CN112100574A - Resampling-based AAKR model uncertainty calculation method and system - Google Patents
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Abstract
The invention discloses a resampling-based method and a resampling-based system for calculating uncertainty of an AAKR model, wherein a sensor historical state data set is divided into a training data set and a testing data set, the training data set is denoised by a wavelet denoising method, noise variance is calculated, data accuracy is improved, then the sensor historical state data is randomly selected and replaced to obtain a new training data set sample, model prediction variances of a plurality of model prediction values can be obtained by optimizing an AAKR model architecture and the change among the plurality of model prediction values, and the mean square error between the prediction values and the testing value is calculated by resampling training data; the model deviation is calculated by combining the variance of the prototype model to form a 95% uncertainty value, an empirical distribution model is not required to perform modeling calculation on the noise estimation value, the resampling process is simplified, the calculation efficiency is improved, the reliability of the confidence interval deviation is guaranteed by combining the Jackknife method, and the estimation efficiency is improved on the basis of keeping the convergence performance.
Description
Technical Field
The invention relates to a quantification method of AAKR model uncertainty, in particular to a resampling-based AAKR model uncertainty calculation method and system.
Background
An online condition monitoring system for critical equipment of a nuclear power plant helps to reduce the risk of catastrophic failure and reduce the excess costs incurred by unnecessary periodic maintenance. The state monitoring method based on the empirical model does not depend on deep understanding of a fault mechanism model, whether the equipment is abnormal or not is judged from historical operation data and operation experience of the equipment, and the method is widely applied along with rapid development of the Internet of things and big data technology. However, when the empirical model is used for monitoring nuclear power key instruments and equipment, the problem of uncertainty affecting the stability of the model is involved, the uncertainty of the empirical model must be estimated, and meanwhile, the accurate estimation of an uncertainty interval can effectively reduce false alarm rate and false alarm rate of the equipment, so that the economic loss caused by equipment shutdown is reduced. At present, uncertain analysis and research on model regression values are few, and the traditional Monte Carlo uncertainty determination method uses probability distribution simulation noise to obtain sampling data, needs total distributed prior knowledge and enough large sample data, is low in efficiency and high in economic cost, and cannot effectively ensure prediction accuracy of the state of a key equipment sensor.
Disclosure of Invention
The invention aims to provide a resampling-based method and a resampling-based system for calculating the uncertainty of an AAKR model, so as to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a resampling-based AAKR model uncertainty calculation method comprises the following steps:
step 1), dividing a sensor historical state data set into a training data set and a testing data set;
step 2), denoising the training data set by a wavelet denoising method and calculating a noise variance;
step 3), resampling the training data sets for multiple times by a Bootstrap method, obtaining a group of new training data sets after resampling for each time, establishing a plurality of new models according to the groups of new training data sets after sampling, obtaining 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 the model prediction variance of the plurality of model predicted values;
step 4), calculating the mean square error between the model predicted value and the test observation value;
step 5), calculating according to the noise variance, the model prediction variance and the mean square error to obtain a model deviation;
and 6) estimating according to the model deviation and the model variance to obtain the Monte Carlo uncertainty estimated value which is 2 times of the square value of the sum of the square of the model deviation and the model variance.
Furthermore, the historical sensor data are loaded, the historical sensor data are detected and abnormal values are corrected, and the historical sensor state data set is divided into a training data set and a testing data set.
Furthermore, a wavelet denoising method is used for denoising the training data set,
wherein,iis the ith training observation X in the training datasetiEstimating the noise of (2);is the ith training observation X in the training datasetiAn estimated value of the true value of (d); the variance of the i variable noise in the training dataset is:
ntrnis the number of training observations;is the expected value of the noise estimate;is the training data set noise variance.
Further, the variance of the model prediction values is calculated by using the following formula:
wherein, variance of ith observation for jth variable; to obtain ntstAnd f, estimating the variance in x p dimension, arranging the variance of each p variable in ascending order, and selecting the maximum value of the 95 th percentile to conservatively estimate the single-point variance.
Furthermore, each new model established by the resampling training data set can give a model predicted value, namelyCalculating the mean square error MSE between the predicted value of the new model and the test observation value:
wherein Xtst,iAndrespectively, the test observed value and the model predicted value of the ith new model. The dimension of the MSE is 1 xp, and N predictors yield N MSEs of dimension 1 xp.
further, according to the Monte Carlo uncertainty estimation value, a confidence interval and a prediction interval corresponding to the 95% confidence level are calculated, and the Jackknife deviation estimation method is used for correcting the deviation of the Confidence Interval (CI) predicted by the AAKR model and calculating the prediction interval.
Further, according to the Monte Carlo uncertainty estimation value, a confidence interval and a prediction interval corresponding to the 95% confidence level are calculated, and the Jackknife deviation estimation method is used for correcting the deviation of the Confidence Interval (CI) predicted by the AAKR model and calculating the prediction interval.
Further, the general equation for the confidence interval is:
wherein,if the model is an estimate of the expected θ of the predicted value of the model, the deviation is as follows:
model prediction valueIs ntst×pA time state sequence is maintained;the estimated value obtained by removing the i (i ═ 1, 2.., N) th predicted value is averaged to obtain the average valueThe Jackknife bias is then estimated as:
the prediction intervals for the 95% confidence levels were:
a resampling-based AAKR model uncertainty calculation system comprises 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 testing data set, and transmitting the training data set to the data denoising module;
the data denoising module denoises a received training data set, calculates a noise variance, transmits the noise variance to the data denoising module, and transmits denoised training data to the data processing module;
the data processing module conducts repeated resampling on the training data set through the data acquisition module, a group of new training data sets are obtained after each repeated resampling, a plurality of new models are built according to the groups of new training data sets after sampling, a plurality of model predicted values are obtained according to the plurality of new models in a predicting mode, and the model prediction variance of the plurality of model predicted values can be obtained by calculating the change among the plurality of model predicted values; simultaneously 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 variance, and outputting a Monte Carlo uncertainty estimation value which is a value 2 times of the square value of the sum of the model deviation and the model variance.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a resampling-based AAKR model uncertainty calculation method, which comprises the steps of dividing a sensor historical state data set into a training data set and a testing data set, denoising the training data set and calculating noise variance through a wavelet denoising method, improving data accuracy, randomly selecting and replacing sensor historical state data to obtain a new training data set sample, obtaining model prediction variances of a plurality of model prediction values by optimizing AAKR model architecture and changes among a plurality of model prediction values, developing and testing a plurality of prototype models by resampling training data through the prototype models and the testing data, and calculating mean square error between the prediction values and the testing values; the model deviation is calculated by combining the variance of a prototype model to form a 95% uncertainty value, an empirical distribution model is not required to perform modeling calculation on a noise estimation value, the resampling process is simplified, the calculation efficiency is improved, the reliability of the uncertainty interval deviation is guaranteed by combining a Jackknife method, the estimation efficiency is improved on the basis of keeping the convergence performance, a set of reliable, efficient and complete method flow is provided for uncertainty estimation of the empirical model of the nuclear power plant key equipment, and the method has important engineering application value for improving the accuracy of state prediction of the key equipment sensor.
Furthermore, by calculating a confidence interval and a prediction interval of a 95% confidence level and correcting the distribution deviation of the confidence interval by using a Jackknife deviation estimation method, the analysis process is simplified, the deviation of the confidence interval is reduced, and the estimation efficiency is improved on the basis of keeping the convergence performance.
The resampling-based AAKR model uncertainty calculation system is simple in structure, training is carried out by acquiring a sensor historical state normal data set, and the analysis process is simplified by the Bootstrap resampling-based experience model uncertainty calculation method, and the reliability of the system is ensured by reducing confidence interval deviation by combining with a Jackknife method.
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FIG. 1 is a schematic diagram of a flow of calculating uncertainty of an AAKR model according to an embodiment of the present invention.
FIG. 2 is a graph illustrating an uncertainty convergence analysis in an embodiment of the present invention.
FIG. 3 is a diagram of confidence interval before rectification of the AAKR model in the embodiment of the present invention.
FIG. 4 is a diagram of confidence intervals after deviation rectification of the AAKR model in the embodiment of the present invention.
FIG. 5 is a diagram illustrating the prediction window of the AAKR model according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1, a resampling-based method for calculating uncertainty of AAKR model includes the following steps:
step 1), dividing a sensor historical state data set into a training data set and a testing data set;
specifically, the historical sensor data is loaded, the historical sensor data is detected and abnormal values are corrected, and the data set is divided into a training data set and a testing data set.
Step 2), denoising the training data set by a wavelet denoising method and calculating a noise variance;
specifically, a wavelet denoising method is used for denoising the training data set,
wherein,iis the ith training observation X in the training datasetiEstimating the noise of (2);is the ith training observation X in the training datasetiThe estimated value of the true value is a result obtained by performing wavelet denoising on the training observed value; the variance of the i variable noise in the training dataset is:
ntrnis the number of training observations;is an expected value of the noise estimate, which is zero or near zero for drift-free data;is the training data set noise variance.
Random error predicted by a variance measurement model of variable noise;
step 3), resampling the training data set for N times by a Bootstrap method (namely, taking a training test observation value to replace the value of the training data set at the current position) to obtain N groups of resampled training data sets, establishing N new models according to the N groups of resampled training data sets, predicting and obtaining N model predicted values according to the N new models, and calculating the change among the N model predicted values to obtain the model prediction variance of the N model predicted values;
the method specifically comprises the following steps:
performing Bootstrap resampling on a group of training data sets for N times, establishing a new model through each obtained new sampling data set, namely N new models, and estimating the change between model prediction values from the N new models;
wherein XiRepresenting a state of the system, XjRepresenting a time state sequence of a monitored variable.
Bootstrap resampling: for monitoring variable XjWith replaced random samples ntrnObtaining Bootstrap resampling sample X of X*。
And adopting LHS resampling technology: applying wavelet denoising method to training data to obtain 'true' value, subtracting the 'true' value from original training data to obtain estimated value of noise; modeling the noise probability distribution as a normal distribution by splitting the distribution into ntrnNon-overlapping compartments (also known as "bins"), each bin havingThe probability of (d); random values are chosen from each bin at equal frequencies and the final noise distribution is uniformly sampled to construct the prototype training set.
The AAKR model established by the resampling training data set can give a test observation value XtstModel predictive value ofModel prediction valueIs to the test observed value XtstEvaluation of (2) test the observed value XtstContaining ntst(ii) an observed value;
wherein,is a test observation XtstPrediction of the kth prototype model, hereTo representAn ith observation for a jth variable; the predicted value of the ith observation of the jth variable is expected to be the average of the predicted values of the N new models, i.e.:
namely XtstThe predicted value of (d) is expressed as:
likewise, variance of ith observation for jth variable:
i.e. the model prediction variance can be written as:
after simplification: the variance of the model predictions, which is the change between the N model predictions, is calculated using the following equation:
to obtain ntstEstimating the variance in x p dimension, arranging the variance of each p variable in ascending order, and selecting the maximum value of the 95 th percentile to conservatively estimate the single-point variance;
the model prediction variance is defined as the expectation of the squared difference of the parameter and its expected value, so the model prediction variance can also be expressed as:
step 4), calculating the Mean Square Error (MSE) between the predicted values of the N models and the test observation value;
each new model established by the resampling training data set can give a model predicted value, namelyCalculating the mean square error MSE between the predicted value of the new model and the test observation value:
wherein Xtst,iAndrespectively, the test observed value and the model predicted value of the ith new model. The dimension of the MSE is 1 x p, N predicted values can generate N MSEs with the dimension of 1 x p, and for p variables, the maximum value of the 95 th percentile is taken as a single-point estimation value of the MSE.
Step 5), calculating according to the noise variance, the model prediction variance and the mean square error to obtain a model deviation;
the deviation measures any systematic error.
The prediction performance of the model is quantified by Mean Square Error (MSE), and the MSE is calculated according to the prediction value of the model:
The reducible error is the model prediction valueAnd test observation XtstTrue model M (X)tst) The square of the distance between; irreducible errors are differences between the true parameter values and the measured parameter values, caused by random processes and measurement noise, and are called irreducible errors because they cannot be modeled deterministically.
The error of treaty explains how the model adequately represents the true model M (X)tst) Depending only on the selected model architecture, training procedure and data set. The error may be further decomposed into a bias component and a variance component.
The model deviation is defined as the systematic error of the model, which is the difference between the expected predicted value and the true target value of the model, and can be expressed as:
The model bias is constant for each variable and can be approximated by its expected value. Then, if the expectation of the squared deviation is negative (i.e., the sum of the model predicted variance and the estimated noise variance is greater than MSE), it is set to zero;
the final available model bias is specifically as follows:
Example (b):
according to the Monte Carlo uncertainty estimation value, a confidence interval and a prediction interval corresponding to the 95% confidence level are calculated, the Jackknife deviation estimation method is used for correcting the deviation of the Confidence Interval (CI) predicted by the AAKR model and calculating the prediction interval, and a diagram of the confidence interval before correction of the AAKR model is shown in figure 3.
The general equation for the confidence interval is given by the following equation:
wherein,if the model is an estimate of the expected θ of the predicted value of the model, the deviation is as follows:
model prediction valueIs ntstA time state sequence of dimension x p,the estimated value obtained by removing the i (i ═ 1, 2.., N) th predicted value is averaged to obtain the average valueThe Jackknife bias is then estimated as:
CI does not contain noise termOnly the uncertainty in the model prediction is estimated, and the natural change of the modeling value is not considered, wherein the confidence interval after rectification of the AAKR model is shown in FIG. 4;
PI at 95% confidence level is expressed as:
since the PI contains a noise variance term, by definition, CI, it is a more conservative estimate of the model uncertainty; the prediction intervals of the AAKR model are shown in FIG. 5
The invention relates to a Bootstrap resampling-based self-association kernel regression model (AAKR) uncertainty calculation method, which randomly selects and replaces sensor historical state data to obtain a Bootstrap sample so as to optimize an AAKR model architecture and determine uncertainty of a current predicted value, and comprises the following steps: loading historical data, detecting and correcting abnormal values, and dividing the data into training and testing data sets; utilizing Bootstrap to resample training data, developing and testing a plurality of prototype models, obtaining a predicted value through the prototype models and the test data, and calculating a Mean Square Error (MSE) between the predicted value and a test observation value; denoising the training data by using a wavelet denoising method to estimate a noise variance; the model deviation is calculated by combining the variance of the prototype model to form 95% uncertainty value estimation, the confidence interval and the prediction interval of 95% confidence level are calculated, and the distribution deviation of the confidence interval is corrected by using a Jackknife deviation estimation method.
Claims (10)
1. A resampling-based AAKR model uncertainty calculation method is characterized by comprising the following steps:
step 1), dividing a sensor historical state data set into a training data set and a testing data set;
step 2), denoising the training data set by a wavelet denoising method and calculating a noise variance;
step 3), resampling the training data sets for multiple times by a Bootstrap method, obtaining a group of new training data sets after resampling for each time, establishing a plurality of new models according to the groups of new training data sets after sampling, obtaining 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 the model prediction variance of the plurality of model predicted values;
step 4), calculating the mean square error between the model predicted value and the test observation value;
step 5), calculating according to the noise variance, the model prediction variance and the mean square error to obtain a model deviation;
and 6) estimating according to the model deviation and the model variance to obtain the Monte Carlo uncertainty estimated value which is 2 times of the square value of the sum of the square of the model deviation and the model variance.
2. The method for calculating the uncertainty of the AAKR model based on resampling as claimed in claim 1, wherein the historical sensor data is loaded, the historical sensor data is detected and abnormal values are corrected, and the corrected data set is divided into a training data set and a testing data set.
3. The method of claim 1, wherein the training data set is denoised by a wavelet denoising method,
wherein,iis the ith training observation X in the training datasetiEstimating the noise of (2);is the ith training observation X in the training datasetiAn estimated value of the true value of (d); trainingThe variance of the i variable noise in the dataset is:
4. The method of claim 3, wherein the model prediction variance is calculated as a change between model predictions using the following equation:
5. The method of claim 4, wherein the new model created for each resampled training data set provides a model prediction value (AAKR model uncertainty) for each resampled training data setCalculating the mean square error MSE between the predicted value of the new model and the test observation value:
7. the method for calculating the uncertainty of the AAKR model based on resampling of claim 1, wherein the confidence interval and the prediction interval corresponding to 95% confidence level are calculated according to the estimated Monte Carlo uncertainty, and the Jackknife deviation estimation method is used to correct the Confidence Interval (CI) predicted by the AAKR model and calculate the prediction interval.
8. The method for calculating the uncertainty of the AAKR model based on resampling of claim 7, wherein the confidence interval and the prediction interval corresponding to 95% confidence level are calculated according to the estimated Monte Carlo uncertainty, and the Jackknife deviation estimation method is used to correct the Confidence Interval (CI) predicted by the AAKR model and calculate the prediction interval.
9. The resampling-based AAKR model uncertainty computation method according to claim 8, wherein the general equation for confidence interval is:
wherein,if the model is an estimate of the expected θ of the predicted value of the model, the deviation is as follows:
model prediction valueIs ntstX p-dimensional time state sequence;the estimated value obtained by removing the i (i ═ 1, 2.., N) th predicted value is averaged to obtain the average valueThe Jackknife bias is then estimated as:
the prediction intervals for the 95% confidence levels were:
10. a resampling-based AAKR model uncertainty calculation system is characterized by 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 testing data set, and transmitting the training data set to the data denoising module;
the data denoising module denoises a received training data set, calculates a noise variance, transmits the noise variance to the data denoising module, and transmits denoised training data to the data processing module;
the data processing module conducts repeated resampling on the training data set through the data acquisition module, a group of new training data sets are obtained after each repeated resampling, a plurality of new models are built according to the groups of new training data sets after sampling, a plurality of model predicted values are obtained according to the plurality of new models in a predicting mode, and the model prediction variance of the plurality of model predicted values can be obtained by calculating the change among the plurality of model predicted values; simultaneously 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 variance, and outputting a Monte Carlo uncertainty estimation value which is a value 2 times of the square value of the sum of the model deviation and the model variance.
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