CN108985335B - Integrated learning prediction method for irradiation swelling of nuclear reactor cladding material - Google Patents

Integrated learning prediction method for irradiation swelling of nuclear reactor cladding material Download PDF

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CN108985335B
CN108985335B CN201810628508.4A CN201810628508A CN108985335B CN 108985335 B CN108985335 B CN 108985335B CN 201810628508 A CN201810628508 A CN 201810628508A CN 108985335 B CN108985335 B CN 108985335B
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李丹宁
杨文�
贺新福
胡长军
王珏
陈丹丹
李建江
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Abstract

The invention provides an integrated learning prediction method for irradiation swelling of nuclear reactor cladding materials, and relates to the technical field of integrated learning material prediction combining results of a plurality of weak supervision models. The invention adopts a stacked multilayer abnormal state regressor model which is a two-layer framework, wherein the first layer comprises four different base learners which are respectively an artificial neural network, a support vector machine, a gradient lifting and a random forest, the first layer adopts 5-fold cross validation training, and the second layer is established by XGboost. The method can reduce deviation and variance, improve the generalization capability of the model and enable the prediction result of the material characteristics to be more accurate.

Description

Integrated learning prediction method for irradiation swelling of nuclear reactor cladding material
Technical Field
The invention relates to the technical field of integrated learning material prediction combining results of a plurality of weak supervision models, in particular to an integrated learning prediction method for irradiation swelling of nuclear reactor cladding materials of a stacked multilayer abnormal state regressor.
Background
Machine Learning (Machine Learning) methods have been gradually applied to material modeling to predict material characteristics more accurately, and the key is to find a mapping model for projecting an input space to an output space for a class of problems, and to predict actual data by using the well-learned model. Common Machine learning methods in material design and characteristic prediction include Artificial Neural networks (Artificial Neural networks), Support Vector machines (Support Vector machines), Decision trees (Decision trees) and the like, and the methods provide advanced scientific and effective means for solving component optimization, heat treatment process research, performance research and post-irradiation performance research of numerical stack materials.
Although many machine learning methods exist in the material field, a single method cannot obtain the best prediction result under all the feature sets in all the fields, and in the actual material prediction process, the single machine learning method has the problems of model overfitting, poor generalization capability, difficulty in ensuring the accuracy of the material prediction result and the like. Document 1(Xue D, Balachandran P V, Hogden J, et al. associated search for materials with targeted properties by adaptive design [ J ]. Nature communications,2016,7:11241.) proposes a data-driven material design framework on the basis of machine learning, and uses uncertainty iteration to guide the experiment to promote the discovery of new materials, and document 2(David h.wolbert.stacked generation. in Neural Networks, volume 5, pages 241-plus 259,1992.) develops a common technical framework of stack integration learning of homologous integration based on the ML algorithm, and verifies that such a framework can achieve better performance than a single classifier. Before classifying a new instance, the stacking integrator integrates a plurality of single classifiers, the integrated classifiers comprise N single artificial neural network classifiers, for the same input, the N artificial neural networks respectively give respective outputs, and finally the outputs are combined to obtain the output result of the integrated classifier as the final classification.
The inventor finds that the stacked integrated learning framework has the characteristics that the trained basic classifiers are homologous, namely the artificial neural network not only causes overfitting, but also greatly reduces the algorithm efficiency due to too long output time. In the field of material prediction at present, the learning precision and the learning effect of a tree model are generally better than those of other models, so that the classification result finally generated by the framework is better than that of a single artificial neural network classifier but not necessarily better than that of a single other model. Moreover, the stacking framework has great flexibility and uncertainty, on one hand, overfitting (over fitting) can be effectively prevented by adopting multi-fold cross validation on the division of the initial data set, and on the other hand, the meta classifier should be replaced by a plurality of regression models in the aspects of selection and use of the training models, so that the precision of each model is higher as much as possible. In addition, in order to optimize the performance of the material prediction model, more information is obtained from the original data as much as possible through initial data preprocessing and feature engineering.
Aiming at the problem that the existing cladding material irradiation swelling field is difficult to observe the swelling mechanism from the swelling incubation period and the transition period to the linear change period through experiments, a new material prediction method is urgently needed to reduce the Bias (Bias) and the Variance (Variance), improve the generalization capability of the model and enable the prediction result of the material characteristics to be more accurate.
Disclosure of Invention
The invention aims to provide an integrated learning prediction method for irradiation swelling of nuclear reactor cladding materials, so as to reduce deviation and variance, improve generalization capability of a model and enable prediction results of material characteristics to be more accurate.
In order to solve the technical problem, an embodiment of the present invention provides an integrated learning prediction method for irradiation swelling of nuclear reactor cladding material, including:
step A: acquiring an original data set related to irradiation and swelling of the cladding, wherein one part of data in the original data set is used as a training set, and the other part of data in the original data set is used as a prediction set;
and B: generating a Pearson correlation thermodynamic diagram to check a characteristic value which is relatively large in relation to swelling capacity of the cladding material and a correlation degree between the characteristic values;
and C: extracting a preset number of characteristic values with large correlation degrees before and carrying out normalization processing;
step D: reducing dimensions and denoising by using a PCA method;
step E: selecting features by using a chi-2 algorithm to remove irrelevant or redundant features;
step F: generating a first-layer machine learning device model which comprises four parallel and different base learning devices, initializing N-1 and K-1, wherein N is the Nth base learning device, and K is the cross validation training times;
step G: performing K-fold cross validation training on the Nth base learner;
step H: judging whether K is larger than 5, if so, continuing to execute the step I; if not, K is K +1, and the step G is returned to;
step I: regarding the training set, taking 5 prediction results as the Nth column of the input training sample of the second layer;
step J: for the test set, taking the average value of 5 times of prediction results as the Nth column of the input test sample of the second layer;
step K: judging whether N is larger than the number of the base learners, if so, continuing to execute the step L; if not, returning to the step G, wherein N is equal to N +1, and K is equal to 1;
step L: taking the output of the first layer of machine learning model as a new characteristic value as input data of a second layer of machine learning model, wherein the second layer of machine learning model is established through XGBOOST;
step M: and outputting the prediction result of the machine learner model of the second layer, and finishing the training of the stacked multilayer abnormal regressor model.
Further, the step C adopts a normalization process of the following formula:
Figure BDA0001699775060000031
wherein x isiRepresenting the original initial value, x, of the ith sample point in the data columnminRepresents the minimum value, x, of the data column in which the sample point is locatedmaxRepresenting the maximum value, x, in the column of data where the sample point is locatedi_newRepresenting the new value of the ith sample point in the data column after the transformation.
Further, the predetermined number in the step C is 10.
Further, in the step F, the four base learners are an artificial neural network ANN, a support vector machine SVM, a Gradient Boost and a random forest RandomForest.
Further, in the step F, each base learner uses a different training set and test set to improve the accuracy of the entire model.
The technical scheme of the invention has the following beneficial effects:
(1) when the method is used for predicting the irradiation swelling amount of the cladding material, the influence factors are multiple and the mechanism is complex, so that the method for researching the swelling gradient effect through the traditional neutron irradiation experiment is high in cost and long in time consumption. The invention constructs a powerful and accurate integrated learning model, and uses an advanced machine learning prediction modeling algorithm to replace a large amount of repeated tests and characterization cycles, thereby reducing the time cost and the research and development cost;
(2) overfitting can easily occur using a single homologous machine learning approach (e.g., an artificial neural network). The novel integrated regression stacking framework is a combination of heterogeneous irrelevant weak supervision models, the final prediction result is formed by two layers of Logistic regression combinations with ANN (artificial neural network), SVM (support vector machine), Gradient Boost and random forest as base learners and XGboost as the last layer of learners, so that the determination coefficient is improved to be more than 0.9, the relative deviation is reduced to be less than 0.1, the prediction precision is improved, and the result is more consistent with the result measured by experiments;
(3) the transformation method for transforming the format of the original data set into the learning format suitable for the model enables the factors influencing the swelling of the cladding material to be more understood, the reliability and the accuracy of the model to be accurately judged, and the implicit swelling mechanism is revealed from irregular data, so that the function relation between the irradiation dose, the temperature, the He content and the swelling amount is quantitatively predicted, the storage cost is reduced, and the complexity of visual analysis is reduced.
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FIG. 1 is a schematic block diagram of a stacked multi-level anomaly regressor model of the present invention;
FIG. 2 is a flow chart of the present invention method for integrated learning prediction of nuclear reactor cladding material radiation swelling;
FIG. 3 is a Pearson correlation heatmap between sample data set feature values in the present invention;
FIG. 4 is an example of a data format of the partial data set according to the next process input after the data preprocessing of step C, D, E;
FIGS. 5(a) and (b) are diagrams of a first level machine learning training and testing process, respectively, in the present invention;
FIG. 6 is a second level machine learning training and testing process of the present invention;
FIG. 7 is a partial data representation of the final result obtained in step M of the present invention;
FIG. 8 is pseudo code of a stacked multi-level anomaly regressor model construction of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
Aiming at the problem that the existing cladding material irradiation swelling field is difficult to observe swelling mechanisms from swelling incubation period and transition period to linear change period through experiments, the invention provides an integrated learning prediction method for nuclear reactor cladding material irradiation swelling, so as to reduce deviation and variance, improve generalization capability of a model and enable prediction results of material characteristics to be more accurate.
FIG. 1 is a schematic block diagram of a stacked multi-layer anomaly regressor model of the present invention. According to the method, a plurality of base learners Meta learners are arranged firstly, then the output of the Meta learners is used as the input of the Last learners to be integrated, and the model is integrally of a two-layer structure. FIG. 2 is a flow chart of the integrated learning prediction method of nuclear reactor cladding material radiation swelling of the present invention.
As shown in fig. 1-2, an embodiment of the present invention provides a method for predicting radiation swelling of nuclear reactor cladding material by integrated learning, including:
step A: acquiring an original data set related to irradiation and swelling of the cladding, wherein one part of data in the original data set is used as a training set, and the other part of data in the original data set is used as a prediction set;
the raw data set may be, for example, a cladding radiation swelling data set of low activation ferrite/martensite steel (RAFM steel) collected from the atomic energy research institute of china, which has 36 characteristic values of composition, cold working process, radiation temperature, radiation dose, etc., and a corresponding result value of a radiation swelling amount, for a total of 220 pieces of data. The original data set may have a portion of the data, e.g., 200 pieces, selected as a training set and another portion, e.g., 20 pieces, selected as a prediction set.
And B: generating a Pearson correlation thermodynamic diagram to check a characteristic value which is relatively large in relation to swelling capacity of the cladding material and a correlation degree between the characteristic values;
fig. 3 is a pearson correlation heat map between characteristic values of a sample data set according to the present invention, as shown in fig. 3, the depth of the gray scale value represents the correlation magnitude between two characteristic values, the deeper the gray scale indicates the greater the correlation degree between the characteristic values, and the top 10 characteristic values with greater correlation degree are listed in the correlation degree ranking chart.
And C: extracting the first 10 characteristic values with large correlation degrees and carrying out normalization processing;
in this step, various normalization processing methods may be adopted, for example, normalization processing of the following formula is performed for each sample point of each line of data in the extracted feature values with large correlation degrees:
Figure BDA0001699775060000061
wherein x isiRepresenting the original initial value, x, of the ith sample point in the data columnminRepresents the minimum value, x, in the data column (each characteristic value corresponds to a column of data) of the sample pointmaxRepresenting the maximum value, x, in the column of data where the sample point is locatedi_newRepresenting the new value of the ith sample point in the data column after the transformation.
Step D: reducing and denoising dimensions by using a PCA method to remove some noise data points;
pca (principal components analysis), a principal component analysis technique, also called principal component analysis, aims to convert multiple indexes into a few comprehensive indexes by using the idea of dimension reduction. The method comprises the following specific steps:
(1) firstly, calculating a covariance matrix of a sample eigenvalue matrix S;
(2) calculating an eigenvector and an eigenvalue of the covariance matrix S;
(3) the data is projected into the space spanned by the feature vectors.
Step E: selecting features by using a chi-2 algorithm to remove irrelevant or redundant features;
chi-2(chi-square test), namely the deviation degree between the actual observed value and the theoretical inferred value of the statistical sample, the deviation degree between the actual observed value and the theoretical inferred value determines the size of the chi-square value, and the chi-square value is greater and less in accordance with the chi-square value; the smaller the chi-square value is, the smaller the deviation is, the more the chi-square value tends to be in line with, and if the two values are completely equal, the chi-square value is 0, which indicates that the theoretical value is completely in line with. Since the chi-2 algorithm is common general knowledge in the art, it is not described herein in detail.
FIG. 4 is an example of the data format of the partial data set of the present invention obtained after the data preprocessing of step C, D, E, which conforms to the input of the next process, as shown in FIG. 4, the original data is shown on the left, wherein the values of Cr column are normalized to the range of [ -0.5,0.5] after the formula transformation of step C, and the other two columns are originally between-0.5 and 0.5, and thus there is no change; after the PCA algorithm in the step D, judging that the two rows of data with the Cr content of 12 in the graph are noise sample data, and filtering the two rows; and (4) calculating by using a chi-2 algorithm in the step E to obtain the minimum chi-square value of the characteristic value row of the cold working process parameter MAT _ CW, thus removing the cold working process parameter MAT _ CW and finally obtaining a right-side image.
Step F: generating a first-layer machine learning device model which comprises four parallel base learning devices, namely an ANN (artificial neural network), an SVM (support vector machine), a Gradient Boost and a random forest, initializing N to 1 and K to 1, wherein N is the Nth base learning device, and K is the cross validation training times;
in this embodiment, each base learner preferably uses a different training set and test set to improve the accuracy of the entire model.
FIGS. 5(a) and (b) are diagrams of a first-level machine learning training and testing process in the present invention, respectively, which includes cross training of a basic Model and prediction during cross testing, Model 1 is subjected to 5 times of cross validation, and a predicted value on a corner mark of a current validation set is obtained each time, and a set having the same size as an initial training set is obtained after 5 times of cross validation; and predicting the initial test set by using the Model 1 at each crossing, averaging all results after 5 times to obtain a prediction result of the current learner in the test set, wherein the prediction result is used as an input of a second-layer machine learner Model.
Step G: performing K-fold cross validation training on the Nth base learner;
step H: k is greater than 5?
a) If yes, continuing to execute the step I;
b) if not, returning to the step G, wherein K is K + 1;
step I: regarding the training set, taking 5 prediction results as the Nth column of the input training sample of the second layer;
step J: for the test set, taking the average value of 5 times of prediction results as the Nth column of the input test sample of the second layer;
step K: n is greater than the number of base learners?
a) If yes, continuing to execute the step L;
b) if not, N is N +1, K is 1, and go back to step G;
step L: taking the output of the first layer machine learner model as a new eigenvalue as input data (including a new training set and a new test set) of a second layer machine learner model, the second layer machine learner model being built by XGBOOST;
FIG. 6 shows the second layer machine learning training and testing process, as shown in FIG. 6, the predicted output of the first layer is adapted to train _ data as a new feature, the XGboost of the second layer is Trained, the Trained Model is used to predict the test set, and the final prediction result is obtained.
Step M: and outputting the prediction result of the machine learner model of the second layer, and finishing the training of the stacked multilayer abnormal regressor model.
FIG. 7 shows partial data of the final result obtained in step M of the present invention, and as shown in FIG. 7, the prediction accuracy is measured by the determination coefficient R-square and the maximum relative deviation E _ max, and it can be determined from the graph that the prediction accuracy meets the experimental requirements. The experiment requires the irradiation swelling capacity prediction of the RAFM steel, requires the determination coefficient to be more than 0.9, and requires the relative deviation to be less than 0.1. Pseudo code for the stacked multi-layer anomaly regressor model construction of the present invention can be written with reference to FIG. 8.
In summary, the embodiment of the invention has the following beneficial effects:
(1) when the method is used for predicting the irradiation swelling amount of the cladding material, the influence factors are multiple and the mechanism is complex, so that the method for researching the swelling gradient effect through the traditional neutron irradiation experiment is high in cost and long in time consumption. The invention constructs a powerful and accurate integrated learning model, and uses an advanced machine learning prediction modeling algorithm to replace a large amount of repeated tests and characterization cycles, thereby reducing the time cost and the research and development cost;
(2) overfitting can easily occur using a single homologous machine learning approach (e.g., an artificial neural network). The novel integrated regression stacking framework is a combination of heterogeneous irrelevant weak supervision models, the final prediction result is formed by two layers of Logistic regression combinations with ANN (artificial neural network), SVM (support vector machine), Gradient Boost and random forest as base learners and XGboost as the last layer of learners, so that the determination coefficient is improved to be more than 0.9, the relative deviation is reduced to be less than 0.1, the prediction precision is improved, and the result is more consistent with the result measured by experiments;
(3) the transformation method for transforming the format of the original data set into the learning format suitable for the model enables the factors influencing the swelling of the cladding material to be more understood, the reliability and the accuracy of the model to be accurately judged, and the implicit swelling mechanism is revealed from irregular data, so that the function relation between the irradiation dose, the temperature, the He content and the swelling amount is quantitatively predicted, the storage cost is reduced, and the complexity of visual analysis is reduced.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (5)

1. An integrated learning prediction method for irradiation swelling of nuclear reactor cladding material, comprising:
step A: acquiring an original data set related to irradiation and swelling of the cladding, wherein one part of data in the original data set is used as a training set, and the other part of data in the original data set is used as a prediction set;
and B: generating a Pearson correlation thermodynamic diagram to check a characteristic value which is relatively large in relation to swelling capacity of the cladding material and a correlation degree between the characteristic values;
and C: extracting a preset number of characteristic values with large correlation degrees before and carrying out normalization processing;
step D: reducing dimensions and denoising by using a PCA method;
step E: selecting features by using a chi-2 algorithm to remove irrelevant or redundant features;
step F: generating a first-layer machine learning device model which comprises four parallel and different base learning devices, initializing N-1 and K-1, wherein N is the Nth base learning device, and K is the cross validation training times;
step G: performing K-fold cross validation training on the Nth base learner;
step H: judging whether K is larger than 5, if so, continuing to execute the step I; if not, K is K +1, and the step G is returned to;
step I: regarding the training set, taking 5 prediction results as the Nth column of the input training sample of the second layer;
step J: for the test set, taking the average value of 5 times of prediction results as the Nth column of the input test sample of the second layer;
step K: judging whether N is larger than the number of the base learners, if so, continuing to execute the step L; if not, returning to the step G, wherein N is equal to N +1, and K is equal to 1;
step L: taking the output of the first layer of machine learning model as a new characteristic value as input data of a second layer of machine learning model, wherein the second layer of machine learning model is established through XGboost;
step M: and outputting the prediction result of the machine learner model of the second layer, and finishing the training of the stacked multilayer abnormal regressor model.
2. The integrated learning prediction method of nuclear reactor cladding material radiation swelling according to claim 1, characterized in that the step C employs a normalization process of the following formula:
Figure FDA0001699775050000021
wherein x isiRepresenting the original initial value, x, of the ith sample point in the data columnminRepresents the minimum value, x, of the data column in which the sample point is locatedmaxRepresenting the maximum value, x, in the column of data where the sample point is locatedi_newRepresenting the new value of the ith sample point in the data column after the normalization transformation.
3. The nuclear reactor cladding material radiation swelling integrated learning prediction method of claim 1, wherein the predetermined number in step C is 10.
4. The integrated learning prediction method for irradiation swelling of nuclear reactor cladding material according to claim 1, wherein in the step F, the four base learners are artificial neural network ANN, support vector machine SVM, Gradient Boost and random forest RandomForest respectively.
5. The method of claim 1, wherein each base learner in step F uses a different training set and test set to improve overall model accuracy.
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