CN112100574B - AAKR model uncertainty calculation method and system based on resampling - Google Patents

Abstract

The present invention discloses a method and system for calculating the uncertainty of an AAKR model based on resampling. A sensor historical state data set is divided into a training data set and a test data set. The training data set is denoised and the noise variance is calculated by a wavelet denoising method to improve data accuracy. Then, the sensor historical state data is randomly selected and replaced to obtain new training data set samples, so as to optimize the AAKR model architecture and the changes between multiple model prediction values to obtain the model prediction variance of multiple model prediction values. The training data is resampled by Bootstrap to calculate the mean square error between the prediction value and the test value. The model deviation is calculated in combination with the prototype model variance to form an uncertainty value of 95%. There is no need to perform modeling and calculation of the noise estimation value using an empirical distribution model, so the resampling process is simplified and the calculation efficiency is improved. In addition, the confidence interval deviation is reduced in combination with the Jackknife method to ensure its reliability, and the estimation efficiency is improved on the basis of maintaining the convergence performance.

Description

A resampling-based AAKR model uncertainty calculation method and system

Technical Field

The present invention relates to a method for quantifying the uncertainty of an AAKR model, and in particular to a method and system for calculating the uncertainty of an AAKR model based on resampling.

Background Art

The online condition monitoring system of key equipment in nuclear power plants helps reduce the risk of catastrophic failures and the excess costs caused by unnecessary regular maintenance. Among them, the condition monitoring method based on the empirical model does not rely on an in-depth understanding of the fault mechanism model. It determines whether the equipment is abnormal based on the historical operating data and operating experience of the equipment. With the rapid development of the Internet of Things and big data technology, it has been widely used. However, when the empirical model is used to monitor key nuclear power equipment, it involves ill-posed problems that affect the stability of the model. It must be accompanied by an estimate of its uncertainty. At the same time, accurate estimation of the uncertainty interval can effectively reduce the false alarm and missed alarm rate of the equipment, thereby reducing the economic losses caused by equipment downtime. However, there is little research on the uncertainty analysis of model regression values. The traditional Monte Carlo uncertainty determination method uses probability distribution to simulate noise to obtain sampling data, which requires prior knowledge of the overall distribution and sufficiently large sample data. It is inefficient and has high economic costs, and cannot effectively ensure the prediction accuracy of the sensor status of key equipment.

Summary of the invention

The purpose of the present invention is to provide a resampling-based AAKR model uncertainty calculation method and system to overcome the deficiencies of the prior art.

In order to achieve the above object, the present invention adopts the following technical scheme:

A resampling-based AAKR model uncertainty calculation method comprises the following steps:

Step 1), divide the sensor historical state data set into a training data set and a test data set;

Step 2), denoising the training data set by wavelet denoising method and calculating the noise variance;

Step 3), the training data set is resampled multiple times by the Bootstrap method, and a new training data set is obtained after each resampling. Multiple new models are established according to each group of new training data sets after sampling, and multiple model prediction values are obtained according to the prediction of the multiple new models. The changes between the multiple model prediction values can be calculated to obtain the model prediction variance of the multiple model prediction values;

Step 4), calculate the mean square error between the model prediction value and the test observation value;

Step 5), the model deviation is calculated based on the noise variance, model prediction variance and mean square error;

Step 6) Estimation is performed based on the model deviation and model variance, and the Monte Carlo uncertainty estimate can be obtained as twice the square root of the sum of the square of the model deviation and the model variance.

Furthermore, the sensor historical data is loaded, and the sensor historical data is detected and corrected for abnormal values, and the sensor historical state data set is divided into a training data set and a test data set.

Furthermore, the wavelet denoising method is used to denoise the training data set.

Where ε _i is the noise estimate of the i-th training observation _Xi in the training data set; is the estimated value of the true value of the i-th training observation _Xi in the training data set; the variance of the i-variable noise in the training data set is:

n _trn is the number of training observations; is the expected value of the noise estimate; is the noise variance of the training dataset.

Furthermore, the following formula is used to calculate the change between multiple model prediction values, namely the model prediction variance:

in, is the variance of the i-th observation of the j-th variable; we get an n _tst ×p-dimensional variance estimate, the variances of each p variable are arranged in ascending order, and the 95th percentile maximum value is selected to conservatively estimate the single-point variance.

Furthermore, each new model established by resampling the training data set can give a model prediction value, namely Calculate the mean squared error (MSE) between the new model's predictions and the test observations:

where _Xtst,i and are the test observations and model predictions of the i-th new model. The dimension of MSE is 1×p, and N predictions will produce N 1×p-dimensional MSEs.

Furthermore, the model deviation is:

Furthermore, the confidence interval and prediction interval corresponding to the 95% confidence level were calculated based on the Monte Carlo uncertainty estimate, and the Jackknife deviation estimation method was used to correct the confidence interval (CI) predicted by the AAKR model and calculate the prediction interval.

Furthermore, the confidence interval and prediction interval corresponding to the 95% confidence level were calculated based on the Monte Carlo uncertainty estimate, and the Jackknife deviation estimation method was used to correct the confidence interval (CI) predicted by the AAKR model and calculate the prediction interval.

Furthermore, the general equation for the confidence interval is:

in, is an estimate of the expected value θ of the model prediction, then its deviation is:

Model prediction value is an n _tst ×p-dimensional time state sequence; It represents the estimated value after removing the i-th (i＝1,2,...,N) predicted value, and the average value is obtained Then the Jackknife deviation is estimated as:

From this we get The correction estimate of :

So the confidence interval after correction is:

The prediction interval at the 95% confidence level is:

A resampling-based AAKR model uncertainty calculation system includes a data acquisition module, a data denoising module and a data processing module;

The data acquisition module is used to acquire the sensor historical state data set and divide the acquired data set into a training data set and a test data set, and transmit the training data set to the data denoising module;

The data denoising module denoises the received training data set and calculates the noise variance and transmits the noise variance to the data denoising module, and transmits the denoised training data to the data processing module;

The data processing module resamples the training data set multiple times through the data acquisition module, and obtains a new training data set after each resampling. Multiple new models are established based on each group of new training data sets after sampling. Multiple model prediction values are obtained based on the multiple new model predictions. The model prediction variance of the multiple model prediction values can be obtained by calculating the changes between the multiple model prediction values; at the same time, the mean square error between the model prediction value and the test observation value is calculated; finally, the model deviation is calculated based on the noise variance, model prediction variance and mean square error; the model deviation and model variance are used for estimation, and the square root of the sum of the square of the model deviation and the model variance is twice the value as the Monte Carlo uncertainty estimate and output.

Compared with the prior art, the present invention has the following beneficial technical effects:

The invention discloses an AAKR model uncertainty calculation method based on resampling. The method divides a sensor historical state data set into a training data set and a test data set, performs denoising on the training data set and calculates the noise variance by using a wavelet denoising method, improves data accuracy, and then randomly selects and replaces the sensor historical state data to obtain new training data set samples, so as to optimize the AAKR model architecture and the changes between multiple model prediction values to obtain the model prediction variance of multiple model prediction values, resamples training data by using Bootstrap, develops and tests multiple prototype models, obtains prediction values by using the prototype models and test data, and calculates the mean square error between the prediction values and the test values; calculates the model deviation in combination with the prototype model variance to form an uncertainty value of 95%, does not need to perform modeling and calculation of noise estimation values by using an empirical distribution model, simplifies the resampling process, improves the calculation efficiency, and reduces the confidence interval deviation in combination with a Jackknife method to ensure its reliability, improves the estimation efficiency on the basis of maintaining the convergence performance, provides a set of reliable, efficient and complete method flows for uncertainty estimation of empirical models of key equipment in nuclear power plants, and has important engineering application value for improving the accuracy of sensor state prediction of key equipment.

Furthermore, by calculating the confidence interval and prediction interval at the 95% confidence level and correcting the confidence interval distribution deviation using the Jackknife deviation estimation method, the analysis process is simplified, the confidence interval deviation is reduced, and the estimation efficiency is improved while maintaining the convergence performance.

The present invention discloses an AAKR model uncertainty calculation system based on resampling, which has a simple structure. The system is trained by acquiring a normal data set of the historical state of the sensor. The uncertainty calculation method of the empirical model based on Bootstrap resampling simplifies the analysis process. The confidence interval deviation is reduced by combining the Jackknife method to ensure its reliability.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of the uncertainty calculation process of the AAKR model in an embodiment of the present invention.

FIG. 2 is a convergence analysis curve diagram of uncertainty in an embodiment of the present invention.

FIG. 3 is a pre-correction confidence interval diagram of the AAKR model in an embodiment of the present invention.

FIG. 4 is a confidence interval diagram of the AAKR model after correction in an embodiment of the present invention.

FIG. 5 is a prediction interval of the AAKR model in an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention is further described in detail below in conjunction with the accompanying drawings:

As shown in FIG1 , a resampling-based AAKR model uncertainty calculation method includes the following steps:

Step 1), divide the sensor historical state data set into a training data set and a test data set;

Specifically, the sensor historical data is loaded, and the sensor historical data is detected and corrected for outliers, and the data set is divided into a training data set and a test data set.

Step 2), denoising the training data set by wavelet denoising method and calculating the noise variance;

Specifically, the wavelet denoising method is used to denoise the training data set.

Where ε _i is the noise estimate of the i-th training observation _Xi in the training data set; is the estimated value of the true value of the i-th training observation _Xi in the training data set, which is the result of wavelet denoising of the training observation; the variance of the i-variable noise in the training data set is:

n _trn is the number of training observations; is the expected value of the noise estimate, which is zero or close to zero for drift-free data; is the noise variance of the training dataset.

The variance of the variable noise measures the random error in the model predictions;

Step 3), resample the training data set N times by the Bootstrap method (i.e., take a training test observation value to replace the value of the current position training data set), obtain N groups of resampled training data sets, establish N new models based on the N groups of resampled training data sets, obtain N model prediction values based on the N new model predictions, and calculate the changes between the N model prediction values to obtain the model prediction variance of the N model prediction values;

The specific steps include:

Perform N Bootstrap resampling on a set of training data sets, and build a new model with each newly sampled data set, that is, there are N new models, and estimate the changes between the model prediction values from these N new models;

Where _Xi represents a state of the system, and _Xj represents a time state sequence of a monitoring variable.

Bootstrap resampling: For the time state series of the monitoring variable _Xj , random sampling with replacement is performed n _trn times, that is, the Bootstrap resampling sample X ^* of X is obtained.

The LHS resampling technique is used: the wavelet denoising method is applied to the training data to obtain its "true" value, and the "true" value is subtracted from the original training data to obtain the estimated value of the noise; the noise probability distribution is modeled as a normal distribution, by dividing the distribution into n _trn non-overlapping intervals (also called "boxes"), each box has ; random values are selected from each bin with equal frequency, and the final noise distribution is uniformly sampled to construct the prototype training set.

Each time the AAKR model built from the resampled training data set gives the model prediction value of the test observation value _Xtst Model prediction value is an estimate of the test observation X _tst , which _{contains n tst observations} ;

in, is the prediction of the k-th prototype model for the test observation X _tst , where express The i-th observation of the j-th variable; the predicted value of the i-th observation of the j-th variable is expected to be the average of the N new model predictions, that is:

That is, the predicted value of X _tst is expressed as:

Similarly, the variance of the ith observation of the jth variable is:

That is, the model prediction variance can be written as:

Simplified: The change between N model prediction values, i.e., model prediction variance, is calculated using the following formula:

Obtain n _tst ×p-dimensional variance estimates, the variances of each p variable are arranged in ascending order, and the 95th percentile maximum is selected to conservatively estimate the single-point variance;

The model prediction variance is defined as the expected square difference between the parameter and its expected value, so the model prediction variance can also be expressed as:

Step 4), calculate the mean square error (MSE) between the N model prediction values and the test observation values;

Each new model established by resampling the training data set can give a model prediction value, that is, Calculate the mean squared error (MSE) between the new model's predictions and the test observations:

where _Xtst,i and are the test observations and model predictions of the ith new model, respectively. The dimension of MSE is 1×p, and N predictions will generate N 1×p-dimensional MSEs. For p variables, the maximum value of the 95th percentile is taken as the single point estimate of MSE.

Step 5), the model deviation is calculated based on the noise variance, model prediction variance and mean square error;

Bias measures any systematic error.

The predictive performance of the model is quantified by the mean squared error (MSE), which is calculated based on the model's predicted values:

in, is the reducible error, and ε _irr is the irreducible error.

E[ε _irr ]＝0,

The reducible error is the model prediction value The expectation of the square of the distance between the true model M(X _tst ) and the test observation X _tst ; The irreducible error is the difference between the true parameter value and the measured parameter value, which is caused by random processes and measurement noise, and is called irreducible error because it cannot be deterministically modeled.

The reducible error explains how well the model represents the true model M(X _tst ), which only depends on the chosen model architecture, training process, and dataset. The reducible error can be further decomposed into a bias component and a variance component.

Model bias is defined as the systematic error of the model as the difference between the expected predicted value of the model and the true target value, which can be expressed as:

Total uncertainty is a combination of model bias, model prediction variance, and irreducible error:

Total uncertainty Quantified by MSE, with the value of MSE, i.e.

Assume that the model bias is constant for each variable and can be approximated by its expected value. Then, if the expected square of the bias is negative (i.e., the sum of the model prediction variance and the estimated noise variance is greater than the MSE), set it to zero;

The final model deviation is as follows:

Step 6) According to the model bias and model variance, the Monte Carlo uncertainty estimate can be obtained as The results of the convergence of the proposed method with the number of prototype models are shown in Figure 2.

Example:

According to the Monte Carlo uncertainty estimate, the confidence interval and prediction interval corresponding to the 95% confidence level are calculated. The confidence interval (CI) predicted by the AAKR model is corrected and the prediction interval is calculated using the Jackknife deviation estimation method. The confidence interval diagram of the AAKR model before correction is shown in Figure 3.

The general equation for the confidence interval is given by:

in, is an estimate of the expected value θ of the model prediction, then its deviation is:

Model prediction value is an n _tst ×p dimensional time state sequence, It represents the estimated value after removing the i-th (i＝1,2,...,N) predicted value, and the average value is obtained Then the Jackknife deviation is estimated as:

From this we get The correction estimate

So the CI after correction is:

CI does not include noise terms It only estimates the uncertainty in the model's expected predictions, without considering the natural variation of the modeled values. The corrected confidence interval of the AAKR model is shown in Figure 4;

The PI at a 95% confidence level is expressed as:

Since PI includes the noise variance term, it includes CI by definition and is therefore a more conservative estimate of model uncertainty; the prediction interval of the AAKR model is shown in Figure 5

The invention discloses an uncertainty calculation method for an auto-associative kernel regression (AAKR) model based on Bootstrap resampling. The method randomly selects and replaces historical state data of a sensor to obtain Bootstrap samples, so as to optimize the AAKR model framework and determine the uncertainty of a current prediction value. The method comprises the following steps: loading historical data, detecting and correcting abnormal values, and dividing the data into training and test data sets; utilizing Bootstrap resampling training data, developing and testing multiple prototype models, obtaining prediction values through the prototype models and test data, and calculating the mean square error (MSE) between the prediction values and the test observation values; utilizing a wavelet denoising method to denoise the training data to estimate the noise variance; calculating a model deviation in combination with the prototype model variance to form a 95% uncertainty value estimate, calculating a confidence interval and a prediction interval at a 95% confidence level, and utilizing a Jackknife deviation estimation method to correct the confidence interval distribution deviation. The invention simplifies the analysis process, reduces the confidence interval deviation, and improves the estimation efficiency while maintaining the convergence performance.

Claims (2)

1. A resampling-based AAKR model uncertainty calculation method, comprising the steps of:

Step 1), dividing a sensor history state data set into a training data set and a test data set;

loading sensor historical data, detecting and correcting abnormal values of the sensor historical data, and dividing a corrected data set into a training data set and a test data set;

step 2), denoising the training data set by a wavelet denoising method and calculating noise variance;

The training data set is denoised using a wavelet denoising method,

Where ε _i is the noise estimate for the ith training observation X _i in the training dataset; Is the estimated value of the true value of the ith training observed value X _i in the training data set; the variance of the ith variable noise in the training dataset is:

n _trn is the number of training observations; Is the expected value of the noise estimate; is the training dataset noise variance;

Step 3), resampling the training data set for a plurality of times by a Bootstrap method, obtaining a group of new training data sets after resampling each time, establishing a plurality of new models according to each group of new training data sets after sampling, predicting a plurality of model predicted values according to the plurality of new models, and calculating the change among the plurality of model predicted values to obtain model predicted variances of the plurality of model predicted values;

The variance of model predictions, which is the variation between model predictions, is calculated using the following equation:

Wherein, Variance of the ith observation for the jth variable; obtaining n _tst multiplied by p-dimensional variance estimation according to model prediction variances, arranging variances of each p variable in an ascending order, and selecting the 95 th percentile maximum value to conservatively estimate single-point variances; Representation of The ith observation of the jth variable,Is the predicted value of the kth prototype model of test observations X _tst, test observations X _tst contains n _tst observations; A predicted value expectation representing an ith observed value of a jth variable;

；

Step 4), calculating the mean square error between the model predicted value and the test observed value;

Step 5), calculating to obtain model deviation according to the noise variance, the model prediction variance and the mean square error;

the new model established by each resampling training data set can give a model predictive value, namely Calculating a mean square error MSE between the new model predictive value and the test observed value:

wherein X _tst,i and The test observation value and the model prediction value of the ith new model are respectively; the dimension of the MSE is 1×p, and N predicted values will generate N1×p-dimension MSEs;

The model bias is:

step 6), estimating according to the model deviation and the model prediction variance, and obtaining a Monte Carlo uncertainty estimated value which is 2 times of an evolution value of the sum of the square of the model deviation and the model prediction variance;

Calculating a confidence interval and a prediction interval corresponding to the 95% confidence level according to the Monte Carlo uncertainty estimation value, correcting the confidence interval predicted by the AAKR model by using a Jackknife deviation estimation method, and calculating the prediction interval;

The general equation for the confidence interval is:

Wherein, Is an estimate of the model predictor expectation θ, then its bias is:

Model predictive value Is an n _tst x p dimensional time state sequence; Represents the estimated quantity after the i-th predicted value is removed, i=1, 2,.. Then Jackknife bias estimates as:

Thereby obtaining Is estimated by the correction:

The confidence interval after correction is:

the prediction interval for the 95% confidence level is:

2. a resampled AAKR model uncertainty computing system based on the method of claim 1, comprising a data acquisition module, a data denoising module, and a data processing module;

the data acquisition module is used for acquiring a sensor historical state data set, dividing the acquired data set into a training data set and a test data set, and transmitting the training data set to the data denoising module;

The data denoising module denoises the received training data set, calculates noise variance and transmits the noise variance to the data processing module, and simultaneously transmits the denoised training data to the data processing module;

The data processing module resamples the training data set for a plurality of times through the data acquisition module, a group of new training data sets are obtained after resampling each time, a plurality of new models are built according to the sampled groups of new training data sets, a plurality of model predicted values are obtained according to the plurality of new model predictions, and model prediction variances of the plurality of model predicted values are obtained by calculating changes among the plurality of model predicted values; meanwhile, calculating the mean square error between the model predicted value and the test observed value; finally, calculating according to the noise variance, the model prediction variance and the mean square error to obtain a model deviation; and estimating by using the model deviation and the model prediction variance, and obtaining and outputting a 2-time value of the square value of the model deviation and the sum of the model prediction variance as a Monte Carlo uncertainty estimated value.