtaining the output prediction values (Zts1_hat and Zts2_hat),

Three optimal constants of the FSVR model obtained in the sixth step

Then, using the quadratic programming technique with the main component Ptr1 of training data and the first signal of training data (first column of Ztr1), the optimization problem is solved. step 8-1 of generating a model of FSVR ₁ by obtaining w ₁ (n × 1) and a bias constant b ₁ ;

Repeat step 8-1 for the second to m th measurement signals

and

Step 8-2 to generate a model of the FSVR ₂ ~ FSVR _m by obtaining the;

The kernel function ( K _ts1 (n × n)) of the Gaussian Radial Basis Function is obtained using the principal component (Ptr1) of the training data and the principal component (Pts1) of the test data. And 8-8-3 obtaining an output of the FSVR ₁ using the support vector weight w ₁ and the bias constant b ₁ of the FSVR model obtained in the 8-8 step;

And step 8-4 of repeating steps 8-3 for the m th sensor from step ₂ to obtain model prediction values output from FSVR ₂ to FSVR _m .

In the present invention, the prediction value for the test data Zts1 is expressed by

(

: Principal component vector of Zts1,

: Principal component vector with index of svi in Ptr1)

(

: The support vector (SV) of the i th sensor of cluster 1

              Weight

: Bias for the i th sensor of cluster 1)

It is characterized by obtaining by.

In the present invention, the prediction value for the test data Zts2 is

(

: The support vector (SV) of the i th sensor of cluster 2

          Weight

: Bias for the i-th sensor of cluster 2)

It is characterized by obtaining by.

In the present invention, the predicted value (Zts_hat) for the entire data in the ninth step is:

It is characterized by obtaining by.

In another aspect, the present invention, the prediction value for each sensor of the original scale in the eleventh step

Expression

It is characterized by obtaining by.

The present invention also provides a twelfth step of determining the drift of the sensor,

A 12-1 step of performing a prediction program to calculate a residual between the predicted value and the measured value for each sensor and calculating the average value and the standard deviation (σ) of the residual when the sensor operates normally after the periodic calibration of the sensor;

Calculating a GT statistic for each window size by increasing the window size w by 5 from minimum to maximum using the residual when the meter is normal;

The equation for the residual to be examined using the optimal window size w for the calculation of GT statistics

And expression

And, expression

Using step 12-3 to calculate the GLR _t (k) (where k = 1, 2, ..., w) and GT while moving the window by 1 time step;

GT is obtained by generating the same number random numbers of normal distributions having the same mean and standard deviation as the mean and standard deviation of the residuals in the normal case calculated in step 12-1, and repeating 1000 times to obtain the maximum GT . Step 12-4, taking the upper control limit (UCL) taken;

It is determined that the drift has occurred in the sensor when the GT deviates from the control limit line (UCL), and if the deviation does not deviate, steps 12-5 of determining whether the sensor is normal and determining whether there is a drift;

In the present invention, the model residual (R), which is the difference between the input value and the predicted value in the step 12-1, is expressed by the equation:

It is characterized by obtaining by.

In addition, the present invention is characterized in that the average value of the residual for the normal case in step 12-2 is -0.00096347, and the standard deviation (σ) is 0.0069.

In addition, the present invention, Generalized Likelihood Ratio (GLR) at the time point t in step 12-2,

(

Recent window size

Means of data)

Saved by

Autumn

It is characterized by represented by.

In addition, the present invention, in step 12-2, the GLRT test statistic GT is defined as the largest within the window size in the GLR obtained at the time point t ,

(only,

Denotes the mean of the most recent k data at time t )

It is characterized by obtaining by.

In another aspect, the present invention, the MSE differences between the GT statistic in each window size GT statistic and the maximum window of the formula

Saved by

It is characterized in that the optimum window size is set in that the decrease of MSE (GT _i ) is slowed down.

In addition, the present invention is characterized in that the control limit line (UCL) in step 12-4 is set to UCL = 28.25.

In addition, the present invention, the sensor data used in the analysis in step 12-5,

Reactor output (%), pressurizer level (%), steam generator steam flow rate (Mkg / hr), steam generator narrow water level data (%), steam generator pressure data (Kg / cm ² ), steam generator wide water level data (% ), Steam generator main feed water flow data (Mkg / hr), turbine output data (MWe), reactor coolant fill flow data (m ³ / hr), residual heat removal flow rate data (m ³ / hr), reactor top coolant temperature data ( It is characterized by the above).

In addition, the present invention, the accuracy of the instrument in step 12-5,

Where N is the number of test data,

: estimate of the model for the i test data,

: measured value of the i-th test data)

It is characterized by represented by.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

2 is a schematic configuration diagram of a performance monitoring system of a power plant instrument according to an embodiment of the present invention.

As can be seen from FIG. 2, the performance monitoring system of the power plant meter according to the present invention includes an input unit 11, a clustering unit 12, a PCA unit 13, an FSVR unit 14, and a comparison operation unit 15. And a GLRT unit 16.

The input unit 11 receives time-series field signals from m field sensors and sends them to the clustering unit 12.

The clustering unit 12 divides the input signal for the time series field signal received from the input unit 11 into N desired data clusters using a fuzzy clustering method.

The PCA unit 13 extracts a principal component for each data cluster divided into N data clusters received from the clustering unit 12.

The FSVR unit 14 calculates a fuzzy membership grade for each data cluster, trains the model, obtains optimal parameters of the model using response surface analysis, and performs signal prediction on the test data. do.

The comparison operation unit 15 compares the signal predicted by the FSVR unit 14 with the input signal to obtain a difference.

The GLRT unit 16 sets the window size optimization and management limit line, and then calculates a GLRT test statistic using the output of the comparison operation unit to determine whether there is a drift of the sensor.

3 is a flowchart of a power plant instrument performance monitoring method using principal component analysis, fuzzy support vector regression (FSVR) and generalized likelihood ratio test (GLRT) method according to the present invention.

As can be seen from Figure 3, the power plant instrument performance monitoring method according to the present invention comprises a first step (ST1) for displaying the entire data set (X) in the form of a matrix; A second step ST2 of normalizing the entire data set; A third step ST3 of dividing the data set into a training (Ztr), an optimization (Zopt), and a test (Zts); A fourth step ST4 of extracting main components Ptr, Popt, and Pts of each normalized data set; A fifth step ST5 of dividing the data set and the main component into as many data clusters as desired using fuzzy clustering; A sixth step (ST6) of obtaining an optimum constant (epsilon, C, sigma) of the FSVR model which minimizes the prediction error of the optimization data using the response surface method; A seventh step (ST7) of calculating a fuzzy membership grade for each cluster of training data; An eighth step (ST8) of training the FSVR model using the data and the optimal parameters for each cluster, and then calculating the output prediction value of each cluster; A ninth step ST9 of concatenating prediction values for each cluster to obtain a total prediction value Zts_hat; A tenth step ST10 of classifying the prediction value Zts_hat for the test data in the original chronological order; An eleventh step (ST11) of denormalizing the prediction value of the normalized test data obtained in the tenth step to the original range to obtain an estimate value (Xts_hat) for each sensor of the original scale; And a twelfth step (ST12) of obtaining a residual of the predicted value obtained from the eleventh step and the measured value as an input value and determining the drift of the sensor using the GLRT technique.

Hereinafter, each of the above steps will be described in detail.

The conventional kernel regression method calculates weights using only the Euclidean distance of training data and test data, and weights them on the training data to calculate the predicted value of the test data. On the contrary, the present invention improves the accuracy of predictive calculation and proposes a new discrimination method for measuring instrument anomalies by using principal component analysis, data clustering, optimization using response surface analysis, and FSVR regression modeling. .

[Step 1]

The entire data set (X) is expressed in the form of a matrix as shown in Equation 6, and divided into training, optimization, and test, respectively, and is called Xtr, Xopt, and Xts, respectively.

Equation 6

[Step 2]

The entire data is normalized according to equation (7).

Equation 7

Where i = 1,2... 3n

The normalized entire data Z is expressed as in Equation 8 below.

Equation 8

[Step 3]

The normalized data set (Z) is divided into training, optimization, and test, and divided into Ztr, Zopt, and Zts, respectively. In this example, the data is divided into n data sets as shown in Equation 9 below.

Equation 9

Where i = 0,1,2... n-1

[Step 4]

The principal component of each normalized data set Ztr, Zop, Zts is extracted. List the variances of the principal components (ie, the eigenvalues of the covariance matrix) in order of magnitude, with the principal components for Ztr, Zop, and Zts starting with the principal component with the largest percentage variance and reaching a cumulative sum of at least 99.5%. Select (Ptr, Pop, Pts).

Here, the method of obtaining a main component is demonstrated.

Principal Component Analysis (PCA) is a useful method for compressing many input variables into a few variables through linear transformation. The compressed variable is called the principal component and the extraction method is as follows.

1) Subtract the mean value of each variable from each data set Ztr, Zopt, and Zts, and call it A matrix, as shown in Eq. Only Ztr is described here.

Equation 10

2) according to equation 11

Eigenvalue of

Calculate and arrange in descending order according to Eq. 12, and find the singular value s of A according to Eq.

Equation 11

Eigenvalues except zero obtained from the characteristic equation of Equation 11 (root; eigenvalue)

Are arranged in descending order according to Eq. 12, and

It is called

Equation 12

Equation 13

3) n × n matrix

Find the eigenvector of.

Equation 14

Eigenvalue from Equation 14

And obtain each eigenvalue by substituting it into

Eigenvector of n × 1 for

Obtain

Equation 15

4) Find the dispersion of each main component according to the following equation.

Equation 16

 5) Calculate the percentage by dividing the variance of each main component by the sum of the variances of all the main components according to the following equations (17) and (18).

Equation 17

Equation 18

6) percentage variance

From this largest one, cumulative calculations are made to select p principal components up to the desired percentage variance (eg 99.98%).

 7) Calculate and extract the main component as in Equation 19 below.

Equation 19

8) Extract the main components by the same procedure as in 1) to 7) for Zopt and Zts.

In this example, seven main components were used. The seven principal components account for 99.98% of the variance, with only 0.02% of the loss of information resulting from the abandonment of the remaining principal components.

Table 1 below shows the dispersion of the main components.

Table 1

Here, FSVR modeling will be described.

As shown in Figure 2, m- dimensional input variable

For

When the predicted value of the first output is obtained using the FSVR, it can be expressed as an optimal regression line (ORL) as shown in Equation 20 below.

Equation 20

only,

In equation 20, the weight of the support vector (SV)

And bias

To obtain the parameters, the normalized risk function using the fuzzy concept is defined as in Equation 21 below, and w _k and b _k are minimized.

Equation 21

here,

Is

The magnitude of the fuzzy membership for the I data of the first signal. Also,

Output variable

The insensitive loss function is defined as in Equation 22 below.

Equation 22

k th output

In order to find the ORL of the equation, the optimization problem is converted into a constrained risk function as shown in Equation 23.

Equation 23

here,

ego,

Wow

Denotes a slack variable shown in FIG. 4. Where

Is the vector of θ

Not the first element

For

The principal component vector corresponding to the first observation vector.

After converting Equation 23 into Lagrangian function, it is solved by quadratic programming.

Wow

After obtaining the value of AAFSVR,

Determine the nonlinear regression equation for the first output variable.

Formula 24

In this embodiment, a Gaussian Radial Basis Function (RBF) is used, as shown in Equation 25 below.

Equation 25

However, the bias term is any SV (Support Vector) as shown in Equation 26 below. And

Calculate using

Equation 26

Constant epsilon of the loss function of the nonlinear regression equation, the dual objective function

If penalty C, RBF (Radial Basis Function) is used as the kernel, the kernel bandwidth σ is obtained by performing step 6. This process is repeated to obtain a total of m SVRs for each output and build an AAFSVR as shown in FIG.

[Step 5]

Using fuzzy clustering, the data set and principal components are divided into as many data clusters as desired. In this embodiment, data is divided into two groups, and the procedure for the present invention will be described based on this.

5.1) The training data (Ztr) is divided into two groups Ztr1 and Ztr2 using the FCM (Fuzzy C-Means) clustering method. At this time, the main component Ptr is also divided into the same number of clusters Ptr1 and Ptr2 by using the same index of each generated data group.

5.2) For optimization data (Zopt) and test data (Zts), divide the normalized data clusters (Zopt1, Zopt2, Zts1, Zts2) and the principal component clusters (Popt1, Popt2, Pts1, Pts2) in the same way.

Here, a description will be given of the FCM (Fuzzy C-Means) clustering method.

(Step 1)

Set of input signals

Cluster Count for

Determine fuzzy coefficient m (= 2), and belong to

Initialize

Equation 27

Where i is the number of clusters, k is the number of patterns, r is the number of repetitions, N is the number of sampled data for each sensor, and u _ik is the membership size of data group X _k belonging to group i.

(Step 2)

The center vector vi ^(r) and membership u _ik for each cluster are calculated as in Equation 28 below.

Equation 28

(Step 3)

The distance between each cluster center and the data is calculated to generate a new membership matrix U ^{(r + 1)} that minimizes the objective function (Q) represented by Eq.

Equation 29

(Step 4)

If the end condition represented by the following expression 30 is satisfied, the process is terminated. Otherwise, r = r + 1 is set, and the process proceeds to step 2 to repeat the algorithm.

Equation 30

[Step 6]

Each FSVR model of reacting with a surface analysis method, the optimization of each data cluster of data (Zopt) for (Z _opt1, Z _opt2) minimizes the prediction error of the optimization data (Zopt) for optimal constant

And

Obtain

6.1) fuzzy membership grade for the first cluster of training data (Ztr1)

Calculate Using the Euclidean distance between each data pointer of Ztr1 and all other input data, the potential (P ₁ ) of each data pointer is calculated according to Equation 31, and using this, fuzzy membership grade

Calculate

Equation 31

= Number of data in a cluster,

: Radius of the first cluster (Ztr1)

5 is a diagram illustrating a measurement example of the fuzzy membership size for each cluster.

6.2) Select the first test point ( v ₁ , v ₂ , v ₃ ) of the test points for cluster 1 (FSVR parameter set, see Table 3-1).

6.3) the first signal of Ztr1 (Ztr1-1) for the selected test point,

After inputting and Ptr1, the FSVR model is trained to obtain svi (support vector index), w ₁ (Support Vector weight), and b ₁ (bias).

6.4) Using Popt 1 and svi, find the radial basis function ( Kopt1 ) according to Eq .

Equation 32

here,

: Principal component vector of Zopt1

: Principal component vector with index of svi in Ptr1

6.5) The prediction for the first instrument signal of the optimization data Zopt1 is obtained according to Eq.

Equation 33

here,

: Beta vector with index of svi among beta vector

6.6) Output the predictive matrix according to Equation 34 after performing the above methods 6.3) to 6.5) for the other instrument signals of Ztr1.

Get

Equation 34

6.7) The residuals of the measured and predicted values of the optimization data (Zopt1)

Find the root mean square (RMS) for this file and store it.

6.8) Repeat 6.2) to 6.7) above for the other test points and store the RMS values for the residuals. However, three tests (test points 15, 16, 17) are performed for the origin of the central synthesis plan (CCD). The whole test is used for the 15th test, half of Zopt for the 16th test, and the other half of Zopt for the 17th test.

6.9) The RMS value of the residual obtained using the optimization data Zopt1 is calculated for the total number of input signals (MSE) (Equation 38), and the natural log value of the average value is obtained.

6.10) Optimal FSVR hyperparameter for minimizing ln {MSE} for Cluster 1 using Response Surface Methodology of Minitap ^TR

Obtain

6.11) Perform the same procedure for cluster 2 as in 6.1) to 6.10) to obtain the optimal FSVR hyperparameter for cluster 2 according to equation 35.

Obtain

Equation 35

The FSVR hyperparameter obtained in this example is

= (2.0, 0.0005, 10)

= (1.1404, 0.0005, 5.247).

6a shows an example of the response surface for cluster 1, and 6b shows the response surface for cluster 2.

Here, the method for obtaining the optimum constant of the FSVR model using the response surface method will be described.

1.Sigma (σ), epsilon (ε), and C, which are FSVR model parameters,

Leave it as.

2.

Determine the search range for. Appropriate search ranges are identified through prior experience or small preliminary experiments. In this example, the search range for Cluster 1 is

: 0.2 to 2.0,

: 0.0005 to 0.05,

: 0.1 to 10.0, and the search range for cluster 2 is

0.3 to 1.9;

: 0.0001 to 0.0009,

: 0.1-10 were set.

3. Set the upper and lower limits of the search range respectively.

Wow

Leave on and normalize the model parameters as shown in Equation 36 below.

Equation 36

4. Standardized Model Parameters

The experimental point, that is, the evaluation point of model performance, is determined by considering the search range of. To do this, we use the central synthesis plan, which is one of the statistical experimental plans. FIG. 7 is a diagram illustrating an experimental point in the central synthesis plan when three model parameters are shown. When the experimental point determined by the central synthesis plan is expressed in three-dimensional space, FIG.

5. The experimental point of the central composition plan consists of eight vertices, one center point, and six axis points. To estimate the magnitude of the experimental error, three or more replicate experiments are performed at the center point. The coordinates of the axes are determined by α = 2 ^3/4 = 1.68179, taking into account the statistical properties of the prediction variances. Is defined by equation 37.

Equation 37

α = [number of factor test points] ^1/4

In the case of three repetitions at the center point, the experimental point according to the central synthesis plan is shown in Table 2 below.

Table 2: According to the central synthesis plan

) Experimental point

6. Model parameters as instructed in Table 2

To determine the value of, obtain the following Table 3-1 and Table 3-2, and use this value as the model parameter to perform the FSVR modeling experiment.

Tables 3-1 and 3-2 show the

Experimental point of), Table 3-1 shows the experimental point of Cluster 1, Table 3-2 shows the experimental point of Cluster 2.

               Table 3-1

               Table 3-2

7. Obtain the beta vector and bias constant of the FSVR model using Ztr, Ptr, and fuzzy membership μ at each experimental point in Table 2. In fact, the No. corresponding to the center point. No. from 15 Up to 17, the same model is obtained.

8. To estimate the accuracy of each model, the data set Pop is input to m AAFSVRs to normalize the predictions of the optimization data.

Obtain From this, the accuracy of the output model, ie MSE, is calculated according to equation 38.

Equation 38

here,

Pop out of the sensor

of

The second input data,

Is an estimate by the model. The experimental results of this example are shown in Table 4 below.

Table 4 shows the experimental MSE calculation results. Table 4-1 shows the MSE of cluster # 1, and Table 4-2 shows the MSE of cluster # 2.

          Table 4-1

           Table 4-2

9. Use log (MSE), which takes the log instead of the MSE, to determine the response surface. In view of this, the model parameters

Estimate the response surface between and log (MSE). The response surface assumes a quadratic model such as

Equation 39

However, e means random error. The estimated response surface in this example is as follows.

10. Minimize log (MSE) using estimated response surface

Find the optimal condition of. Since the second response surface is assumed, the optimal condition is confirmed by partial differential. That is, satisfying the following 40 at the same time

Obtain

Expression 40

For the response surface obtained for cluster # 1 in this example, the optimal condition is

= (0,0.04525,0).

Also, the optimal condition for cluster # 2 is

= (1.1364, -0.0005,5.2487).

11. Optimum conditions

Is converted to the original unit using the following Equation 41.

Equation 41

In this example, the optimal parameters for cluster # 1 are

,

,

The estimated log (MSE) under this condition is -5.3249.

Also, the optimal parameters for cluster # 2 are

,

,

The estimated log (MSE) under this condition is -5.4170.

FIG. 8 is a diagram illustrating a method of extracting an optimal point from a response surface for cluster 2. FIG.

[Step 7]

Fuzzy membership grade according to step 6.1) for each cluster of training data Ztr.

Calculate

[Step 8]

After training the FSVR model using the training data for each cluster, the principal component vector of the training data, the optimal parameters obtained in step 6, and the fuzzy membership grade obtained in step 7, the test data ( The output prediction values Zts1_hat and Zts2_hat are obtained by inputting each cluster principal component vector Pts1 and Pts2 of Zts) as follows.

8.1) Three optimal constants of the FSVR model obtained in step 6 above

And the principal component of training data (Ptr1) and the first signal of training data (column 1 of Ztr1) as inputs to solve the optimization problem using quadratic programming, and the difference between the Lagrangian multipliers w ₁ (n × 1) and the bias constant b ₁ are obtained to generate a model of FSVR ₁ in FIG. 2.

8.2) In the same manner as in 8.1), repeat this with respect to the second to m- th instrument signal

and

The model of FSVR _m is generated in FSVR ₂ . FSVR model for all sensors as shown in FIG.

8.3) Using the principal component (Ptr1) of the training data and the principal component (Pts1) of the training data, the kernel function ( K _ts1 (n × n)) of the Gaussian Radial Basis Function is obtained and the FSVR model obtained above. The output of FSVR ₁ is obtained using w ₁ , the bias constant b ₁ , which is the weight of SV (Support vector) of.

8.4) In the same manner as in 8.3), it is repeated for the second to m th sensors to obtain a model prediction value that is the output of FSVR _m at FSVR ₂ .

The predicted value for the test data Zts1 is obtained as shown in Equation 42 below.

Expression 42

: Principal component vector of Zts1,

: Principal component vector with index of svi in Ptr1,

: Addition of the support vector (SV) to the i th sensor of cluster 1.

              Weight

: Bias for the i th sensor of cluster 1

The prediction value for the test data Zts2 is obtained as shown in Equation 43 below.

Equation 43

: Addition of the support vector (SV) to the i th sensor of cluster 2.

     Weight

: Bias for the i th sensor of cluster 2

[Step 9]

The prediction values (Zts_hat) for the entire data are obtained by connecting the prediction values (Zts1_hat and Zts2_hat) for each cluster according to Equation 44.

Equation 44

[Step 10]

Estimates for Experimental Data

Is sorted in chronological order using the original time index.

[Step 11]

The normalized test data obtained in step 10 is denormalized to the original range to estimate the estimated value for each sensor of the original scale.

Is obtained according to equation 45.

Formula 45

[Step 12]

Follow the steps below to calculate the residuals for the predicted values and to determine the drift of the sensor using GLRT.

12.1) Calculation of residuals

When the sensor operates normally after regular calibration (after periodic inspection), the prediction program is executed to calculate the difference (residual) between the predicted value and the measured value for each sensor. In addition, the mean value and standard deviation (σ) for the residuals are calculated.

The model residual (R) is a difference between an input value and a predicted value, as shown in Equation 46 below.

Formula 46

FIG. 9 is a diagram showing an example of a steady state residual and a residual when a shift of δ = 0.01 occurs, using an example of 151 data which is part of the residual for the sensor # 7 (steam generator main water flow rate). Seemed. In this example, it is assumed that the standard deviation (σ) is increased by +0.01 in the time step 50 to 150, and the residual of the output signal of the model with respect to the shifted signal is also shown.

In this example, the mean value of the residuals for the normal case is -0.00096347 and the standard deviation is 0.0069.

12.2) Setting Window Size

The GT statistic for each window size is calculated using the residual when the meter is normal, increasing the window size w by 5 from minimum (eg, 5) to maximum (eg, 150).

The generalized likelihood ratio (GLR) at time t is given by

Equation 47

Recent window size

Means the average of the data, and 48 is expressed as follows.

Formula 48

The test statistic GT of GLRT is defined as the largest within the window size among the GLRs obtained at time t , and is obtained as in Equation 49 below.

Formula 49

only,

Denotes the average obtained from time t with k recent data.

MSE calculated by the difference between the GT statistic in each window size GT statistic and the maximum window in the formula 50.

Formula 50

Set the optimal window size in that the decrease of MSE (GT _i ) is slowed down.

FIG. 10 is a diagram illustrating an example of calculating a value of MSE (GT _i ) according to a window size. The horizontal axis represents window size, the vertical axis represents MSE (GT _i ) , and the optimal window size is w = 50.

12.3) GT Statistics Calculation

Optimal window sizewUsing the equations 47, 48 and 49 for the residuals to be examined using theGLR                  _t                 (k) and GTCalculate only,k = 1, 2, ..., w             

12.4) UC

The 12.1) to generate the same number of random numbers has mean and standard deviation values and the same mean and standard deviation of the residuals for, if the normal calculated normal distribution obtain and GT in, by repeating 1000 times this takes the maximum value of GT management limit Set to (UCL: Upper Control Limit).

In this example, UCL is set to 28.25.

12.5) Determination of Drift

Draw GT and UCL on the graph. When the GT deviates from the control limit line UCL, it is determined that a drift has occurred in the sensor, and when it is below, the sensor is determined to be normal.

FIG. 11 is a diagram illustrating an example of failure determination for a case where the meter is in a normal state and an abnormal state. FIG. 11A is a case where a shift drift occurs in the meter when the meter is in a normal state. will be. In FIG. 11B, the occurrence of the drift of the sensor is detected at the 58th step.

In order to confirm the effectiveness of the present invention and the superiority of the new methodology, the output of the actual nuclear power plant was increased from 0% to 100%. The data used in the analysis was measured on a total of 11 sensors.

Table 5 is a table comparing the accuracy of the instrument prediction according to the conventional kernel regression method and the present invention.

As shown in Table 5, the data used in the analysis were measured from a total of 11 sensors as follows.

 -1: reactor output (%)

 -2: Pressurizer water level (%)

 -3: Steam generator steam flow rate (Mkg / hr)

 -4: Steam generator narrow level data (%)

-5: Steam generator pressure data (Kg / cm ² )

 6: Steam generator wide area water level data (%)

 -7: Steam generator main water supply flow rate data (Mkg / hr)

 -8: turbine output data (MWe)

9: reactor coolant charge flow rate data (m ³ / hr)

10: residual heat removal flow rate data (m ³ / hr)

 11: Upper reactor coolant temperature data (° C.)

Accuracy is the most basic measure for applying predictive models to driving surveillance. In most cases, accuracy is expressed as the mean square error between model predictions and actual measurements. The following 51 is a formula for the accuracy of one instrument.

Equation 51

Where N is the number of test data

: Estimate of model for the i test data

: Measurement value of the i test data

Table 5: Accuracy Comparison between Instrument Kernel Regression and Instrument Prediction According to the Present Invention

The present invention extracts the principal component of the measuring instrument signal, obtains the optimal constant of the FSVR model using the response data, using the response analysis surface method, and trained the model using the training data and tested the test data using the existing data. Improve the accuracy of prediction calculations compared to kernel regression. In addition, even when a very fine shift drift occurs that cannot be detected by an ordinary alarm system, failure can be identified early by using the GLRT method according to the present invention.

A graph of the data as a function of time is as follows.

12 is a graph showing the reactor core output data of a nuclear power plant for accuracy test, the "Measured" line corresponds to the test input data X _{ts_1} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimated data for test input X _{ts_1} of Equation 45

Indicates.

13 is a graph showing the nuclear power plant pressurizer water level data for accuracy test, the "Measured" line corresponds to the test input data X _{ts_2} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimated Data for Test Input X _{ts_2} in Equation 45

Indicates.

14 is a graph illustrating steam flow rate data of a nuclear power plant steam generator for accuracy test, in which the "Measured" line corresponds to the test input data X _{ts_3} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_3} of Equation 45 above

Indicates.

FIG. 15 is a graph showing the narrow-range water level data of a nuclear power plant steam generator for accuracy test, wherein a "Measured" line corresponds to the test input data X _{ts_4} of Equation 6, and a "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_4} in Equation 45

Indicates.

16 is a graph showing the steam generator pressure data for the accuracy test, the "Measured" line corresponds to the test input data X _{ts_5} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_5} in equation 45

Indicates.

17 is a graph showing the water level data of the nuclear power plant steam generator for accuracy test, the line "Measured" corresponds to the test input data X _{ts_6} of Equation 6, and the line "Predicted" is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_6} in Equation 45

Indicates.

18 is a graph showing the main water supply flow rate data of the nuclear power plant steam generator for accuracy test, the "Measured" line corresponds to the test input data X _{ts_7} of Equation 6, and the "Predicted" line using the algorithm of the present invention. Estimate data for experimental input X _{ts_7} in predicted equation 45

Indicates.

FIG. 19 is a graph showing nuclear power plant turbine output data for accuracy test, in which the "Measured" line corresponds to the test input data X _{ts_8} of Equation 6 and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_8} at 45

Indicates.

20 is a graph showing the primary side charge flow rate data for the nuclear power plant for accuracy test, the "Measured" line corresponds to the test input data X _{ts_9} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_9} in Equation 45

Indicates.

21 is a graph showing the residual heat removal flow rate data of a nuclear power plant for accuracy test, where the "Measured" line corresponds to the test input data X _{ts_10} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_10} in equation 45

Indicates.

FIG. 22 is a graph showing temperature data of the upper reactor coolant temperature of a nuclear power plant for accuracy test, in which the "Measured" line corresponds to the test input data X _{ts_11} of Equation 6, and the "Predicted" line is predicted using the algorithm of the present invention. Estimate data for test input X _{ts_11} in Equation 45

Indicates.

Claims (47)

1. an input unit 11 receiving time-series field signals for the m field sensors and sending them to the clustering unit 12;

   A clustering unit 12 dividing an input signal for the time series field signal received from the input unit 11 into N desired data clusters using a fuzzy clustering method;

   A PCA unit 13 for extracting a main component for each data cluster divided into N data clusters received from the clustering unit 12;

   An FSVR unit 14 for calculating fuzzy membership grade for each data cluster, training a model, obtaining optimal parameters of the model using response surface analysis, and performing signal prediction on test data;

   A comparison operation unit 15 for comparing a signal predicted by the FSVR unit 14 with an input signal to obtain a difference;

   FSVR (Fuzzy Support), characterized in that it comprises a GLRT unit 16 for determining the drift of the sensor by calculating the GLRT test statistic using the output of the comparison operation unit after setting the window size optimization and management limit line. Power plant instrument performance monitoring system using Vector Regression and Generalized Likelihood Ratio Test (GLRT).
2. A first step of displaying the entire data set (X) in the form of a matrix and subdividing it into training (Xtr), optimization (Xopt), and test (Xts);

   A second step of normalizing the entire data displayed in matrix form in the first step;

   A third step of dividing the data set Z normalized in the second step into training (Ztr), optimization (Zopt), and test (Zts);

   A fourth step of extracting a principal component of each data set (Ztr) for training (Ztr), optimization (Zopt), and test (Zts) normalized and divided in the third step;

   A fifth step of dividing the data set and the principal components into as many data clusters as desired using Fuzzy C-Means (FCM) clustering;

   Each FSVR model of reacting with a surface analysis method, the optimization of each data cluster of data (Zopt) for (Z _opt1, Z _opt2) minimizes the prediction error of the optimization data (Zopt) for optimal constant

   

   And

   

   Obtaining a sixth step;

   Fuzzy membership grade according to step 6-1 above for each cluster of training data Ztr

   

   Calculating a seventh step;

   After training the FSVR model using the training data for each cluster, the principal component vector of the training data, the optimal parameters obtained in the sixth step, and the fuzzy membership grade obtained in the seventh step, An eighth step of obtaining output prediction values Zts1_hat and Zts2_hat by inputting each cluster principal component vector Pts1 and Pts2 of the test data Zts;

   A ninth step of connecting prediction values Zts1_hat and Zts2_hat for each cluster to obtain prediction values Zts_hat for the entire data;

   Estimates for Experimental Data

   

   Classifying the data in chronological order using the original time index;

   The normalized test data obtained in step 10 is normalized to the original range by denormalizing the predicted value of each sensor of the original scale.

   

   Eleventh step of obtaining according to equation 45 and;

   12. A method for monitoring plant performance using a FSVR (Generalized Likelihood Ratio Test) and a GFVR (Generalized Likelihood Ratio Test), comprising a twelfth step of calculating a residual for a predicted value and determining a drift of a sensor using a GLRT.
3. The method of claim 2,

   The matrix in the first step is

   

   Power station instrument performance monitoring method using FSVR and GLRT, characterized in that displayed by.
4. The method of claim 2,

   In the second step, the normalization is

   

   Where i = 1,2 ... 3n

   Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that made by.
5. The method of claim 4, wherein

   The normalized entire data set (Z) is

   

   Power station instrument performance monitoring method using FSVR and GLRT, characterized in that displayed by.
6. The method of claim 2,

   The normalized training (Ztr), optimization (Zopt), and trial (Zts) data sets are

   

   Where i = 0,1,2… n-1

   Performance monitoring method for power plant instrumentation using FSVR and GLRT, characterized in that divided by.
7. The method of claim 2,

   In the fourth step, the variances of the principal components are listed in order of magnitude, and the training (Ztr), optimization (Zopt) and test ( A method for monitoring the performance of a power plant instrument using FSVR and GLRT, characterized by extracting the principal components by selecting the principal components (Ptr, Pop, Pts) of each data set of Zts).
8. The method of claim 7, wherein

   The main component extraction,

   In each data set of training (Ztr), optimization (Zopt), and testing (Zts), the mean value of each variable is subtracted.

   

   Step 4-1 represented by;

   expression

   

   Depending on the

   

   Eigenvalue of

   

   Finding the equation

   

   Sort in descending order according to the formula

   

   Step 4-2 to obtain a singular value s of A according to;

   

   Eigenvalue from

   

   And obtain the eigenvalue

   

   Expression

   

   Assigning to each eigenvalue

   

   Eigenvector of n × 1 for

   

   By finding n × n matrix

   

   A fourth to third step of obtaining an eigenvector;

   expression

   

   4-4 to obtain the dispersion of each main component according to;

   expression

   

   And expression

   

   4-5 to obtain a percentage by dividing the variance of each main component by the sum of the variances of all the main components in accordance with;

   Percent variance

   

   Steps 4-6 of performing the cumulative calculation from this largest one to selecting p principal components up to a desired percentage variance (eg, 99.98%);

   Formulated the main ingredient

   

   4-7 to calculate and extract according to;

   Using the FSVR and GLRT, characterized in that it comprises a; 4-8 step for extracting the main components in the Zopt, Zts data set in the above steps 4-1 to 4-7 How to monitor power plant instrument performance.
9. The method of claim 8,

   A method for monitoring plant performance using FSVR and GLRT, characterized in that the desired percentage dispersion in steps 4-6 is 99.98%.
10. The method of claim 2,

    In the fifth step, the training data Ztr is divided into two groups Ztr1 and Ztr2 by using a Fuzzy C-Means (FCM) clustering method, and the same principal component is also used by using the same index of each generated data group. A fifth step of dividing into a number of clusters Ptr1 and Ptr2;

    Repeating step 5-1 for the optimization data (Zopt) and the test data (Zts), and dividing them into normalized data clusters (Zopt1, Zopt2, Zts1, Zts2) and principal component clusters (Popt1, Popt2, Pts1, Pts2), respectively. A method for monitoring power plant instrument performance using FSVR and GLRT, comprising steps 5-2.
11. The method of claim 10,

    Fuzzy C-Means (FCM) clustering method,

    Set of input signals

    

    Cluster Count for

    

    Determine fuzzy coefficient m (= 2), and belong to

    

    Initiating step 1;

    Obtaining a center vector vi ^(r) and membership u _ik for each cluster;

    Calculating a distance between each cluster center and data to generate a new belonging matrix U ^{(r + 1)} which minimizes the objective function Q;

    FSVR, characterized in that: if the end condition is satisfied, if the end condition is not met, set r = r + 1, and then proceed to step 2 and repeat step 2 to step 3; Monitoring Method for Power Plant Instrument Performance Using GLRT.
12. The method of claim 11,

    Step 1 above,

    expression

    

    (Where, i is the cluster number, k is the number of the pattern, r is the number of iterations, N is the number of sample data of each sensor, u _ik is pointer data X _k being the membership size belonging to the group i)

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that performed by.
13. The method of claim 11,

    Step 2 above,

    expression

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that performed by.
14. The method of claim 11,

    The objective function (Q) in the step 3,

    expression

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that represented by.
15. The method of claim 11,

    The termination condition in step 4 is expressed by

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that represented by.
16. The method of claim 2,

    Optimal Constants for Each FSVR Model

    

    And

    

    The sixth step of obtaining

    The potential (P ₁ ) of each data pointer is calculated using the Euclidean distance between each data pointer of the first cluster of training data (Ztr1) and all other input data, and the fuzzy membership grade is used. )

    

    6-1 step of calculating the;

    Step 6-2 selecting the first test point ( v ₁ , v ₂ , v ₃ ) of the test point for the cluster 1;

    The first signal of Ztr1 (Ztr1-1) for the selected test point,

    

    And step 6-3, after inputting Ptr1, training the FSVR model to obtain svi (support vector index), w ₁ (weight of SV) and b ₁ (bias);

    Step 6-4 by using a Popt svi 1 and to obtain a radial basis function (radial basis function) (Kopt1) ;

    6-5 to obtain a prediction value for the first instrument signal of the optimization data Zopt1;

    After repeating steps 6-3 to 6-5 with respect to the other instrument signals of Ztr1, the prediction matrix output is performed.

    

    Step 6-6 to obtain;

    Residual of measured and predicted values of optimization data (Zopt1)

    

    Calculating a root mean square (RMS) for each of the sixth and sixth steps of storing the root mean square (RMS);

    Steps 6-8 for repeating steps 6-2 to 6.7 for other test points and storing RMS values for the residuals;

    Steps 6-9 of calculating an average value MSE (Equation 38) of the RMS value of the residual value obtained by using the optimization data Zopt1 with respect to the total number of input signals and calculating a natural log value with respect to the average value;

    Optimal Constants of FSVR Model Using Minimized ln {MSE} for Cluster 1 Using Response Surface Methodology

    

    Step 6-10 to obtain and;

    Repeat steps 6-1 to 6-10 for cluster 2, and use the FSVR model constant for cluster 2 according to equation 35.

    

    6-11 step of obtaining a; power plant instrument performance monitoring method using FSVR and GLRT, characterized in that made.
17. The method of claim 16,

    The potential (P ₁ ) of each data pointer is

    

    (here,

    

    = Number of data in a cluster,

    

    : Radius of first cluster (Ztr1)

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that calculated by.
18. The method of claim 16,

    Steps 6-4 to obtain the radial basis function Kopt1 are given by

    

    (here,

    

    : Principal component vector of Zopt1,

    

    : Principal component vector with index of svi in Ptr1)

     Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
19. The method of claim 16,

    Steps 6-5 above to obtain a prediction value for the first instrument signal of the optimization data Zopt1,

    

    (here,

    

    : Beta vector with index of svi among beta vector)

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
20. The method of claim 16,

    The prediction matrix output

    

    The sixth to sixth steps of

    

    Performance monitoring method for power station instrumentation using FSVR and GLRT, characterized in that obtained by.
21. The method of claim 16,

    In Steps 6-8, three tests (test points 15, 16, and 17) are performed for the origin of the central synthesis plan (CCD), but the entire Zopt is used for the 15th test, and 1 of Zopt is used for the 16th test. / 2, 17th test is to monitor the performance of power plant instrumentation using FSVR and GLRT, characterized in that the test is performed on the other half of Zopt.
22. The method of claim 16,

    The average value (MSE) in step 6-9 is expressed by

    

    Power station instrument performance monitoring method using FSVR and GLRT, characterized in that calculated by.
23. The method of claim 16,

    Optimal Constant of FSVR Model for Cluster 2

    

    The sixth to sixth steps to find the equation,

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
24. The method of claim 16,

    The optimal constant of the FSVR model,

    

    = (2.0, 0.0005, 10)

    

    = (1.1404, 0.0005, 5.247) power station instrument performance monitoring method using FSVR and GLRT.
25. The method of claim 16,

    The method for obtaining the optimal constant of the FSVR model using the response surface analysis method in step 6-10,

    Sigma (σ), epsilon (ε), and C, respectively, are the FSVR model parameters.

    

    Step 6-10-1;

    

    6-10-2 to determine a search range for each;

    The upper and lower bounds of the search range

    

    Wow

    

    6-10-3, which standardizes the model parameters.

    Standardized Model Parameters Using Central Synthesis Plan

    

    A step 6-10-4 of setting an evaluation point of the model performance in response to the search range of;

    6-10-5 steps of estimating the magnitude of the experimental error and defining the coordinate α of the axial point by the equation α = [number of factor test points] ^1/4 ;

    By central composition plan

    

    Model parameters according to the experimental point of

    

    After determining the value of, follow the central synthesis plan (

    

    Test points of) and by the central synthesis plan

    

    Step 6-10-6 of performing an FSVR modeling experiment using the experimental point value of n) as a model parameter;

    By central composition plan

    

    6-10-7 obtaining the beta vector and the bias constant of the FSVR model using Ztr, Ptr and fuzzy membership μ at the experimental points of

    To estimate the accuracy of each model, the data set Pop is input into m AAFSVRs to normalize the predictions of the optimization data.

    

    6-10-8 calculating the MSE, which is the accuracy of the output model, from Equation 38;

    Model Parameter

    

    Steps 6-10-9 of estimating a response surface equation between the log and the log (MSE);

    Minimize log (MSE) using estimated response surface

    

    Optimum condition of

    

    6-10-10 to obtain;

    Optimal condition

    

    Step 6-10-11 of converting to the original unit; Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that made.
26. The method of claim 25,

    Search range for cluster 1 in step 6-10-2

    

    : 0.2 to 2.0,

    

    : 0.0005 to 0.05,

    

    : 0.1 to 10.0, and the search range for cluster 2 is

    

    0.3 to 1.9;

    

    : 0.0001 to 0.0009,

    

    : Performance monitoring method for power plant instrumentation using FSVR and GLRT, characterized by setting from 0.1 to 10.
27. The method of claim 25,

    The standardization of the model parameters in step 6-10-3 is

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that made by.
28. The method of claim 25,

    MSE which is the accuracy of the output model in step 6-10-8,

    

    (here,

    

    Pop out of the sensor

    

    of

    

    The second input data,

    

    Is an estimate by model)

    Power station instrument performance monitoring method using FSVR and GLRT, characterized in that calculated by.
29. The method of claim 25,

    The reaction surface is

    

    ( e means random error)

    By taking a quadratic model,

    The estimated response surface is

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that represented by.
30. The method of claim 25,

    In the above steps 6-10-10

    

    The optimal condition of

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained through partial differential.
31. The method of claim 30,

    For the response surface obtained for cluster # 1, the optimal condition is

    

    = (0,0.04525,0) and the optimal conditions for the response surface obtained for cluster # 2

    

    = (1.1364, -0.0005,5.2487) Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that.
32. The method of claim 25,

    Optimal Conditions in Steps 6-10-11

    

    Is converted into the original unit,

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that made by.
33. The method of claim 25,

    Each of the best parameters for cluster # 1

    

    ,

    

    ,

    

    The estimated log (MSE) under this condition is -5.3249,

    Each of the best parameters for cluster # 2

    

    ,

    

    ,

    

    And the log (MSE) predicted under these conditions is -5.4170.
34. The method of claim 2,

    The eighth step of obtaining the output prediction values (Zts1_hat and Zts2_hat),

    Three optimal constants of the FSVR model obtained in the sixth step

    

    Then, using the quadratic programming technique with the main component Ptr1 of training data and the first signal of training data (first column of Ztr1), the optimization problem is solved. step 8-1 of generating a model of FSVR ₁ by obtaining w ₁ (n × 1) and a bias constant b ₁ ;

    Repeat step 8-1 for the second to m th measurement signals

    

    and

    

    Step 8-2 to generate a model of the FSVR ₂ ~ FSVR _m by obtaining the;

    The kernel function ( K _ts1 (n × n)) of the Gaussian Radial Basis Function is obtained using the principal component (Ptr1) of the training data and the principal component (Pts1) of the test data. And 8-8-3 obtaining an output of the FSVR ₁ using the support vector weight w ₁ and the bias constant b ₁ of the FSVR model obtained in the 8-8 step;

    A power plant using FSVR and GLRT, comprising steps 8 to 4 to obtain model prediction values output from FSVR ₂ to FSVR _m by repeating steps 8-3 for the second to m th sensors. Instrument performance monitoring method.
35. The method of claim 34, wherein

    The estimate for the experimental data Zts1 is

    

    (

    

    : Principal component vector of Zts1,

    

    : Principal component vector with index of svi in Ptr1)

    

    (

    

    : The support vector (SV) of the i th sensor of cluster 1

                  Weight

    

    : Bias for the i th sensor of cluster 1)

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
36. The method of claim 34, wherein

    The estimate for the experimental data Zts2 is

    

    (

    

    : The support vector (SV) of the i th sensor of cluster 2

              Weight

    

    : Bias for the i-th sensor of cluster 2)

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
37. The method of claim 2,

    In the ninth step, the prediction value Zts_hat for the entire data is

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
38. The method of claim 2,

    Prediction value for each sensor of the original scale in the eleventh step

    

    Expression

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
39. The method of claim 2,

    The 12th step of determining the drift of the sensor,

    A 12-1 step of performing a prediction program to calculate a residual between the predicted value and the measured value for each sensor and calculating the average value and the standard deviation (σ) of the residual when the sensor operates normally after the periodic calibration of the sensor;

    Calculating a GT statistic for each window size by increasing the window size w by 5 from minimum to maximum using the residual when the meter is normal;

    The equation for the residual to be examined using the optimal window size w for the calculation of GT statistics

    

    And expression

    

    And, expression

    

    Using step 12-3 to calculate the GLR _t (k) (where k = 1, 2, ..., w) and GT while moving the window by 1 time step;

    GT is obtained by generating the same number random numbers of normal distributions having the same mean and standard deviation as the mean and standard deviation of the residuals in the normal case calculated in step 12-1, and repeating 1000 times to obtain the maximum GT . Step 12-4, taking the upper control limit (UCL) taken;

    If the GT deviates from the control limit line (UCL), it is determined that drift has occurred in the sensor, and if it does not deviate, steps 12-5 of determining whether the sensor is normal and determining whether there is a drift are provided using the FSVR and GLRT. How to monitor power plant instrument performance.
40. The method of claim 39,

    The model residual (R), which is the difference between the input value and the predicted value in step 12-1, is expressed by the equation

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
41. The method of claim 39,

    Method of monitoring power plant instrument performance using FSVR and GLRT, characterized in that the average value of the residual for the normal case in step 12-2 is -0.00096347, and the standard deviation (σ) is 0.0069.
42. The method of claim 39,

    In step 12-2, the generalized likelihood ratio (GLR) at time t is

    

    (

    

    Recent window size

    

    Means of data)

    Saved by

    

    Autumn

    

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that represented by.
43. The method of claim 39,

    In step 12-2, the GLRT's test statistic GT is defined as the largest within the window size in the GLR obtained at time t .

    

    (only,

    

    Denotes the mean of the most recent k data at time t )

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that obtained by.
44. The method of claim 43,

    Expression the MSE differences between the GT statistic in each window size GT statistic and the maximum window at,

    

    Saved by

    A method for monitoring the performance of power plant instrumentation using FSVR and GLRT, characterized in that the optimal window size is set in that MSE (GT _i ) decreases.
45. The method of claim 39,

    Power line instrument performance monitoring method using FSVR and GLRT, characterized in that the control limit line (UCL) in step 12-4 is set to UCL = 28.25.
46. The method of claim 39,

    Sensor data used for the analysis in step 12-5,

    Reactor output (%), pressurizer level (%), steam generator steam flow rate (Mkg / hr), steam generator narrow water level data (%), steam generator pressure data (Kg / cm ² ), steam generator wide water level data (%) ), Steam generator main feed water flow data (Mkg / hr), turbine output data (MWe), reactor coolant fill flow data (m ³ / hr), residual heat removal flow rate data (m ³ / hr), reactor top coolant temperature data ( Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that the ().
47. The method of claim 39,

    In step 12-5, the accuracy of the instrument is

    

    Where N is the number of test data,

    

    : estimate of the model for the i test data,

    

    : measured value of the i-th test data)

    Power plant instrument performance monitoring method using FSVR and GLRT, characterized in that represented by.

Images