Industrial data semi-supervised feature selection method based on granular fuzzy granular entropy

Abstract

This invention discloses a semi-supervised feature selection method for industrial data based on fuzzy sphere entropy. First, it acquires status monitoring data from multiple sensors of industrial equipment to construct a semi-supervised monitoring dataset containing labeled and unlabeled samples. Then, it divides the data into spheres based on the local structure and nearest neighbor relationships of the spheres, achieving adaptive sphere splitting through sphere purity gain. Further, it combines sample nearest neighbors and sphere nearest neighbors to propagate category information from labeled data to unlabeled data, constructing sphere labeled distribution data. Subsequently, it measures the importance of industrial monitoring features based on fuzzy sphere entropy. Finally, it inputs the selected monitoring features into an equipment fault status identification model to achieve industrial equipment operating status identification. This invention can effectively utilize the local structure of data even when label information is partially missing, improving the efficiency of industrial equipment fault diagnosis and the stability of status identification.

Description

Technical Field

[0001] This invention relates to feature selection methods, specifically a semi-supervised feature selection method for industrial data based on granular fuzzy entropy. Background Technology

[0002] In applications such as industrial equipment condition monitoring, fault diagnosis, and intelligent manufacturing, a large number of sensors are typically used to collect multi-source monitoring data such as vibration, temperature, current, and pressure during equipment operation in real time. Because industrial monitoring data is generally characterized by high dimensionality, strong coupling, nonlinearity, and redundancy, directly using raw data for model training not only increases computational complexity but also easily leads to a decrease in model generalization ability. Therefore, feature selection, as a key preprocessing technique in industrial data analysis, can filter out key features with high discriminative power and representativeness from the original high-dimensional feature space. This reduces data dimensionality and computational costs while improving the accuracy and stability of subsequent fault identification and condition classification models.

[0003] Most existing feature selection methods rely on training samples possessing complete labeled information. However, in real-world industrial scenarios, due to factors such as complex equipment operating conditions, high costs of manual labeling, and scarcity of fault samples, a large amount of industrial monitoring data often contains only a small number of labeled samples, while the vast majority of samples remain unlabeled, thus creating a semi-supervised data environment. Under conditions of missing labeled information, traditional supervised feature selection methods struggle to fully utilize the potential structural information in unlabeled samples, leading to a decrease in the discriminative power and stability of the obtained feature subset.

[0004] To address the aforementioned issues, semi-supervised feature selection methods utilize data distribution information from both labeled and unlabeled samples to effectively screen key features. However, industrial monitoring data typically exhibits complex nonlinear distribution structures and local clustering characteristics. Effectively characterizing the data's intrinsic structure and achieving reliable label propagation remains a critical technical challenge in the field of semi-supervised feature selection. Failure to accurately describe the local and global structural relationships of the data can easily lead to the accumulation of label propagation errors, thereby affecting the feature evaluation results.

[0005] Particle-sphere computation, as a multi-granularity data representation method, can uniformly describe the local neighborhood relationships and overall distribution characteristics of data by constructing particle-sphere structures at different scales. Compared with traditional sample-level processing methods, particle-sphere structures can effectively reduce data complexity and enhance the ability to express data structure information. Existing research shows that introducing particle-sphere computation into feature selection and pattern recognition tasks can improve algorithm efficiency while ensuring classification performance. Therefore, how to combine particle-sphere structures to achieve label propagation and construct a feature evaluation mechanism suitable for semi-supervised industrial monitoring data has significant research value and application significance. Summary of the Invention

[0006] The purpose of this invention is to address the problems of insufficient data structure utilization, poor reliability of label propagation, and low stability of feature evaluation in existing semi-supervised feature selection methods under the condition of missing labels in industrial monitoring data. This invention proposes a semi-supervised feature selection method for industrial data based on granular fuzzy entropy.

[0007] The technical solution adopted in this invention is:

[0008] A semi-supervised feature selection method for industrial data based on granular fuzzy entropy includes the following steps:

[0009] Step 1: Acquire condition monitoring data collected by multiple sensors during the operation of industrial equipment. This condition monitoring data includes a set of labeled monitoring samples and a set of unlabeled monitoring samples, thus constructing a semi-supervised industrial monitoring dataset. , It is a set of conditional attributes. It is a set of decision attributes. It is the attribute value range. yes and arrive The mapping function, the particle purity threshold Minimum number of samples for spheres The number of particles and the number of nearest neighbor particles in the sample are . The set of markers is ,in for The first in One tag;

[0010] Step 2: Construct an initial set of data spheres from the industrial monitoring data. The initial set of data spheres consists of all the monitoring samples.

[0011] Step 3: Divide the spheres in the initial sphere set into spheres. When a sphere contains a labeled monitoring sample, determine whether the current sphere meets the splitting condition based on the sphere purity. When a sphere contains only an unlabeled monitoring sample, calculate the sphere splitting gain based on the state category information of the nearest neighbor sphere, and determine whether the sphere should continue to split based on the splitting gain.

[0012] Step 4: Based on the set of spheres obtained in Step 3, for spheres containing labeled monitoring samples, calculate the class membership degree of the monitoring samples using the state category information of the labeled monitoring samples, and combine the labeled nearest neighbor monitoring samples to propagate the equipment state category information to the unlabeled monitoring samples, thereby obtaining the class membership degree of the monitoring samples and the class membership degree of the spheres. For spheres containing only unlabeled monitoring samples, estimate the state category membership degree of the current sphere using the class membership degree of its labeled nearest neighbor spheres.

[0013] Step 5: Based on the particle marker distribution data obtained in Step 4, calculate the fuzzy similarity between particles, and calculate the particle fuzzy mutual information and particle fuzzy conditional mutual information between industrial monitoring features and equipment status categories.

[0014] Step 6: Establish an industrial monitoring feature importance evaluation function. Taking into account the correlation between monitoring features and equipment status categories, the redundancy between monitoring features, and the irrelevance between monitoring features and equipment status categories, iteratively screen industrial monitoring features to obtain the optimal subset of monitoring features.

[0015] Step 7: Input the selected optimal subset of monitoring features into the industrial equipment fault status identification model to realize the identification of the operating status of industrial equipment.

[0016] When the granules in step three contain labeled monitoring samples, the purity of the equipment is considered. Generate using formula (1): (1)

[0017] in For the sample The corresponding marker, For granules The total number of samples in the sample. Indicates granules The middle mark is The number of samples.

[0018] In step three, when the pellets contain labeled monitoring samples, the pellet purity is... Generate using formula (2): (2)

[0019] The final purity of the pellets is taken as the maximum value among all equipment status categories.

[0020] Step 3 calculates the number of particles The set of nearest neighbor particles Generate using formula (3): (3)

[0021] in This represents the candidate set of nearest neighbor particles. For any particle in the set of neighboring particles, For granules The center, For granules The center, Indicates granules and pellets Euclidean distance between centers, set of neighboring spheres It is to find out and The closest Each ball.

[0022] In step three, for spheres containing only label-free monitoring samples, the purity of the device state is... Generate using formula (4): (4)

[0023] in For granules Equipment status category The membership degree is obtained through the propagation of the device state category of the nearest neighbor particle.

[0024] In step three, for granules containing only label-free monitoring samples, their purity is calculated using formula (5): (5)

[0025] The purity of the pellets is obtained by taking the highest purity value for the equipment condition category.

[0026] In step three, the granulocyte splitting judgment condition, which only includes unlabeled monitoring samples, is calculated using formula (6): (6)

[0027] in It is by Split sub-spheres Indicates the splitting of daughter grains Total number For granules The total number of monitored samples is used to determine the purity of the child particles after splitting. When the splitting gain is greater than 0, it indicates that the overall purity of the child particles is higher than that of the parent particles, and then particle splitting is performed.

[0028] In step four, the set of labeled nearest neighbors of unlabeled monitoring samples in a sphere containing labeled monitoring samples is calculated using formula (7): (7)

[0029] when hour, Represents the candidate set of nearest neighbor samples. For any sample in the set of labeled nearest neighbors, Represents the Euclidean distance between monitored samples, and the set of neighboring particles of a sample. It is to find the closest one to the currently monitored sample. It consists of 10 labeled monitoring samples.

[0030] In step four, for spheres containing labeled monitoring samples, the membership degree of the monitoring sample class is generated using formula (8): (8)

[0031] in This is an indicator function that takes the value 1 when the condition is true and 0 otherwise. , The normalized similarity weights for the monitoring samples , Label-free monitoring samples Compared with recently tagged monitoring neighbor samples Gaussian kernel similarity between them The sum of squares of the Euclidean distance. for and The standard deviation between them.

[0032] In step four, the membership degree of the granules in the labeled monitoring samples is generated using formula (9): (9)

[0033] in The weighted average of the class membership degrees of all monitored samples within the pellet is used as the class membership degree of the pellet equipment status.

[0034] In step four, for granules containing only unlabeled monitoring samples, their granule class membership degree is generated using formula (10): (10)

[0035] in, and They represent granules and balls respectively. and The center point, , , The normalized particle-sphere similarity weights, for and between standard deviations For granules With neighboring grains Gaussian kernel similarity between them The sum of squared Euclidean distances is used to propagate device status category information from labeled particles to unlabeled particles by weighted averaging of the membership degrees of labeled neighboring particles.

[0036] In step five, the similarity between any two spheres is generated using formula (11): (11)

[0037] in, .

[0038] Step five involves any industrial monitoring feature set. and device status category set The fuzzy interparticle information between particles and spheres is generated by formula (12): (12)

[0039] in The total number of balls. Indicates in the attribute set The complement of the fuzzy similarity class of particles and spheres is defined as follows: .

[0040] In step five, for any set of attributes Under the condition, equipment status category set and industrial monitoring characteristics The fuzzy particle conditional mutual information between particles is generated by formula (13): (13)

[0041] The granular fuzzy granular conditional mutual information is used to represent the new state classification information provided by candidate monitoring features under given feature subset conditions.

[0042] In step six, the particle entropy of the spherical fuzzy particle is generated by formula (14): (14)

[0043] in This represents the cardinality of granular-spherical fuzzy similarity classes under the industrial monitoring feature set.

[0044] In step six, the correlation between industrial monitoring features and equipment status categories is generated using formula (15): (15)

[0045] For the selected feature subset, correlation Mutual information between granular and spherical fuzzy particles This indicates that it reflects the characteristics of the candidate monitoring. For the set of tags The importance of.

[0046] The redundancy among industrial monitoring features in step six is ​​generated by formula (16): (16)

[0047] The redundancy between candidate monitoring features and the selected feature subset is measured by using the joint mutual information of fuzzy particles, and candidate monitoring features with lower overlap of classification information are selected first.

[0048] The independence between industrial monitoring features and equipment status categories in step six is ​​generated by formula (17): (17)

[0049] The irrelevance is used to represent the amount of information in candidate monitoring features that is irrelevant to the equipment status category.

[0050] In step six, when the feature subset is empty, the first monitoring feature is generated using formula (18): (18).

[0051] The importance of industrial monitoring features in step six is ​​generated by formula (19):

[0052] Repeat the feature scoring and feature selection process in step six until the termination condition is met. When the current feature subset is determined to contain discriminative information equivalent to the complete feature set, the iteration process is terminated, and the optimal monitoring feature subset for industrial equipment status identification and fault diagnosis is finally obtained.

[0053] The advantages of this invention are as follows:

[0054] The semi-supervised data particle generation method provided by this invention combines the local structural relationships and global distribution characteristics of particles, and utilizes the labeled sample information inside the particles to fuse... The nearest neighbor relationship method is used to estimate the purity of granules containing only a small number of labeled samples or no labeled samples, thereby improving the stability and reliability of granule purity assessment and providing an effective structured data representation for subsequent semi-supervised industrial monitoring data analysis.

[0055] The granule labeling distribution method constructed in this invention combines samples at the local level of granules. Nearest neighbor relationships enable label propagation from labeled samples to unlabeled samples, and estimate the class membership of unlabeled samples; at the global level of the particle sphere, it is combined with particle spheres. By leveraging nearest neighbor relationships, the method enables label propagation from labeled spheres to unlabeled spheres, thereby converting semi-supervised data into sphere label distribution data. This approach fully utilizes sphere structure information in industrial monitoring data, mitigating the problem of incomplete data representation caused by missing label information and providing more comprehensive and reliable label information support for subsequent feature selection.

[0056] This invention constructs a semi-supervised feature selection method based on granular fuzzy entropy. Using granular label distribution as a foundation, it comprehensively considers multiple evaluation factors such as feature relevance, redundancy, and irrelevance to establish a unified feature evaluation criterion. Compared to existing feature selection methods with relatively singular evaluation dimensions, this invention can more comprehensively measure the importance of features even when some sample labels are missing. It effectively filters highly discriminative features and reduces the impact of redundant and irrelevant features on the feature selection results, thereby improving the stability of feature selection and classification performance. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the workflow of the present invention. Detailed Implementation

[0058] The workflow of this invention is as follows: Figure 1 The present invention specifically describes a semi-supervised feature selection method for industrial data based on granular fuzzy entropy as follows:

[0059] Step 1: Acquire condition monitoring data collected by multiple sensors during the operation of industrial equipment. This condition monitoring data includes a set of labeled monitoring samples and a set of unlabeled monitoring samples, thus constructing a semi-supervised industrial monitoring dataset. , It is a set of conditional attributes. It is a set of decision attributes. It is the attribute value range. yes and arrive The mapping function, the particle purity threshold Minimum number of samples for spheres The number of particles and the number of nearest neighbor particles in the sample are . The set of markers is ,in for The first in One tag;

[0060] Step 2: Construct an initial set of data spheres from the industrial monitoring data. The initial set of data spheres consists of all the monitoring samples.

[0061] Step 3: Divide the spheres in the initial sphere set into spheres. When a sphere contains a labeled monitoring sample, determine whether the current sphere meets the splitting condition based on the sphere purity. When a sphere contains only an unlabeled monitoring sample, calculate the sphere splitting gain based on the state category information of the nearest neighbor sphere, and determine whether the sphere should continue to split based on the splitting gain.

[0062] When the granules in step three contain labeled monitoring samples, the purity of the equipment is considered. Generate using formula (1): (1)

[0063] in For the sample The corresponding marker, For granules The total number of samples in the sample. Indicates granules The middle mark is The number of samples.

[0064] In step three, when the pellets contain labeled monitoring samples, the pellet purity is... Generate using formula (2): (2)

[0065] The final purity of the pellets is taken as the maximum value among all equipment status categories.

[0066] Step 3 calculates the number of particles The set of nearest neighbor particles Generate using formula (3): (3)

[0067] in This represents the candidate set of nearest neighbor particles. For any particle in the set of neighboring particles, For granules The center, For granules The center, Indicates granules and pellets Euclidean distance between centers, set of neighboring spheres It is to find out and The closest Each ball.

[0068] In step three, for spheres containing only label-free monitoring samples, the purity of the device state is... Generate using formula (4): (4)

[0069] in For granules Equipment status category The membership degree is obtained through the propagation of the device state category of the nearest neighbor particle.

[0070] In step three, for granules containing only label-free monitoring samples, their purity is calculated using formula (5): (5)

[0071] The purity of the pellets is obtained by taking the highest purity value for the equipment condition category.

[0072] In step three, the granulocyte splitting judgment condition, which only includes unlabeled monitoring samples, is calculated using formula (6): (6)

[0073] in It is by Split sub-spheres Indicates the splitting of daughter grains Total number For granules The total number of monitored samples is used to determine the purity of the child particles after splitting. When the splitting gain is greater than 0, it indicates that the overall purity of the child particles is higher than that of the parent particles, and then particle splitting is performed.

[0074] In step four, the set of labeled nearest neighbors of unlabeled monitoring samples in a sphere containing labeled monitoring samples is calculated using formula (7): (7)

[0075] when hour, Represents the candidate set of nearest neighbor samples. For any sample in the set of labeled nearest neighbors, Represents the Euclidean distance between monitored samples, and the set of neighboring particles of a sample. It is to find the closest one to the currently monitored sample. It consists of 10 labeled monitoring samples.

[0076] In step four, for spheres containing labeled monitoring samples, the membership degree of the monitoring sample class is generated using formula (8): (8)

[0077] in This is an indicator function that takes the value 1 when the condition is true and 0 otherwise. , The normalized similarity weights for the monitoring samples , Label-free monitoring samples Compared with recently tagged monitoring neighbor samples Gaussian kernel similarity between them The sum of squares of the Euclidean distance. for and The standard deviation between them.

[0078] In step four, the membership degree of the granules in the labeled monitoring samples is generated using formula (9): (9)

[0079] in The weighted average of the class membership degrees of all monitored samples within the pellet is used as the class membership degree of the pellet equipment status.

[0080] In step four, for granules containing only unlabeled monitoring samples, their granule class membership degree is generated using formula (10): (10)

[0081] in, and They represent granules and balls respectively. and The center point, , , The normalized particle-sphere similarity weights, for and between standard deviations For granules With neighboring grains Gaussian kernel similarity between them The sum of squared Euclidean distances is used to propagate device status category information from labeled particles to unlabeled particles by weighted averaging of the membership degrees of labeled neighboring particles.

[0082] In step five, the similarity between any two spheres is generated using formula (11): (11)

[0083] in, .

[0084] Step five involves any industrial monitoring feature set. and device status category set The fuzzy interparticle information between particles and spheres is generated by formula (12): (12)

[0085] in The total number of balls. Indicates in the attribute set The complement of the fuzzy similarity class of particles and spheres is defined as follows: .

[0086] In step five, for any set of attributes Under the condition, equipment status category set and industrial monitoring characteristics The fuzzy particle conditional mutual information between particles is generated by formula (13): (13)

[0087] The granular fuzzy granular conditional mutual information is used to represent the new state classification information provided by candidate monitoring features under given feature subset conditions.

[0088] In step six, the particle entropy of the spherical fuzzy particle is generated by formula (14): (14)

[0089] in This represents the cardinality of granular-spherical fuzzy similarity classes under the industrial monitoring feature set.

[0090] In step six, the correlation between industrial monitoring features and equipment status categories is generated using formula (15): (15)

[0091] Correlation Mutual information between granular and spherical fuzzy particles This indicates that it reflects the characteristics of the candidate monitoring. For the set of tags The importance of.

[0092] The redundancy among industrial monitoring features in step six is ​​generated by formula (16): (16)

[0093] The redundancy between candidate monitoring features and the selected feature subset is measured by using the joint mutual information of fuzzy particles, and candidate monitoring features with lower overlap of classification information are selected first.

[0094] The independence between industrial monitoring features and equipment status categories in step six is ​​generated by formula (17): (17)

[0095] The irrelevance is used to represent the amount of information in candidate monitoring features that is irrelevant to the equipment status category.

[0096] In step six, when the feature subset is empty, the first monitoring feature is generated using formula (18): (18).

[0097] The importance of industrial monitoring features in step six is ​​generated by formula (19):

[0098] Repeat the feature scoring and feature selection process in step six until the termination condition is met. When the current feature subset is determined to contain discriminative information equivalent to the complete feature set, the iteration process is terminated, and the optimal monitoring feature subset for industrial equipment status identification and fault diagnosis is finally obtained.

[0099] This invention performs multi-granularity modeling of industrial monitoring data through granular structure, and combines a dual label propagation mechanism at the sample and granular levels. It can make full use of the potential structural information in semi-supervised data, and achieve a comprehensive evaluation of feature relevance, redundancy and irrelevance based on fuzzy granular entropy, thereby improving the stability and effectiveness of feature selection under label missing conditions.

[0100] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A semi-supervised feature selection method for industrial data based on granular fuzzy entropy, characterized in that, Includes the following steps: Step 1: Acquire condition monitoring data collected by multiple sensors during the operation of industrial equipment. This condition monitoring data includes a set of labeled monitoring samples and a set of unlabeled monitoring samples, thus constructing a semi-supervised industrial monitoring dataset. , It is a set of conditional attributes. It is a set of decision attributes. It is the attribute value range. yes and arrive The mapping function, the particle purity threshold Minimum number of samples for spheres The number of particles and the number of nearest neighbor particles in the sample are . The set of markers is ,in for The first in One tag; Step 2: Construct an initial set of data spheres from the industrial monitoring data. The initial set of data spheres consists of all the monitoring samples. Step 3: Divide the spheres in the initial sphere set into spheres. When a sphere contains a labeled monitoring sample, determine whether the current sphere meets the splitting condition based on the sphere purity. When a sphere contains only an unlabeled monitoring sample, calculate the sphere splitting gain based on the state category information of the nearest neighbor sphere, and determine whether the sphere should continue to split based on the splitting gain. Step 4: Based on the set of spheres obtained in Step 3, for spheres containing labeled monitoring samples, calculate the class membership degree of the monitoring samples using the state category information of the labeled monitoring samples, and combine the labeled nearest neighbor monitoring samples to propagate the equipment state category information to the unlabeled monitoring samples, thereby obtaining the class membership degree of the monitoring samples and the class membership degree of the spheres. For spheres containing only unlabeled monitoring samples, estimate the state category membership degree of the current sphere using the class membership degree of its labeled nearest neighbor spheres. Step 5: Based on the particle marker distribution data obtained in Step 4, calculate the fuzzy similarity between particles, and calculate the particle fuzzy mutual information and particle fuzzy particle information between industrial monitoring features and equipment status categories; Step 6: Establish an industrial monitoring feature importance evaluation function. Taking into account the correlation between monitoring features and equipment status categories, the redundancy between monitoring features, and the irrelevance between monitoring features and equipment status categories, iteratively screen industrial monitoring features to obtain the optimal subset of monitoring features. Step 7: Input the selected optimal subset of monitoring features into the industrial equipment fault status identification model to realize the identification of the operating status of industrial equipment.

2. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: In step three, for spheres containing labeled monitoring samples, the purity of each equipment state category is calculated by statistically analyzing the proportion of samples from each category within the sphere. The purity of the highest category is taken as the sphere purity. The calculation formula is as follows: Equipment State Category Purity Generate using formula (1): (1) in Indicates the equipment status category corresponding to the monitored sample. For granules The total number of monitored samples; Pellet purity Generate using formula (2): (2) The final purity of the pellets is taken as the maximum value among all equipment status categories.

3. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: In step three, for spheres containing only unlabeled monitoring samples, the device state class purity of the current sphere is estimated by the membership degree of the state classes of neighboring spheres. The decision to perform sphere splitting is based on the purity gain before and after the split, calculated using the following formula: Calculate the number of particles The set of nearest neighbor particles Generate using formula (3): (3) in This represents the candidate set of nearest neighbor particles. For any particle in the set of neighboring particles, For granules The center For granules The center Indicates granules and pellets Euclidean distance between centers, set of neighboring spheres It is to find out and The closest Each ball; Label-free pellet equipment state-of-the-art purity Generate using formula (4): (4) in For granules Equipment status category The membership degree is obtained through the propagation of the device state category of the nearest neighbor particle; Particle purity is calculated using formula (5): (5) The purity of the pellets is obtained by taking the highest purity value for the equipment condition category. The criteria for determining granulocyte splitting in unlabeled monitoring samples are calculated using formula (6): (6) in It is by Split sub-spheres Indicates the splitting of daughter grains Total number For granules The total number of monitored samples is used to determine the purity of the child particles after splitting. When the splitting gain is greater than 0, it indicates that the overall purity of the child particles is higher than that of the parent particles, and then particle splitting is performed.

4. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: In step four, for spheres containing labeled monitoring samples, the class membership degree of the monitoring samples is calculated using the state category information of the labeled monitoring samples. This is then combined with the state category information of the labeled nearest neighbor monitoring samples to propagate the equipment state category information to the unlabeled monitoring samples, resulting in the class membership degree of the monitoring samples and the sphere class membership degree. For spheres containing only unlabeled monitoring samples, the state category membership degree of the current sphere is estimated using the class membership degree of its labeled nearest neighbor spheres. The calculation formula is as follows: In a sphere containing labeled monitoring samples, the set of labeled nearest neighbors of unlabeled monitoring samples is calculated using formula (7): (7) when hour, Represents the candidate set of nearest neighbor samples. For any sample in the set of labeled nearest neighbors, Represents the Euclidean distance between monitored samples, and the set of neighboring particles of a sample. It is to find the closest one to the currently monitored sample. It consists of 10 labeled monitoring samples; The membership degree of the monitoring sample class of the granules containing the labeled monitoring samples is generated by formula (8): (8) in This is an indicator function that takes the value 1 when the condition is true and 0 otherwise. , The normalized similarity weights of the monitoring samples , Label-free monitoring samples Compared with recently tagged monitoring neighbor samples Gaussian kernel similarity between them The sum of squares of the Euclidean distance. for and Standard deviation between; For granules in labeled monitoring samples, their granule class membership is generated using formula (9): (9) in The weighted average of the class membership degrees of all monitored samples within the pellet is used as the class membership degree of the pellet equipment status. For granules containing only unlabeled monitoring samples, their granule class membership is generated using formula (10): (10) in, and They represent granules and balls respectively. and The center point, , , The normalized particle-sphere similarity weights, for and between standard deviations For granules With neighboring grains Gaussian kernel similarity between them The sum of squared Euclidean distances is used to propagate device status category information from labeled particles to unlabeled particles by weighted averaging of the membership degrees of labeled neighboring particles.

5. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: The formulas for calculating the particle-sphere fuzzy particle mutual information and the particle-sphere fuzzy particle conditional mutual information between industrial monitoring features and equipment status categories in step five are as follows: For any industrial monitoring feature set and device status category set The fuzzy interparticle information between particles and spheres is generated by formula (12): (12) in The total number of balls. Indicates in the attribute set The complement of the fuzzy similarity class of particles and spheres is defined as follows: ; For any set of attributes Under the condition, equipment status category set and industrial monitoring characteristics The fuzzy particle conditional mutual information between particles and spheres is generated by formula (13): (13) The granular fuzzy granular conditional mutual information is used to represent the new state classification information provided by candidate monitoring features under given feature subset conditions.

6. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: Step six establishes an industrial monitoring feature importance evaluation function, comprehensively considering the correlation between monitoring features and equipment status categories, the redundancy between monitoring features, and the irrelevance between monitoring features and equipment status categories. The calculation formula is as follows: In step six, the particle entropy of the spherical fuzzy particle is generated by formula (14): (14) in This represents the cardinality of granular-spherical fuzzy similarity classes under the industrial monitoring feature set; The correlation between industrial monitoring characteristics and equipment status categories is generated by formula (15): (15) This indicates that a subset of features has been selected, and the relevance is... Mutual information between granular and spherical fuzzy particles This indicates that it reflects the characteristics of the candidate monitoring. For the set of tags The importance of; Redundancy among industrial monitoring features is generated by formula (16): (16) The redundancy between candidate monitoring features and the selected feature subset is measured by using the joint mutual information of fuzzy particles, and candidate monitoring features with lower overlap of classification information are selected first. The independence between industrial monitoring features and equipment status categories is generated by formula (17): (17) The irrelevance is used to represent the amount of information in candidate monitoring features that is irrelevant to the equipment status category.

7. The semi-supervised feature selection method for industrial data based on granular fuzzy entropy according to claim 1, characterized in that: In step six, the monitoring feature with the highest correlation to the equipment status category is first selected as the initial feature. Then, the feature scoring and feature selection process is repeated. The iteration terminates when the current feature subset contains discriminative information equivalent to the complete feature set, thus obtaining the optimal monitoring feature subset. The calculation formula is as follows: When the feature subset is empty, the first monitoring feature is generated using formula (18): (18) In the initial stage of iteration, the monitoring feature with the strongest correlation to the equipment fault state and the lowest redundancy that is irrelevant to itself is selected as the first element of the optimal feature subset; The importance of industrial monitoring features is generated by formula (19): 。

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