# A Correlation-Based Feature Selection Algorithm for Operating Data of Nuclear Power Plants

Authors: Yuxuan He; Hongxing Yu; Ren Yu; Jian Song; Haibo Lian; Jiangyang He; Jiangtao Yuan
Journal: Science and Technology of Nuclear Installations
 (2021)

---

## Abstract

Nuclear power plant operating data are characterized by a large variety, strong coupling, and low data value density. When using machine learning techniques for fault diagnosis and other related research, feature selection enables dimensionality reduction while maintaining the physical meaning of the original features, thus improving the computational efficiency and generalization ability of the learning model. In this paper, a correlation-based feature selection algorithm is developed to implement feature selection of nuclear power plant operating data. The proposed algorithm is verified by experiments and compared with traditional correlation-based feature selection algorithms. The experiments and comparison results show that the proposed algorithm is effective in realizing the dimensionality reduction of nuclear power plant operating data.


---

## Body

## 1. Introduction

During the real-time operation of a nuclear power plant, the parameters such as temperature and pressure are monitored constantly and recorded. When studies based on machine learning are carried out for fault diagnosis or anomaly detection using nuclear power plant operating data, dimensionality reduction is required to avoid the calculation delay caused by the excessive data volume and the interference of weakly related parameters on the prediction accuracy [1–5]. Feature selection is interpretable because it retains the physical meaning of the original feature, which makes it more advantageous in related research [6, 7]. Currently, the feature selection method for nuclear power plant operating data mainly uses expert knowledge or simple data preprocessing. Santhosh et al. obtained a new feature set by artificially selecting features according to professional knowledge [8–10]. Wang et al. comprehensively considered the reliability requirements of the nuclear power system and the coupling relationship between the parameters and expert experience feedback to determine the strong correlation parameters [11]. Wang et al. used statistical methods to remove low variance features in time-series data [12]. The work of Peng et al. was based on relevance analysis and used the Pearson coefficient to evaluate correlation to delete features that have little impact on classification [13]. Na et al. proposed a method, which combines correlation analysis with a genetic algorithm to realize automatic input selection [14, 15]. However, faced with specific classification problems, some important features may be mistakenly removed or the new feature set may contain a large number of redundant features, which makes it impossible to achieve satisfactory dimensionality reduction effects with guaranteed model performance. Since nuclear power plant operating data have many types and strong coupling characteristics, common feature selection algorithms sometimes cannot accurately identify redundant features. In this context, this paper proposes a correlation-based feature selection algorithm for operating data of nuclear power plants (NPP-FS).The main contributions of the proposed method can be summarized as follows:(i)
We consider the characteristics of nuclear power plant operating data and propose that the maximal information coefficient should be used to determine the strength of the correlation between features and class. The results are used as the basis for feature ranking to delete irrelevant features.(ii)
We propose an improved approximate Markov blanket concept, which can avoid the risk of excessively removing redundant features when making redundant judgments on nuclear power plant operating data.(iii)
We conduct a series of experiments on the data generated by the simulation based on different backgrounds. The effects of the proposed method are investigated, and the feature selection performance is compared with traditional feature selection methods. The results show that the proposed method outperforms the conventional method in the dimensionality reduction effect.The remainder of this article is arranged as follows. Section2 reviews classical correlation-based feature selection algorithms and points out the problems in applying these algorithms to nuclear power plant operating data. Sections 3 and 4 introduce the details of the proposed feature selection algorithm. Section 5 evaluates the validity of the proposed theory and method through experiments. Conclusions are given in Section 6, which summarizes the advantages and disadvantages of the proposed approach as well as some future topics.


## 2. Related Work

The feature selection algorithm based on correlation is a common method to obtain the input features of model learning, and it has received widespread attention in many fields such as text classification [16–19], bioinformatics [20], and genetic analysis [21]. The correlation theory regards the feature-class correlation as feature relevance and the feature-feature correlation as redundancy [22]. Then, an original feature set is considered to be composed of strongly relevant features, weakly relevant but nonredundant features, redundant features, and irrelevant features. It is expected that a feature subset containing only nonredundant features and strongly relevant features can be obtained through feature selection algorithms. The most representative of these algorithms are correlation-based feature selection (CFS) [23], minimal-redundancy-maximal-relevance criterion (mRMR) [24], and fast correlation-based filter (FCBF) [25, 26]. CFS uses a forward search strategy to estimate the performance of a subset of features rather than a single feature. It uses Merits as an evaluation function to examine the effect of adding a certain feature to the Merits value. The mRMR is similar to the CFS algorithm in that it uses a mutual information-based evaluation function to estimate the correlation and redundancy while also taking into account the performance of the feature subset as a whole. FCBF uses symmetric uncertainty as to the correlation measure and decouples the relevance analysis and redundancy analysis to sequentially perform feature ranking and feature search to gradually remove irrelevant and redundant features.Unlike the publicly available datasets used to validate such feature selection algorithms, nuclear power plant operating data have the following characteristics. (1) Various data sources: in addition to variables such as temperature, pressure, water level, and flow from the loop, process parameters such as neutron detection and radiation monitoring are also involved. (2) Strong coupling between variables: for example, the reactor physical and thermal-hydraulic parameters influence each other. (3) Low data value density: fault or abnormality data are low, and the occurrence of a certain fault or abnormality is often reflected only by individual variables.The characteristics possessed by nuclear power plant operating data can amplify the shortcomings of the above feature selection algorithm. CFS and mRMR sometimes have poor recognition performance for strongly coupled features to take into account the overall performance of feature subsets. The symmetric uncertainty used in FCBF is weak in identifying nonlinear relationships, which can cause the results of feature ranking to fail. These problems pose challenges for the application of correlation-based feature selection algorithms.To overcome the problems of existing algorithms based on correlation and meet the needs of nuclear power plant operating data feature selection, we develop a novel algorithm that can provide a collection of features with strong correlation and low redundancy.


## 3. Correlation-Based Measures

Choosing an appropriate measure of correlation is crucial for a correlation-based feature selection algorithm. The mutual information is first introduced in this section. We then focus on two mutual information-based correlation measures adopted by the NPP-FS algorithm. Maximal information coefficient is applied to measure nuclear power plant operating data. Symmetric uncertainty is used to improve the approximate Markov blanket.


### 3.1. Mutual Information

There are many measures based on the information-theoretical concept of entropy among nonlinear correlation measures. It solves the measurement of the uncertainty of random variables. The entropy of variableX can be defined as(1)HX=−∑iPxilogPxi,where Pxi represents the prior probabilities for all values of X.Conditional entropy is the conditional probability distribution of random variableX when random variable Y occurs alone. It is defined as(2)HX|Y=−∑jPyj∑iPxi|yjlogPxi|yj,where Pxi|yj represents the posterior probabilities of X given the values of Y.Mutual information can be expressed by equations (1) and (2), given by [27](3)IGX|Y=HX−HX|Y.We can easily know thatIGX|Y=IGY|X by derivation, and it can be expressed as IX,Y. Mutual information is not normalized, and it tends to have more values. It is generally not directly used for correlation measurement.


### 3.2. Maximal Information Coefficient

The maximal information coefficient is a nonparametric statistical method proposed by Reshef et al. that can measure the correlation between two variables [28]. Under the condition of sufficient sample data and information, it can identify any type of functional relationship (including the superposition of noise-free functions), and it is more equitable than mutual information. The calculation method of the maximal information coefficient (MIC) is as follows.Given a data setD consisting of n‐ordered pairs of variables, and a scatter plot consisting of all pairs of variables in this set, the X-axis and Y-axis are divided into a grid according to the number of x, y, and the grid G is obtained. Under the condition that x and y remain unchanged, grid G has multiple division methods. If ID|G represents the mutual information of the dataset D divided by G, then the highest mutual information is expressed as follows:(4)I∗D,x,y=maxID|G.Normalize the highest mutual information obtained under the condition of differentx and y to form the characteristic matrix MDx,y, and it can be expressed by the following equation:(5)MDx,y=I∗D,x,ylogminx,y.On the datasetD, the MIC can be calculated as follows:(6)MICD=maxxy<BnMDx,y,where xy≤Bn=nα, n is the number of samples, and α is an adjustable parameter. The value of α will affect the density of the grid so that it will affect the judgment of the correlation. According to Reshef’s suggestion, α is 0.6 in the experiment involved in this article.The MIC is symmetric due to the symmetry of mutual information and its score is in the range [0, 1]. When there is a noise-free relationship between two variables, the MIC tends to 1, and when the two variables are statistically independent, the MIC tends to 0.


### 3.3. Symmetric Uncertainty

Symmetric uncertainty (SU) is a correlation measure based on normalized mutual information proposed by Kvalseth [29] and is often used in feature selection algorithms based on correlation. The calculation method of SU is shown in the following equation [30]:(7)SUX,Y=2IX,YHX+HY,where SUX,Y is the SU of random variables X and Y, IX,Y is the mutual information between X and Y, and H· represents the information entropy of the random variable.SU can compensate for the bias that mutual information tends to have more value features and at the same time normalizes its values to the range [0, 1].SUX,Y=0 indicates X and Y are independent, and SUX,Y=1 means that one variable can be completely predicted by another variable. In addition, SU is also symmetric to a pair of variables because of the symmetry of mutual information.


## 3.1. Mutual Information

There are many measures based on the information-theoretical concept of entropy among nonlinear correlation measures. It solves the measurement of the uncertainty of random variables. The entropy of variableX can be defined as(1)HX=−∑iPxilogPxi,where Pxi represents the prior probabilities for all values of X.Conditional entropy is the conditional probability distribution of random variableX when random variable Y occurs alone. It is defined as(2)HX|Y=−∑jPyj∑iPxi|yjlogPxi|yj,where Pxi|yj represents the posterior probabilities of X given the values of Y.Mutual information can be expressed by equations (1) and (2), given by [27](3)IGX|Y=HX−HX|Y.We can easily know thatIGX|Y=IGY|X by derivation, and it can be expressed as IX,Y. Mutual information is not normalized, and it tends to have more values. It is generally not directly used for correlation measurement.


## 3.2. Maximal Information Coefficient

The maximal information coefficient is a nonparametric statistical method proposed by Reshef et al. that can measure the correlation between two variables [28]. Under the condition of sufficient sample data and information, it can identify any type of functional relationship (including the superposition of noise-free functions), and it is more equitable than mutual information. The calculation method of the maximal information coefficient (MIC) is as follows.Given a data setD consisting of n‐ordered pairs of variables, and a scatter plot consisting of all pairs of variables in this set, the X-axis and Y-axis are divided into a grid according to the number of x, y, and the grid G is obtained. Under the condition that x and y remain unchanged, grid G has multiple division methods. If ID|G represents the mutual information of the dataset D divided by G, then the highest mutual information is expressed as follows:(4)I∗D,x,y=maxID|G.Normalize the highest mutual information obtained under the condition of differentx and y to form the characteristic matrix MDx,y, and it can be expressed by the following equation:(5)MDx,y=I∗D,x,ylogminx,y.On the datasetD, the MIC can be calculated as follows:(6)MICD=maxxy<BnMDx,y,where xy≤Bn=nα, n is the number of samples, and α is an adjustable parameter. The value of α will affect the density of the grid so that it will affect the judgment of the correlation. According to Reshef’s suggestion, α is 0.6 in the experiment involved in this article.The MIC is symmetric due to the symmetry of mutual information and its score is in the range [0, 1]. When there is a noise-free relationship between two variables, the MIC tends to 1, and when the two variables are statistically independent, the MIC tends to 0.


## 3.3. Symmetric Uncertainty

Symmetric uncertainty (SU) is a correlation measure based on normalized mutual information proposed by Kvalseth [29] and is often used in feature selection algorithms based on correlation. The calculation method of SU is shown in the following equation [30]:(7)SUX,Y=2IX,YHX+HY,where SUX,Y is the SU of random variables X and Y, IX,Y is the mutual information between X and Y, and H· represents the information entropy of the random variable.SU can compensate for the bias that mutual information tends to have more value features and at the same time normalizes its values to the range [0, 1].SUX,Y=0 indicates X and Y are independent, and SUX,Y=1 means that one variable can be completely predicted by another variable. In addition, SU is also symmetric to a pair of variables because of the symmetry of mutual information.


## 4. Method

### 4.1. Improved Approximate Markov Blanket

Markov blanket is a method proposed by Koller to eliminate redundant features, and its definition is as follows [31].Mj does not contain fj, and we say that Mj is a Markov blanket for fj iff PF−Mj−fj,C|fj,Mj=PF−Mj−fj,C|Mj.The meaning of the above formula is thatMj contains all the information of fj about C and F−Mj−fj, that is, when there is a feature subset Mj, feature fj does not contribute to classification. The redundancy feature based on the Markov blanket is defined as follows.A featurefj is redundant iff fj is weakly relevant and there is a Markov blanket in F.Because obtaining a feature’s Markov blanket is an NP-hard problem, the approximate Markov blanket method is usually used to eliminate redundant features in applications. A commonly used approximate Markov blanket is defined as follows.fj forms an approximate Markov blanket for fi iff Jfj,C≥Jfi,C and Jfj,fi≥Jfi,C, and J· is optional correlation measure.This approximation method takes the feature-class correlation and the feature-feature correlation as the solution condition of the Markov blanket at the same time, and the time complexity isONlogN. This can avoid enumerating all combinations of features under nonapproximate conditions. However, the use of this approximation method in practical applications may misjudge strongly relevant features as redundant features and eliminate them, which will cause the subset obtained by feature selection to lose part of the information needed for classification [32]. Therefore, this paper proposes an improved approximate Markov blanket method, which is defined as follows.fj forms an approximate Markov blanket for fi iff MICfj,C≥MICfi,C, MICfj,fi≥MICfi,C, and SUfj,fi>γ.In the formula, the value ofγ is in the range [0, 1], which is used to constrain the Markov blanket to contain the information amount of the eliminated feature. The larger the value of γ, the higher the feature-feature correlation of the eliminated features and the stronger the redundancy. This improvement can be explained by Figure 1 as follows. When eliminating redundant features, the feature-feature correlation consists of two parts: class-related (yellow parts) and class-independent (red parts). We impose a constraint through SU so that the deleted feature has high class-related rather than class-independent. The reason for not using the MIC as a constraint is its strong ability to mine the correlation between variables, and it may introduce more class-independent correlations into the results.Figure 1
Venn diagram showing the relationships among featurei, feature j, and class C.Through this improvement, it is possible to ensure that the deleted redundant features have high feature-feature correlation, thereby avoiding misjudgment of strongly relevant features and obtaining a feature set with better performance.


### 4.2. Algorithm

Based on the selected correlation measures and the improved approximate Markov blanket presented before, we develop a two-stage algorithm, named NPP-FS. Given a dataset withd features and a class C, the final output is a selected subset after two stages. The detailed process of the algorithm is shown in Figure 2.Figure 2
NPP-FS algorithm.The first stage uses the original dataset as input for relevance analysis (lines 5–11). First, the MIC is used to calculate the correlation of each feature, and then the feature correlation ranking method is used to eliminate some features. In this process, set a thresholdσ with a value of [0, 1], add all the features with a feature-class correlation higher than σ to an empty set Slist′, and finally arrange the features in Slist′ in descending order of the feature-class correlation to obtain the relevance analysis subset. The feature of the first stage is that only the correlation of a single feature is considered, and the time complexity is low, but the redundant features in the dataset cannot be eliminated. The features in the relevance analysis subset should be strongly correlated or weakly correlated, and the features whose feature-class correlation is less than σ are regarded as irrelevant features and are eliminated in relevance analysis. Therefore, when σ takes different values, a relevance analysis subset with different dimensions can be obtained, which also determines the minimum feature-class correlation of the features in the final subset that can be selected by the NPP-FS algorithm.The second stage uses a subset of relevance analysis as input for redundancy analysis (lines 12–22). Based on the feature correlation ranking results, the redundancy of features is evaluated through MIC and SU, and then the improved approximate Markov blanket is used to eliminate redundant features. The process of redundancy analysis includes a nested loop. The inner loop applies an improved approximate Markov blanket to the featurefj and all features in the current set whose ranking is lower than fj under the condition of a given γ threshold. Only one feature is judged at a time. If the judgment condition is met, fi is regarded as a redundant feature and eliminated from the current set. After completing the inner loop, the outer loop uses the next feature of fj in the current set as the new fj. The outer loop ends when there is no new fj. The feature set at this time is the final subset obtained by the NPP-FS algorithm. The feature of the second stage is that the relevance and redundancy of features are comprehensively considered, and finally a feature selection subset with higher relevance and lower redundancy can be obtained.Combining the first stage and second stage, it can be seen that under the condition of a given relevance analysis subset, the result of redundancy analysis is only affected by the value ofγ. When the σ value is fixed, the dimension of the final feature selection subset can be further controlled by selecting different γ values. Therefore, in practical applications, the values of σ and γ can be adjusted at the same time to generate feature selection subsets composed of different features and having lower dimensions to adapt to different datasets and classification problems.


## 4.1. Improved Approximate Markov Blanket

Markov blanket is a method proposed by Koller to eliminate redundant features, and its definition is as follows [31].Mj does not contain fj, and we say that Mj is a Markov blanket for fj iff PF−Mj−fj,C|fj,Mj=PF−Mj−fj,C|Mj.The meaning of the above formula is thatMj contains all the information of fj about C and F−Mj−fj, that is, when there is a feature subset Mj, feature fj does not contribute to classification. The redundancy feature based on the Markov blanket is defined as follows.A featurefj is redundant iff fj is weakly relevant and there is a Markov blanket in F.Because obtaining a feature’s Markov blanket is an NP-hard problem, the approximate Markov blanket method is usually used to eliminate redundant features in applications. A commonly used approximate Markov blanket is defined as follows.fj forms an approximate Markov blanket for fi iff Jfj,C≥Jfi,C and Jfj,fi≥Jfi,C, and J· is optional correlation measure.This approximation method takes the feature-class correlation and the feature-feature correlation as the solution condition of the Markov blanket at the same time, and the time complexity isONlogN. This can avoid enumerating all combinations of features under nonapproximate conditions. However, the use of this approximation method in practical applications may misjudge strongly relevant features as redundant features and eliminate them, which will cause the subset obtained by feature selection to lose part of the information needed for classification [32]. Therefore, this paper proposes an improved approximate Markov blanket method, which is defined as follows.fj forms an approximate Markov blanket for fi iff MICfj,C≥MICfi,C, MICfj,fi≥MICfi,C, and SUfj,fi>γ.In the formula, the value ofγ is in the range [0, 1], which is used to constrain the Markov blanket to contain the information amount of the eliminated feature. The larger the value of γ, the higher the feature-feature correlation of the eliminated features and the stronger the redundancy. This improvement can be explained by Figure 1 as follows. When eliminating redundant features, the feature-feature correlation consists of two parts: class-related (yellow parts) and class-independent (red parts). We impose a constraint through SU so that the deleted feature has high class-related rather than class-independent. The reason for not using the MIC as a constraint is its strong ability to mine the correlation between variables, and it may introduce more class-independent correlations into the results.Figure 1
Venn diagram showing the relationships among featurei, feature j, and class C.Through this improvement, it is possible to ensure that the deleted redundant features have high feature-feature correlation, thereby avoiding misjudgment of strongly relevant features and obtaining a feature set with better performance.


## 4.2. Algorithm

Based on the selected correlation measures and the improved approximate Markov blanket presented before, we develop a two-stage algorithm, named NPP-FS. Given a dataset withd features and a class C, the final output is a selected subset after two stages. The detailed process of the algorithm is shown in Figure 2.Figure 2
NPP-FS algorithm.The first stage uses the original dataset as input for relevance analysis (lines 5–11). First, the MIC is used to calculate the correlation of each feature, and then the feature correlation ranking method is used to eliminate some features. In this process, set a thresholdσ with a value of [0, 1], add all the features with a feature-class correlation higher than σ to an empty set Slist′, and finally arrange the features in Slist′ in descending order of the feature-class correlation to obtain the relevance analysis subset. The feature of the first stage is that only the correlation of a single feature is considered, and the time complexity is low, but the redundant features in the dataset cannot be eliminated. The features in the relevance analysis subset should be strongly correlated or weakly correlated, and the features whose feature-class correlation is less than σ are regarded as irrelevant features and are eliminated in relevance analysis. Therefore, when σ takes different values, a relevance analysis subset with different dimensions can be obtained, which also determines the minimum feature-class correlation of the features in the final subset that can be selected by the NPP-FS algorithm.The second stage uses a subset of relevance analysis as input for redundancy analysis (lines 12–22). Based on the feature correlation ranking results, the redundancy of features is evaluated through MIC and SU, and then the improved approximate Markov blanket is used to eliminate redundant features. The process of redundancy analysis includes a nested loop. The inner loop applies an improved approximate Markov blanket to the featurefj and all features in the current set whose ranking is lower than fj under the condition of a given γ threshold. Only one feature is judged at a time. If the judgment condition is met, fi is regarded as a redundant feature and eliminated from the current set. After completing the inner loop, the outer loop uses the next feature of fj in the current set as the new fj. The outer loop ends when there is no new fj. The feature set at this time is the final subset obtained by the NPP-FS algorithm. The feature of the second stage is that the relevance and redundancy of features are comprehensively considered, and finally a feature selection subset with higher relevance and lower redundancy can be obtained.Combining the first stage and second stage, it can be seen that under the condition of a given relevance analysis subset, the result of redundancy analysis is only affected by the value ofγ. When the σ value is fixed, the dimension of the final feature selection subset can be further controlled by selecting different γ values. Therefore, in practical applications, the values of σ and γ can be adjusted at the same time to generate feature selection subsets composed of different features and having lower dimensions to adapt to different datasets and classification problems.


## 5. Empirical Study

### 5.1. Data Sources

Due to irresistible reasons, it is very difficult to obtain fault data in nuclear power plants, so the amount of fault data that can be collected is limited [33]. To verify the effectiveness of the NPP-FS algorithm and apply it to the classification of steady conditions and typical accident conditions, 12 conditions were simulated by nuclear power plant simulation software [34]. It generated a total of 10800 sample data, and each sample point includes 90 parameters (not considering time series). The dataset needed for the experiment can be constructed from the generated sample data. Table 1 lists the detailed information of the sample data.Table 1
Original data.
NumberConditionInitial conditionCriteriaSample size150% power——900275% power——9003100% power——9004Loss of coolant accident (hot leg)100% power2/10/100 cm2300/300/3005Loss of coolant accident (cold leg)100% power2/10/100 cm2300/300/3006Steam generator A tube rupture100% power0.5/1/2 (∗100%)300/300/3007Steam generator B tube rupture100% power0.5/1/2 (∗100%)300/300/3008Steam line break inside containment100% power25/50/75 cm2300/300/3009Steam line break outside containment100% power25/50/75 cm2300/300/30010Loss of flow (locked rotor)50%/75%/100% power—300/300/30011Turbine trip50%/75%/100% power—300/300/30012Loss of feedwater accident50%/75%/100% power—300/300/300Total10800


### 5.2. Correlation Measure Verification

This experiment is mainly used to verify the validity of the MIC as a correlation measure of nuclear power plant operating data. The experimental program is shown in Figure3.Figure 3
Program of correlation measure verification experiment.First, we construct the experimental dataset shown in Table2 according to the original data in Table 1. To reflect the advantage of the MIC to evaluate the correlation, the SU is used for comparative experiments and combined with professional knowledge to evaluate the use of the MIC as a correlation measure of nuclear power plant operating data.Table 2
Correlation measure verification experiment data.
NumberClassesData number in Table1Class label13{1} {2} {3}50% power/75% power/100% power22{1, 2, 3} {4, 5}Normal condition/loss of coolant accident32{1, 2, 3} {12}Normal condition/loss of feedwater42{1, 2, 3} {10}Normal condition/loss of flow (locked rotor)52{1, 2, 3} {6, 7}Normal condition/steam generator tube ruptureThe MIC is calculated by the minepy module [35]. When the features are continuous data, the calculation of SU is discretized by the histogram method [36]. The experimental results are retained to 6 decimal places.Figure4 shows the calculation results of feature-class correlation, and the meaning of the abbreviations can be found in [34]. In experiments 1–5, the average value of the MIC is higher than the average value of the SU. In experiment 1, the difference between the MIC and the SU is the smallest, which is 0.236. In experiment 2, the difference between the two is the largest, which is 0.437. This shows that in the nuclear power plant operating data, the MIC is stronger than the SU as a whole to measure the correlation. But when the calculated value is less than 0.2, the difference between the calculation results of the two correlation measures is small, indicating that the performance of the two indicators is relatively close at this time. In addition, the situation where the two measures are 0 is the same, indicating that the two measures have the same effect in identifying features that are completely unrelated to classification. The above analysis shows that the results of calculating the operating data of nuclear power plant by the two measures are different, and the order of the features according to the number of the correlation measure is also inconsistent.Figure 4
Results of correlation measure verification experiment. (a)–(e) represent experiments 1 to 5, and the dotted line represents the average value.
(a)(b)(c)(d)(e)The mechanism of different operating conditions in experiments 1–5 is clear. Combined with professional knowledge, it can be found that the use of SU to evaluate feature-class correlation will assign lower values to some features that are more important for classification, such as TAVG, PSGA, and PSGB in experiment 1, P in experiment 2, WFWA and WFWB in experiment 3, WRCA and WRCB in experiment 4, and LVPZ in experiment 5.The reason for this phenomenon is illustrated in Figure5, which shows the TAVG and TBLD data contained in the class label “75% power” in experiment 1. It can be found from Figure 5 that the parameters of the feature TAVG fluctuate around the setting value, while the parameters of the TBLD have a fixed value. Combining Figure 4, it can be seen that when the operating parameters of a feature fluctuate in the data under the same class label, the SU cannot accurately identify its correlation, but this type of feature is widely present in the operating data of nuclear power plants.Figure 5
Data with the class label of “75% power” in experiment 1.Based on the above comparative analysis, when the MIC is used to evaluate the correlation, its ability to mine the correlation is overall stronger, and the relative value of different features is also in good agreement with the professional knowledge.


### 5.3. Sensitivity Analysis Experiment

The NPP-FS algorithm contains two adjustable parameters,σ and γ. σ is used to delete irrelevant features, and γ is used as a constraint to approximate the Markov blanket to avoid eliminating strongly relevant features. This experiment mainly explores the influence of the different values of these two parameters on the results of the NPP-FS algorithm. The experimental program is shown in Figure 6.Figure 6
Program of sensitivity analysis experiment.The experiment uses the method of establishing a classifier model to evaluate the feature selection results of the NPP-FS algorithm when different parameters are selected. First, we construct the experimental dataset shown in Table3 according to the simulated data in Table 1. In data preprocessing, the NPP-FS algorithm is first used for feature selection, and the grid search method shown in Figure 6 is used to obtain the feature selection results when different parameter values are taken. After the experimental dataset obtains the feature selection subset by the NPP-FS algorithm, to avoid the inconsistency of the feature value range from affecting the classifier, the data are normalized. Since the maximum and minimum values of each feature in the dataset are known, the following formula is used for normalization:(8)X=x−xminxmax−xmin.Table 3
Sensitivity analysis experiment data.
NumberClassesSamplesData number in Table1124500{1, 2, 3} {4, 5}224500{1, 2, 3} {6, 7}321800{4} {5}423600{4, 5} {6, 7}565400{4}{5}{6}{7}{8}{9}61210800{1}{2}{3}{4}{5}{6}{7}{8}{9}{10}{11}{12}After data preprocessing is completed, three classifiers of logistic regression (LR) [37], support vector machine (linear kernel, SVM) [38], and k nearest neighbors (KNN) [39] are used for evaluating the selected subset of features. The evaluation of the classifier uses the average of 10-fold cross-validation accuracy. Finally, through the performance of the classifier on different feature selection subsets, the results of the NPP-FS algorithm in different parameter values are evaluated.Figure7 shows how the accuracy of the classifier varies with σ and γ. The results show that the accuracy of the nuclear power plant operating data on the three classifiers is different. This is caused by the different calculation principles of the classifier. On the same experimental dataset, the results of LR and SVM are relatively consistent, and the results of the two and KNN are different.Figure 7
Results of the sensitivity analysis experiment. (a)–(f) represent experiments 1 to 6 with (i) LR, (ii) SVM, and (iii) KNN.
(a)(b)(c)(d)(e)(f)


#### 5.3.1. The Results of LR and SVM

The classification accuracy obtained by the sensitivity analysis experiment using LR and SVM shows an obvious partition phenomenon. In each graph, there is a transition zone with a relatively large accuracy gradient. According to the theory of the NPP-FS algorithm, in the relevance analysis, irrelevant, weakly relevant, and strongly relevant features will be eliminated in turn asσ increases. In the redundancy analysis, with the increase of γ, there is a tendency to keep the strongly relevant and weakly relevant features in the feature subset in turn. Therefore, the shape of the transition zone is the result of the combined effect of σ and γ. When the parameter values in the vicinity of the transition zone change, the strongly relevant features will be eliminated or remain in the feature subset, resulting in a relatively large gradient of accuracy in the transition zone.According to the NPP-FS algorithm shown in Figure8, the dimensionality of the subset generated by σ and γ changes can be further found, that is, the results of LR and SVM have a strong correlation with the change of the feature selection subset dimension with the parameters. σ with higher accuracy should be taken in the σ interval smaller than the transition zone, but when σ is less than 0.2, the change of the feature selection subset dimension has no obvious effect on the accuracy. The value of γ to obtain results with higher accuracy is usually greater than 0.4. However, when σ∈0.1,0.3 and γ∈0,0.4, affected by the approximate Markov blanket, the dimension of the subset of experiment 4 first increases and then decreases with the increase of the value of γ. This also shows that the improved approximate Markov blanket can effectively alleviate the problem of incorrectly eliminating nonredundant features.Figure 8
The reciprocal of the subset dimension changes with the parameter value. (a)–(f) represent experiments 1 to 6.
(a)(b)(c)(d)(e)(f)


#### 5.3.2. The Results of KNN

According to the results shown in Figure7, KNN has better adaptability to the classification of operating conditions of nuclear power plants and can achieve higher accuracy in a larger parameter range. In binary classification, the accuracy of experiments 1 and 4 is above 99% in the full parameter experiment range; when σ>0.1, the accuracy of experiment 2 is above 94%; experiment 3 has an accuracy higher than 96% in the full parameter experiment range. In combination with Figure 8, it can be found that in binary classification, the dimensionality of the feature selection subset has little effect on the accuracy of KNN, and only a few features are needed to obtain a higher classification accuracy. The results of experiments 5 and 6 show that in the multiclassification problem, the accuracy of KNN is also strongly related to the change of the feature selection subset dimension with parameters, but the range of parameters with higher accuracy is larger than that of LR and SVM.


### 5.4. Comparative Experiment and Analysis

To reflect the advantages of the NPP-FS, the same dataset and experimental program as mentioned in Section5.3 are used to compare the NPP-FS algorithm with the feature selection algorithms CFS, mRMR, and FCBF. Using the data in Table 3 as input, we run the original feature set (Fullset) and all four feature selection algorithms, NPP-FS, CFS, mRMR, FCBF, respectively, in the three classifiers of LR, SVM, and KNN. The normalization method adopts equation (8), and the way to evaluate models is the average of 10-fold cross-validation. We use the sklearn library to build these models with default parameters, which can avoid the uncertain effects caused by parameter tuning. Tables 4–6, respectively, show the classification accuracy and the number of selected features (round half to integer) in the three classifiers of LR, SVM, and KNN in the above five cases.Table 4
Comparison of feature selection algorithms under LR classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)198.62 ± 0.55 (90)96.84 ± 0.89 (2)96.42 ± 0.86 (2)98.62 ± 0.67 (2)96.42 ± 0.62 (2)2100.00 ± 0.00 (90)100.00 ± 0.00 (6)97.49 ± 0.59 (6)100.00 ± 0.00 (3)92.47 ± 0.89 (2)398.89 ± 0.93 (90)96.94 ± 1.52 (3)98.22 ± 0.10 (4)83.17 ± 1.74 (20)52.72 ± 2.49 (2)499.30 ± 0.53 (90)99.53 ± 0.34 (2)98.92 ± 0.53 (7)98.92 ± 0.50 (2)98.92 ± 0.47 (3)597.57 ± 0.87 (90)96.44 ± 0.62 (17)86.52 ± 1.00 (11)96.29 ± 0.74 (20)67.41 ± 1.44 (4)698.34 ± 0.45 (90)96.24 ± 0.65 (18)93.94 ± 0.67 (17)81.48 ± 1.01 (30)70.67 ± 0.45 (6)Average98.79 ± 0.56 (90)97.67 ± 0.67 (8)95.25 ± 0.63 (8)93.08 ± 0.78 (13)79.77 ± 1.06 (3)Table 5
Comparison of feature selection algorithms under SVM classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)1100.00 ± 0.00 (90)98.42 ± 0.90 (2)96.42 ± 0.86 (2)98.62 ± 0.47 (2)96.42 ± 0.62 (2)2100.00 ± 0.00 (90)100.00 ± 0.00 (6)98.11 ± 0.60 (6)100.00 ± 0.00 (3)95.29 ± 0.92 (2)398.67 ± 1.00 (90)97.22 ± 1.52 (3)98.17 ± 0.07 (4)83.61 ± 2.29 (20)52.78 ± 2.43 (2)4100.00 ± 0.00 (90)99.47 ± 0.22 (2)98.92 ± 0.53 (7)98.92 ± 0.50 (2)98.92 ± 0.47 (3)599.43 ± 0.28 (90)96.44 ± 0.82 (12)91.19 ± 0.98 (11)97.07 ± 0.98 (15)70.33 ± 1.45 (4)699.54 ± 0.19 (90)97.33 ± 0.37 (21)96.19 ± 0.55 (17)82.72 ± 1.20 (30)70.35 ± 0.97 (6)Average99.61 ± 0.25 (90)98.15 ± 0.64 (8)96.50 ± 0.60 (8)93.49 ± 0.91 (12)80.68 ± 1.14 (3)Table 6
Comparison of feature selection algorithms under KNN classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)1100.00 ± 0.00 (90)99.78 ± 0.01 (1)98.60 ± 0.61 (2)98.64 ± 0.48 (2)96.42 ± 0.62 (2)299.93 ± 0.10 (90)99.96 ± 0.07 (1)99.96 ± 0.13 (3)100.00 ± 0.00 (3)99.98 ± 0.07 (2)399.44 ± 0.43 (90)99.83 ± 0.12 (6)99.50 ± 0.39 (5)95.89 ± 1.37 (4)81.94 ± 2.27 (2)4100.00 ± 0.00 (90)99.94 ± 0.01 (1)99.94 ± 0.11 (3)99.89 ± 0.18 (6)99.94 ± 0.11 (3)599.54 ± 0.35 (90)99.52 ± 0.19 (6)99.41 ± 0.26 (6)94.52 ± 1.03 (7)78.44 ± 0.74 (4)699.75 ± 0.12 (90)99.66 ± 0.23 (11)99.33 ± 0.22 (9)97.71 ± 0.35 (11)74.13 ± 0.80 (6)Average99.78 ± 0.17 (90)99.78 ± 0.11 (4)99.46 ± 0.29 (5)97.78 ± 0.57 (6)88.48 ± 0.77 (3)It can be seen from Table4 that the classification accuracy of NPP-FS on the LR model is lower than that of mRMR in experiment 1 and CFS in experiment 3, but the performance of NPP-FS is better than other algorithms in other experiments. The average accuracy of NPP-FS in six experiments is 2.42% higher than that of the CFS algorithm, 4.59% higher than that of the mRMR algorithm, and 17.9% higher than that of the FCBF algorithm. Although the average number of feature subsets generated by NPP-FS is larger than that of FCBF, NPP-FS has an obvious advantage in terms of classification accuracy. The results shown in Table 5 on the SVM classifier are relatively similar to those on the LR classifier. The classification accuracy of NPP-FS is slightly lower than that of mRMR in experiment 1 and experiment 5 and slightly lower than that of CFS in experiment 3, but in all other experiments, NPP-FS outperformed the other algorithms. The mean of the six experiments’ accuracy is 1.65% higher than that of CFS, 4.66% higher than that of mRMR, and 17.47% higher than that of FCBF. Similarly, although the NPP-FS algorithm produces a larger average number of feature subsets than FCBF in SVM, it has a remarkable advantage in terms of classification accuracy. As shown in Table 6, the results of NPP-FS, CFS, mRMR, and FCBF on the KNN classifier are better than those on LR and SVM classifiers overall. The accuracy of NPP-FS is slightly lower than that of FCBF in experiment 2, but in all other experiments, NPP-FS is superior to the rest of the algorithms. The average accuracy of NPP-FS in six experiments is 0.32% higher than that of the CFS algorithm, 2% higher than that of the mRMR algorithm, and 11.3% higher than that of the FCBF algorithm. The average number of NPP-FS feature subsets is the only one greater than the smallest FCBF among the four.According to Tables4–6, we can conclude that the overall performance of the NPP-FS algorithm is better than that of CFS, mRMR, and FCBF. This is made possible by the fact that NPP-FS obtains a subset of features that perform well on each experimental dataset. The remaining three feature selection algorithms suffer, to varying degrees, from the problem of making the model performance sharply decline, such as CFS in experiment 5, mRMR in experiment 3 and experiment 6, and FCBF in experiment 3, experiment 5, and experiment 6. The reasons for this phenomenon are explained below. The strong coupling between nuclear power plant operating data features is often complex, and at the same time, deterministic mathematical relationships and features with such relationships are difficult to identify whether they are redundant features by general feature selection algorithms. When these features contain information necessary for classification, the feature selection algorithm incorrectly removes them as redundant features. If these features are not relevant to the classification, the results are not influenced by this factor. NPP-FS uses the MIC to evaluate the correlation, which can effectively identify the complex nonlinear relationships in the nuclear power plant operating data. Meanwhile, the misjudgment of redundant features is mitigated by an approximate Markov blanket improved for nuclear power plant operating data. Therefore, the overall performance of NPP-FS is superior in the experimental dataset.


## 5.1. Data Sources

Due to irresistible reasons, it is very difficult to obtain fault data in nuclear power plants, so the amount of fault data that can be collected is limited [33]. To verify the effectiveness of the NPP-FS algorithm and apply it to the classification of steady conditions and typical accident conditions, 12 conditions were simulated by nuclear power plant simulation software [34]. It generated a total of 10800 sample data, and each sample point includes 90 parameters (not considering time series). The dataset needed for the experiment can be constructed from the generated sample data. Table 1 lists the detailed information of the sample data.Table 1
Original data.
NumberConditionInitial conditionCriteriaSample size150% power——900275% power——9003100% power——9004Loss of coolant accident (hot leg)100% power2/10/100 cm2300/300/3005Loss of coolant accident (cold leg)100% power2/10/100 cm2300/300/3006Steam generator A tube rupture100% power0.5/1/2 (∗100%)300/300/3007Steam generator B tube rupture100% power0.5/1/2 (∗100%)300/300/3008Steam line break inside containment100% power25/50/75 cm2300/300/3009Steam line break outside containment100% power25/50/75 cm2300/300/30010Loss of flow (locked rotor)50%/75%/100% power—300/300/30011Turbine trip50%/75%/100% power—300/300/30012Loss of feedwater accident50%/75%/100% power—300/300/300Total10800


## 5.2. Correlation Measure Verification

This experiment is mainly used to verify the validity of the MIC as a correlation measure of nuclear power plant operating data. The experimental program is shown in Figure3.Figure 3
Program of correlation measure verification experiment.First, we construct the experimental dataset shown in Table2 according to the original data in Table 1. To reflect the advantage of the MIC to evaluate the correlation, the SU is used for comparative experiments and combined with professional knowledge to evaluate the use of the MIC as a correlation measure of nuclear power plant operating data.Table 2
Correlation measure verification experiment data.
NumberClassesData number in Table1Class label13{1} {2} {3}50% power/75% power/100% power22{1, 2, 3} {4, 5}Normal condition/loss of coolant accident32{1, 2, 3} {12}Normal condition/loss of feedwater42{1, 2, 3} {10}Normal condition/loss of flow (locked rotor)52{1, 2, 3} {6, 7}Normal condition/steam generator tube ruptureThe MIC is calculated by the minepy module [35]. When the features are continuous data, the calculation of SU is discretized by the histogram method [36]. The experimental results are retained to 6 decimal places.Figure4 shows the calculation results of feature-class correlation, and the meaning of the abbreviations can be found in [34]. In experiments 1–5, the average value of the MIC is higher than the average value of the SU. In experiment 1, the difference between the MIC and the SU is the smallest, which is 0.236. In experiment 2, the difference between the two is the largest, which is 0.437. This shows that in the nuclear power plant operating data, the MIC is stronger than the SU as a whole to measure the correlation. But when the calculated value is less than 0.2, the difference between the calculation results of the two correlation measures is small, indicating that the performance of the two indicators is relatively close at this time. In addition, the situation where the two measures are 0 is the same, indicating that the two measures have the same effect in identifying features that are completely unrelated to classification. The above analysis shows that the results of calculating the operating data of nuclear power plant by the two measures are different, and the order of the features according to the number of the correlation measure is also inconsistent.Figure 4
Results of correlation measure verification experiment. (a)–(e) represent experiments 1 to 5, and the dotted line represents the average value.
(a)(b)(c)(d)(e)The mechanism of different operating conditions in experiments 1–5 is clear. Combined with professional knowledge, it can be found that the use of SU to evaluate feature-class correlation will assign lower values to some features that are more important for classification, such as TAVG, PSGA, and PSGB in experiment 1, P in experiment 2, WFWA and WFWB in experiment 3, WRCA and WRCB in experiment 4, and LVPZ in experiment 5.The reason for this phenomenon is illustrated in Figure5, which shows the TAVG and TBLD data contained in the class label “75% power” in experiment 1. It can be found from Figure 5 that the parameters of the feature TAVG fluctuate around the setting value, while the parameters of the TBLD have a fixed value. Combining Figure 4, it can be seen that when the operating parameters of a feature fluctuate in the data under the same class label, the SU cannot accurately identify its correlation, but this type of feature is widely present in the operating data of nuclear power plants.Figure 5
Data with the class label of “75% power” in experiment 1.Based on the above comparative analysis, when the MIC is used to evaluate the correlation, its ability to mine the correlation is overall stronger, and the relative value of different features is also in good agreement with the professional knowledge.


## 5.3. Sensitivity Analysis Experiment

The NPP-FS algorithm contains two adjustable parameters,σ and γ. σ is used to delete irrelevant features, and γ is used as a constraint to approximate the Markov blanket to avoid eliminating strongly relevant features. This experiment mainly explores the influence of the different values of these two parameters on the results of the NPP-FS algorithm. The experimental program is shown in Figure 6.Figure 6
Program of sensitivity analysis experiment.The experiment uses the method of establishing a classifier model to evaluate the feature selection results of the NPP-FS algorithm when different parameters are selected. First, we construct the experimental dataset shown in Table3 according to the simulated data in Table 1. In data preprocessing, the NPP-FS algorithm is first used for feature selection, and the grid search method shown in Figure 6 is used to obtain the feature selection results when different parameter values are taken. After the experimental dataset obtains the feature selection subset by the NPP-FS algorithm, to avoid the inconsistency of the feature value range from affecting the classifier, the data are normalized. Since the maximum and minimum values of each feature in the dataset are known, the following formula is used for normalization:(8)X=x−xminxmax−xmin.Table 3
Sensitivity analysis experiment data.
NumberClassesSamplesData number in Table1124500{1, 2, 3} {4, 5}224500{1, 2, 3} {6, 7}321800{4} {5}423600{4, 5} {6, 7}565400{4}{5}{6}{7}{8}{9}61210800{1}{2}{3}{4}{5}{6}{7}{8}{9}{10}{11}{12}After data preprocessing is completed, three classifiers of logistic regression (LR) [37], support vector machine (linear kernel, SVM) [38], and k nearest neighbors (KNN) [39] are used for evaluating the selected subset of features. The evaluation of the classifier uses the average of 10-fold cross-validation accuracy. Finally, through the performance of the classifier on different feature selection subsets, the results of the NPP-FS algorithm in different parameter values are evaluated.Figure7 shows how the accuracy of the classifier varies with σ and γ. The results show that the accuracy of the nuclear power plant operating data on the three classifiers is different. This is caused by the different calculation principles of the classifier. On the same experimental dataset, the results of LR and SVM are relatively consistent, and the results of the two and KNN are different.Figure 7
Results of the sensitivity analysis experiment. (a)–(f) represent experiments 1 to 6 with (i) LR, (ii) SVM, and (iii) KNN.
(a)(b)(c)(d)(e)(f)


### 5.3.1. The Results of LR and SVM

The classification accuracy obtained by the sensitivity analysis experiment using LR and SVM shows an obvious partition phenomenon. In each graph, there is a transition zone with a relatively large accuracy gradient. According to the theory of the NPP-FS algorithm, in the relevance analysis, irrelevant, weakly relevant, and strongly relevant features will be eliminated in turn asσ increases. In the redundancy analysis, with the increase of γ, there is a tendency to keep the strongly relevant and weakly relevant features in the feature subset in turn. Therefore, the shape of the transition zone is the result of the combined effect of σ and γ. When the parameter values in the vicinity of the transition zone change, the strongly relevant features will be eliminated or remain in the feature subset, resulting in a relatively large gradient of accuracy in the transition zone.According to the NPP-FS algorithm shown in Figure8, the dimensionality of the subset generated by σ and γ changes can be further found, that is, the results of LR and SVM have a strong correlation with the change of the feature selection subset dimension with the parameters. σ with higher accuracy should be taken in the σ interval smaller than the transition zone, but when σ is less than 0.2, the change of the feature selection subset dimension has no obvious effect on the accuracy. The value of γ to obtain results with higher accuracy is usually greater than 0.4. However, when σ∈0.1,0.3 and γ∈0,0.4, affected by the approximate Markov blanket, the dimension of the subset of experiment 4 first increases and then decreases with the increase of the value of γ. This also shows that the improved approximate Markov blanket can effectively alleviate the problem of incorrectly eliminating nonredundant features.Figure 8
The reciprocal of the subset dimension changes with the parameter value. (a)–(f) represent experiments 1 to 6.
(a)(b)(c)(d)(e)(f)


### 5.3.2. The Results of KNN

According to the results shown in Figure7, KNN has better adaptability to the classification of operating conditions of nuclear power plants and can achieve higher accuracy in a larger parameter range. In binary classification, the accuracy of experiments 1 and 4 is above 99% in the full parameter experiment range; when σ>0.1, the accuracy of experiment 2 is above 94%; experiment 3 has an accuracy higher than 96% in the full parameter experiment range. In combination with Figure 8, it can be found that in binary classification, the dimensionality of the feature selection subset has little effect on the accuracy of KNN, and only a few features are needed to obtain a higher classification accuracy. The results of experiments 5 and 6 show that in the multiclassification problem, the accuracy of KNN is also strongly related to the change of the feature selection subset dimension with parameters, but the range of parameters with higher accuracy is larger than that of LR and SVM.


## 5.3.1. The Results of LR and SVM

The classification accuracy obtained by the sensitivity analysis experiment using LR and SVM shows an obvious partition phenomenon. In each graph, there is a transition zone with a relatively large accuracy gradient. According to the theory of the NPP-FS algorithm, in the relevance analysis, irrelevant, weakly relevant, and strongly relevant features will be eliminated in turn asσ increases. In the redundancy analysis, with the increase of γ, there is a tendency to keep the strongly relevant and weakly relevant features in the feature subset in turn. Therefore, the shape of the transition zone is the result of the combined effect of σ and γ. When the parameter values in the vicinity of the transition zone change, the strongly relevant features will be eliminated or remain in the feature subset, resulting in a relatively large gradient of accuracy in the transition zone.According to the NPP-FS algorithm shown in Figure8, the dimensionality of the subset generated by σ and γ changes can be further found, that is, the results of LR and SVM have a strong correlation with the change of the feature selection subset dimension with the parameters. σ with higher accuracy should be taken in the σ interval smaller than the transition zone, but when σ is less than 0.2, the change of the feature selection subset dimension has no obvious effect on the accuracy. The value of γ to obtain results with higher accuracy is usually greater than 0.4. However, when σ∈0.1,0.3 and γ∈0,0.4, affected by the approximate Markov blanket, the dimension of the subset of experiment 4 first increases and then decreases with the increase of the value of γ. This also shows that the improved approximate Markov blanket can effectively alleviate the problem of incorrectly eliminating nonredundant features.Figure 8
The reciprocal of the subset dimension changes with the parameter value. (a)–(f) represent experiments 1 to 6.
(a)(b)(c)(d)(e)(f)


## 5.3.2. The Results of KNN

According to the results shown in Figure7, KNN has better adaptability to the classification of operating conditions of nuclear power plants and can achieve higher accuracy in a larger parameter range. In binary classification, the accuracy of experiments 1 and 4 is above 99% in the full parameter experiment range; when σ>0.1, the accuracy of experiment 2 is above 94%; experiment 3 has an accuracy higher than 96% in the full parameter experiment range. In combination with Figure 8, it can be found that in binary classification, the dimensionality of the feature selection subset has little effect on the accuracy of KNN, and only a few features are needed to obtain a higher classification accuracy. The results of experiments 5 and 6 show that in the multiclassification problem, the accuracy of KNN is also strongly related to the change of the feature selection subset dimension with parameters, but the range of parameters with higher accuracy is larger than that of LR and SVM.


## 5.4. Comparative Experiment and Analysis

To reflect the advantages of the NPP-FS, the same dataset and experimental program as mentioned in Section5.3 are used to compare the NPP-FS algorithm with the feature selection algorithms CFS, mRMR, and FCBF. Using the data in Table 3 as input, we run the original feature set (Fullset) and all four feature selection algorithms, NPP-FS, CFS, mRMR, FCBF, respectively, in the three classifiers of LR, SVM, and KNN. The normalization method adopts equation (8), and the way to evaluate models is the average of 10-fold cross-validation. We use the sklearn library to build these models with default parameters, which can avoid the uncertain effects caused by parameter tuning. Tables 4–6, respectively, show the classification accuracy and the number of selected features (round half to integer) in the three classifiers of LR, SVM, and KNN in the above five cases.Table 4
Comparison of feature selection algorithms under LR classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)198.62 ± 0.55 (90)96.84 ± 0.89 (2)96.42 ± 0.86 (2)98.62 ± 0.67 (2)96.42 ± 0.62 (2)2100.00 ± 0.00 (90)100.00 ± 0.00 (6)97.49 ± 0.59 (6)100.00 ± 0.00 (3)92.47 ± 0.89 (2)398.89 ± 0.93 (90)96.94 ± 1.52 (3)98.22 ± 0.10 (4)83.17 ± 1.74 (20)52.72 ± 2.49 (2)499.30 ± 0.53 (90)99.53 ± 0.34 (2)98.92 ± 0.53 (7)98.92 ± 0.50 (2)98.92 ± 0.47 (3)597.57 ± 0.87 (90)96.44 ± 0.62 (17)86.52 ± 1.00 (11)96.29 ± 0.74 (20)67.41 ± 1.44 (4)698.34 ± 0.45 (90)96.24 ± 0.65 (18)93.94 ± 0.67 (17)81.48 ± 1.01 (30)70.67 ± 0.45 (6)Average98.79 ± 0.56 (90)97.67 ± 0.67 (8)95.25 ± 0.63 (8)93.08 ± 0.78 (13)79.77 ± 1.06 (3)Table 5
Comparison of feature selection algorithms under SVM classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)1100.00 ± 0.00 (90)98.42 ± 0.90 (2)96.42 ± 0.86 (2)98.62 ± 0.47 (2)96.42 ± 0.62 (2)2100.00 ± 0.00 (90)100.00 ± 0.00 (6)98.11 ± 0.60 (6)100.00 ± 0.00 (3)95.29 ± 0.92 (2)398.67 ± 1.00 (90)97.22 ± 1.52 (3)98.17 ± 0.07 (4)83.61 ± 2.29 (20)52.78 ± 2.43 (2)4100.00 ± 0.00 (90)99.47 ± 0.22 (2)98.92 ± 0.53 (7)98.92 ± 0.50 (2)98.92 ± 0.47 (3)599.43 ± 0.28 (90)96.44 ± 0.82 (12)91.19 ± 0.98 (11)97.07 ± 0.98 (15)70.33 ± 1.45 (4)699.54 ± 0.19 (90)97.33 ± 0.37 (21)96.19 ± 0.55 (17)82.72 ± 1.20 (30)70.35 ± 0.97 (6)Average99.61 ± 0.25 (90)98.15 ± 0.64 (8)96.50 ± 0.60 (8)93.49 ± 0.91 (12)80.68 ± 1.14 (3)Table 6
Comparison of feature selection algorithms under KNN classifier.
NumberFullset (%)NPP-FS (%)CFS (%)mRMR (%)FCBF (%)1100.00 ± 0.00 (90)99.78 ± 0.01 (1)98.60 ± 0.61 (2)98.64 ± 0.48 (2)96.42 ± 0.62 (2)299.93 ± 0.10 (90)99.96 ± 0.07 (1)99.96 ± 0.13 (3)100.00 ± 0.00 (3)99.98 ± 0.07 (2)399.44 ± 0.43 (90)99.83 ± 0.12 (6)99.50 ± 0.39 (5)95.89 ± 1.37 (4)81.94 ± 2.27 (2)4100.00 ± 0.00 (90)99.94 ± 0.01 (1)99.94 ± 0.11 (3)99.89 ± 0.18 (6)99.94 ± 0.11 (3)599.54 ± 0.35 (90)99.52 ± 0.19 (6)99.41 ± 0.26 (6)94.52 ± 1.03 (7)78.44 ± 0.74 (4)699.75 ± 0.12 (90)99.66 ± 0.23 (11)99.33 ± 0.22 (9)97.71 ± 0.35 (11)74.13 ± 0.80 (6)Average99.78 ± 0.17 (90)99.78 ± 0.11 (4)99.46 ± 0.29 (5)97.78 ± 0.57 (6)88.48 ± 0.77 (3)It can be seen from Table4 that the classification accuracy of NPP-FS on the LR model is lower than that of mRMR in experiment 1 and CFS in experiment 3, but the performance of NPP-FS is better than other algorithms in other experiments. The average accuracy of NPP-FS in six experiments is 2.42% higher than that of the CFS algorithm, 4.59% higher than that of the mRMR algorithm, and 17.9% higher than that of the FCBF algorithm. Although the average number of feature subsets generated by NPP-FS is larger than that of FCBF, NPP-FS has an obvious advantage in terms of classification accuracy. The results shown in Table 5 on the SVM classifier are relatively similar to those on the LR classifier. The classification accuracy of NPP-FS is slightly lower than that of mRMR in experiment 1 and experiment 5 and slightly lower than that of CFS in experiment 3, but in all other experiments, NPP-FS outperformed the other algorithms. The mean of the six experiments’ accuracy is 1.65% higher than that of CFS, 4.66% higher than that of mRMR, and 17.47% higher than that of FCBF. Similarly, although the NPP-FS algorithm produces a larger average number of feature subsets than FCBF in SVM, it has a remarkable advantage in terms of classification accuracy. As shown in Table 6, the results of NPP-FS, CFS, mRMR, and FCBF on the KNN classifier are better than those on LR and SVM classifiers overall. The accuracy of NPP-FS is slightly lower than that of FCBF in experiment 2, but in all other experiments, NPP-FS is superior to the rest of the algorithms. The average accuracy of NPP-FS in six experiments is 0.32% higher than that of the CFS algorithm, 2% higher than that of the mRMR algorithm, and 11.3% higher than that of the FCBF algorithm. The average number of NPP-FS feature subsets is the only one greater than the smallest FCBF among the four.According to Tables4–6, we can conclude that the overall performance of the NPP-FS algorithm is better than that of CFS, mRMR, and FCBF. This is made possible by the fact that NPP-FS obtains a subset of features that perform well on each experimental dataset. The remaining three feature selection algorithms suffer, to varying degrees, from the problem of making the model performance sharply decline, such as CFS in experiment 5, mRMR in experiment 3 and experiment 6, and FCBF in experiment 3, experiment 5, and experiment 6. The reasons for this phenomenon are explained below. The strong coupling between nuclear power plant operating data features is often complex, and at the same time, deterministic mathematical relationships and features with such relationships are difficult to identify whether they are redundant features by general feature selection algorithms. When these features contain information necessary for classification, the feature selection algorithm incorrectly removes them as redundant features. If these features are not relevant to the classification, the results are not influenced by this factor. NPP-FS uses the MIC to evaluate the correlation, which can effectively identify the complex nonlinear relationships in the nuclear power plant operating data. Meanwhile, the misjudgment of redundant features is mitigated by an approximate Markov blanket improved for nuclear power plant operating data. Therefore, the overall performance of NPP-FS is superior in the experimental dataset.


## 6. Conclusion

In this study, we propose a novel correlation-based feature selection algorithm for solving the problem of poor performance in identifying redundant features when the existing correlation-based feature selection algorithm analyzes nuclear power plant operating data. We propose the MIC as a correlation measure for the characteristics of nuclear power plant operating data and conduct correlation analysis experiments on the MIC and SU by combining professional knowledge. The results of this section show that the MIC is more applicable to the nuclear power plant operating data. In addition, we purposefully improved an approximate Markov blanket to enable the task of eliminating redundant features of nuclear power plant operating data under a given constraint. Then, we demonstrate the validity of the proposed theory and method through parametric sensitivity analysis experiments. Finally, we compare the performance of the proposed algorithm with several typical correlation-based feature selection algorithms. The results show that the proposed algorithm performs better than the conventional algorithm.Our proposed approach provides a general dimensionality reduction method for the application of machine learning techniques on nuclear power plant operating data. It can generate a feature-selected subset with good classification performance from labeled data under appropriate given parameters, resulting in a remarkable reduction of feature dimensionality, thus improving the computational efficiency and generalization ability of the model. However, there are two points to note in the application of this algorithm. (1) The MIC is less efficient to calculate compared to the traditional correlation measure. We can improve the efficiency of this algorithm by using SU to preprocess irrelevant features based on the characteristics that the MIC and SU respond consistently to irrelevant features. (2) The sensitivity of the two parameters of the algorithm is poorly generalized across different datasets, and the parameters still need to be selected according to the specific dataset and classifier. When applying this algorithm, it is recommended to sample the data with class labels into a small sample dataset and then perform feature selection.There are several topics for further focus in the future. First, it would be interesting to explore the performance of additional correlation measures on nuclear power plant operating data and methods for evaluating that performance. Second, the proposed approach can be combined with association rules and causal analysis in the field of nuclear power plants for studies such as anomaly detection.



---

*Source: 9994340-2021-08-29.xml*